EP1709729A4  Transmitter predistortion circuit and method therefor  Google Patents
Transmitter predistortion circuit and method thereforInfo
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 EP1709729A4 EP1709729A4 EP20050711985 EP05711985A EP1709729A4 EP 1709729 A4 EP1709729 A4 EP 1709729A4 EP 20050711985 EP20050711985 EP 20050711985 EP 05711985 A EP05711985 A EP 05711985A EP 1709729 A4 EP1709729 A4 EP 1709729A4
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 H—ELECTRICITY
 H04—ELECTRIC COMMUNICATION TECHNIQUE
 H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
 H04L27/00—Modulatedcarrier systems
 H04L27/32—Carrier systems characterised by combinations of two or more of the types covered by groups H04L27/02, H04L27/10, H04L27/18 or H04L27/26
 H04L27/34—Amplitude and phasemodulated carrier systems, e.g. quadratureamplitude modulated carrier systems
 H04L27/36—Modulator circuits; Transmitter circuits
 H04L27/366—Arrangements for compensating undesirable properties of the transmission path between the modulator and the demodulator
 H04L27/367—Arrangements for compensating undesirable properties of the transmission path between the modulator and the demodulator using predistortion
 H04L27/368—Arrangements for compensating undesirable properties of the transmission path between the modulator and the demodulator using predistortion adaptive predistortion

 H—ELECTRICITY
 H03—BASIC ELECTRONIC CIRCUITRY
 H03F—AMPLIFIERS
 H03F1/00—Details of amplifiers with only discharge tubes, only semiconductor devices or only unspecified devices as amplifying elements
 H03F1/32—Modifications of amplifiers to reduce nonlinear distortion
 H03F1/3241—Modifications of amplifiers to reduce nonlinear distortion using predistortion circuits
 H03F1/3247—Modifications of amplifiers to reduce nonlinear distortion using predistortion circuits using feedback acting on predistortion circuits

 H—ELECTRICITY
 H03—BASIC ELECTRONIC CIRCUITRY
 H03F—AMPLIFIERS
 H03F3/00—Amplifiers with only discharge tubes or only semiconductor devices as amplifying elements
 H03F3/189—High frequency amplifiers, e.g. radio frequency amplifiers

 H—ELECTRICITY
 H03—BASIC ELECTRONIC CIRCUITRY
 H03F—AMPLIFIERS
 H03F3/00—Amplifiers with only discharge tubes or only semiconductor devices as amplifying elements
 H03F3/20—Power amplifiers, e.g. Class B amplifiers, Class C amplifiers
 H03F3/24—Power amplifiers, e.g. Class B amplifiers, Class C amplifiers of transmitter output stages

 H—ELECTRICITY
 H03—BASIC ELECTRONIC CIRCUITRY
 H03F—AMPLIFIERS
 H03F2200/00—Indexing scheme relating to amplifiers
 H03F2200/165—A filter circuit coupled to the input of an amplifier

 H—ELECTRICITY
 H03—BASIC ELECTRONIC CIRCUITRY
 H03F—AMPLIFIERS
 H03F2200/00—Indexing scheme relating to amplifiers
 H03F2200/171—A filter circuit coupled to the output of an amplifier

 H—ELECTRICITY
 H03—BASIC ELECTRONIC CIRCUITRY
 H03F—AMPLIFIERS
 H03F2200/00—Indexing scheme relating to amplifiers
 H03F2200/336—A I/Q, i.e. phase quadrature, modulator or demodulator being used in an amplifying circuit

 H—ELECTRICITY
 H03—BASIC ELECTRONIC CIRCUITRY
 H03F—AMPLIFIERS
 H03F2200/00—Indexing scheme relating to amplifiers
 H03F2200/451—Indexing scheme relating to amplifiers the amplifier being a radio frequency amplifier
Abstract
Description
TRANSMITTER PREDISTORTION CIRCUIT AND METHOD THEREFOR
TECHNICAL FIELD OF THE INVENTION The present invention relates generally to the field of digital RF communications. More specifically, the present invention relates to the control and reduction of inaccuracies introduced into a digital communication signal by analog components of a transmitter.
BACKGROUND OF THE INVENTION Vast amounts of digital processing can be applied to a communication signal in a digital communications transmitter at low cost. Even a relatively wideband communications signal may be described digitally and processed digitally at great accuracy for a reasonable cost. The digital description of the signal comes from providing a stream of samples at a rate suitable for the bandwidth and at a desired resolution. But the digitallydescribedcommunications signal is nevertheless conventionally converted into an analog form, upconverted, filtered, and amplified for transmission by analog components. Unlike digital components, analog components achieve only limited accuracy. Moreover, even poor levels of analog accuracy tend to be relatively expensive, and greater accuracy is achieved only at even greater expense. Consequently, a recent trend in digital communications transmitters is to replace analog processing by extending the digital processing as far as possible toward an antenna from which an RF communications signal will be broadcast. Two other recent trends are the use of modulation forms that require linear amplification and the use of less expensive, but also less accurate, analog components. The modulation forms that require linear amplification are. desirable because they, allow more information to be conveyed during a given period, over a given bandwidth, and using a given transmission power level. Using less expensive components is always a desirable goal, but it is also an important goal in applications that have massmarket appeal and/or highly competitive markets. A linear power amplifier is an analog component that is one of the most expensive and also most powerconsuming devices in the transmitter. To the extent that a linear power amplifier fails to reproduce and amplify its input signal in a precisely linear manner, signal distortion results. And, as a general rule the distortion worsens as lessexpensive and lowerpower amplifiers are used. One type of poweramplifier distortion that has received considerable attention is nonlinearity. Nonlinearity is a particularly prominent characteristic of linear power amplifiers and refers to the extent to which inaccuracy in an amplifier's output signal fails to be linearly related to the amplifier's input signal. Nonlinearity is particularly troublesome in an RF transmitter because it causes spectral regrowth. While an amplifier's RFinput signal may be wellconfined in a predetermined portion of the electromagnetic spectrum, any amplifier nonlinearity causes intermodulation so that the amplifier's RFoutput signal covers a larger portion of the electromagnetic spectrum. Transmitters desirably utilize as much of the spectrum as permitted by regulations in order to efficiently convey information. Consequently, spectral regrowth would typically cause a transmitter to be in violation of regulations. To avoid violating regulations, linear poweramplifiers desirably amplify the communications signal they process in as precisely a linear manner as possible. Another trend faced in digitalcommunicationstransmitter designs is that standards and regulations are continually tightening the spectralregulatory masks within which transmitters must operate. So the need to minimize the spectral regrowth consequences of power amplifier nonlinearity is greater than ever. One way to address the spectralregrowth consequences of power amplifier nonlinearity is to use a higherpower amplifier and operate that higherpower amplifier at a greater backoff. Backoff refers to the degree to which an amplifier is producing a weaker signal than it is capable of producing. Typically, power amplifiers become increasingly linear as they operate further beneath their maximum capabilities, and a greater backoff maintains amplifier operation in the amplifier's more highly linear operating range. Not only does this solution require the use of a moreexpensive, higherpower amplifier, but it also usually requires operating the power amplifier in a less efficient operating range, thereby causing the transmitter to consume more power than it might if the amplifier were operated more efficiently. This problem becomes much more pronounced when the communications signal exhibits a high peaktoaverage power ratio, such as when several digital communications signals are combined prior to amplification. And, the practice of combining several signals prior to amplification is a common one in cellsite base stations, for example. Another way to address the consequences of poweramplifier nonlinearity is though digital predistortion. Digital predistortion has been applied to digital communications signals to permit the use of less expensive power amplifiers and also to improve the performance of more expensive power amplifiers. Digital predistortion refers to digital processing applied to a communications signal while it is still in its digital form, prior to analog conversion. The digital processing attempts to distort the digital communications signal in precisely the right way so that after inaccuracies are applied by linear amplification and other analog processing, the resulting communications signal is as precisely accurate as possible. To the extent that amplifier nonlinearity is corrected through digital predistortion, lowerpower, lessexpensive amplifiers may be used, the amplifiers may be operated at their moreefficient, lowerbackoff operating ranges, and spectral regrowth is reduced. And, since the digital predistortion is performed through digital processing, it should be able to implement whatever distortion functions it is instructed to implement in an extremely precise manner and at reasonable cost. While prior digital predistorting techniques have achieved some successes, those successes have been limited, and the more modern regulatory requirements of tighter spectralregulatory masks are rendering the conventional predistortion techniques inadequate. Predistortion techniques require knowledge of the way in which analog components will distort the communications signal in order to craft the proper inversepredistortiontransfer function that will precisely compensate for distortion introduced by the analog components. The more accurate conventional digital predistortion techniques use a feedback signal derived from the power amplifier output in an attempt to gain this knowledge in real time and to have this knowledge accurately reflect the actual analog components and actual operating conditions. Conventionally, in response to monitoring this feedback signal, an extensive amount of processing is perfonned to derive a distortiontransfer function. Then, after deriving the distortiontransfer function, the inverse of the distortiontransfer function is computed and translated into instructions that are programmed into a digital predistorter. In many conventional applications, the transmitter is required to transmit a predetermined sequence of training data to reduce the complexity and improve the accuracy of the extensive processing needed to derive a distortiontransfer function. Less accurate or narrowband conventional predistortion techniques may resort to configuring a digital predistorter as a simple communicationssignal filter that is programmed to implement the inversetransferfunction as best it can. But in many of the more accurate, and usually more expensive, conventional applications, the digital predistorter itself includes one or more lookuptables whose data serve as the instructions which define the character of the predistortion the digital predistorter will impart to the communications signal. At the cost of even greater complexity, prior art techniques in highend applications attempt to compensate for memory effects. In general, memory effects refer to tendencies of power amplifiers to act differently in one set of circumstances than in another. For example, the gain and phase transfer characteristics of a power amplifier may vary as a function of frequency, instantaneous power amplifier bias conditions, temperature, and component aging. In order to address memory effects, predistorter design is typically further complicated by including multiple lookuptables and extensive processing algorithms to first characterize the memory effects, then derive suitable inversetransfer functions, and alter predistorter instructions accordingly. The vast array of conventional predistortion techniques suffers from a variety of problems. The use of training sequences is particularly undesirable because it requires the use of spectrum for control rather than payload purposes, and it typically increases complexity. Generally, increased processing complexity in the path of the feedback signal and in the predistorter design is used to achieve increased accuracy, but only minor improvements in accuracy are achieved at the expense of great increases in processing complexity. Increases in processing complexity for the feedback signal are undesirable because they lead to increased transmitter expense and increased power consumption. Following conventional digital predistortion techniques, the cost of digital predistortion quickly meets or exceeds the cost of using a higherpower amplifier operated at greater backoff to achieve substantially the same result. Thus, digital predistortion has conventionally been practical only in higherend applications, and even then it has achieved only a limited amount of success. More specifically, the processing of the feedback signal suffers from some particularly vexing problems using conventional techniques. An inversing operation is conventionally performed to form an inversetransfer function to use in programming a digital predistorter. While the inversing operation may be somewhat complex on its own, a more serious problem is that it is sensitive to small errors in the feedback signal. Even a small error processed through an inversing operation can result in a significantly inaccurate inversetransfer function. Using conventional predistortion techniques, the feedback signal should be captured with great precision and accuracy to precisely and accurately compute the inversetransfer function. Using conventional techniques, this requires high precision analogtodigital conversion circuits (A/D) to capture the feedback signal, followed by high resolution, low error, digital circuitry to process the feedback signal. To complicate matters, the feedback signal typically exhibits an expanded bandwidth due to the spectral regrowth caused by power amplifier nonlinearity. To accurately capture the expanded bandwidth of the feedback signal using conventional techniques, the A/D should also consist of highspeed circuits. But such high speed, highresolution A/D's are often such costly, highpower components that they negate any power amplifier cost savings achievable through digital predistortion in all but the most highend applications. In order to avoid the requirement of highspeed, highresolution A/D's, some conventional predistortion techniques have adopted the practice of processing only the power of the outofband portion of the feedback signal. But the power of the outofband portion of the feedback signal only indirectly describes analogcomponent distortion, again causing increased errors and reduced accuracy in inverse transfer functions. Even when conventional designs use highspeed, highresolution A/D's to capture feedback signals, they still fail to control other sources of error that, after an inversion operation, can lead to significant inaccuracy in an inversetransferfunction. Phase jitter in clocking the A D adds to error, as does any analog processing that may take place prior to A/D conversion. And, conventional practices call for digital communications signals to be complex signals having inphase and quadrature components which are conventionally processed separately in the feedback signal prior to A/D conversion. Any quadrature imbalance introduced in the feedback signal by analog processing leads to further error that, after an inversion operation, can cause significant inaccuracy in an inversetransfer function. Linear distortion introduced into the communications signal by analog components is believed to be another source of error that plagues conventional digital predistortion techniques. Linear distortion refers to signal inaccuracies that are faithfully reproduced by, or introduced by, the power amplifier and fall inband. Examples of linear distortion include imbalances of quadrature gain, phase, and group delay. And, as the communication signal becomes more wideband, frequencydependent gain and phase variances assert a greater lineardistortion influence. Additional examples of linear distortion include certain types of signal images and intermodulation. Linear distortion is typically viewed as being a more benign form of error than nonlinear distortion because it does not lead to spectral regrowth. Typically, linear distortion is compensated for in a receiver after the transmission channel and the receiver's frontendanalog components have added further linear distortions. But in at least one example, a communication system has been configured so that the receiver determines some lineardistortioncorrection parameters that are then communicated back to the transmitter, where the transmitter then implements some corrective action. The reduction of linear distortion in a transmitted communications signal is desirable because it reduces the amount of linear distortion that a receiver must compensate for in the received signal, which leads to improved performance. And, reduction of linear distortion becomes even more desirable as the communications signal becomes more wideband. But using a receiver to specify the corrective action that a transmitter should take to reduce linear distortion is undesirable because it does not separate channel induced distortion from transmitterinduced distortion. Since multipath usually asserts a dynamic influence on a transmitted RF communications signal as the signal propagates through a channel, such efforts are usually unsuccessful. In addition, it wastes spectrum for transmitting control data rather than payload data, and it requires a population of receivers to have a compatible capability. Not only is the failure to address linear distortion in conventional transceivers a problem in its own right, but it is believed to lead to further inaccuracy in characterizing nonlinear transfer functions. Most algorithms which transform raw data into transfer functions are based upon amplifier models that are reasonably accurate under controlled conditions. But the use of linearlydistorted signals to derive transfer functions based upon such models, and particularly over wide bandwidths, can violate the controlled conditions. Consequently, the transfer functions derived therefrom are believed to be less accurate than they might be, and any inversetransfer functions calculated for use in a digital predistorter can be significantly inaccurate as a result. In some digital communication applications (e.g., a cellular base station), a wide bandwidth communication signal is composed of a plurality of independent narrowerbandwidth signals frequency multiplexed together to form the wide bandwidth communication signal. This situation poses particular challenges for predistortion circuits. In such a multiplenarrowerbandwidthsignal application, some of the narrowerbandwidth signals are likely to exhibit considerably less signal strength than the others. In a typical scenario, communication system specifications insist that all transmitted channels meet a minimum error vector magnitude (EVM) or signaltonoise (S/N) requirement. Accordingly, a need exists to perform predistortion and other transmitter processing in a way that meets these requirements for both weaker and stronger channels.
DISCLOSURE OF THE INVENTION It is an advantage of at least one embodiment of the present invention that an improved transmission predistortion circuit and method are provided. Another advantage of at least one embodiment of the present invention is that a quantization error compensator is provided to compensate for quantization errors introduced by an analogtodigital circuit (A/D) that monitors a feedback signal generated by analogtransmitter components. Another advantage of at least one embodiment of the present invention is that a process is provided that compensates for distortions introduced in a feedback signal path prior to using that feedback signal path to counteract distortions introduced by analogtransmitter components. Yet another advantage of at least one embodiment of the present invention is that distortions introduced by analogtransmitter components are counteracted in a manner responsive to the relative strengths of frequencymultiplexed communication channels. These and other advantages are realized in one form by a method of compensating for distortion introduced by analogtransmitter components of a digital communications transmitter. The method calls for obtaining a forwarddata stream configured to convey a plurality of frequencymultiplexed communication channels. The forwarddata stream is processed through the analogtransmitter components. A returndata stream responsive to the forwarddata stream after it has been influenced by the analogtransmitter components is obtained. A communicationsignal strength is identified for each of the communication channels in response to the forwarddata stream, and an errorsignal strength is identified for each of the communication channels in response to the returndata stream. The distortion introduced by the analog transmitter components is counteracted in response to relative communicationsignal strengths and error signal strengths for said communication channels. These and other advantages are realized in another form by a predistortion circuit for compensating distortion introduced by analogtransmitter components of a digital communications transmitter. The predistortion circuit includes an adaptive equalizer configured to receive a forwarddata stream and to generate a processedforwarddata stream. A digitaltoanalog converter (D/A) is coupled to the adaptive equalizer and configured to convert the processedforwarddata stream into a forwardanalog signal which propagates through the analogtransmitter components. An analogtodigital converter (A/D) is adapted to receive a returnanalog signal from the analogtransmitter components. The returnanalog signal is responsive to the forwardanalog signal, and the A/D is configured to produce a returnrawdigitizeddata stream. An A/D compensation section is adapted to receive the forwarddata stream. The A/D compensation section is configured to compensate for errors introduced into the returnrawdigitizeddata stream by the A/D and to produce a returndata stream. A control circuit is coupled to the adaptive equalizer. The control circuit is configured to alter the processedforwarddata stream in response to the returndata stream.
BRIEF DESCRIPTION OF THE DRAWINGS A more complete understanding of the present invention may be derived by referring to the detailed description and claims when considered in connection with the Figures, wherein like reference numbers refer to similar items throughout the Figures, and: Fig. 1 shows a block diagram of a digital communications transmitter configured in accordance with the teaching of the present invention; Fig. 2 shows a block diagram of a first embodiment of a linearandnonlinearpredistortion section of the transmitter depicted in Fig. 1; Fig. 3 shows a block diagram of a digital downconversion section suitable for use in the linearand nonlinearpredistortion section of the transmitter depicted in Fig. 1; Fig. 4 shows a flowchart of a first embodiment of a transmissiondistortionmanagement process ^{•} performed by the transmitter depicted in Fig. 1; Fig. 5 shows a flowchart of a subprocess of the process depicted in Fig. 4, wherein this subprocess compensates for linear distortion introduced upstream of a high power amplifier (HP A); Fig. 6 shows a flowchart of a subprocess of the subprocesses depicted in Figs. 5 and 14, wherein this subprocess implements one example of a timealignmentestimationandconvergence algorithm; Fig. 7 shows a block diagram of a commonmodetimealign section suitable for use in the linear andnonlinearpredistortion section of the transmitter depicted in Fig. 1; Fig. 8 shows a block diagram of a differentialmodetimealign section suitable for use in the linear andnonlinearpredistortion section of the transmitter depicted in Fig. 1; Fig. 9 shows a flowchart of a subprocess of the subprocesses depicted in Figs. 5 and 14, wherein this subprocess implements a commonmodephasealignmentestimationandconvergence algorithm; Fig. 10 shows a block diagram of a phaserotate section suitable for use in the linearandnonlinear predistortion section of the transmitter depicted in Fig. 1; Fig. 11 shows a flowchart of a subprocess of the subprocesses depicted in Figs. 5, 14 and 15, wherein this subprocess implements an equalizationestimationandconvergence algorithm; Fig. 12 shows a block diagram of a representative equalizer suitable for use in several sections of the linearandnonlinearpredistortion section of the transmitter depicted in Fig. 1; Fig. 13 shows a block diagram of an adaptation engine section suitable for use in the linearand nonlinearpredistortion section of the transmitter depicted in Fig. 1; Fig. 14 shows a flow chart of a subprocess of the process depicted in Fig. 4, wherein this subprocess compensates for linear distortion introduced through the HPA; Fig. 15 shows a flow chart of a subprocess of the process depicted in Fig. 4, wherein this subprocess compensates for nonlinear distortion of the HPA; Fig. 16 shows a block diagram of a basisfunctiongeneration section suitable for use in the linear andnonlinearpredistortion section of the transmitter depicted in Fig. 1; Fig. 17 shows a block diagram of a representative heatestimation section suitable for use in the linearandnonlinearpredistortion section of the transmitter depicted in Fig. 1; Fig. 18 shows a block diagram of a second embodiment of the linearandnonlinearpredistortion section of the transmitter depicted in Fig. 1; Fig. 19 shows a flowchart of a second embodiment of the transmissiondistortionmanagement process performed by the transmitter depicted in Fig. 1; Fig. 20 shows a model of an analogtodigital converter (A/D); Fig. 21 shows a graph depicting quantization and quantization error characteristics of an exemplary 2bit A/D; Fig. 22 shows a block diagram of a first representative quantizationerror compensator for use in the linearandnonlinearpredistortion section of the transmitter depicted in Fig. 1; Fig. 23 shows a flowchart of a subprocess of the process depicted in Fig. 19, wherein this subprocess programs the quantizationerror compensator depicted in Fig. 22 to compensate for dissymmetry in quantization error; Fig. 24 shows a flowchart of a subprocess of the process depicted in Fig. 19, wherein this subprocess compensates for linear distortion introduced through the A/D; Fig. 25 shows a block diagram of a multiplexing section that works in conjunction with the second embodiment of the linearandnonlinearpredistortion section shown in Fig. 18 to generate signals which drive taps of adaptive equalizers; Fig. 26 shows a flowchart of a subprocess of the process depicted in Fig. 19, wherein this subprocess compensates for nonlinear distortion introduced through the A/D; Fig. 27 shows a graph which depicts a few spectral plots that characterize various features of a communications signal that conveys a plurality of frequencymultiplexed channels; Fig. 28 shows a block diagram of a third embodiment of the linearandnonlinearpredistortion section of the transmitter depicted in Fig. 1; Fig. 29 shows a block diagram of a representative spectral management section for use in the linear andnonlinearpredistortion section of the transmitter depicted in Fig. 1; Fig. 30 shows a flow chart depicting the operation of a representative gain controller for use in the spectral management section shown in Fig. 29; Fig. 31 shows a block diagram of a second representative quantizationerror compensator for use in the linearandnonlinearpredistortion section of the transmitter depicted in Fig. 1; and Fig. 32 shows a flowchart of a third embodiment of the transmissiondistortionmanagement process performed by the transmitter depicted in Fig. 1.
BEST MODE FOR CARRYING OUT THE INVENTION Fig. 1 shows a block diagram of a digitalcommunications radiofrequency (RF) transmitter 100 configured in accordance with the teaching of the present invention. Transmitter 100 is the type of transmitter that may be used at a cellular telephony, cellsite base station, but transmitter 100 may be used in other applications as well. In transmitter 100 a plurality of digitaldata streams 102 is provided to a corresponding plurality of digital modulators 104. In a cellsite base station application, data streams 102 may convey information to be transmitted to a plurality of different users. The different streams 102 may bear some relation to one another, or they may bear no relation whatsoever. Modulators 104 may implement any type of digital modulation, but the benefits of the present invention are best appreciated with forms of modulation where both amplitude and phase are used to digitally convey the information. Such types of modulation typically require the use of linear highpower amplifiers (HPA's). Examples of such types of modulation include any type of quadratureamplitude modulation (QAM), codedivisionmultipleaccess (CDMA), orthogonalfrequencydivision modulation (OFDM), multipleinput, multipleoutput (MIMO) systems, and the like. In the preferred embodiment, the modulated data output from modulators 104 digitally conveys information using complex data streams. Those skilled in the art will appreciate that complexdata streams include two parallel streams. Using a conventional nomenclature, Fig. 1 depicts one of the streams as an inphase (I) stream and the other as a quadrature (Q) stream, reflecting an orthogonal relationship the two streams will share as they are processed and combined together downstream. Although not specifically shown, modulators 104 may include pulse shaping filters that are configured to minimize intersymbol interference (ISI) in a manner wellunderstood by those skilled in the art, and other forms of postmodulation signal processing. In one preferred embodiment, modulators 104 couple to a combining section 106 in which the plurality of independentlymodulated complexdata streams are combined together into a single digital communications signal, referred to herein as complexforwarddata stream 108. For the purposes of this description, complexforwarddata stream 108 and all variants thereof produced by downstream processing between combining section 106 and an antenna from which transmission occurs are referred to as forward data streams to distinguish them from returndata streams that are discussed below and which propagate in the opposite direction. Even if data streams 102 were narrowbanddata streams, the combined complex forwarddata stream 108 may be viewed as a widebanddata stream. One of the consequences of combining the separate modulateddata streams is that the peaktoaverage ratio of complexforwarddata stream 108 increases, placing greater demands on linear amplification to be performed downstream. An output of combining section 106 couples to an input of a peakreduction section 110. Peak reduction section 110 reduces the peaktoaverage ratio of forwarddata stream 108 so that a resulting complexpeakreducedforwarddata stream 112 will place fewer demands on linear amplification to be performed downstream. In the preferred embodiments, peakreduction section 110 uses a peakreduction or crestreduction technique that introduces only inband distortion on forwarddata stream 108. Consequently, no significant spectral regrowth should occur in complexpeakreducedforwarddata stream 112 or elsewhere as a result of applying peak reduction. In addition, peakreduction section 110 desirably applies peak reduction in a controllable manner so as to respond to a peakreductionfeedback signal 114. In particular, feedback signal 114 may provide a residualnonlinearEVM value that may be transformed into a threshold value by peakreduction section 110. The threshold value indicates the minimum magnitude that needs to be exhibited by forwarddata stream 108 before any peak reduction will be applied. Typically, greater amounts of peak reduction will be applied to forwarddata stream 108 as the magnitude of forwarddata stream 108 exceeds this threshold by greater amounts. An increase in peak reduction can be achieved by lowering the magnitude threshold where peak reduction is applied to forwarddata stream 108, and it will have the effect of introducing greater in band distortion into peakreducedforwarddata stream 112. Suitable peakreduction techniques are described in U.S. Patent Nos. 6,104,761 and 6,366,619, both of which are incorporated herein by reference, but techniques other than those described therein may be used as well. In the preferred embodiment, feedback signal 114 indicates the amount of residual nonlinear distortion in an RFcommunications signal 116 transmitted from transmitter 100. The development of feedback signal 114 is discussed below. In one preferred embodiment, peakreduction section 110 is operated so that the amount of peak reduction applied to forwarddata stream 108 increases when an excessive amount of nonlinear distortion is present, as compared with a predetermined value. Desirably, transmitter 100 is designed so that under normal, steadystate, operating conditions the amount of nonlinear distortion in RFcommunications signal 116 is not excessive and the total errorvector magnitude (EVM) is slightly less that the maximum allowed by a system specification. But abnormal operating conditions may lead to excessive nonlinear distortion, which in turn could result in spectral regrowth that exceeds regulatory requirements and EVM specifications. Accordingly, feedback signal 114 has the ability to manage the amount of distortion in RF communication signal 116 and cause that distortion to be more inband and less outofband, regardless of other operating conditions. Feedback signal 114 permits peakreduction section 110 to increase peak reduction, which then causes HPA 136 to operate at a greater backoff. Operating HPA 136 at greater backoff will result in reduced nonlinear distortion and reduced outofband emissions. But by increasing peak reduction, inband distortion will also increase. Thus, overall distortion may remain roughly constant, but its character will be shifted from outofband to inband. Peakreduction section 110, if present, serves as a source of forwarddata stream 112 for a linear andnonlinearpredistortion circuit 200. Predistortion circuit 200 uses a variety of features to intentionally introduce both linear distortion and nonlinear distortion into forwarddata stream 112 through the use of digital processing. This variety of features is discussed in detail below. It is predistortion circuit 200 that generates feedback signal 114. After processing in predistortion circuit 200, forwarddatastream 112 becomes a complexquadraturebalancedequalizedforwarddata stream 118. To the extent that forwarddata streams 108 and 112 represent wideband signals, forwarddata stream 118 now represents a superwideband signal. Forwarddata stream 118 passes to analog components 120 of transmitter 100. Forwarddata stream 118 conveys not only the baseband communications signal, but also conveys inverseintermodulation distortion introduced by predistortion circuit 200 that will compensate for nonlinear distortions to be introduced by analog components 120. In one embodiment, an optional peakreduction control signal 114' may be supplied from peak reduction section 110 to predistortion circuit 200. Peakreduction control signal 114' desirably indicates, either by estimation, measurement, or calculation, the amount of noise added to forwarddata stream 112 by the operation of peakreduction section 110. In a presently preferred embodiment, peakreduction control signal 114' conveys the shortterm average noise added to each of the abovediscussed independently modulated complexdata streams output from modulators 104, as determined by filtered magnitudes of post lowpassfiltering excursion energy. The use of peakreduction control signal 114' is discussed below in connection with Fig. 29. Analog components 120 include separate digitaltoanalog converters (D/A's) 122 for each leg of complexforwarddata stream 118. D/A's 122 convert forwarddata stream 118 from digital to analog signals. Subsequent processing of the forwardcommunications signal will be analog processing and subject to the inaccuracies characteristic of analog processing. For example, the two different D/A's 122 may not exhibit precisely the same gain and may introduce slightly different amounts of delay. Such differences in gain and delay can lead to linear distortion in the communication signal. Moreover, so long as the different legs of the complex signal are processed separately in different analog components, the components are likely to apply slightly different frequency responses so that linear distortion is worsened by the introduction of frequencydependent gain and phase imbalances. And, the frequencydependent gain and phase imbalances worsen as the bandwidth of the communication signal widens. The two complex legs of the analog signal pass from D/A's 122 to two lowpass filters (LPF's) 124. LPF's 124 can be the source of additional linear distortion by applying slightly different gains and phase shifts in addition to slightly different frequencydependent characteristics. From LPF's 124 the two complex legs of the analog signal pass to a direct quadrature upconversion section 126. Upconversion section 126 mixes the two complex legs with a localoscillator signal exhibiting a localoscillator frequency and obtained from a local oscillator 128 in a manner known to those skilled in the art. Additional linear distortion in the form of gain and phase imbalance may be introduced, and localoscillator leakage may produce an unwanted DC offset. In addition, upconversion section 126 combines the two distinct legs of the complex signal and passes the combined signal, now an RFanalog signal 130, to a bandpass filter (BPF) 132. Section 126 preferably performs a direct upconversion for cost reasons, at least up to frequencies less than around 2.5 GHz. For higher frequencies multiple stages of upconversion may be used. BPF 132 is configured to block unwanted sidebands in RFanalog signal 130, but will also introduce additional phase delay into the communications signal, now referred to as RFanalog signal 134. RFanalog signal 134 drives a power amplifier 136, also conventionally called a highpower amplifier (HPA). HPA 136 couples to an antenna 138 and produces an amplifiedRFanalog signal, referred to above as RF communications signal 116. HPA 136 is likely to be the source of a variety of linear and nonlinear distortions introduced into the communications signal. Fig. 1 depicts HPA 136 using the WienerHammerstein RFamplifier model, which may be used to explain some of these distortions, at least for the controlled conditions of ideal signals. According to the WienerHammerstein HPA model, HPA 136 acts like an input bandpass filter (BPF) 140, followed by a memoryless nonlinearity, labeled amp 142 in Fig. 1, which is followed by an output bandpass filter (BPF) 144. Amp 142 generates an output signal that may be a higherorder complex polynomial function of its input. Each of BPF's 140 and 144 may introduce linear distortion, but probably little significant nonlinear distortion. On the other hand, amp 142 is a significant source of nonlinear distortion. In the preferred embodiment, linearandnonlinearpredistortion circuit 200 receives at least three or four analog input signals. One signal is the localoscillator signal used by upconversion section 126 for upconversion. Another signal is an optional feedback signal from the output of at least one of the two legs of the complex signal from D/A's 122. This output is labeled baseband (BB) signal 123 in Fig. 1. Other analog inputs are feedback signals derived from RFanalog signal 134, which serves as the input signal to HPA 136, and RFcommunications signal 116 through a directive coupler 115, which serves as the output signal from HPA 136. Through monitoring these feedback signals, linearandnonlinearpredistortion circuit 200 learns how to apply predistortion so as to minimize the linear, then the nonlinear distortion. While a variety of different distortion sources are present, the physical attributes of the analog components that cause the distortions tend to change slowly. This allows circuit 200 to implement estimationandconvergence algorithms to determine suitable predistortion characterizations and to tolerate slow convergence rates in such algorithms. The use of estimationandconvergence algorithms reduces processing complexity and also reduces sensitivity to errors in the feedback signals. Moreover, the use of slow convergence rates allows circuit 200 to reduce the effectiveerror levels of the feedback signals so that accurate predistortion characterizations are obtained. Since errors in the feedback signals can be tolerated, the feedback signals may be processed using low resolution circuits, thereby achieving a circuit component count and power savings. Fig. 2 shows a block diagram of a first embodiment of linearandnonlinearpredistortion circuit 200 of transmitter 100. A second embodiment, referred to as linearandnonlinearpredistortion circuit 1800, is discussed below in connection with Fig. 18, and a third embodiment, referred to as linearandnonlinear predistortion circuit 2800, is discussed below in connection with Fig. 28. Complexforwarddata stream 112, which is configured to convey digital data, is applied at an input port 202 of circuit 200. Compared to a returndata steam discussed below, forwarddata stream 112 exhibits a higher resolution, as indicated in Fig. 2 by the letter "H". Those skilled in the art will appreciate that the resolution is determined, at least in part, by the number of bits with which each sample in forwarddata stream 112 is described. A higherresolution data stream is usually conveyed using more bits per sample than a lowerresolutiondata stream. Likewise, forwarddata stream 112 exhibits a relatively low error level from quantization noise, phase jitter, and the like. As discussed above, any signal flowing toward analog components 120 that is based on forwarddata stream 112 is also considered to be a form of the forwarddata stream. As forwarddata stream 112 flows through predistortion circuit 200, it retains its high resolution, low error level characteristic. In the preferred embodiment, forwarddata stream 112 is routed to a rate multiplier 204. In this preferred embodiment, forwarddata stream 112 conveys only a baseband digital communications signal and needs to flow at a data rate that supports the Nyquist criteria for the baseband digital communications signal. But in one preferred embodiment, subsequent processing of forwarddata stream 112 will introduce higher frequency components to compensate for nonlinear distortion. Thus, rate multiplier 204 steps up the data rate to be at least equal to and preferably greater than the Nyquist rate for the highestfrequency components that will be introduced. At this point, the forwarddatastream may be thought of as a superwideband data stream. Rate multiplier 204 may be implemented using interpolators in a manner wellknown to those skilled in the art. Or, rate multiplier 204 may be omitted altogether if nonlinear compensation is to be omitted. The forwarddata stream output from multiplier 204 passes to a highpass filter (HPF) 205 configured merely to remove DC. Highpass filter 205 desirably has substantially the same filtering characteristics as another highpass filter inserted in the returndata stream, as discussed below. Highpass filter 205 may alternatively be located prior to rate multiplier 204, as depicted below in connection with Figs. 18 and 25, or at other equivalent locations. An increasedratecomplexforwarddata stream 206 flows from highpass filter 205 to a delay section 208, a basisfunctiongeneration section 1600, and a heatchangeestimation section 1700. Basis functiongeneration section 1600 is used in connection with nonlinear compensation and may be omitted if nonlinear compensation is to be omitted. Basisfunctiongeneration section 1600 generates a plurality of complexbasisfunctiondata streams 214. Each complexbasisfunctiondata stream 214 is responsive to X(n) X(n)^{K}, where X(n) represents the forwarddata stream 206 received by section 1600, and K is an integer number greater than or equal to one. Thus, section 1600 generates a variety of higherorder harmonics of and from the forwarddata stream 206. A complexbasisfunctiondata stream 214' supplies the highestorderedbasisfunctiondata stream 214 (i.e., has the greatest value of K). Data stream 214' is routed to a first data input of a multiplexer (MUX) 222. Basisfunctiongeneration section 1600 is discussed below in more detail in connection with Figs. 15 and 16. Likewise, heatchangeestimation section 1700 is used in connection with nonlinear compensation and may be omitted if nonlinear compensation is to be omitted. Generally, heatchangeestimation section 1700 generates a deltaheat signal (ΔHeat) 216 that describes the relative power in the forwarddata stream 206 in a way that characterizes the instantaneous change in heat buildup in HPA 136 relative to a longer termheat average. Deltaheat signal 216 is then used to influence basisfunctiondata streams 214 to compensate for the heat memory effect of a typical HPA 136. Heatchangeestimation section 1700 is discussed below in more detail in connection with Figs. 15 and 17. In the preferred embodiment, all basisfunctiondata streams 214 exhibit equal delay in basis functiongeneration section 1600. Delay section 208 inserts a constant delay equal to this basisfunction delay. Accordingly, a complexforwarddata stream 218 output from delay section 208 has the same timing as each of basisfunctiondata streams 214, including highestorderbasisfunctiondata stream 214'. The complexforwarddata stream 218 output from delay section 208 is routed to a combining circuit 220 and to a second data input of multiplexer 222. Combining circuit 220 is depicted in Fig. 2 as a complex subtracting circuit having one subtraction element for each leg of the complex signal path. Complexforwarddata stream 218 is routed to positive inputs of the subtraction elements. All complexbasisfunctiondata streams 214 are routed to a nonlinear predistorter 224, which may be omitted if nonlinear compensation is to be omitted from transmitter 100. Nonlinear predistorter 224 includes a plurality of equalizers (EQ) 226, with one equalizer 226 being provided for each complexbasis functiondata stream 214. Fig. 2 labels equalizers 226 as being associated with a 2^{nd}order basis function, a 3^{rd}order basis function, and so on up to a (K+l)^{th}order basis function. Each of equalizers 226 is a complex equalizer, like an equalizer 1200 shown in more detail in Fig. 12, and outputs from each equalizer 226 are combined together in adders 228 to form a complexfilteredbasisfunctiondata stream 230. Data stream 230, which serves as a nonlinearpredistortedcompensation stream, is routed to the subtraction inputs of combining circuit 220. For the purposes of this description, an equalizer, such as any of equalizers 226, is a programmable filter. The filter is programmed by specifying its filter coefficients to define how it will alter the signal it processes. In the preferred embodiments, a wide range in filter complexity is contemplated. Each of equalizers 226 may have as few as one tap or any number of taps greater than that. An adaptive equalizer is an equalizer configured to determine its own filter coefficients and to continuously alter its filter coefficients, while a nonadaptive equalizer is an equalizer which accepts filter coefficients programmed into it but does not alter those filter coefficients until they are updated by further programming. But as discussed below, in some locations deltaheat signal 216 may cause some alteration in filter coefficients programmed into a nonadaptive equalizer. In the preferred embodiment, equalizers 226 are nonadaptive equalizers. But when coupled to an adaptation engine 1300, the combination of an equalizer 226 with adaptation engine 1300 forms an adaptive equalizer. Each of equalizers 226, other equalizers included in linearandnonlinearpredistortion circuit 200, and adaptation engine 1300 belong to an equalizer section 234. In the preferred embodiment, adaptation engine 1300 is selectively coupled to and decoupled from the various equalizers within equalizer section 234 from time to time to determine filter coefficients through the implementation of an estimationand convergence algorithm. Fig. 2 depicts this selective coupling and decoupling through feature 236 in nonlinear predistorter 224 and in adaptation engine 1300. Deltaheat signal 216 is one of the inputs to adaptation engine 1300, and deltaheat signal 216 is also input to nonlinear predistorter 224. Equalizers 226, adaptation engine 1300, and the estimationandconvergence algorithm implemented therewith are discussed below in more detail in connection with Figs. 1113. An output of combining circuit 220 provides a complexnonlinearpredistortedforwarddata stream 238. Forwarddata stream 238 drives a differentialmodetimealignment section 800 in one embodiment of the present invention. Timealignment section 800 may be omitted if linear compensation is to be omitted from transmitter 100. Timealignment section 800 inserts different amounts of delay into the I and Q complex legs of forwarddata stream 238 to compensate for an opposing differential time delay that may be introduced through analog components 120. Timealignment section 800 is discussed in more detail below in connection with Figs. 5 and 8. An output of timealignment section 800 produces a complexdifferentialtimealignedforwarddata stream 242 that drives a linear predistorter 244. Alternatively, timealignment section 800 may be located after linear predistorter 244, rather than before as depicted in Fig. 2, if desired. And, linear predistorter 244 may be omitted altogether if linear compensation is to be omitted from transmitter 100. Linear predistorter 244 performs a variety of adjustments on the forwarddata stream 242. For example, linear predistorter 244 performs quadraturebalance functions and therefore serves as a quadrature balanceadjustment section. Thus, linear predistorter 244 introduces gain and phase adjustments into the I and Q legs of complexforwarddata stream 242, and introduces such adjustments independently for the I and Q legs so that quadrature balance can be affected. In addition, linear predistorter 244 compensates for frequencydependent quadrature gain and phase imbalances. Accordingly, even wideband and the above discussed superwideband communications signal are quadrature balanced through linear predistorter 244. In the preferred embodiment, linear predistorter 244 is implemented using a complex equalizer 246, which may be configured as equalizer 1200 but most likely has a greater number of taps. If the number of taps is sufficiently generous, then differential mode time alignment section 800 may be omitted altogether. Equalizer 246 is labeled EQ_{F}, with the subscript "F" indicating that equalizer 246 filters the forwarddata stream. As discussed above in connection with equalizers 226, equalizer 246 serves as one part of equalizer section 234. And, equalizer 246 is desirably a nonadaptive equalizer that, when coupled through feature 236 to adaptation engine 1300, becomes an adaptive equalizer. By properly programming forwardfilter coefficients (i.e., filter coefficients for forward equalizer EQ_{F}) into equalizer 246, linear predistorter 244 compensates for linear distortion introduced by analog components 120. The forwardfilter coefficients are determined through a training process that is discussed below in connection with Figs. 5, 1114, and 19. When trained, the forwardfilter coefficients serve as quadraturebalance coefficients or parameters in addition to correcting for frequencydependent phase and gain imbalance and distortion between the I and Q legs. Linear predistorter 244 generates complexquadraturebalancedequalizedforwarddata stream 118 which is passed to analog components 120. Forwarddata stream 118 desirably maintains the high resolution, lowerrorlevel characteristic that it demonstrated upstream. It has been distorted in the preferred embodiment to compensate for both nonlinear and linear distortions that have not yet been introduced into the communications signal but will be introduced by analog components 120. Moreover, it is desirably provided at a rate that supports the abovediscussed superwideband that includes the baseband signal plus higher harmonics. But other embodiments may nevertheless benefit from compensating for only linear distortions or compensating for only nonlinear distortions. Referring to Fig. 1, feedback from analog components 120 is obtained through feedback signals 117 and 134. Feedback signal 117 is derived from the RFanalog signal output by HPA 136, and feedback signal 134 is derived from the RFanalog signal input to HPA 136. Back on Fig. 2 then, feedback signals 117 and 134 are supplied to a feedback section 248 of linearandnonlinearpredistortion circuit 200 at a multiplexer 250. Feedback section 248 also includes a digitaldownconversion section 300, which receives an output from multiplexer 250. Downconversion section 300 also receives substantially the same localoscillator signal from local oscillator 128 that is used by upconversion section 126. Downconversion section 300 first downconverts feedback signal 134 for use in training linearandnonlinearpredistortion circuit 200 to compensate for various forms of linear distortion introduced into the signal input to HPA 136. Then, downconversion section 300 downconverts feedback signal 117 for use in training linearandnonlinear predistortion circuit 200 to compensate for various forms of linear and nonlinear distortion introduced into the signal output from HPA 136. Downconversion section 300 is discussed in more detail below in connection with Fig. 3. Downconversion section 300 generates a complex returndata stream 254. As indicated by the letter "L" in Fig. 2, returndata stream 254 exhibits a low resolution and higherror level, compared to the various forms of the forwarddata stream. For purposes of this discussion, all data streams that propagate away from analog components 120 and are based on returndata stream 254 are considered to be a form of the return data stream. Complexreturndata stream 254 drives an adjustable attenuator circuit 256. Adjustable attenuator circuit 256 desirably serves as a fine adjustment or vernier that is programmed or otherwise determines how to attenuate the signal level of returndata stream 254 to compensate for the gain inserted into the forward propagating communication signal by HPA 136, and attenuation provided by coupler 115. Adjustable attenuation circuit 256 may be implemented using a complex multiplier. Adjustable attenuator 256 produces an attenuatedcomplexreversedata stream 258 that is routed to a complex equalizer 260, which may be configured like equalizer 1200 but most likely has a greater number of taps. Fig. 2 applies the label EQ_{R} to equalizer 260, with the subscript "R" indicating that equalizer 260 filters the returndata stream. As discussed above in connection with equalizers 226 and 246, equalizer 260 serves as one part of equalizer section 234. And, equalizer 260 is desirably a nonadaptive equalizer that, when coupled through feature 236 to adaptation engine 1300, becomes an adaptive equalizer. By properly programming return filter coefficients (i.e., filter coefficients for return equalizer EQ_{R}) into equalizer 260, linear distortion that is introduced primarily by HPA 136 itself is compensated so that this form of linear distortion does not contaminate subsequent training that will take place to compensate for nonlinear distortion. The returnfilter coefficients are determined through a training process that is discussed below in connection with Figs. 1114. Equalizer 260 generates an equalizedcomplexreturndata stream 262 that maintains the relatively low resolution and high error level discussed above. The use of low resolution for processing the returndata stream leads to power and component savings. An output of multiplexer 222 drives a commonmodetimealignment section 700. Timealignment section 700 inserts the same amount of delay into the I and Q complex legs of either the forwarddata stream 218 or highestorderbasisfunctiondata stream 214', depending upon which stream has been selected at multiplexer 222. And, the amount of delay that timealignment section 700 inserts is programmable. Time alignment section 700 generates a delayedcomplexforwarddata stream 266. Timealignment section 700 is programmable so that stream 266 may be brought into temporal alignment with the returndata stream 262. Timealignment section 700 is discussed in more detail below in connection with Figs. 57. Delayedcomplexforwarddata stream 266 is routed to a phaserotate section 1000 and to a first data input of a multiplexer (MUX) 270. Phaserotate section 1000 rotates delayedcomplexforwarddata stream 266 by a programmable amount and generates an alignedcomplexforwarddata stream 272. Phaserotate section 1000 is programmable so that stream 272 may be brought into phasealignment with returndata stream 262 to compensate for the delay imposed by filters 132, 140, and/or 144 of analog components 120. Phaserotate section 1000 is discussed in more detail below in connection with Figs. 5 and 910. Alignedcomplexforwarddata stream 272 is routed to adaptation engine 1300 and to a second data input of multiplexer 270. In addition, alignedcomplexforwarddata stream 272 and equalizedcomplex returndata stream 262 are routed to a complexcombining circuit 274, depicted in Fig. 2 as two subtraction elements. Combining circuit 274 subtracts returndata stream 262 from forwarddata stream 272 to form an error signal or error stream 276. Both equalizedreturndata stream 262 and error stream 276 are routed to data inputs of a multiplexer (MUX) 278, as is deltaheat signal 216. And, error stream 276 is routed to a third data input of multiplexer 270 and to adaptation engine 1300, while a deltacoefficient (ΔCOEFF) signal 279 generated by adaptation engine 1300 is routed to a fourth data input of multiplexer 270. Outputs from multiplexers 270 and 278 are each routed to a correlation engine 280. In particular, outputs from multiplexers 270 and 278 are supplied to different data inputs of a complex multiplier 282, and a complex output from multiplier 282 couples to an input of an accumulator 284. Through multiplexers 270 and 278, a variety of different data streams may be correlated together in correlation engine 280. Multiplier 282 performs a basic correlation operation, and the correlation results are integrated in accumulator 284. One of the data streams correlated by correlation engine 280 is based upon the returndata stream and exhibits the lowresolution and higherror level discussed above. In the preferred embodiment, accumulator 284 desirably permits a massive amount of accumulation (e.g., between 2^{16} and 2^{24} samples) so that a multiplicity of samples are processed before making decisions based on correlation results. That way the effects of the low resolution and higherror level of the returndata stream are negated so that an effectiveerror level resulting after the integration is less, and can even be much less, than the error level of the returndata stream. Generally, the noise variance of a sampled signal decreases as the squareroot of the number of samples averaged together increases, so long as the "noise" is more or less uncorrelated. Thus, for example, the effectiveerror level of the return stream may be decreased by an amount equivalent to increasing resolution 10 bits (i.e., approximately 60 dB) over the error level of the return stream by accumulating correlations over 2^{20}, or roughly 10^{6}, samples. Fig. 2 depicts a controller 286 with numerous inputs and outputs. Although not explicitly shown to simplify the block diagram of Fig. 2, these inputs and outputs couple to the various subsections of linear andnonlinearpredistortion circuit 200 to provide controlling data thereto and to read data therefrom. For example, controller 286 controls multiplexers 278 and 270 to specify which data streams or signals are correlated together in correlation engine 280, and an output from accumulator 284 of correlation engine 280 is routed to controller 286. Controller 286 may be provided using any of a variety of conventional microprocessors or microcontrollers in a manner wellunderstood by those skilled in the art. As such, controller 286 may perform tasks defined by computer software instructions stored in a memory portion (not shown) of controller 286. In one embodiment, controller 286 may provide control functions for linearand nonlinearpredistortion circuit 200 as well as other sections of transmitter 100. Controller 286 and the tasks performed by linearandnonlinearpredistortion circuit 200 in response to the controlling influence of controller 286 are discussed in more detail below in connection with Figs. 46, 9, 11, and 1415. Fig. 3 shows a block diagram of a digitaldownconversion section 300 suitable for use in linearand nonlinearpredistortion circuit 200 of transmitter 100. Section 300 receives an RFanalog input from multiplexer 250, and routes that input to a programmableanalog attenuator 302. Control inputs of attenuator 302 determine the amount of attenuation provided by attenuator 302 and are provided by controller (C) 286. Attenuator 302 desirably serves as a coarse adjustment that operates in conjunction with digital adjustable attenuator 256 to attenuate the signal level of returndata stream 254 to compensate for the gain inserted into the forwardpropagating communication signal by HPA 136 and attenuation provided by coupler 115. An output of attenuator 302 couples to an input of an analogtodigital converter (A/D) 304. In addition, the same localoscillator signal used by upconversion section 126 is input to section 300 and received at a synthesizer 306. Synthesizer 306 is desirably configured to multiply the localoscillator frequency by four and divide the resulting product by an odd number, characterized as 2N±1, where N is a positive integer chosen to satisfy the Nyquist criteria for the superwideband signal discussed above, and is usually greater than or equal to ten. As a result, A/D 304 performs a direct downconversion through subharmonic sampling. In one embodiment, an averagepower calculator (not shown) may be included in section 300. This average power calculator is responsive to returndata stream 254. Desirably, average power is held to a constant level. Accordingly, analog attenuator 302 may be adjusted to optimize loading for A/D 304 in response to the average power, and digital adjustable attenuator 256 can then be adjusted to substantially equal the reciprocal gain applied by analog attenuator 302. This maintains the overall gain substantially at a constant. The directsubharmonicsamplingdownconversion process performed by A/D 304 requires that A/D 304 be capable of highspeed conversions. In addition, the subharmonic sampling process tends to sum thermal noise from several harmonics of the baseband into the resulting baseband signal, thereby increasing noise over other types of downconversion. While these factors pose serious problems in many applications, they are no great burden in section 300 because, as discussed above, only low resolution is required. Moreover, the low resolution demanded of A/D 304 likewise places no particular burden on the phasenoise in the clock signal generated by synthesizer 306 or aperturejitter characteristic of A/D 304. The low resolution requirement is permitted due to the operation of various estimationandconvergence algorithms, discussed below, that result in an averaging effect which reduces the impact of noise, phase jitter, and/or aperture jitter. In particular, A/D 304 is required only to provide a resolution at most four bits less than the forward resolution exhibited by the forwarddata stream 112 flowing through linearandnonlinearpredistortion circuit 200. In one embodiment, A/D 304 may be implemented by providing only one or two bits of resolution. As discussed above, various techniques, such as estimationandconvergence algorithms and integration, are used to translate increased arithmetic processing time into a reduced effectiveerror level for the returndata stream. Thus, the low resolution is effectively increased by processing a multiplicity of samples before decisions are made based on feedback signals, and no single sample or even small or medium size groups of samples have a significant influence by themselves on decisions made based on the feedback signals. Highquantization error and highthermalnoise error pose no particular problem for linearand nonlinearpredistortion circuit 200. In the preferred embodiment, linearandnonlinearpredistortion circuit 200 is provided on a common semiconductor substrate that may be predominantly manufactured using a CMOS process. But the high speed requirements of A/D 304 and synthesizer 306 may be provided for by using a SiGe process which is compatible with CMOS processing. The processing of the feedback signal upstream of A/D 304 has been performed using analog techniques and is therefore subject to the inaccuracies characteristic of analog processing. But A/D 304 provides a digitaldata stream, and subsequent processing will not be subject to analog inaccuracies. That digitaldata stream characterizes the complex feedback signal as a combination signal in which the I and Q legs are combined together. Subsequent processing is performed to appropriately position the subharmonic of interest at baseband and to separate the I and Q legs of the complex signal. Although processing is subsequently performed independently on the I and Q legs of the complex signal, such processing is performed digitally, so no linear distortion is introduced due to quadrature imbalances and/or diverse frequencydependent gain and phase characteristics. In particular, the digitaldata stream output from A/D 304 is routed to a demultiplexer (DEMUX) 308, which separates the stream into evenandoddsampledata streams. One of these evenandoddsample data streams is merely delayed in a delay element 310, while the other is transformed in a Hilbert transformation section 312. Outputs from element 310 and section 312 are filtered in highpass filters (HPF's) 314 to remove DC, where they then collectively serve as complexreturndata stream 254. Of course, the rates of the data streams slow as they propagate through section 300, and clock signals are appropriately divided down (not shown) to support the decreasing data rates. It is highpass filters 314 that are matched by highpass filter 205. Fig. 3 depicts one form of a complexdigitalsubharmonicsampling downconverter suitable for use as digitaldownconversion section 300. But those skilled in the art can devise other forms of directdigital subsampling downconversion that will also be acceptable. While direct downconversion is desirable because it does not introduce different analog inaccuracies into the I and Q legs which can lead to linear distortion or other analog inaccuracies that can lead to nonlinear distortion, in higherfrequency applications (e.g., greater than 2.5 GHz) downconversion may be performed in two stages, with the first stage being an analog downconversion. In this situation distortion introduced by the first analog downconversion stage will be less significant because it will be applied over a significantly narrower bandwidth as a percentage of the carrier frequency. Fig. 4 shows a flowchart of a first embodiment of a transmissiondistortionmanagement process 400 performed by transmitter 100. Process 400, as well as the subprocesses and subsubprocesses included therein, are carried out under the control of controller 286 through the performance of software in a manner wellunderstood by those skilled in the art. A second embodiment of process 400 is discussed below in connection with Fig. 19 and is referred to as process 1900. A third embodiment of process 400 is discussed below in connection with Fig. 32 and is referred to as process 3200. Process 400 may be initiated immediately after transmitter 100 is energized, or at any time while transmitter 100 is operating. Generally, analog components 120 introduce distortion into RF communications signal 116 from a variety of sources. In other words, RFcommunications signal 116 may be viewed as exhibiting a variety of different types of distortions rather than a single distortion. Not only is there a distinction between linear and nonlinear distortions, but linear distortions have a variety of different causes. Process 400 trains linearandnonlinearpredistortion circuit 200 to compensate for the worst of these distortions on a onebyone basis. Training is performed using estimationandconvergence algorithms so that complex processing may be avoided and so that sensitivity to error in the feedback signal is reduced. But the calculation of forward transfer functions and inversing operations are avoided. Process 400 first performs a subprocess 500 to compensate for linear distortion introduced upstream of HPA 136. Fig. 5 shows a flowchart of subprocess 500. Subprocess 500 first performs an initialization task 502. Task 502 initializes the various sections of linearandnonlinear predistortion circuit 200 so that training may begin. In particular, forward equalizer 246 and reverse equalizer 260 are both programmed with filter coefficients that cause them to merely pass, and not alter, the forward and reverse data streams, respectively. Adaptation engine 1300 is decoupled from all equalizers. Adjustable attenuators 256 and 302 are programmed to apply a gain of one (i.e., neither gain nor attenuation). A selectioncontrol value is provided to multiplexer 250 to route RFanalog feedback signal 134 (RF1) to downconversion section 300. Basis functions are zeroed by controlling nonlinear predistorter 224 to produce constant zero values regardless of input. Multiplexer 222 is controlled to route forwarddata stream 218 to timealignment section 700. Correlation engine (CE) 280 is configured to correlate "ideal"delayedforwarddata stream 266 and returndata stream 262 by appropriate selection values being supplied to multiplexers 278 and 270. Delayed forwarddata stream 266 is considered to be ideal because it has not been distorted either by predistortion circuit 200 or analog components 120. Time alignment implemented by timealignment sections 700 and 800 is set to midrange values, and the processing of deltaheat signal 216 is disabled. At this point, linearand nonlinearpredistortion circuit 200 is prepared to begin training for linear compensation. Following task 502, a task 504 invokes a subprocess 600 to implement a timealignmentestimation andconvergence algorithm. In particular, subprocess 600 implements this algorithm in task 504 for a programmable delay element provided by commonmodetimealignment section 700. Thus, subprocess 600 will now temporally align delayedcomplexforwarddata stream 266 with the complexreturndatastream 262. Following task 504, a task 506 invokes subprocess 600 again, or an equivalent process, to again implement the timealignmentestimationandconvergence algorithm, but this time for a programmable delay element provided by differentialmodetimealignment section 800. During task 506 subprocess 600 temporally aligns the I and Q legs of complexforwarddata stream 238. Fig. 6 shows a flowchart of a subprocess 600 that may be applied during each of tasks 502 and 504 in connection with timealignment sections 700 and 800, respectively. In commonmode task 504, control of timealignment section 700 adjusts the delay imposed in delayedcomplexforwarddata stream 266, but in differentialmode task 506, control of timealignment section 800 adjusts the delay imposed in one of the I and Q legs of complexreturndatastream 262 relative to the other. Subprocess 600 performs a task 602 to couple correlation engine (CE) 280 to the "ideal" delayed complexforwarddata stream 266 and to complexreturndatastream 262 by appropriate selection at multiplexers 270 and 278. Next, a task 604 sets correlation convergence criteria. The convergence criteria determine how many samples correlation engine 280 needs to correlate and integrate before it can be deemed as having converged upon a correlation solution. As discussed above, a greater number of samples processed leads to a greater increase in effective resolution, or reduction in error level, in the returndata stream. An increase in algorithmic processing time is thus transformed into a reduced effectiveerror level for the returndata stream. Through task 604, the rate of convergence is controlled to achieve a predetermined effective return error level less than the error level associated with the returndata stream. In one example, approximately 10^{6} samples may be processed to achieve a signaltonoise improvement of around 60 dB. Of course, subprocess 600 is not required to set different convergence criteria in different situations, but correlation engine 280 may be hardwareprogrammed to use the same criteria for all situations. In this situation, task 604 is performed by correlation engine 280 and not controller 286. After task 604, subprocess 600 performs a query task 606. Task 606 determines when correlation engine 280 has converged upon a correlation solution. During task 606, correlation engine 280 processes a multiplicity of samples. Correlation is performed between the returndata stream and the delayedforward data stream as delayed through a programmable delay element that has been programmed to impose some duration of delay. That programmable delay element was initialized to a midrange value. When that correlation solution occurs, an initializing task 608 then makes an initializing estimate of a large step and positive offset to use in an upcoming binarysearch algorithm. The step size of "large" refers to how different the programmed duration for an upcoming iteration of the binarysearch algorithm will be from delay imposed in the previous correlation. The offset of "positive" is an arbitrary value that indicates that the upcoming iteration delay will be greater than the previous. After task 608, a task 610 adjusts the programmable timealignment hardware (either section 700 or section 800) to reflect the current step size and offset direction. Fig. 7 shows a block diagram of one embodiment of commonmodetimealignment section 700. This embodiment is desirable because it achieves accurate and precise results using a relatively simple hardware implementation. But while timealignment section 700 provides suitable results for the purposes of linearandnonlinearpredistortion circuit 200, those skilled in the art will be able to devise alternate embodiments that will also work. Timealignment section 700 includes a minimumdelay element 702 that receives the complexdata stream from multiplexer 222. Minimumdelay element 702 is a nonprogrammable element that inserts an integral number of clockcycle delays roughly equivalent to the minimum delay that is expected to be imposed by the combination of: combining circuit 200, timealignment section 800, linear predistorter 244, analog components 120, feedback section 248, attenuator 256, and equalizer 260. A clocked, complextappeddelay line 704 is driven by minimumdelay element 702. Each leg of the complex signal is equivalently delayed in delay line 704. While Fig. 7 depicts eight taps 706, those skilled in the art will appreciate that any number of taps 706 may be provided. Taps 706 couple to data inputs of a multiplexer 708, which has an output that routes a selected tap to an input of a complex interpolator 710. Interpolator 710 may be implemented using a Farrow or other architecture and delays both legs of the complex signal by equal amounts. An output of interpolator 710 provides delayedcomplex forwarddata stream 266. Controller (C) 286 provides control inputs to multiplexer 708 and interpolator 710. A clock signal 712 is also provided to minimumdelay element 702, delay line 704, and interpolator 710. Clock 712 is desirably synchronized to the data rate of the forwarddata and returndata streams. When task 610 is being used for commonmodetimealignment section 700 (i.e., during task 504), timealignment section 700 may be adjusted by providing appropriate controlling inputs to multiplexer 708 and interpolator 710. An integral section 714 includes delay line 704 and multiplexer 708 and serves to provide an integral number of cycles of clock 712 delay, as specified by control data provided by controller 286. A fractional section 716 includes interpolator 710 and serves to provide a fraction of a cycle of a clock 712 delay. An integral portion of any delay to be programmed into timealignment section 700 is accomplished by controlling multiplexer 708, and a fractional portion of the delay is accomplished by controlling interpolator 710. Fig. 8 shows a block diagram of one embodiment of differentialmodetimealignment section 800. This embodiment is desirable because it achieves accurate and precise results using a relatively simple hardware implementation. But while timealignment section 800 provides suitable results for the purposes of linearandnonlinearpredistortion circuit 200, those skilled in the art will be able to devise alternate embodiments that will also work. Differentialmodetimealignment section 800 is in many ways similar to commonmodetimealignment section 700, but has a different effect. One leg, shown as the I leg in Fig. 8, of complexforwarddata stream 238 is routed to a clocked, tappeddelay line 802. The other leg, shown as the Q leg in Fig. 8, is routed to a fixeddelay element 804. Delay element 804 is configured to implement about Vi of the delay of delay line 802. While Fig. 8 depicts delay line 802 as having eight taps 806, those skilled in the art will appreciate that any number of taps 806 may be provided. Taps 806 couple to data inputs of a multiplexer 808, which has an output that routes a selected tap to an input of an interpolator 810. Interpolator 810 may be implemented using a Farrow or other architecture. An output of interpolator 810 provides the I leg of complexforwarddata stream 242 while an output of delay element 804 provides the Q leg of data stream 242. Controller (C) 286 provides control inputs to multiplexer 808 and interpolator 810. A clock signal 812 is also provided to delay line 802, delay element 804, and interpolator 810. Clock 812 is desirably synchronized to the data rate of the forwarddata and returndata streams. When task 610 is being used for differentialmodetimealignment section 800 (i.e., during task 506), timealignment section 800 may be adjusted by providing appropriate controlling inputs to multiplexer 808 and interpolator 810. An integral section 814 includes delay line 802 and multiplexer 808 and serves to provide an integral number of cycles of clock 812 delay, as specified by control data provided by controller 286. A fractional section 816 includes interpolator 810 and serves to provide a fraction of a cycle of a clock 812 delay. An integral portion of any delay to be programmed into timealignment section 800 is accomplished by controlling multiplexer 808, and a fractional portion of the delay is accomplished by controlling interpolator 810. Referring back to Fig. 6, after task 610 adjusts timealignment hardware to reflect a new delay duration based upon the old delay duration and the current step size and polarity, a query task 612 is perfonned. During task 612, correlation engine 280 performs its correlation and integration operation until the correlation criteria have been met. When task 612 determines that the correlation criteria have been met, a query task 614 determines whether the current correlation results are greater than the maximum correlation recorded so far during this invocation of process 600. If the current correlation results are not greater than prior correlations, then a task 616 makes the step estimate the same size as before but changes the offset polarity, and program control proceeds to a query task 618. If the current correlation results are greater than the maximum correlation, a task 620 estimates a step size reduced from the previous step size, and typically 0.5 to 1.0 times the previous step size, and also estimates the same polarity offset. Then, program control proceeds to task 618. Task 618 determines whether the timealignmentestimationandconvergence algorithm has now converged on either a commonmodedelay value or differentialmodedelay value that maximizes the correlation between the forwarddata and returndata streams. Convergence may be determined by monitoring the current step size and concluding that convergence has been reached when the current step size is less than the resolution of interpolator 710 or 810. When task 618 determines that delay convergence has not yet occurred, program control loops back to task 610. At task 610 the previous estimate of delay is altered in accordance with the current step size and offset polarity, and the correlation process repeated. When task 618 determines that delay convergence has occurred, subprocess 600 is complete. At this point, delayedcomplexforwarddata stream 266 has been temporally aligned with complexreturndata stream 262. And, linearcompensation process 500 may proceed to perform another alignmentprocess which is a prerequisite in the preferred embodiment to actual linear compensation. Referring back to Fig. 5, after the invocation of subprocess 600 two times, once for commonmode time alignment and once for differentialmode time alignment in tasks 504 and 506 respectively, a subprocess 900 is performed to implement an estimationandconvergence algorithm in which aligned complexforwarddata stream 272 is rotated in phase relative to delayedcomplexforwarddata stream 266 by phase rotator 1000. Fig. 9 shows a flowchart of subprocess 900. Subprocess 900 includes a task 902 that controls multiplexer 270 so that correlation engine 280 is coupled to perform correlation between the "ideal" aligned complexforwarddata stream 272 and the complexreturndata stream 262. Then, a task 904 deselects CORDIC cells. Task 904 is directed to a specific hardware implementation for phase rotator 1000 that is implemented in the preferred embodiment. Fig. 10 shows a block diagram of one embodiment of phaserotate section 1000. This embodiment is desirable because it achieves accurate and precise results using a relatively simple hardware implementation. But while phaserotate section 1000 provides suitable results for the purposes of linearandnonlinear predistortion circuit 200, those skilled in the art will be able to devise alternate embodiments that will also work. Phaserotate section 1000 includes a quadrant selection cell 1002, followed by a cascaded series of CORDIC cells 1004. Fig. 10 depicts only two of CORDIC cells 1004 in detail, labeled cells 1004 and 1004'. But the remaining cells 1004 should have a structure similar to cell 1004'. Any number of CORDIC cells 1004 may be included, with the preferred embodiment having between 6 and 16 cells 1004. If ten CORDIC cells 1004 are included, then precision may be provided to within about 0.112 degrees. Delayedcomplexforwarddata stream 266 is received at quadrantselection cell 1002. Each leg of the complexdata stream is received at its own selective inversion circuit 1006, depicted in Fig. 10 as a multiplier. Selective inversion circuits 1006 are independently controlled by controller 286 to either invert, or let the data stream pass unaltered. Fig. 10 depicts each cell 1002 and 1004 as terminating at a latch 1008. By controlling circuits 1006 to exhibit all combinations of inversion and passing, four possible quadrants are estimated, wherein cell 1002 can shift the incomingdata stream 266 either 0°, 90°, 180°, or 270° degrees. Within each CORDIC cell 1004, the I and Q legs of the cell's incomingcomplexdata stream are respectively routed to shifters 1010. Fig. 10 depicts shifters 1010 as being multiplication circuits because shifters 1010 perform mathematical multiplication by the inverse of a power of two. For the first CORDIC cell 1004, shifters 1010 may be omitted because they shift the incoming data to the right by zero bits and perform a multiplication by one. In the second cell 1004' and subsequent cells 1004, shifters 1010 shift the incoming data to the right by one additional bit from the shift of the previous cell. Thus, Fig. 10 depicts shifters 1010 as multiplying by 0.5 in cell 1004'. The third CORDIC cell 1004 would effectively multiply by 0.25, and so on. Those skilled in the art will appreciate that shifters 1010 need not be implemented using physical components but may be implemented merely through interconnections. Within each CORDIC cell 1004, outputs from shifters 1010 are routed to inputs of a selective enablement circuit 1012, depicted as a couple of AND gates in this embodiment, with one gate for each leg of the complex signal. The other input of each AND gate is controlled by controller 286. Thus, controller 286 either enables the output from shifters 1010 to pass unimpeded, or forces a zero value. In the I leg of each CORDIC cell 1004, a subtractor 1014 subtracts the output of the selective enablement circuit 1012 in the Q leg from the I leg of the incomingdata stream. In the Q leg of each CORDIC cell 1004, an adder 1016 adds the output of the selectiveenablement circuit 1012 in the I leg with the Q leg of the incomingdata stream. From subtractor 1014 and adder 1016, the I and Q legs exit the CORDIC cell 1004 through latch 1008. Each CORDIC cell 1004 rotates its incoming complex signal by progressively smaller angles, as indicated in the following example:
Each cell's rotation is slightly more, than Vi of the previous cells' rotation. Thus, by selectively combining the rotation of various CORDIC cells 1004, any angle within the range of 0°  90° may be achieved, to a resolution determined by the number of CORDIC cells included in phase rotator 1000. Although not shown, a scaling stage may be used to compensate for the magnitude scaling caused by processing the signal through the CORDIC cells 1004. In one embodiment, each CORDIC cell 1004 may be set to either a positive or negative value to maintain the scaling at a constant level for different rotations. Referring to Figs. 9 and 10, task 904 disables selectiveenablement circuits 1012 in each cell 1004 so that in no cell 1004 is any portion of one leg's signal crosscoupled to the other leg. Consequently, CORDIC cells 1004 do not rotate as a result of task 904. Following task 904, a task 906 sets the convergence criteria. As discussed above in connection with task 604, setting the convergence criteria controls the rate of correlation convergence to achieve a predetermined effectiveerror level using the lowresolution returndata stream. Through task 906, increased algorithmic processing time is transformed into reduced effectiveerror levels for the returndata stream. After task 906, a task 908 selects another quadrant by adjusting the control inputs at selective inverters 1006. The current amount of rotation imparted by phaserotation section 1000 represents an estimate of the phase rotation needed to bring alignedcomplexforwarddata stream 272 into phase alignment with complexreturndata stream 262. Following task 908, correlation engine 280 integrates the correlation between alignedcomplex forwarddata stream 272 and complexreturndata stream 262 at the current phase rotation estimate. A query task 910 determines whether the convergence criteria set above in task 906 have been met. Program control remains at task 910 until the criteria are met. When the convergence criteria are met, a query task 912 determines whether all four quadrants have been selected yet. If fewer than four quadrants have been tried, the correlation results are saved and program control loops back to task 908 until all four quadrants have been tested. While tasks 908, 910, and 912 depict one embodiment of quadrant evaluation, in an alternate embodiment one of the legs of the forwarddata and reversedata streams may be correlated with both legs of the other stream. Moreover, results from a prior correlation subprocess, such as subprocess 600 may be used. Then, quadrant selection may be made based on the relative magnitudes and polarities of the correlation results. When all four quadrants have been tested or otherwise evaluated, a task 914 selects the quadrant that generated or should generate the maximum correlation from the four quadrants and so programs selective inverters 1006. Then, a task 916 selects the nextmostsignificant CORDIC cell 1004 by enabling that cell 1004. For the first iteration of task 916, the CORDIC cell 1004 that shifts by 45° is selected. At this point another estimate of the phase rotation needed to bring alignedcomplexforwarddata stream 272 into phase alignment with complexreturndata stream 262 has been made, and correlation engine 280 performs its correlation and integration task. Following task 918, a query task 916 determines whether the convergence criteria set above in task 906 have been met. When the convergence criteria are met, a query task 920 determines whether the maximum correlation recorded so far for this invocation of subprocess 900 has been increased by the most recent estimate. If no increase is detected, then a task 922 deselects the current CORDIC cell 1004. Following task 922 and when task 920 detects an increase in maximum correlation, a task 924 deteπnines whether the last, leastsignificant CORDIC cell 1004 has been selected. So long as lesssignificant CORDIC cells 1004 remain to be tested, program control loops back to task 916. When task 924 determines that the last CORDIC cell 1004 has been evaluated, subprocess 900 is complete. At this point subprocess 900 has tested all CORDIC cells 1004 and selected that combination of cells 1004 that yielded the phaserotation estimate achieving the maximum correlation, as determined by correlation engine 280. This subprocess brings alignedcomplexforwarddata stream 272 into phase alignment with complexreturndata stream 262, to a degree of precision determined by the convergence criteria used by correlation engine 280 and the number of CORDIC cells 1004 included in phaserotate section 1000. Referring back to Fig. 5, after the completion of subprocess 900, a task 508 optimizes the gain adjustment provided by adjustable attenuators 302 and 256. Accordingly a suitable optimization algorithm is implemented in task 508 to increase and/or decrease programmable attenuation provided in coarse adjustment and fineadjustment attenuators 302 and 256, respectively. The optimization algorithm may desirably make attenuation adjustments in order to minimize the integrated difference between forwarddata stream 272 and returndata stream 262. The optimization algorithm may use techniques similar to those discussed above in connection with Figs. 610, or other techniques may be applied. Following task 508, linearandnonlinearpredistortion circuit 200 is now sufficiently trained so that it is prepared to more directly address the problem of compensation for linear distortion introduced by analog components 120. At this point the "ideal" forwarddata stream and the reversedata stream are in time and phase alignment with each other at complex combining circuit 274. Accordingly, error stream 276 now describes distortion introduced by analog components 120. But as described above, error stream 276 is formed, at least in part, from the returndata stream and exhibits a high error level and low resolution. A subprocess 1100 is now invoked to perform an equalizationestimationandconvergence algorithm for forward equalizer 246. Fig. 11 shows a flowchart of subprocess 1100. Subprocess 1100 is configured to operate with a particular embodiment of a nonadaptive equalizer 1200 and a particular embodiment of an adaptation engine 1300. Fig. 12 shows a block diagram of a representative nonadaptive equalizer 1200 suitable for use in several sections of the linearandnonlinearpredistortion circuit 200 and for use in connection with subprocess 1100. Forward equalizer 246 may be configured similarly to nonadaptive equalizer 1200 but is likely to have more taps. Likewise, Fig. 13 shows a block diagram of an adaptation engine 1300 suitable for use in connection with the nonadaptive equalizer 1200 depicted in Fig. 12 and with linearandnonlinear predistortion circuit 200. But those skilled in the art will understand that other embodiments of nonadaptive equalizer 1200, adaptation engine 1300, and subprocess 1100 may be devised to achieve many of the goals of the present invention. Referring to Fig. 12, nonadaptive equalizer 1200 is a complex equalizer depicted for convenience as having only three taps, but those skilled in the art will understand that the number of taps may be easily expanded or shrunk as needed for a particular application. The I and Q legs of the complexinputdata stream are applied at nodes 1202 and 1204, respectively. Equalizer 1200, or the equivalent, may be used in a variety of locations in linearandnonlinearpredistortion circuit 200, such as for equalizers 226, 246, and/or 260. Consequently, the precise identity of the complexinputdata stream will depend upon its location of use. Inode 1202 couples to and drives clockedtappeddelay lines 1206 and 1208, and Qnode 1204 couples to and drives clockedtappeddelay lines 1210 and 1212. Delay line 1206 drives an inphase, direct path 1214 of equalizer 1200; delay line 1210 drives a quadrature, direct path 1216 of equalizer 1200; delay line 1208 drives an inphasetoquadrature, crossover path 1218 of equalizer 1200; and, delay line 1212 drives a quadraturetoinphase, crossover path 1220 of equalizer 1200. Each tap 1222 from each delay lines 1206, 1208, 1210, and 1212 drives a first input of its own multiplier 1224, and outputs of multipliers 1224 drive adders 1226. An output from inphase path 1214 is provided by the sum of all multiplier 1224 outputs in that path to a positive input of a subtractor 1228, and an output from quadraturetoinphase path 1220 is provided by the sum of all multiplier 1224 outputs in that path to a negative input of subtractor 1228. An output from quadrature path 1216 is provided by the sum of all multiplier 1224 outputs in that path to a first input of an adder 1230, and an output from inphaseto quadrature path 1218 is provided by the sum of all multiplier 1224 outputs in that path to a second input of adder 1230. An output of subtractor 1228 provides the I leg of the complexoutputdata stream while the output of adder 1230 provides the Q leg of the complexoutputdata stream. Each tap 1222 of the inphase and quadrature direct paths 1214 and 1216 has the same filter coefficient, provided by a multiplexer 1232 through an optional heatadapter unit 1234, which has one output for each tap 1222. Fig. 12 shows two heatadapter units 1234, with details provided for only one of the two heatadapter units 1234. If heatadapter units 1234 are omitted, then each tap's filter coefficient is provided directly from multiplexer 1232. That filtercoefficient output couples to a second input of the corresponding two multipliers 1224 in direct paths 1214 and 1216. Likewise, each tap 1222 of the crossover paths 1218 and 1220 has the same filter coefficient, provided by a multiplexer 1236 through an optional heatadapter unit 1234, which has one output for each tap 1224. That filtercoefficient output couples to a second input of the corresponding two multipliers 1224 for crossover paths 1218 and 1220. Multiplexers 1232 and 1236 receive filter coefficients either from adaptation engine 1300 at feature 236 or from controller 286. When heatadapter units 1234 are included, a heatsensitivity coefficient is also received either from adaptation engine 1300 or controller 286. Controller 286 also controls selection inputs of multiplexers 1232 and 1234 to couple and decouple equalizer 1200 from adaptation engine 1300 by routing filter coefficients and heatsensitivity coefficients either from controller 286 or from adaptation engine 1300. When filter coefficients and optional heatsensitivity coefficients are supplied from controller 286, equalizer 1200 operates in a nonadaptive mode. In the nonadaptive mode a set of directfilter coefficients and directheatsensitivity coefficients are programmed into the direct paths 1214 and 1216 by controller 286, and a set of crossoverfilter coefficients and crossoverheatsensitivity coefficients are programmed into the crossover paths 1218 and 1220 by controller 286. Neither set of filter coefficients changes unless controller 286 alters the programming. But the filter coefficients may optionally be adjusted within heatadapter units 1234 in response to deltaheat signal 216. In the preferred embodiment, optional heatadapter units 1234 are included with nonadaptive equalizers 226, but may be included with other equalizers or omitted from all equalizers in other applications. Each heatadapter unit 1234 includes a multiplier 1238 for each tap and an adder 1240 for each tap. Deltaheat signal 216 couples to first inputs of each of multipliers 1238. For each tap, multiplexer 1232 or 1238 provides a heatsensitivity coefficient "α" to second inputs of the tap's multiplier 1238. Respective outputs of multipliers 1238 couple to corresponding first inputs of adders 1240. And, for each tap, multiplexer 1232 or 1236 provides a filter coefficient "w" to second inputs of adders 1240. The outputs of adders 1240 provide the filtercoefficient outputs of heatadapter units 1234. Thus, filter coefficients are offset, either positively or negatively, in response to deltaheat signal 216 as weighted by heatsensitivity coefficients. When filter coefficients and optional heatsensitivity coefficients are supplied from adaptation engine 1300, equalizer 1200 operates in an adaptive mode. In the adaptive mode at least one of the direct and crossover sets of filter coefficients and heatsensitivity coefficients are supplied by adaptation engine 1300, and these sets of filter coefficients and heatsensitivity coefficients can continuously change so long as equalizer 1200 remains in its adaptive mode. Referring to Fig. 13, in one embodiment adaptation engine 1300 is configured to accommodate a partial complex equalizer to reduce the number of components of linearandnonlinearpredistortion circuit 200. In particular, when adaptation engine 1300 is coupled to a nonadaptive equalizer 1200, it is coupled to either the direct paths 1214 and 1216 or to the crossover paths 1218 and 1220, but not both. For consistency with the threetap complex equalizer 1200 depicted in Fig. 12, Fig. 13 depicts a threetap arrangement. But those skilled in the art will understand that the number of taps may be easily expanded or shrunk as needed for a particular application. The I and Q legs of the "ideal" alignedcomplexforwarddata stream 272 are respectively supplied to clockedtappeddelay lines 1302 and 1304, with each delay line being depicted as having three taps for convenience. The I and Q legs of error stream 276 are supplied to delay elements 1306 and 1308, where delay elements 1306 and 1308 are each configured to delay the error stream 276 to the middle of tapped delay lines 1302 and 1304, when adaptation engine 1300 is operated in the mode where it is coupled to direct paths 1214 and 1216 of nonadaptive equalizer 1200. The Q and I legs of error stream 276 are supplied to delay elements 1306 and 1308 when adaptation engine 1300 is operated in the mode where it is coupled to crossover paths 1218 and 1220. Taps 1310 from the inphase delayline 1302 respectively couple to first inputs of corresponding inphase multipliers 1312, and taps 1314 from the quadrature delayline 1304 respective couple to first inputs of corresponding quadraturephase multipliers 1316. Outputs from inphase multipliers 1312 respectively couple to first inputs of corresponding adders 1318, and outputs from quadrature multipliers 1316 respectively couple to second inputs of the corresponding adders 1318 through selective inversion elements 1320. Selective inversion elements 1320 are depicted in Fig. 13 as being multipliers, with one of the multiplier inputs being controlled by controller 286. Controller 286 causes inversion of the weighted quadrature signals output by quadrature multipliers 1316 when adaptation engine 1300 is operated in the mode where it is coupled to crossover paths 1218 and 1220 of nonadaptive equalizer 1200, but no inversion of the weightedquadrature signals output by quadrature multipliers 1316 when adaptation engine 1300 is operated in the mode where it is coupled to direct paths 1214 and 1216. Those skilled in the art will appreciate that multipliers need not be used to implement selective inversion elements 1320. Likewise, those skilled in the art will appreciate that complexity may be reduced in adaptation engine 1300 by quantizing error signal 276, idealaligned signal 272, or both to a single bit or to a /0/+ triplet. In this alternative, the above discussed multipliers may be replaced by simpler circuits. Respective outputs of adders 1318 present noisy signals because they are based on the returndata stream. These outputs couple to first inputs of corresponding multipliers 1322, with the second inputs of multipliers 1322 all being coupled to controller 286. Controller 286 provides a convergence factor "μ" which determines how much filter coefficients are allowed to change from clockcycle to clockcycle. In the preferred embodiment, a small value is used for μ to prevent any single instance or even moderatesized groups of instances of the noisy signals output by adders 1318 from exerting a great influence by allowing a significant amount of change. Respective outputs of multipliers 1322 couple to first inputs of corresponding adders 1324. Respective outputs of each adder 1324 couple through first data inputs of corresponding multiplexers (MUX) 1326 to corresponding onecycle delay elements 1328. Second data inputs and selection control inputs of multiplexers 1326 are provided by controller 286. Delay elements 1328 may be initialized to predetermined filter coefficients by controller 286. But in normal adaptationoperating conditions, each adder 1324 adds a changeinfiltercoefficient value to the previous coefficient value that has been retained in the corresponding delay element 1328. In addition, for each tap, the output of adder 1324 provides filter coefficient "w" that is output by adaptation engine 1300 at feature 236. Filter coefficients "w" are provided to equalizers 1200 when operating in their adaptive modes and are also readable by controller 286. Subsequent processing of filter coefficients is directed to the heatrelated memory effect. In particular, the filter coefficients "w" output from respective adders 1324 are routed to corresponding IIR filter circuits. The filter circuits each include a subtraction circuit 1330, a multiplier 1332, an adder 1334, and a onecycle delay element 1336. Outputs from respective adders 1324 couple to positive inputs of corresponding subtraction circuits 1330. Respective outputs of corresponding subtraction circuits 1330 provide the filter output and couple to first inputs of sensitivity multipliers 1332. Second inputs of each of sensitivity multipliers 1332 are adapted to receive a coefficientsensitivity factor γ supplied by controller 286. Outputs of respective multipliers 1332 provided to first inputs of corresponding adders 1334, and outputs of respective adders 1334 are delayed for one clock cycle through corresponding delay elements 1336. Respective outputs of delay elements 1336 are routed to second inputs of the corresponding adders 1334 and to negative inputs of the corresponding subtraction circuits 1330. An averagecoefficient output in each filtering circuit is provided by adder 1334. This output represents a longterm average or filtered signal for the filter coefficient "w". Subtraction circuit 1330 determines the difference between the current instantaneous value for the filter coefficient "w" and the long terra average, as set forth in the previous clock cycle. Coefficientsensitivity factor γ determines the sensitivity of the longterm average to the influence of instantaneous filter coefficients, with smaller values for γ making the average reflect a longer terra and less sensitive to the filter coefficient from any one clock cycle. A deltacoefficient stream 1338 is provided by the output of subtraction circuit 1330. For the middle tap of adaptation engine 1300, deltacoefficient stream 1338 forms deltacoefficient signal 279 that is selectively routed toward correlation engine 280. It is the change in filter coefficients determined in response to average filter coefficient values over a preceding duration that can correlate with changes in temperature when HPA 136 experiences the heat related memory effect. Accordingly, subsequent adaptation processing implements an LMS estimationand convergence adaptation algorithm on deltacoefficient streams 1338. In particular, respective delta coefficient streams 1338 are routed to positive inputs of corresponding subtraction circuits 1340. Outputs of respective subtraction circuits 1340 are routed to first inputs of corresponding multipliers 1342, and outputs of respective multipliers 1342 are routed to first inputs of corresponding convergence multipliers 1344. Outputs of respective convergence multipliers 1344 are routed to first inputs of corresponding adders 1346, and outputs of respective adders 1346 are routed back to second inputs of the same adders 1346 through corresponding onecycle delay elements 1348, thereby forming integrators from adders 1346 and delay elements 1348. In addition, the outputs of respective adders 1346 are routed to first inputs of corresponding multipliers 1350, and outputs of respective multipliers 1350 are routed to negative inputs of corresponding adders 1340. Deltaheat signal 216 drives second inputs of all multipliers 1350 and all multipliers 1342. And second inputs of convergence multipliers 1344 are supplied with a convergence value λ from controller 286. The outputs of adders 1346 provide heatsensitivity coefficients α output from adaptation engine 1300 at feature 236. Heatsensitivity coefficients α are provided to equalizers 1200 when operating in their adaptive modes and are also readable by controller 286. Over time, heatsensitivity coefficients α converge to increasingly accurate estimates of the sensitivity of changes in filter coefficients "w" to the deltaheat signal 216. As discussed below in connection with Fig. 17, deltaheat signal 216 characterizes the change in heat in HPA 136. Thus, heatsensitivity coefficients α are used with the heat signal and filter coefficients in heatadapter units 1234 to remove correlation that may exist between changes in heat in HPA 136 and changes in equalizer filter coefficients. In other words, heatsensitivity coefficients α are determined which, when multiplied by deltaheat signal 216, cause the heat signal to become maximally correlated with the corresponding deltacoefficient signals 1338. Fig. 13 depicts all onecycle delay elements 1348 as having a clear input driven by an output from controller 286. This input allows controller 286 to initialize delay elements 1348 to a zero condition and to disable heat processing. In one alternative embodiment of adaptation engine 1300, integrateanddump operations (not shown) may be performed on deltaheat signal 216 and deltacoefficient signals 1338 to slow their data rates. This is permitted because heat changes take place on a slower time scale than the symbolbysymbol basis at which data is processed through transmitter 100. By slowing the data rates at this point, power may be conserved downstream of deltacoefficient signals 1338. Referring back to Fig. 11, subprocess 1100 operates with an equalizer 1200 and with adaptation engine 1300 to implement an estimationandconvergence algorithm that is tolerant of the low resolution and higherror level characteristic of error stream 276. When subprocess 1100 is being operated to address lineardistortion compensation and for initial stages of nonlineardistortion compensation, heat processing is disabled through the operation of initialization task 502. Heat processing may be disabled by forcing one cycle delay elements 1348 to exhibit zero values and by setting the convergence value λ to zero. This causes heatadapter units 1234 to have no effect. But the disabling of heat processing is a moot point in connection with the equalizers 1200 that serve as forward or return equalizers 246 and 260 and that omit heatadapter units 1234 in the preferred embodiment. Subprocess 1100 performs a task 1102 to lock adaptation engine 1300. Adaptation engine 1300 may be locked by supplying a convergence factor of μ=0 to adaptation engine 1300. By locking adaptation engine 1300, filter coefficients "w" supplied through feature 236 cannot change. After task 1102, a task 1104 initializes the mode of adaptation engine (AE) 1300 to determine the filter coefficients for direct paths 1214 and 1216 of equalizer 1200. The choice of direct paths 1214 and 1216 over crossover paths 1218 and 1220 is arbitrary at this point. Adaptation engine 1300 may be initialized to directpathfiltercoefficient adaptation by controlling selective inversion circuits 1320 so that they do not invert the weightedquadrature signals they process. Following task 1104, subprocess 1100 begins a routine 1106 in which a set of filter coefficients is determined using an estimationandconvergence algorithm for 1/2 of a complex equalizer 1200. Of course, nothing requires adaptation engine 1300 to adapt only a portion of the paths of an equalizer 1200. If adaptation engine 1300 is configured to simultaneously adapt all paths of an equalizer 1200, then the circuitry of adaptation engine depicted in Fig. 13 is substantially doubled, but selective inversion circuits 1320 and task 1104 may be omitted. In this case, onehalf of adaptation engine 1300 would perform addition in circuits 1318, and the other half of adaptation engine 1300 would perform subtraction in circuits 1318. In particular, following task 1104, a task 1108 initializes adaptation engine (AE) filter coefficients. Task 1108 may initialize filter coefficients by forcing onecycle delay elements 1328 to exhibit the filter coefficient set currently in use by the subject equalizer paths. But upon initialization and in other circumstances, onecycle delay elements may be set to random values, to predetennined values, or not explicitly set at all. After task 1108, a task 1110 couples adaptation engine (AE) 1300 to the subject Vi section of non adaptive equalizer 1200. Coupling is performed by controlling multiplexer 1232 or 1236, as appropriate, to select filter coefficients from adaptation engine 1300 rather than from controller 286. Next, a task 1112 sets the convergence criteria, in part, for the estimationandconvergence algorithm and unlocks adaptation engine (AE) 1300. The partial setting of the convergence criteria and the unlocking of adaptation engine 1300 may both be accomplished by supplying adaptation engine 1300 with a positive value for the convergence variable μ. Desirably, this value is a fraction far less than one. The convergence criteria determine how many samples adaptation engine 1300 will process before it can be deemed as having converged upon a filtercoefficientset solution. As discussed above, a greater number of samples processed leads to a greater increase in effective resolution, or reduction in error level, in the return data stream. An increase in algorithmic processing time is thus transformed into a reduced effectiveerror level for the returndata stream. Through task 1112, the rate of convergence is controlled to achieve a predetermined effective returnerror level less than the error level associated with the returndata stream. In one embodiment, the convergence variable μ is initially set to a somewhat higher value, but decreases over time. This approach allows rapid convergence to an approximate solution, followed by decreasing convergence rates which achieve smaller final tracking jitter. Following task 1112, adaptation engine 1300 will implement a least mean square (LMS), estimation andconvergence algorithm where filtercoefficient estimates are continuously altered to minimize the error signal. The LMS, estimationandconvergence algorithm repetitively revises filter coefficients to minimize the error signal and to decorrelate the error signal from the forwarddata stream. This operation also increases correlation between the forwarddata and returndata streams. More particularly, filter coefficients are adjusted until the error signal resulting from either the HPA input signal 134 or the HPA output signal 117, depending upon the current state of multiplexer 250, becomes a substantially uncorrelated signal (e.g., is as close to white noise as possible). At this point, a query task 1114 determines whether the filter coefficients being determined by adaptation engine 1300 may be deemed as having converged. Task 1114 works in conjunction with task 1112 to set the convergence criteria. Along with smaller values of μ, longer durations spent at task 1114 further increase the effective resolution and further decrease the effectiveerror level of the returndata stream. Task 1114 may simply determine whether sufficient time has been spent to achieve convergence, or task 1114 may monitor filter coefficients being generated by adaptation engine 1300 and determine that convergence has occurred when no consistent pattern of change in filter coefficients is detected. When task 1114 has determined that convergence has occurred, a query task 1115 determines whether subprocess 1100 has been invoked to include heat processing along with filtercoefficient determination. In connection with forward and return equalizers 246 and 260 and in connection with the initial coefficientdetermination iterations of equalizers 226, no heat processing is included. In these scenarios, program control passes to a task 1116. The heat processing scenarios are discussed below in connection with Figs. 15 and 17. Task 1116 locks adaptation engine 1300 by setting the filtercoefficientconvergence factor μ=0 and the heatconvergence factor λ=0. Next, a task 1118 reads the set of filter coefficients and heatsensitivity coefficients at feature 236 of adaptation engine (AE) 1300. After tasks 1116 and 1118, a task 1120 programs this set of filter coefficients into the subject nonadaptive equalizer 1200, and a task 1122 decouples adaptation engine (AE) 1300 from the nonadaptive equalizer 1200. When subprocess 1100 is being used to determine heatsensitivity coefficients, task 1120 also programs the set of heatsensitivity coefficients into the subject nonadaptive equalizer 1200. Decoupling may be accomplished by selecting the controller data input at the subject multiplexer 1232 or 1234 rather than the adaptation engine data input. At this point, a set of filter coefficients and possibly a set of heatsensitivity coefficients has been determined by adaptation engine 1300, that filter coefficient set and heatsensitivity coefficient set has been programmed back into nonadaptive equalizer 1200, adaptation engine 1300 is now available to determine another filtercoefficient set, and routine 1106 is complete. The justdetermined filtercoefficient set and heatsensitivity coefficient set will desirably remain static. But, the filtercoefficient set may continue to be adjusted within nonadaptive equalizers in response to deltaheat signal 216 and heatsensitivity coefficients. Following task 1122 and routine 1106, a task 1124 initializes the mode of adaptation engine 1300 to determine crosspath coefficients for the subject nonadaptive equalizer 1200. Adaptation engine 1300 may be initialized to crosspathfiltercoefficient adaptation by controlling selective inversion circuits 1320 so that they invert the weighted quadrature signals they process. Next, a task 1126 repeats routine 1106 for this other filtercoefficient set. When task 1126 has completed the other filtercoefficient set, subprocess 1100 is complete. Referring back to Fig. 5, upon the completion of subprocess 1100, subprocess 500 is likewise complete. At this point, forward equalizer 246 of linear predistorter 244 has been programmed with forward filter coefficients that compensate for linear distortion in the RFanalog signal 134 at the input of HPA 136 caused by analog components 120. In particular, forward equalizer 246 can now compensate for frequency dependent gain and phase imbalance and also for quadrature imbalance caused by differences in gain and delay between the legs of the complex communication signal. Accordingly, the RFanalog signal at the input of HPA 136 is as nearly an ideal signal as possible, with the linear distortion caused by analog components 120 upstream of HPA 136 accounted for by predistortion introduced through linear predistorter 244. Referring back to highpass filter 205 in Fig. 1 and to highpass filters 314 in Fig. 3, each highpass filter asserts only a very small influence. In particular, in order to block DC, some small amount of nearDC energy is also blocked by highpass filters 314 in the return path. But for this nearDC hole in the spectrum, the return path is used to drive forward equalizer 246 to match the return path. Thus, adaptation engine 1300 has determine forwardfilter coefficients that control the linear distortion in forward stream, except for near DC energy. Highpass filter 205 merely removes this nearDC energy from the forward stream so that all energy passing through forward equalizer 246 is controlled for linear distortion. Upon the completion of subprocess 500, a subprocess 1400 is performed to extend the compensation of linear distortion through HPA 136. Since a substantially undistorted signal is now present at the input to HPA 136, HPA 136 will now amplify a signal that more closely meets the controlled conditions that HPA models are designed to model. Moreover, at this point, no nonlinear compensation has been introduced into the forwarddata stream, and the substantially undistorted signal presented to HPA 136 includes substantially only inband frequency components. Fig. 14 shows a flow chart of subprocess 1400. Subprocess 1400 includes a task 1402 which switches the feedback signal provided to downconversion section 300 by multiplexer 250 from the input of HPA 136 to the RFanalog signal generated at the output of HPA 136. Since the feedback signal now propagates through HPA 136, it experiences additional delay and additional phase rotation compared to the feedback signal derived from the input of HPA 136. Next, a task 1404 invokes subprocess 600 to implement an estimationandconvergence algorithm for commonmodetimealignment section 700. As a result, the "ideal" delayedcomplexforwarddata stream 266 is brought back into temporal alignment with complex returndata stream 262. No further differentialtime alignment should be required at this point because both legs of the complex communication signal have been combined prior to processing in HPA 136. Since the same analog component (i.e., HPA 136) processes both legs of the combined signal, no opportunity for further differential quadrature time imbalance exists. After task 1404, a task 1406 invokes subprocess 900 to implement an estimationandconvergence algorithm to realign the phase of alignedcomplexforwarddata stream 272 with complexreturndata stream 262. As a result, the "ideal" alignedcomplexforwarddata stream 272 is brought back into phase alignment with complexreturndata stream 262. Following phase realignment in task 1406, a task 1408 optimizes the gain adjustment provided by adjustable attenuators 302 and 256 in a manner similar to that performed above in task 508. After task 1408, a task 1414 invokes subprocess 1100 to implement an estimationandconvergence algorithm for forward equalizer 246 to increase correlation between HPAoutputRFanalog signal 117 and the "ideal" forward data stream. As a result the forwardfilter coefficients programmed into forward equalizer 246 are revised to compensate for linear distortion introduced by HPA 136. In particular, such linear distortion may be introduced by input bandpass filter (BPF) 140 and output bandpass filter (BPF) 144 of the Wiener Hammerstein HPA model. But, at this point, the linear compensation covers the wideband signal that does not include nonlinear components. After task 1414 a task 1416 controls multiplexer 222 to route highestorderedbasisfunctiondata stream 214', rather than forwarddata stream 218, toward adaptation engine 1300. As discussed above, highestorderedbasisfunctiondata stream 214' exhibits the same timing as forwarddata stream 218, and basisfunction generation section 1600 does not implement processing to rotate the quadrature phase of highestorderedbasisfunctiondata stream 214' in the preferred embodiment. Consequently, no further time or phase alignment should be required to bring highestorderedbasisfunctiondata stream ,214' into alignment with returndata stream 262. For purposes of linear compensation, one significant difference between highestorderedbasisfunctiondata stream 214' and forwarddata stream 218 is that highest orderedbasisfunctiondata stream 214' exhibits the superwideband discussed above. Referring to the WienerHammerstein HPA model depicted in Fig. 1, amp 142 can introduce nonlinear distortion, which will result in outofband frequency components being processed by output bandpass filter (BPF) 144, where they may experience linear distortion. In order to compensate for this linear distortion of output bandpass filter (BPF) 144, a task 1418 again invokes subprocess 1100 to implement an estimationandconvergence algorithm. But this time subprocess 1100 is invoked for return equalizer 260 to adjust the returndata stream so that the HPARFanalogoutput signal 117 reflected by the returndata stream is maximally correlated with the superwideband, highestorderedbasisfunctiondata stream 214'. The higherordered terms do not appear to a significant degree in the forwardpropagating signal until the output of the memoryless nonlinearity portion (i.e., amp 142) of the WienerHammerstein HPA model. But as these higherordered terms pass through output BPF 144 of the WienerHammerstein HPA model, they may experience linear distortion. Thus, linear distortion is compensated over the wider bandwidth that output BPF 144 must process. This operation further compensates for linear distortion appearing at the output of HPA 136 but does not adjust the HPA output signal. Rather, this operation makes an adjustment in the returnsignal path that allows subsequent training for nonlinear compensation to rely on lineardistortioncompensated signals. As a result of task 1418, returnfilter coefficients are determined tlirough an estimationandconvergence algorithm and programmed into return equalizer 260. And, the returndata stream is as precise a replica of the output of the memoryless nonlinearity portion (i.e., amp 142) of the WienerHammerstein HPA model as can be achieved. Next, a task 1420 controls multiplexer 222 to route forwarddata stream 218 toward adaptation engine 1300 rather than highestorderedbasisfunctiondata stream 214'. Then, a task 1422 again invokes subprocess 1100 to implement an estimationandconvergence algorithm. This time subprocess 1100 is invoked for forward equalizer 246 to remove any correlation that may appear between the returndata and forwarddata streams now that return equalizer 260 has been programmed to address linear distortion of output bandpass filter 144. This operation is particularly aimed at compensating for linear distortion that may be introduced by input bandpass filter (BPF) 140. Following task 1422, subprocess 1400 is complete and linearandnonlinearpredistortion circuit 200 has been trained to compensate for linear distortions. As nearly an ideal signal as possible is provided to HPA 136 so that HPA 136 now amplifies a signal that most closely matches the controlled conditions for which amplifier models are devised. Moreover, sources of linear distortion following amp 142 have been compensated so that nonlinear distortion training can now take place without substantial degradation from linear distortion. Referring back to Fig. 4, following subprocess 1400, transmissiondistortionmanagement process 400 now performs a task 402 to invoke a subprocess 1500. Subprocess 1500 compensates for nonlinear distortion introduced by HPA 136. More specifically, at task 402 subprocess 1500 compensates for nonlinear distortion without compensating for heatinducedmemory effects. Fig. 15 shows a flow chart of subprocess 1500. Generally, subprocess 1500 is configured for compatibility with the WienerHammerstein HPA model. In particular, nonlinear distortion is assumed to be in the form of higherordered harmonics of the signal being amplified. The signal being amplified at amp 142 in this model is now closely matched to the "ideal" signal that drives basisfunctiongeneration section 1600 due to the abovediscussed linear compensation. And, basisfunctiongeneration section 1600 generates higherordered harmonics of this signal. Nonlinear predistorter 224 filters these higherordered harmonics, where they are then combined together with the ideal signal in a subtractive fashion. Subprocess 1500 includes a task 1502 to select a next basis function from the basis functions generated by basisfunctiongeneration section 1600. At the first iteration of task 1502, any of the basis functions, from the 2^{nd} order basis function to the K^{th} order basis function may be selected. Otherwise, task 1502 preferably selects the basis function that has not been selected for the longest period of time by a prior iteration of task 1502. Subsequent tasks will train the equalizer 226 allocated for the selected basis function by determining filter coefficients for the equalizer 226 and programming those filter coefficients into the equalizer 226. In the preferred embodiments, the basis functions are substantially orthogonal to one another. By being orthogonal to one another, filtering applied to one of the basis functions will have a minimal impact on other basis functions. Moreover, when the filtering changes for one basis function, those changes are less likely to influence the other basis functions. Fig. 16 shows a block diagram of one embodiment of a basisfunctiongeneration section 1600 suitable for use in the linearandnonlinearpredistortion circuit 200. This embodiment is desirable because it achieves substantially orthogonal basis functions using a relatively simple hardware implementation. Moreover, it is responsive to a highresolution, low error input data stream and likewise provides high resolution, low error output data streams as a result. But while basisfunctiongeneration section 1600 provides suitable results for the purposes of linearandnonlinearpredistortion circuit 200, those skilled in the art will be able to devise acceptable alternate embodiments. Complexforwarddata stream 206 is received at a magnitude circuit 1602 and at a multiplier 1604. Magnitude circuit 1602 generates a scalardata stream that describes the magnitude of complexforwarddata stream 206 and routed to multiplier 1604, as well as multipliers 1606 and 1608. Fig. 16 indicates that basis functiongeneration section 1600 is segmented into cells 1610, with each cell generating one basis function. Multipliers 1604, 1606, and 1608 are respectively associated with different cells 1610. Generally, each basis function is responsive to X(n) X(n)^{K}, where X(n) represents the forwarddata stream 206 received by section 1600, and K is an integer number greater than or equal to one. The outputs of multipliers 1604, 1606, and 1608 are X(n) X(n)^{K} streams. But in order to achieve substantial orthogonality, each basis function equals the sum of an appropriately weighted X(n) X(n)^{K} stream and all appropriately weighted lowerordered X(n) X(n)^{K} streams. Accordingly, the output from multiplier 1604 directly serves as the 2^{nd} order basis function, and provides one of complexbasisfunctiondata streams 214. The output from multiplier 1606 is multiplied by a coefficient W_{22} at a multiplier 1612, and the output from multiplier 1604 is multiplied by a coefficient W_{2}ι at a multiplier 1614. The outputs of multipliers 1612 and 1614 are added together in an adder 1616, and the output of adder 1616 serves as the 3^{rd} order basis function and provides another of complexbasisfunction data streams 214. Likewise, the output from multiplier 1604 is multiplied by a coefficient W_{3}j in a multiplier 1618; the output from multiplier 1606 is multiplied by a coefficient W_{32} in a multiplier 1620; and, the output of multiplier 1608 is multiplied by a coefficient W_{33} in a multiplier 1622. Outputs of multipliers 1618, 1620, and 1622 are added together in an adder 1624. The output of adder 1624 serves as the 4^{th} order basis function and provides yet another of complexbasisfunctiondata streams 214. In the preferred embodiment, the coefficients are determined during the design process by following a GramSchmidt orthogonalization technique, or any other orthogonalization technique known to those skilled in the art. As such, the coefficients remain static during the operation of transmitter 100. But nothing prevents the coefficients from changing from timetotime while transmitter 100 is operating if conditions warrant. Those skilled in the art will appreciate that basisfunctiongeneration section 1600 may be expanded by adding additional cells 1610 to provide any desired number of basis functions. Moreover, those skilled in the art will appreciate that pipelining stages may be added as needed to accommodate the timing characteristics of the components involved and to insure that each basis function has substantially equivalent timing. The greater the number of basis functions, the better nonlinear distortion may be compensated for. But the inclusion of a large number of basis functions will necessitate processing a very wideband, super wideband signal. The preferred embodiments contemplate the use of 25 basis functions, but this is no requirement of the present invention. Referring back to Fig. 15, after a basis function has been selected in task 1502, a task 1504 either disables or enables heat processing. Task 1504 disables heat processing if subprocess 1500 is being invoked from task 402. Next, a task 1506 calls subprocess 1100 to implement an estimationandconvergence algorithm to determine appropriate filter coefficients for the nonadaptive equalizer 226 associated with the selected basis function. During initialization and during linear compensation, the selected nonadaptive equalizer may have been disabled by setting all its filter coefficients to zero. During task 1506, filter coefficients are determined for this nonadaptive equalizer 226 that minimize any correlation between the forwarddata and error streams, and maximize correlation between the forwarddata and returndata streams. To the extent that orthogonal basis functions are used, the increase in correlation between the forwarddata and returndata streams for any one basis function will have no correlating influence on the other basis functions. Following task 1506, a query task 1508 determines whether all basis functions have been processed by subprocess 1500, so long as other basis functions remain to be processed, program control loops back to task 1502 to determine filter coefficients for the remaining basis functions. When task 1508 determines that all basis functions have been processed, subprocess 1500 is complete. Referring back to Fig. 4, after task 402 invokes subprocess 1500, a task 404 again invokes subprocess 1500. This time subprocess 1500 to train for nonlinear compensation with heat processing. Thus, the processing of deltaheat signal 216 will be enabled at task 1504 in subprocess 1500. Referring to Fig. 13, heat processing may be enabled by enabling onecycle delay elements 1348 in adaptation engine 1300. Fig. 17 shows a block diagram of one embodiment of a representative heatchangeestimation section 1700 suitable for use in the linearandnonlinearpredistortion circuit 200. This embodiment is desirable because it configures deltaheat signal 216 to be responsive to instantaneous changes from the longterm average relative power exhibited by the forwarddata stream and it uses a relatively simple hardware implementation. But while heatchangeestimation section 1700 provides suitable results for the purposes of linearandnonlinearpredistortion circuit 200, those skilled in the art will be able to devise alternate embodiments that will also work. Complexforwarddata stream 206 is received at a magnitudedetermining circuit 1702 in heat changeestimation section 1700. At circuit 1702, the magnitude of the complex signal is formed, thereby making a scalar magnitude signal that drives a programmable timealignment section 1704. In one embodiment, magnitudedetermining circuit 1702 provides a stream of magnitude values responsive to the magnitude of complexforwarddata stream 206, and in another embodiment, circuit 1702 provides this stream of magnitude values raised to a power greater than one. Programmable timealignment section 1704 receives programming inputs from controller (C) 286. Programmable timealignment section 1704 may be configured in a manner similar to that described above in connection with Figs. 7 and 8. In other words, section 1704 allows controller 286 to alter the delay the stream of magnitude values experiences in section 1704. Section 1704 provides a delayed stream of magnitude values to an IIR filter in one embodiment. The IIR filter provides an averagemagnitude output at an output of an adder 1706, but this average magnitude output is not the output for heatchangeestimation section 1700. The averagemagnitude output provides a presenttime representation of a longterm average magnitude signal. This signal is routed to a onecycle delay element 1708, whose output provides a previous representation of the longterm average magnitude signal. The previous representation of the longterm average magnitude signal is routed to a first input of adder 1706 and to a negative input of a subtraction circuit 1710. The delayed stream of magnitude values from timealignment section 1704 is provided to a positive input of subtraction circuit 1710, and the output of subtraction circuit 1710 provides deltaheat signal 216, which is the output for heatchange estimation section 1700. Deltaheat signal 216 is routed back to a first input of a convergence multiplier 1712, and a convergence value η is supplied by controller (C) 286 to a second input of convergence multiplier 1712. An output of convergence multiplier 1712 couples to a second input of adder 1706. Thus, the longterm average magnitude signal reflects the average magnitude, or a power greater than one thereof, over time of forwarddata stream 206, and it is updated during each clock cycle by a fraction of the current instantaneous magnitude value. The size of that fraction is determined by convergence value η. Smaller convergence values η make the longterm average magnitude signal less responsive to instantaneous magnitude values. Moreover, deltaheat signal 216 characterizes the deviation of the instantaneous magnitude from the longterm average magnitude signal. Referring back to Figs. 4 and 15, during task 404 of transmission distortion management process 400, filter coefficients for equalizers 226 continue to be adjusted. In addition, during task 404 heat sensitivity coefficients for equalizers 226 are adjusted in response to deltaheat signal 216. Each iteration of task 1506, which is invoked through task 404, now invokes equalization estimationandconvergence algorithm subprocess 1100 to determine both filter coefficients and heatsensitivity coefficients. Referring to Fig. 11, the query task 1115 is performed when subprocess 1100 has converged to a solution for a set of filter coefficients. Task 1115 determines whether heat processing is to be included. During task 404, when heat processing is to be included, program control proceeds to a tasks 1128, 1130, and 1132. Tasks 1128, 1130, and 1132 are optional tasks that are desirably performed the first time program control proceeds along this path for the purposes of initialization, and thereafter performed only occasionally. In one embodiment, tasks 1128, 1130, and 1132 are performed only during the first iteration of the programming loop set forth in subprocess 1500. Task 1128 couples correlation engine (CE) 280 to correlate deltaheat signal 216 with delta coefficient signal 279 by making the appropriate selections at multiplexers 270 and 278. Then, task 1130 performs a time alignment optimization operation. In particular, deltaheat signal 216 is delayed by making increasingly accurate delay estimates until convergence is reached where maximum correlation results are observed when deltaheat signal 216 is correlated with deltacoefficient signal 279. An optimizing algorithm similar to that discussed above in connection with Fig. 6 may be used in task 1130, or another optimizing algorithm may also be used. At this point, deltaheat signal 279 has been brought into time alignment at the middle of adaptation engine 1300. Changes in the heat of HPA 136, as indicated by the power of the forwarddata stream, track changes in the filter coefficient for the middle tap to the maximum extent possible. After task 1130, task 1132 performs another optimizing operation. At task 1132 the convergence values η and γ are optimized. Convergence values η and γ determine the sensitivity of longterm averages to instantaneous changes in the power and middlefiltercoefficient signals. Desirably, convergence values η and γ are small positive values so that the longterm averages are fairly insensitive to instantaneous changes. But convergence values η and γ are optimized by making increasingly accurate estimates for these values until substantially maximal correlation results are observed at correlation engine 280. Next, a task 1134 sets the convergence criteria, in part, for the heat portion of the estimationand convergence algorithm and unlocks adaptation engine (AE) 1300 to perform heatsensitivitycoefficient processing along with filtercoefficient processing. The partial setting of the convergence criteria and the unlocking of adaptation engine 1300 may both be accomplished by supplying adaptation engine 1300 with a positive value for the convergence variable λ. Desirably, this value is a fraction far less than one. The convergence criteria determine how many samples adaptation engine 1300 will process before it can be deemed as having converged upon a heatsensitivitycoefficientset solution. As discussed above, a greater number of samples processed leads to a greater increase in effective resolution, or reduction in error level, in the returndata stream. An increase in algorithmic processing time is thus transformed into a reduced effectiveerror level for the returndata stream. Through task 1134, the rate of convergence is controlled to achieve a predetermined effective returnerror level less than the error level associated with the returndata stream. In one embodiment, the convergence variable λ is initially set to a somewhat higher value, but decreases over time. Following task 1134, adaptation engine 1300 will now implement two least mean square (LMS), estimationandconvergence algorithms. In one algorithm filtercoefficient estimates are continuously altered to minimize the error signal provided by data stream 276. In the other, heatsensitivity coefficient estimates are continuously altered to minimize the error signal provided by the difference between deltaheat signal 216 and deltacorrelation signals 1338. Both LMS, estimationandconvergence algorithms repetitively revise filter coefficients and heatsensitivity coefficients to minimize the respective error signals. At this point, a query task 1136 determines whether the heatsensitivity coefficients being determined by adaptation engine 1300 may be deemed as having converged. Task 1 136 works in conjunction with task 1134 to set the convergence criteria. Task 1136 may simply determine whether sufficient time has been spent to achieve convergence, or task 1136 may monitor heatsensitivity coefficients being generated by adaptation engine 1300 and detennine that convergence has occurred when no consistent pattern of change in filter coefficients is detected. When task 1136 has determined that convergence has occurred, heatsensitivity coefficients α have been determined which, when multiplied by deltaheat signal 216, cause the heat signal to become maximally correlated with corresponding deltacoefficient signals 1338. At this point, program control proceeds to task 1116 to lock adaptation engine 1300, extract filter coefficients and heatsensitivity coefficients from adaptation engine 1300, and program those coefficients back into the subject nonadaptive equalizer 226. Heatadapter units 1234 will then subsequently adjust filter coefficients in response to delta heat signal 216 as weighted by corresponding heatsensitivity coefficients, to compensate for heat buildup or drainage in HPA 136. Referring back to Fig. 4, after task 404, linearandnonlinearpredistortion circuit 200 has compensated for both linear and nonlinear distortion introduced by analog components 120. But not all distortion has been removed from HPARFanalogamplifier signal 117 by predistortion circuit 200, and some residual amount will remain. The residual distortion will contribute to errorvector magnitude (EVM). Two forms of residual distortion will contribute to EVM, one linear and the other nonlinear. Desirably, overall EVM resulting from the use of transmitter 100 is held as low as possible so that reception of communications signal 116 is as good as possible. But industry standards are configured to achieve acceptable reception while nevertheless permitting a certain amount of EVM. Of the two forms of residual distortion contributing to EVM, nonlinear distortion is considered worse because it leads to spectral regrowth in addition to degraded reception. The component of EVM resulting from linear distortion may lead to degraded reception but does not substantially worsen spectral regrowth. Distortion introduced by peakreduction section 110 is another contributor to EVM. In general, peakreduction section 110 will introduce greater amounts of distortion as greater amounts of peak reduction are applied to the forwarddata stream. But the distortion introduced by peakreduction section 110 will be inband distortion, and will not substantially contribute to spectral regrowth. It may therefore be desirable in some applications to detect if EVM resulting from nonlinear distortion has increased, and tradeoff this form of distortion for the more benign form of inband distortion. Accordingly, after task 404 a task 406 obtains a residualnonlinearEVM value. The residual nonlinearEVM value is an estimate of the amount or residual distortion remaining in HPARFanalog amplifier signal 117 after linear and nonlinear compensation that is due to nonlinear distortion. Task 406 may, for example, obtain the residualnonlinearEVM value by controlling multiplexers 270 and 278 so that the error stream 276 is correlated with itself in correlation engine 280, then do at least two correlations. One of the two correlations will measure the error signal resulting from the analog signal that is input to HPA 136 and the other will measure the error signal resulting from the analog signal that is output from HPA 136. Of course, timing, phase alignment, and gain adjustments may be performed as described herein prior to each correlation. Desirably, suitable convergence criteria are used for the two correlation operations so that the effectiveerror level of error stream 276 is significantly decreased as discussed above. Then task 406 can obtain the residualnonlinearEVM value by evaluating the difference between the two correlations. The difference results primarily from the memoryless nonlinearity 142 of HPA 136 and represents nonlinear distortion. While a variety of noise sources will contribute to the results of each correlation, those noise sources are, for the most part, common to each correlation operation. Thus, the difference between the two correlations yields a residualnonlinearEVM value that is substantially isolated from the noise sources. Following task 406, a task 408 evaluates whether the residualnonlinearEVM value is excessive when compared to a predetermined value. An excessive value may result from an aging but not yet failed HPA 136, power supply aging, operation at extreme temperature, or a variety of other scenarios. If the residualnonlinearEVM value is excessive, then task 408 provides peakreductionfeedback signal 114 to peakreduction section 110. Feedback signal 114 is based upon the residualnonlinearEVM value obtained above in task 406. In response to feedback signal 114, peakreduction section 110 will alter the peak reduction it applies to the forwarddata stream as discussed above. In particular, when an excessive residual nonlinearEVM value is detected, peak reduction is increased so that HPA 136 may operate at a greater backoff, which will lead to reduced nonlinear distortion. The increase in peak reduction will likewise increase linear distortion, but should also decrease nonlinear distortion somewhat. Transmitter 100 will henceforth operate with less nonlinear distortion but more linear distortion. Reception will gracefully degrade, but spectral regrowth will be substantially prevented. In addition, task 408 may activate alarms or otherwise automatically send control messages indicating the excessive residualnonlinear EVM condition. After task 408 program control loops back to any of the subprocesses and tasks in process 400 so that each subprocess and task is repeated from time to time on a suitable schedule. The abovediscussed embodiment of predistortion circuit 200 and of transmissiondistortion management process 400 provides beneficial results when A/D 304 of DDC 300 introduces only a negligible amount of distortion exhibited as a frequencydependent influence imposed on the superwideband feedback signal processed by A/D 304. Mere quantizationerror amplitude and uncorrelated errors caused by phase noise or aperturejitter at A/D 304 pose no significant problem because the abovediscussed estimationand convergence algorithms used to process the feedback signal are tolerant of such errors, noise, and jitter. But even a lowresolution, high error A/D 304 can be a sophisticated component, and the overall expense of predistortion circuit 200 may be further reduced by permitting the use of a lesssophisticated A/D 304 that may nevertheless introduce some distortion into the feedback signal. Such distortion, if not compensated, will be mistakenly interpreted by transmissiondistortionmanagement process 400 as being introduced by analogtransmitter components 120. Thus, in addition to removing the sources of distortion discussed above, equalizers 226, 246, and 260 will be programmed with tap values that could also introduce an unwanted distortion in the forwarddata stream, where the unwanted distortion is inverse to the A/D introduced distortion. Fig. 18 shows a block diagram of a second embodiment of the linearandnonlinearpredistortion section 200, referred to below as predistortion circuit 1800, of transmitter 100. Predistortion circuit 1800 is configured to compensate for some A/Dintroduced distortions in addition to the linear and nonlinear distortions discussed above in connection with Figs. 217. Through the use of predistortion circuit 1800, transmitter 100 may even use an inexpensive A/D that introduces significant amounts of distortion into the feedback signals it processes. Predistortion circuit 1800 is configured much like predistortion circuit 200, and the abovepresented discussion concerning predistortion circuit 200 for the most part applies to predistortion circuit 1800. Like reference numbers refer to similar components between the block diagrams of Figs. 1, 2 and 18. However, for convenience certain segments of predistortion circuit 200, such as gain adjustment circuits 302 and 256, heatchange estimation circuit 1700, and circuits for generating clock signals for A/D 304 have been omitted from Fig. 18. Those skilled in the art will appreciate that such segments are nevertheless desirably included in predistortion circuit 1800 and used substantially as discussed above in connection with Figs. 217. Predistortion circuit 1800 also includes rate multiplier 204, which generates increasedratecomplex forwarddata stream 206. Forwarddata stream 206 drives basisfunctiongeneration section 1600, delay element 208, a realconversion section 1802, and programmable delay section 700, which is equivalent to commonmodetimealignment section 700 from Fig. 2. Basisfunctiongeneration section 1600 provides a plurality of basisfunctiondata streams 214 to nonlinear predistorter 224 and to a corresponding plurality of programmable delay sections 700". Nonlinear predistorter 224 is included in an analogtransmittercomponent compensator 1803 and includes a plurality of equalizers 226 and combining circuit 228, as discussed above in connection with Fig. 2. But combining circuit 228 is omitted from Fig. 18 for convenience. Analogtransmittercomponent compensator 1803 is provided to counteract distortion introduced by analogtransmitter components 120. Fig. 18 denotes equalizers 226 with the notation Eθ _{A}, where the superscript "k" designates the basis function with which the equalizer 226 is associated, and the subscript "HPA" indicates that the equalizer 226 is provided to compensate for nonlinear distortion introduced by HPA 136. Nonlinear predistorter 224 provides complex filteredbasisfunctiondata stream 230 to a negative input of combining circuit 220, and delay element 208 provides complexforwarddata stream 218 to a positive input of combining circuit 220. Combining circuit 220 provides complexnonlinearpredistortedforwarddata stream 238 to forward equalizer 246 and to programmable delay section 800 as discussed above, but Fig. 18 depicts equalizer 246 and delay section 800 in a different order. Forward equalizer 246 is also included in analogtransmittercomponent compensator 1803. Delay section 800 is substantially equivalent to differentialmodetimealignment section 800 discussed above in connection with Figs. 217. Delay section 800 provides complexquadraturebalancedequalizedforwarddata stream 118 to digitaltoanalog converters (D/A's) 122, which drive the remainder of analogtransmitter components 120. As discussed above, D/A's 122 preferably exhibit a significantly higher resolution than A/D 304. The box labeled "XPF" in Fig. 18 includes lowpass filters 124, upconversion section 126, and bandpass filter 132 from Fig. 1. An output from bandpass filter 132 provides RFanalog signal 134 to multiplexer 250 and to HPA 136. RFanalog signal 117 is derived from the output of HPA 136 and routed to multiplexer 250. Unlike predistortion circuit 200 discussed above in connection with Fig. 2, one of D/A's 122 also directly generates baseband signal 123, which is routed to multiplexer 250. Baseband signal 123 is an unfiltered signal because it does not pass through the filtering provided in analogtransmitter components 120. Consequently, it does not suffer from the distortions imposed by that filtering. In one embodiment, D/A's 122 are substantially equivalent to one another in resolution and in other parameters. In another embodiment, the D/A 122 that generates baseband signal 123 is of a higher resolution and/or quality than the other D/A 122. In yet another embodiment, a third D/A (not shown) is dedicated to driving baseband signal 123 but need not also drive other analogtransmitter components 120. Desirably, the D/A that drives baseband signal 123 is of high resolution and high quality because, as discussed in more detail below, that D/A is used to establish compensation for A/D 304, and such compensation will be limited by any distortion introduced by the D/A. Fortunately, high resolution, high quality D/A's are readily available at low cost. Programmable delay section 700 provides delayedcomplexforwarddata stream 266 to phaserotate section 1000, and phaserotate section 1000 provides alignedcomplexforwarddata stream 272'. Forward data stream 272' drives a digital upconversion (DUC) section 1806. DUC section 1806 digitally upconverts forwarddata stream 272' to F_{s}/4, where F_{s} is the sampling frequency. An output of DUC section 1806 drives a realconversion section 1808. Each of programmable delay elements 700" is configured similarly to delay section 700, and each couples to its own phaserotate section 1000'. Phaserotate sections 1000' are all configured similarly to phaserotate section 1000. Phaserotate sections 1000' each provide an aligned basisfunctiondata stream 1804 to a nonlinear predistorter 224'. Nonlinear predistorter 224' is desirably configured similarly to nonlinear predistorter 224, but is included in an A/D compensation section 1805. In particular, nonlinear predistorter 224' includes a plurality of linear equalizers 226', with one equalizer 226' being dedicated to independently filter each basis function. Fig. 18 labels equalizers 226' with the notation EQ_{A}/_{D,} where the superscript "k" designates the basis function with which the equalizer 226' is associated, and the subscript "A/D" indicates that the equalizer 226' is provided to compensate for A/Dintroduced distortion. Outputs from equalizers 226' are combined together as discussed above (not shown), and a complexfilteredbasis functiondata stream 1809 is then generated by nonlinear predistorter 224' and provided to a digital upconversion (DUC) section 1810, which in turn drives a realconversion section 1812. Realconversion sections 1802, 1808, and 1812 each convert their respective versions of the complex forwarddata stream into realdata streams. Using techniques well known to those skilled in the art, from every set of four pairs of samples in the complex forwarddata stream, realconversion sections 1802, 1808, and 1812 each select the I, Q, I, and Q samples. Realconversion section 1802 couples to a programmable delay section 700', which may be configured substantially similar to programmable delay section 700. Delay section 700' couples to a fixed delay section 1814, which implements a fixed delay substantially equivalent to the delay imposed by phaserotate sections 1000 and 1000'. Delay section 1814 provides a delayedforwarddata stream 1816 to a fixed delay element 1818. Delay element 1818 imposes a fixed delay substantially equivalent to the delay imposed by digital upconversion section 1806. The outputs of realconversion section 1808 and of delay element 1818 couple to a switching section 1820, which is included in A/D compensation section 1805. Switching section 1820 has a first output that couples to a lineardistortion compensator 1822. Lineardistortion compensator 1822 is provided by a linear equalizer 1824, which is labeled EQ ) in Fig. 18, where the "1" superscript denotes a linear operator and the "A/D" subscript denotes that equalizer 1824 is provided to compensate for A/Dintroduced distortion. In the preferred embodiment of the present invention, equalizer 1824 is desirably configured similarly to equalizers 226, 246, 260, and 226', except that equalizer 1824 need only process a realdata stream rather than a complex data stream and the number of taps may differ. But like equalizers 226, 246, 260, and 226', equalizer 1824 is desirably configured as an adaptive equalizer, either directly or through the operation of adaptation engine 1300. Thus, as discussed below in more detail in connection with Figs. 19 and 24, equalizer 1824 is adjusted to compensate for linear distortion introduced by A/D 304. Switching section 1820 has a second output that couples to a quantizationerror compensator 2200, which is also included in A/D compensation section 1805. Generally, quantizationerror compensator 2200 omits compensation for the amplitude of quantization error. But quantizationerror compensator 2200 symmetrizes the compensation error. Quantizationerror compensator 2200 is discussed in more detail below in connection with Figs. 2122. A second embodiment of quantizationerror compensator 2200 which both symmetrizes and compensates for the amplitude of quantization error is discussed below in connection with Fig. 31. Outputs of real conversion section 1812, lineardistortion compensator 1822, and quantizationerror compensator 1826 are added together in a combining circuit 1828. The version of the forwarddata stream output from combining circuit 1828 is provided to a negative input of a combining circuit 1830. Combining circuit 1830 provides a compensation point where the processed forwarddata stream is combined with the returndata stream output from A/D 304. An output of combining circuit 1830 provides an A/Dcompensatedreturndata stream 1832 to direct digital downconversion section 1834. In this second embodiment, DDC 1834 includes only components 308, 310, and 312 from DDC 300 in the abovediscussed first embodiment. In general, A/D 304 effectively downconverts the feedback signal it samples into a real signal at an intermediate frequency (IF) of F_{s}/4, where F_{s} is the sampling frequency. DDC 1834 generates complex returndata stream 254, which is a complex signal substantially at baseband. As discussed above in connection with the first embodiment, complex returndata stream 254 may exhibit higher error and lower resolution than the forwarddata stream. Complex returndata stream 254 drives return equalizer 260, which in turn generates equalizedcomplex returndata stream 262, as discussed above in connection with Figs. 217. Return equalizer 260 is also included in analogtransmittercomponent compensator 1803. In this second embodiment of predistortion circuit 1800, as discussed above in connection with Figs 217, controller 286, adaptation engine 1300, and correlation engine 280 desirably couple to various components of predistortion circuit 1800 to control the flow and timing of data streams and to process the various versions of the returndata stream. Fig. 19 shows a flowchart of a second embodiment of transmissiondistortionmanagement process 400 performed by transmitter 100. This second embodiment is referred to as process 1900. Process 1900 differs from process 400, discussed above, in that additional subprocesses are included to compensate for some forms of distortion introduced by A/D 304. Process 1900 is discussed in more detail below. Fig. 20 shows a model 2000 of a typical analogtodigital converter, such as may describe A/D 304. Model 2000 illustrates various sources of distortion that may be introduced by A/D 304. An input analog signal 2002 is provided to an amplifier 2004. Fig. 20 designates amplifier 2004 as "NL AMP" to signify that amplifier 2004 is a potential source of nonlinear distortion. An output of amplifier 2004 drives a lowpass filter (LPF) 2006. LPF 2006 is potentially a source of only a minor amount of linear distortion because the "knee" of the filter is typically well above the frequency band of interest. An output of LPF 2006 couples to a switch 2008, which drives a sampleandhold circuit 2010. Sampleandhold circuit 2010 resembles a low pass filter that can contribute a significant amount of linear distortion. Sampleandhold circuit 2010 drives an adder 2012 through a switch 2014. At adder 2012, a DC offset may be contributed. While the DC offset is usually an unwanted effect, it need not present a distortionrelated problem. Adder 2012 drives a quantizer 2016. Quantizer 2016 digitizes the analog voltage captured by sampleandhold circuit 2010, and provides the digital output from the A/D. Quantizer 2016 may be the source of a couple of different types of error. Fig. 21 shows a graph depicting quantization and quantization error characteristics of an exemplary 2bit resolution A/D. The 2bit resolution characteristic is not a requirement of the present invention. Fig. 21 depicts a twodimensional representation of all possible input analog voltages to the A/D in a line 2102, an exemplary scenario of how the A/D might digitize the various possible input analog voltages in a trace 2104, and the resulting quantization error in a trace 2106. A column of binary numbers on the left side of Fig. 21 depicts a conventional two'scomplement representation of the quantized output from the A/D. A column of binary numbers on the right side of Fig. 21 depicts an alternate /4bit offset representation of the quantized output from A/D which is desirable for use in the preferred embodiment. The /4bit offset representation is expressed using one additional bit of resolution when compared to the two'scomplement representation, but includes no zero state, or any other evennumbered state, and has an equal number of nonzero positive and nonzero negative states. Quantizer 2016 of A D model 2000 is characterized by switching thresholds 2108. Desirably, a 2bit A/D has three switching thresholds 2108 precisely at zero and at ± ^{>}/_{2} X full scale (FS/2). A/D's with greater resolution have more switching thresholds 2108. At an input voltage marginally below a switching threshold 2108 the A/D will output one code, and at an input voltage marginally above the switching threshold 2108 the A/D will output another code. At the switching thresholds 2108, the quantization error will instantly jump from a local minimum to a local maximum. If all switching thresholds 2108 are precisely positioned, the absolute values of all local minimum and all local maximum quantization errors will equal one another. The amplitude of the quantization error can lead to one type of A/Dinduced distortion in certain RF communication applications, as is discussed below in connection with Figs. 2732. But in other applications the amplitude of the quantization error is of minor concern because the estimationandconvergence algorithms based upon the returndata stream 1832 cause this form of error to average to zero. Regardless of whether quantization error amplitude will pose a problem, if switching thresholds 2108 are not appropriately positioned, then a dissymmetry can result. Fig. 21 illustrates one such dissymmetry, where the actual +FS/2 switching threshold 2108 has been shifted from its ideal position in a negative direction, but the FS/2 switching threshold is located in its proper position. This dissymmetry in the quantization error introduces another type of distortion into the signal processed by A/D 304. If not compensated for, then that distortion may cause inaccurately resolved tap coefficients for equalizers 226, 246, and 260. The particular form of dissymmetry that is of interest is about a DC offset, which may, but is not required to, equal zero. The use of the — bit offset representation further promotes symmetry because the negative of each code in the z— bit offset representation has a corresponding positive value that represents a corresponding analog input. In other words, the coding scheme is symmetrical about zero. Predistortion circuit 1800 compensates for A/D quantization error, but more particularly dissymmetry, using quantizationerror compensator 2200. Fig. 22 shows a block diagram of a first embodiment of a representative quantizationerror compensator 2200. In general, quantizationerror compensator 2200 allows the formation of effective switching thresholds 2108' that are ideally positioned, at least to within the precision of D/A 122. Another embodiment for quantizationerror compensator 2200 is discussed below in connection with Fig. 31. Referring to Fig. 22, a positive offset is added at a combining circuit 2202 to the analog feedback input signal driving A/D 304. The positive offset is not a requirement but is used here merely to simplify the hardware. Desirably, the positive offset is slightly greater than the maximum amount by which an actual switching threshold 2108 may be displaced in a negative direction from an ideal switching threshold. Thus, the positive offset has the effect of shifting all actual switching thresholds 2108 to exhibit a negative error relative to the analog input signal. This negative switching threshold error causes the A/D digital output to be too positive for some analog inputs, but the toopositive output can then be corrected by applying only negative offsets. A/D 304 is adapted to provide the abovediscussed Vibit offset representation discussed above, by adding an additional LSB of resolution to a two'scomplement output from A/D 304 and permanently setting that bit to a "1". As discussed above, the output of A/D 304 is routed to combining circuit 1830. In this embodiment, controller (C) 286 is configured to monitor compensatedreturndata stream 1832 output from combiner 1830. Controller 286 is also configured to write data into registers 2204, 2206, and 2208. Outputs from registers 2204, 2206, and 2208 respectively couple to positive inputs of comparators 2210, 2212, and 2214. Negative inputs of comparators 2210, 2212, and 2214 are all driven by the output from switch 1820. Negative inputs to comparators 2216, 2218, and 2220 are respectively adapted to receive values of FS/2, 0, and +FS/2, where "FS" refers to full scale. Positive inputs of comparators 2216, 2218, and 2220 are also driven by the output from switch 1820. Greaterthan outputs from comparators 2210 and 2216 generate an active signal when the positive inputs are greater than the negative inputs and couple to inputs of an AND gate 2222; greaterthan outputs from comparators 2212 and 2218 couple to inputs of an AND gate 2224; and, greaterthan outputs from comparators 2214 and 2220 couple to inputs of an AND gate 2226. Outputs from AND gates 2222, 2224, and 2226 couple to inputs of an OR gate 2228, and an output of OR gate 2228 couples to a selection input of a multiplexer (MUX) 2230. A "0" value is supplied to a zero data input of multiplexer 2230, and a "1" value is supplied to a one data input of multiplexer 2230. An output of multiplexer 2230 provides a stream 2232 of offset values through a delay element 2234 to combining circuit 1828, where this stream is combined with outputs from realconversion section 1812 and equalizer 1824. The delay inserted in data stream 2232 by delay element 2234 desirably causes quantization error compensator 2200 to exhibit the same delay as is exhibited by equalizer 1824. As discussed above, the output of combining circuit 1828 couples to a negative input of combining circuit 1830. Referring briefly back to Fig. 19, process 1900 initially performs a subprocess 2300 which works in conjunction with quantizationerror compensator 2200 to symmetrize A/D quantization error. In connection with the second embodiment of the quantizationerror compensator discussed below in connection with Fig. 31, subprocess 2300 both compensates for quantization error amplitude and symmetrizes quantization. Fig. 23 shows a flowchart of subprocess 2300. Subprocess 2300 is configured to be performed on a powerup basis or at a time when transmitter 100 is not transmitting data. Subprocess 2300 first performs a task 2302 to initialize predistortion circuit 1800. Task 2302 may, for example, set basis functiongenerator 1600 to output only zeros. Multiplexer 250 is desirably set so that baseband (BB) feedback signal 123 is routed to A/D 304. Equalizer 1824 is desirably set so that it outputs only zeros, and switch 1820 is desirably controlled so that the baseband path through delay section 700' is routed to quantizationerror compensator 2200. And, registers 2204, 2206, and 2208 are desirably programmed with maximum negative values. In this state, no distortion from analogtransmitter components 120, other than the D/A 122 driving baseband feedback signal 123, is introduced into the signal being monitored by A/D 304. Likewise, no influence is applied to the output of A/D 304 at the compensation point of combining circuit 1830. Forcing registers 2204, 2206, and 2208 to exhibit maximum negative values likewise prevents quantizationerror compensator 2200 from influencing the output of A/D 304. Following task 2302, a task 2304 identifies an actual switching threshold used by A/D 304. The first switching threshold may, for example, be the FS/2 threshold, and the positive offset added at combining circuit 2202 forces the actual switching threshold to be less than the identified ideal threshold. Next, a task 2306 causes D/A 122 to output a value in analog form. Due to the higher resolution of D/A 122 than A/D 304, this analog value is output to great precision, and it is fed directly to A/D 304 through multiplexer 250. Next, after waiting an appropriate duration a query task 2308 determines whether the A/D output value has switched from its previous value. Assuming, that no switching is detected in task 2308, a task 2310 increments the output value by one LSB of the highresolution forwarddata stream, and program flow returns to task 2306 to output this new, marginallygreater value. Program flow remains in the loop of tasks 2306, 2308, and 2310 until a value is output that causes the A/D output to switch to a new output code. Due to the positive offset which causes the switching threshold to exhibit a negative error, the output of A/D 304 will exhibit a positive error at this point. An actual switching threshold has been identified. A task 2312 then records the actual switching threshold, and a query task 2314 determines whether the previous actual switching threshold detected was the last threshold to detect. So long as other switching thresholds remain to be detected, program flow returns to task 2304 to detect another actual switching threshold. When task 2314 determines that the last actual switching threshold has been detected, a task 2316 programs registers 2204, 2206, and 2208 with the respective actual switching thresholds. In an alternative embodiment, the actual switching thresholds programmed in task 2316 may be an LSB or one LSB less than the actual switching thresholds detected and recorded in task 2312. At this point subprocess 2300 is finished. Actual switching thresholds have been detected to the degree of precision provided by D/A 122. During subsequent operation, the forwarddata stream which drives D/A 122 is also provided to comparators 2210, 2212, 2214, 2216, 2218, and 2220 (Fig. 22). Whenever forwarddata stream values between the ideal and actual switching thresholds are detected through comparators 2210, 2212, 2214, 2216, 2218, and 2220 and AND gates 2222, 2224, and 2226, an offsetting value of 1 is supplied through combining circuits 1828 and 1830 to compensate the output of A/D 304. As a result, the quantization error is symmetrized. For each effective switching threshold 2108' used by A/D 304 that is more positive than any DC offset, A/D 304 also uses an effective switching threshold 2108' that is more negative than the DC offset, wherein, an average of the morepositive and morenegative switching thresholds approximately equals the DC offset. More precisely, actual switching thresholds 2108 are converted into effective switching thresholds 2108' that are as close to their ideals as possible given the resolution of D/A 122. This sets the DC offset approximately at zero and makes all effective switching thresholds 2108' symmetrical about zero. While the embodiment of quantizationerror compensator 2200 described above in connection with Figs. 2223 relies upon no data being transmitted from transmitter 100 while process 2300 operates, this is not a requirement of the present invention. In an alternate embodiment transmitter 100 may transmit data while identifying actual switching thresholds 2108. In this alternate quantizationerror compensator 2200, the forwarddata stream may be monitored in quantizationerror compensator 2200 over a long period of time, and the greatest forwarddata stream value associated with each A/D output state recorded. Actual switching thresholds 2108 may then be determined to be the slightly less than or equal to the recorded greatest values. In yet another alternate embodiment, the greatest and least forwarddata stream values associated with each A/D output state may be recorded while transmitting a vast amount of data. The actual switching thresholds may then be determined as the average between the greatest value recorded for one state and the least value recorded for the next greater state. Referring briefly back to process 1900, after completion of subprocess 2300 a subprocess 2400 is performed to compensate for linear distortion introduced by A/D 304. Referring to Fig. 20, A/D 304 may introduce linear distortion primarily through the operation of sampleandhold circuit 2010 and secondarily through LPF 2006. Fig. 24 shows a flowchart of an exemplary subprocess 2400. Subprocess 2400 is performed at any time while transmitter 100 transmits data, and preferably after subprocess 2300 has setup quantizationerror compensator 2200 to compensate for A/D quantization error. After compensation for quantization error distortion introduced within A/D 304 downstream of the sources of linear distortion, the quantization error distortion is then unlikely to harm the resolution of an appropriate compensation for linear distortion. Thus, quantizationerror compensator 2200 is desirably enabled and operational during subprocess 2400. Subprocess 2400 performs an initialization task 2402 to initialize predistortion circuit 1800 for the performance of subprocess 2400. Task 2402 may control multiplexer 250 so that baseband (BB) feedback signal 123 is routed to A/D 304. Switch 1820 may be controlled so that the baseband path of the forward data stream passing through delay section 700' is routed to lineardistortion compensator 1822. Equalizer 1824 of lineardistortion compensator 1822 is initialized to a desirable state that passes but does not filter data. And, an adaptation multiplexer 2500 (Fig. 25) may be adjusted to route appropriate idealaligned and error signals to adaptation engine 1300 directly to equalizer 1824 when equalizer 1824 is implemented as an adaptive equalizer. Fig. 25 shows a block diagram of a multiplexing section 2500 that works in conjunction with predistortion circuit 1800 to generate signals which drive taps of the various adaptive equalizers, including equalizer 1824. The taps may be driven through equalization engine 1300. Alternatively, the various equalizers, including equalizer 1824, may be configured as adaptive equalizers. Fig. 25 omits a depiction of complex signal notation for convenience, but those skilled in the art will appreciate that complex signals may be routed through multiplexing section 2500 as needed. In general, error signal 276, which drives equalizer taps in adaptation engine 1300, is generated in subtraction circuit 274 by subtracting the return data stream from a version of the forwarddata stream. The returndata stream is routed to subtraction circuit 274 through a multiplexer 2502, and various versions of the forwarddata stream are routed to subtraction circuit 274 through a multiplexer 2504. Idealaligned signal 272 also drives taps of the various adaptive equalizers, including equalizer 1824. Idealaligned signal 272 is obtained from a version of the forwarddata signal by appropriate routing through a multiplexer 2506. Multiplexing section 2500 is configured to route the appropriate forwarddata and returndata streams so that suitable idealaligned and error signals 272 and 276 are generated. In this embodiment, highpass filter (HPF) 314 has been combined with HPF 205 from the Fig. 2 embodiment and placed downstream of subtraction circuit 274. Thus, error signal 276 is generated most directly from HPF 314. And, a delay element 2508 is inserted following multiplexer 2506. Delay element 2508 inserts a delay approximately equal to the delay inserted by HPF 314 so that error signal 276 and idealaligned signal 272 maintain temporal alignment. Referring to Figs. 24 and 25, task 2402 may initialize multiplexing section 2500 to select the multiplexer inputs designated with a "0" in Fig. 25. These selections route a 0 through multiplexer 2502 to subtractor 274 and A/Dcompensatedreturndata stream 1832 through a delay element 2510 and multiplexer 2504. Consequently, error signal 276 is essentially provided by combination circuit 1830. Idealaligned signal 272 is provided by delayedforwarddata stream 1816 through multiplexer 2506 and a delay element 2512. Delay element 2510 inserts a fixed delay equivalent to the collective signal delay imposed by DDC 1834 and return equalizer 260. Delay element 2512 inserts a fixed delay equivalent to the collective signal delay imposed by DDC 1834, return equalizer 260, digital upconverter 1806, and equalizer 1824. The delays of delay elements 2510 and 2512 cause the error and idealaligned signals 276 and 272 to maintain temporal alignment in lateroccurring processes where the different components are switched into the signal paths. Following task 2402, subprocess 2400 desirably performs subprocess 600, discussed above, or a similar process to implement an estimationandconvergence algorithm that causes the forwarddata and returndata streams to temporally align at the compensation point provided by combining circuit 1830. Temporal alignment may be established by varying the programmable delay inserted by delay element 700' while monitoring an output from a Root Mean Square (RMS) estimator 2514. RMS estimator 2514 has an input coupled to the output of subtractor 274, which reflects the timing at the compensation point. Desirably, RMS estimator 2514 performs a similar function to correlation engine 280 and is configured to accumulate the estimated RMS values of a vast number of samples, as discussed above in connection with correlation engine 280. Temporal alignment is achieved when delay element 700' is programmed so that a minimum RMS value is detected at RMS estimator 2514. In an alternate embodiment, correlation engine 280 may be used to maximize the correlation between the forwarddata and returndata signals at the compensation point. Following the performance of subprocess 600 from subprocess 2400, subprocess 2400 performs subprocess 1100, discussed above, to implement an estimationandconvergence algorithm which resolves tap coefficients for equalizer 1824. Following the completion of subprocess 1100, coefficients have been determined and programmed into equalizer 1824, and the justdetermined coefficients result in a maximum level of correlation between the returndata stream output from A/D 304 and the forwarddata stream. At this point equalizer 1824 has been adjusted to compensate for linear distortion introduced by A/D 304, and subprocess 2400 is complete. Referring back to Fig. 19, following the completion of subprocess 2400, process 1900 then performs subprocess 500, discussed above, to compensate for linear distortion introduced upstream of HPA 136. During subprocess 500 and subsequent subprocesses, quantizationerror compensator 2200 and linear distortion compensator 1822 remain programmed and operational to apply A/D distortion compensation while these subsequent compensation subprocesses take place. During initialization task 502 of subprocess 500, multiplexer 250 is switched to route RF feedback signal 134 to A/D 304. RF feedback signal 134 is an upconverted form of baseband feedback signal 123 and includes distortions not present in baseband feedback signal 123. Consequently, task 502 desirably switches switch 1820 to route the forwarddata stream passing through delay element 700 and digital upconverter 1806 to quantizationerror compensator 2200 and lineardistortion compensator 1822. While upconversion section 126 need not, and preferably does not, upconvert to F_{s}/4, as does digital upconverter 1806, A/D 304 performs a subsampling downconversion that centers its output at Fs/4. Consequently, upconversion section 126 and A/D 304 act together as though an upconversion to F_{s}/4 has been performed. The quantization error and linear distortion compensation previously determined for baseband are now applied at F_{s}/4. In addition, initialization task 502 desirably controls multiplexing section 2500 to select the multiplexer inputs designated with a "1" in Fig. 25. These selections route a returndata stream 262 through multiplexer 2502 to subtractor 274 and forwarddata stream 272' through a delay element 2516 and multiplexer 2504 to form error signal 276. Idealaligned signal 272 is provided by forwarddata stream 272' delayed through delay element 2516. Delay element 2516 inserts a fixed delay equivalent to the collective signal delay imposed by DDC 1834, return equalizer 260, digital upconverter 1806, and equalizer 1824 to maintain temporal alignment with other processes where the different components are switched into the signal paths. Following initialization task 502, subprocess 500 then adjusts common mode and differential time alignment by programming delay sections 700 and 800, as discussed above in connection with Figs. 58, and adjusts phaserotate section 1000 to align phase as discussed above in connection with Fig. 910. Then, subprocess 500 implements an estimationandconvergence algorithm to resolve tap coefficients for forward equalizer 246. At this point, linear distortions introduced into the forwarddata stream upstream of HPA 136 have been compensated. Referring again to Fig. 19, following the completion of subprocess 500, process 1900 next perfonns a subprocess 2600 to compensate for nonlinear distortion introduced by A/D 304. Referring to Fig. 20, A/D 304 may introduce nonlinear distortion primarily through the operation of NL amp 2004. Fig. 26 shows a flowchart of subprocess 2600. Process 2600 is desirably performed after predistortion circuit 1800 has been programmed to compensate for A/D quantization error distortion, A/D linear distortion, and linear distortion upstream of HPA 136. At this point, RF feedback signal 134 has been adjusted to remove linear distortion. And, no source of a substantial amount of nonlinear distortion is present in the path of RF feedback signal 134. Consequently, any nonlinear distortion is primarily from A/D 304. Process 2600 includes an initialization task 2602 to set up predistortion circuit 1800 to determine the corrective actions needed to compensate for A/D nonlinear distortion. Task 2602 may switch multiplexer 250 to route RF feedback signal 134 to A/D 304, and control switch 1820 to route the forwarddata stream passing through delay element 700 and digital upconverter 1806 to quantizationerror compensator 2200 and lineardistortion compensator 1822. And, multiplexing section 2500 may be controlled to select the multiplexer inputs designated with a "2" in Fig. 25. These selections route returndata stream 262 through multiplexer 2502 to subtractor 274 and forwarddata stream 272' through delay element 2516 and multiplexer 2504 to form error signal 276. Idealaligned signal 272 is provided by one of the basisfunction data streams 1804, such as the one labeled D_{2}, delayed through delay element 2518. Delay element 2518 inserts a fixed delay equivalent to the collective signal delay imposed by DDC 1834, return equalizer 260, digital upconverter 1806, and an equalizer 1826' to maintain temporal alignment with other processes where the different components are switched into the signal paths. Initialization task 2602 may also enable basisfunction generator 1600 to generate basis functions, but equalizers 226 are desirably disabled to generate a zero data stream. The equalizer 226' for the subject basis function, such as EQ_{A©} for D_{2} basis functiondata stream 1804, is desirably set to an initial value, but any other equalizers 226' that have not been processed are desirably initialized to output a zero data stream. Following initialization task 2602, subprocess 2600 performs a task 2604 to program delay sections 700" and phaserotate sections 1000'. Task 2604 may, but need not, employ estimationandconvergence algorithms to determine appropriate delay and phase settings. If such algorithms are employed they may be configured substantially as discussed above in connection with Figs. 610. But delay sections 700" and phaserotate sections 1000' have a fixed relationship to delay section 700 and phaserotate section 1000, respectively. That fixed relationship is determined by the relative delays inserted by the components in the respective forwarddata stream paths. Consequently, delay sections 700" may be programmed merely by applying predetermined offsets to the parameters determined above for delay section 700 and phaserotate section 1000. The goal of this programming is to have the forwarddata stream flowing in this path arrive at combination circuits 1828 and 1830 in temporal alignment with the forwarddata streams propagating through delay sections 700 and 700'. Next, subprocess 2600 performs subprocess 1100 to implement an estimationandconvergence algorithm for the EQ_{AΏ} equalizer 226'. At the completion of subprocess 1100, the EQ_{AΉ} equalizer 226' is programmed with coefficients that cause the secondorder basis function to be filtered so that it exhibits maximum correlation with the returndata stream from A/D 304. This then minimizes the secondorder distortion component of the returndata stream. Fig. 26 depicts an exemplary scenario where three basis functions are utilized by predistortion circuit 1800. Consequently, for this exemplary scenario subprocess 2600 repeats subprocess 1100 two additional times to resolve coefficients for the EQ_{A©} equalizer 226' and the EQ^{K+} _{AΈ}> equalizer 226'. In the subsequent iterations of subprocess 1100, multiplexing section 2500 is desirably controlled to select the multiplexer inputs designated with a "3" and a "4" in Fig. 25. Both selections route returndata stream 262 through multiplexer 2502 to subtractor 274 and forwarddata stream 272' through delay element 2516 and multiplexer 2504 to form error signal 276. In the "3" selection, idealaligned signal 272 is provided by the basisfunctiondata stream 1804 labeled D_{3}, delayed through delay element 2520. In the "4" selection, ideal aligned signal 272 is provided by the basisfunctiondata stream 1804 labeled D_{κ+}ι, delayed through delay element 2522. Delay elements 2520 and 2522 each impose the same delay as delay element 2518. Those skilled in the art will appreciate that nothing requires that any set number of basis functions be used. After the requisite number of iterations of subprocess 1100, subprocess 2600 is complete and nonlinear predistorter 224' has been programmed to compensate for nonlinear distortion introduced by A/D 304. Referring back to Fig. 19, following the execution of subprocess 2600, all substantial forms of distortion introduced by A/D 304 have now been compensated. Consequently, the remaining portion of process 1900 tracks corresponding components of process 400, discussed above. Subprocess 1400 is performed to compensate for linear distortion introduced through HPA 136. Thus, as shown in Fig. 14 initialization task 1402 in subprocess 1400 controls multiplexer 250 to route RF feedback signal 117 from the output of HPA 136 to the input of A/D 304. Time and phase alignment is readjusted to compensate for the insertion of HPA 136 into the feedback signal path by monitoring forwarddata stream 272' and return data stream 1832. Then, subprocess 1100 is executed three times. The first iteration of subprocess 1100 takes place at task 1414, which may control multiplexing section 2500 to select the multiplexer inputs designated with a "5" in Fig. 25, which has the same effect as selecting a "1". During the first iteration, forward coefficients for forward equalizer 246 are determined. The second iteration of subprocess 1100 takes place at task 1418, but the previous task 1416 may control multiplexing section 2500 to select multiplexer inputs designated with a "6" in Fig. 25. This selection routes returndata stream 262 through multiplexer 2502 to subtractor 274 and the highest ordered basis function (i.e., D_{κ+1}) through delay element 2522 and multiplexer 2504 to form error signal 276. Idealaligned signal 272 is also provided by the highest ordered basis function (i.e., D _{+}ι) delayed through delay element 2522. During the second iteration, return coefficients for return equalizer 260 are determined. The third iteration of subprocess 1100 takes place at task 1422, but the previous task 1420 may control multiplexing section 2500 to again select multiplexer inputs designated with a "1" or "5" in Fig. 25. During the third iteration, forward coefficients for forward equalizer 246 are readjusted. Following the performance of subprocess 1400, process 1900 performs task 402, substantially as discussed above in connection with Figs. 4 and 15. Task 402 performs subprocess 1500 to compensate for nonlinear distortion from HPA 136 without including heatinducedmemory effects. Subprocess 1500 iteratively routes different basis functions to adaptation engine 1300 and executes subprocess 1100 to perform an estimationandconvergence algorithm to determine equalizer coefficients. Following the three basisfunction scenario discussed above, for these iterations multiplexing section 2500 may be controlled to respectively select the multiplexer inputs designated with a "7", "8", and "9" in Fig. 25. Each selection routes returndata stream 262 through multiplexer 2502 to subtractor 274 and forwarddata stream 272' through delay element 2516 and multiplexer 2504 to form error signal 276. In the "7" selection, ideal aligned signal 272 is provided by the basisfunctiondata stream 1804 labeled D_{2}, delayed through delay element 2518, and coefficients are determined for the EQ^_{A} equalizer 226. In the "8" selection idealaligned signal 272 is provided by the basisfunctiondata stream 1804 labeled D_{3}, delayed through delay element 2520, and coefficients are determined for the EQ^_{A} equalizer 226. And, in the "9" selection idealaligned signal 272 is provided by the basisfunctiondata stream 1804 labeled D_{κ+1}, delayed through delay element 2522, and coefficients are determined for the EQ^{K+} _{HPA} equalizer 226. But those skilled in the art will appreciate that nothing requires that any set number of basis functions be used. As discussed above in connection with process 400, following task 402, a task 404 repeats subprocess 1500, but this time heatinducedmemory effects are also compensated. Then, following task 404, tasks 406 and 408 obtain a residual EVM value and use that value to adjust peak reduction. Following task 408, any of the subprocesses and tasks in process 1900 may be repeated as needed to allow the compensation provided by predistortion circuit 1800 to track over time and temperature. Fig. 27 shows a graph which depicts a few spectral plots that characterize various features of an exemplary wide bandwidth communications signal that conveys four frequencymultiplexed channels. Referring to Figs. 1 and 27, in this example four of modulators 104 generate four independent data streams 2700. Each of the independent data streams 2700 is positioned at baseband when generated by their respective modulators 104. In other words, each is characterized using a bandwidth centered at 0 Hz and extending between 3.8 MHz and +3.8 MHz. In this example, combiner 106 uses frequency multiplexing to combine these four independent data streams to produce complexforwarddata stream 108, as depicted in a trace 2702. Two of channels 2704, labeled "A" and "B" in Fig. 27, are centered at negative frequencies (e.g., 7.5 MHz and 2.5 MHz) and two of channels 2704, labeled "C" and "D" in Fig. 27, are centered at positive frequencies (e.g., +2.5 MHz and +7.5 MHz). The use of negative and positive frequencies to represent the frequencymultiplexed channels 2704 permits a reduction in the clock rate used for processing forwarddata stream 108 from the clock rate that would be required if all channels 2704 were characterized using only frequencies of a common polarity. Trace 2702 depicts the spectral character of wide bandwidth forwarddata stream 108 as it is processed downstream of combiner 106 in transmitter 100. For purposes of illustration, one of channels 2704, specifically channel B, in this example is significantly weaker than the others. This situation, where a wideband digital communication signal is configured to include a plurality of discrete frequency multiplexed channels and the discrete channels exhibit varying signal strength relative to one another, represents certain cellular base station and other digital communications applications. But those skilled in the art will appreciate that the present invention is not limited to addressing only this particular application, nor is this particular application limited to any particular number of discrete channels 2704 or to any specific constraint concerning relative channel strengths. Trace 2706 depicts a challenge faced in this application where forwarddata stream 108 is configured to include a plurality of discrete frequencymultiplexed channels and the discrete channels exhibit varying signal strength relative to one another. If complexforwarddata stream 118 could be perfectly upconverted in upconversion section 126, the upconverted inphase component would initially frequencyshift and split each channel to sum and difference frequencies and the upconverted quadrature component would also initially frequencyshift and split each channel to sum and difference frequencies. Then the upconverted inphase and quadrature components would be combined, and either the sum frequencies would completely cancel one another or the difference frequencies would completely cancel one another, depending upon how the inphase and quadrature upconverted components were combined. In other words, in a perfect upconversion of a complex signal no image signal results. However, a perfect upconversion is unlikely to result from the operation of upconversion section 126. While one of the goals of forward equalizer 246 and differential time alignment section 800 is to balance the inphase and quadrature components of complex forwarddata stream 118 as much as they can, some residual imbalance will invariably remain. The residual imbalance will, after upconversion in upconversion section 126, cause image signals 2708 to appear in RFanalog signal 130 because the crossover terms from the opposing complex components will not perfectly cancel each other out. And, since channel A is placed at the negative of the frequency used for channel D and since channel B is placed at the negative of the frequency used for channel C, image signals 2708 fall in band. In other words, the image signal 2708 from channel A falls in channel D in RFanalog signal 130; the image signal 2708 from channel B falls in channel C in RFanalog signal 130; the image signal 2708 from channel C falls in channel B in RFanalog signal 130; and, the image signal 2708 from channel D falls in channel A in RFanalog signal 130. Image signals 2708 are unwanted because they represent error, noise, or interference in the channels where they fall. Trace 2706 illustrates that image signals 2708 are much weaker than the signals of which they are an image. Consequently, when channels located at the image frequencies of one another are of approximately equal communicationchannel strength 2710, such as channels A and D, the image problem is easily managed by the embodiments and techniques discussed above in connection with Figs. 126. Receivers tuned to receive channels A and D will be able to successfully demodulate their signals because the error signal strengths 2712 caused by the image signals are sufficiently weak compared to the communication signal strengths 2710 of channels A and D. But when channels located at the image frequencies of one another exhibit significantly different strengths, such as channels B and C, an image concern occurs. In particular, trace 2706 depicts an exemplary situation where communicationsignal strength 2710 of weak channel B is low compared to, and perhaps even lower than, errorsignal strength 2712 resulting from the image of strong channel C. A receiver tuned to receive channel C will be easily able to demodulate its signal because errorsignal strength 2712 in channel C, caused by the image from channel B, is very weak compared to the communicationsignal strength 2710 in channel C. On the other hand, a receiver tuned to receive channel B may not be able to successfully demodulate its signal. In channel B the errorsignal strength 2712, caused by the image from channel C, is very strong compared to communicationsignal strength 2710 for channel B. Fig. 28 shows a block diagram of a third embodiment of the linearandnonlinearpredistortion section 200, referred to below as predistortion circuit 2800, of transmitter 100. Predistortion circuit 2800 is configured to perform predistortion and other transmitter processing in a way that meets errorvector magnitude (EVM) and/or signaltonoise (S/N) requirements for both weaker and stronger channels transmitted from transmitter 100. Predistortion circuit 2800 is configured much like predistortion circuits 200 and 1800, and the abovepresented discussion concerning predistortion circuits 200 and 1800 for the most part applies to predistortion circuit 2800. Like reference numbers refer to similar components between the block diagrams of Figs. 1, 2, 18 and 28. However, for convenience certain segments of predistortion circuits 200 and 1800, such as gain adjustment circuits 302 and 256, heatchange estimation circuit 1700, and circuits for generating clock signals for A/D 304, rate multiplier 204, controller 286, adaptation engine 1300, correlation engine 280, and certain delay stages have been omitted from Fig. 28. Those skilled in the art will appreciate that such segments may nevertheless be included in predistortion circuit 2800 and used substantially as discussed above in connection with Figs. 226. Increasedratecomplexforwarddata stream 206 drives a nonlinear processing section 2802, commonmodetimealignment section 700, and a positive input of combining circuit 220. Nonlinear processing section 2802 includes abovediscussed sections that are useful in addressing nonlinear distortions caused by HPA 136 and A/D 304. Such sections include basis function generation section 1600, equalizers 226 and 226' (see Fig. 18) and the like. As discussed above, a complex signal output from nonlinear processing section 2802 couples to a negative input of combining circuit 220. Combining circuit 220 provides forwarddata stream 238 to forward equalizer 246 and to differential modetimealignment section 800. A processedforwarddata stream 118 is generated by forward equalizer 246. Although not depicted in Fig. 28, an alternate embodiment may place combining circuit 220 downstream of forward equalizer 248, rather than upstream as shown in Fig. 28. In this alternate embodiment, forward equalizer 248 may then operate at a lower clock rate. As in the previouslydiscussed embodiments, forward equalizer 246 is positioned in series with analogtransmitter components 120. Timealignment, or delay, section 800 provides forwarddata stream 118 to digitaltoanalog converters (D/A's) 122, which convert the forwarddata stream into a forwardanalog signal and drive the remainder of analogtransmitter components 120. As discussed above, D/A's 122 preferably exhibit a significantly higher resolution than A/D 304. The box labeled "XPF" in Fig. 28 includes lowpass filters 124, upconversion section 126, and bandpass filter 132 from Fig. 1. As the forwarddata signal continues to be processed through analogtransmitter components 120, an output from bandpass filter 132 provides RFanalog signal 134 to multiplexer 250 and to HPA 136. RFanalog signal 117 is derived from the output of HPA 136 and routed to multiplexer 250. As discussed above in connection with Fig. 18, one of D/A's 122 also directly generates baseband signal 123, which is routed to multiplexer 250. But a dedicated D/A (not shown) may also be used to generate baseband signal 123. The output of multiplexer 250 couples to an input of A/D 304. Desirably, the D/A that drives baseband signal 123 is of high resolution and high quality because, as discussed in more detail below, that D/A is used to establish compensation for A/D 304, and such compensation will be limited by any distortion introduced by the D/A. One difference between this third embodiment and the abovediscussed embodiments is that time alignment section 700 directly provides alignedidealforwarddata stream 272, and phase rotator 1000 is positioned in returndata stream 262. But an inverse phase rotator 2804, which is included in A/D compensation section 1805, has an input driven by alignedidealforwarddata stream 272, and produces forwarddata stream 272'. Inverse phase rotator 2804 causes a phase rotation opposite to the phase rotation imparted by phase rotator 1000. In an alternate embodiment, common mode alignment section 700 may be split into an integral portion 714 (Fig. 7) and two (not shown) fractional sections 716. One of the fractional sections 716 may operate on the forwarddata stream and feed one input of subtraction circuit 274, while the other fractional section 716 may then operate on the returndata stream and feed the other input of subtraction circuit 274. The two fractional sections 716 would desirably be controlled to generate equal but opposite, relative to a midpoint of a clock cycle, fractional delays. Any linear distortions then produced by the two fractional sections 716 would tend to equal one another and diminish any influence such distortions might otherwise exert over equalizer tap adjustments. Forwarddata stream 272' drives digital upconversion (DUC) section 1806 and a fixed delay element 1818, which imposes a fixed delay substantially equivalent to the delay imposed by digital upconversion section 1806. DUC section 1806 digitally upconverts forwarddata stream 272' to an intermediate frequency (IF) of F_{s}/4, where F_{s} is the sampling frequency. Outputs of DUC section 1806 and of delay element 1818 couple to switching section 1820, which is included in A/D compensation section 1805. Switching section 1820 has an output that couples through realconversion section 1808 to linear equalizer 1824, which is labeled EQ_{AD} in Fig. 28, where the "1" superscript denotes a linear operator and the "A/D" subscript denotes that equalizer 1824 is provided to compensate for A/Dintroduced distortion. The output from switching section 1820 also drives, through real conversion section 1808, quantizationerror compensator 3100, which is also included in A/D compensation section 1805. Generally, quantizationerror compensator 3100 compensates for quantization error amplitude and dissymmetry. Quantizationerror compensator 3100 is discussed in more detail below in connection with Fig 31. Outputs from nonlinear processing section 2802, equalizer 1824, and quantizationerror compensator 3100 are added together in combining circuit 1828. The version of the forwarddata stream output from combining circuit 1828 is provided to a negative input of combining circuit 1830. Combining circuit 1830 provides the compensation point where the processed forwarddata stream is combined with a returnrawdigitizeddata stream 304' output from A/D 304 to form A/Dcompensatedreturndata stream 1832. But, Fig. 28 depicts that returnrawdigitizeddata stream 304' has its resolution adjusted, if necessary, in a resolution adjuster 2806 prior to this combination. Resolution may be adjusted by implementing the Vj bit offset representation discussed above in connection with Figs. 2122 and/or by increasing the resolution to approximately the same resolution at which the forwarddata stream is processed. In some embodiments, no explicit activity needs to occur in resolution adjuster 2806. A/Dcompensatedreturndata stream 1832 feeds direct digital downconversion section (DDC) 1834. In this third embodiment, DDC 1834 includes only components 308, 310, and 312 from DDC 300 in the abovediscussed first embodiment. In general, A/D 304 effectively downconverts the feedback signal it samples into a real signal at the intermediate frequency (IF) of F_{s}/4, where F_{s} is the sampling frequency. DDC 1834 generates complex returndata stream 254, which is a complex signal substantially at baseband. Complex returndata stream 254 drives return equalizer 260, which in turn drives phase rotator 1000. An output of phase rotator 1000 generates complexreturndata stream 262, which is fed to subtraction circuit 274, a first input of a phase estimator 2808 and a first input of a differential delay estimator 2810. The output of subtraction circuit 274 generates error stream 276, which is fed to a spectral management section 2900 and to a spectral management switch 2814. Alignedidealforwarddata stream 272 is fed to phase estimator 2808, differential delay estimator 2810, spectral management section 2900, and switch 2814. An output from phase estimator 2808 couples to a control input of phase rotator 1000 and to a control input of inverse phase rotator 2804. And, an output from differential delay estimator 2810 couples to a control input of differential mode time alignment section 800. As with the abovediscussed embodiments, equalizers 246, 260, 1824, and other equalizers which may be included in predistortion circuit 2800 are desirably either programmable equalizers that become adaptive equalizers when coupled to adaptation engine 1300 or adaptive equalizers that include coefficient adapting circuits. Differential delay estimator 2810 is a hardware block that achieves a similar result to that achieved by time alignment subprocess 600. Generally, delay estimator 2810 closes a feedback loop that drives the variable delay imparted by differential mode time alignment section 800. Accordingly, the delay imparted by section 800 is dynamically and continuously adjusted. Dynamic adjustment of the differential delay between inphase and quadrature components of the forwarddata stream is desirable because the image problem is particularly sensitive to differential delay. Likewise, phase estimator 2808 is a hardware block that achieves a similar result to that achieved by phase alignment subprocess 900. Generally, phase estimator 2808 closes a feedback loop that drives the phase rotation needed to align returndata stream 262 with forwarddata stream 272 at subtraction circuit 274. The phase rotations imparted by phase rotator 1000 and by inverse phase rotator 2804 are desirably identical to one another, but in opposite directions. And, these phase rotations are dynamically and continuously adjusted. Dynamic adjustment of the phase rotation is desirable because differential delay calculations are more accurate when the forwarddata and returndata streams are phase aligned. Spectral management section 2900 also addresses the abovediscussed image problem that can occur when the forwarddata stream conveys a plurality of frequencymultiplexed communication channels. Fig. 29 shows a block diagram of a representative spectral management section 2900 which is suitable for use in linearandnonlinearpredistorter 2800. Spectral management section 2900 receives alignedidealforwarddata stream 272 at a signalstrengthmeasuring circuit 2902 and receives error stream 276 at a signalstrengthmeasuring circuit 2904. Streams 272 and 276 are complex signal streams, but the complex notation is omitted from Fig. 29. Within signalstrengthmeasuring circuit 2902, forwarddata stream 272 is fed to a transmultiplexer 2906, which separates forwarddata stream 272 into a plurality of discrete communication signals 2908, where the discrete communication signals 2908 have a onetoone correspondence with communication channels 2704. Signalstrength measuring circuit 2902 also includes one magnitudedetecting circuit 2910 for each of discrete communication signals 2908. Magnitudedetecting circuits 2910 identify communicationsignal strengths 2710 for channels 2704. Likewise, within signalstrengthmeasuring circuit 2904, error stream 276 is fed to a transmultiplexer 2912, which separates error stream 276 into a plurality of discrete error signals 2914, where the discrete error signals 2914 also have a onetoone correspondence with communication channels 2704. Signalstrength measuring circuit 2904 also includes one magnitude detecting circuit 2916 for each of discrete error signals 2914. Magnitudedetecting circuits 2916 identify errorsignal strengths 2712 for channels 2704. In the preferred embodiment, each magnitudedetecting circuit 2910 and 2916 measures the power present in its respective discrete communication or error signal 2908 or 2914. Outputs from magnitudedetecting circuits 2910 and 2916 are fed to an errorvector magnitude (EVM) calculator 2918. EVM calculator 2918 calculates an EVM statistic for each of communication channels 2704. In general, these EVM calculations are performed by dividing the error power, obtained from error stream 276, by the communication channel power, obtained from forwarddata stream 272. But the purposes of the present invention may also be fulfilled by other calculations that account for the relative communicationsignal strengths 2710 and the relative errorsignal strengths 2712 among channels 2704. EVM calculator 2918 passes the EVM statistics to a gain controller 3000. EVM calculator 2918 need not assume that forwarddata stream 272 is an absolutely "ideal" data stream that conveys no error. In an embodiment of transmitter 100 which includes peak reduction section 110 (Fig. 1), forwarddata stream 272 may include some distortion introduced by peak reduction section 110. It is desirable that distortion introduced into forwarddata stream 112 by peak reduction section 110 be accounted for by EVM calculator 2918. Thus, peakreduction control signal 114' conveys the shortterm average noise added to forwarddata stream 112. Preferably, peakreduction control signal 114' conveys the shortterm average noise added to each of the independentlymodulated complexdata streams output from modulators 104 (Fig. 1), as determined by filtered magnitudes of postlowpassfiltering excursion energy. In this embodiment EVM calculator 2918 may then, for each channel 2704, calculate EVM's in response to the RMS sum of the peakreduction noise obtained from control signal 114' and error noise obtained from magnitudedetecting circuits 2916. In general, gain controller 3000 forms scale factors 2920, 2922, and 2924 which are used to scale the relative influence of channels 2704 in instructing forward equalizer 246 how to adapt its coefficients to reduce correlation between the forwarddata and error streams. More specifically, gain controller 3000 implements an algorithm that tends to emphasize the influence of the weaker ones of discrete communication signals 2908 in the adaptation of coefficients within forward equalizer 246 and deemphasize the influence of the stronger ones of discrete communication signals 2908 in the adaptation of coefficients within forward equalizer 246. Stronger signals 2908 tend, but are not required to, exhibit lower EVM's and weaker signals 2908 tend to exhibit higher EVM's. So, in a preferred embodiment the EVM metric, or the equivalent, is used by this algorithm. Signals 2908 with higher EVM values are emphasized with respect to those with lower EVM values in adapting coefficients within forward equalizer 246. Four of scale factors 2920 are provided to first inputs of multipliers 2926. Second inputs of multipliers 2926 are adapted to receive the four discrete communication signals 2908, and outputs of multipliers 2926 provide scaled discrete communication signals 2928 to an inverse transmultiplexer 2930. Inverse transmultiplexer 2930 performs the inverse operation of transmultiplexer 2906 and forms a merged communication signal 272". Mergedcommunication signal 272" again conveys four frequencymultiplexed communication channels 2704 and generally corresponds to forwarddata stream 272 in data rate and resolution. But the spectral content of mergedcommunication signal 272" has been altered to emphasize the higherEVM, and typically weaker, channels over the lowerEVM, and typically stronger, channels. Four of scale factors 2922 are provided to first inputs of multipliers 2932. Second inputs of multipliers 2932 are adapted to receive the four discrete error signals 2914, and outputs of multipliers 2932 provide scaled discrete error signals 2934 to an inverse transmultiplexer 2936. Inverse transmultiplexer 2936 performs the inverse operation of transmultiplexer 2912 and forms a mergeddirectpatherror signal 276". Mergeddirectpatherror signal 276" again describes four frequencymultiplexed communication channels 2704 and generally corresponds to error stream 276 in data rate and resolution. But the spectral content of mergeddirectpatherror signal 276" has been altered to emphasize the higherEVM, and typically weaker, channels over the lowerEVM, and typically stronger, channels. Four of scale factors 2924 are provided to first inputs of multipliers 2938. Second inputs of multipliers 2938 are adapted to receive the four discrete error signals 2914, and outputs of multipliers 2938 provide scaled discrete error signals 2940 to an inverse transmultiplexer 2942. Inverse transmultiplexer 2942 performs the inverse operation of transmultiplexer 2912 and forms a mergedcrossoverpatherror signal 276". During normal operations, forward equalizer 246 adapts its coefficients in response to the correlation between mergedcommunication signal 272" and either mergeddirectpatherror signal 276" or mergedcrossoverpatherror signal 276", depending upon whether coefficients for direct paths 1214 and 1216 or for crossover paths 1218 and 1220 are being adapted. Fig. 30 shows a flow chart depicting the operation of an exemplary gain controller 3000 for use in spectral management section 2900. Gain controller 3000 may be implemented within controller 286, an independent controller device, or by hardware dedicated to providing similar functions. The algorithm implemented by gain controller 3000 includes a task 3002, which identifies the channel 2704 with the greatest EVM. In other words, the worst channel is identified, which is also the channel whose EVM is in the most need of improvement. After task 3002, a query task 3004 determines whether coefficients are being calculated for direct paths 1214 and 1216 of equalizer 1200, which also serves as forward equalizer 246, or for crossover paths 1218 and 1220. If crossover paths 1218 and 1220 are detected in task 3004, then a task 3006 selects scale factors currently being applied for the crossover paths. If direct paths 1214 and 1216 are detected in task 3004, then a task 3008 selects scale factors currently being applied for the direct paths. Gain controller 3000 may be configured to switch backandforth from timeto time between calculating scale factors for the direct and crossover paths. Switching may occur on a regular schedule or based upon a failure to detect significant improvement in EVM statistics which result from previous scale factor updates. Alternatively, gain controller 3000 may be configured to first focus on direct paths, lock equalizer coefficients in the direct paths, then switch to crossover paths. Or, gain controller 3000 may use still other switching algorithms which may be devised by those skilled in the art. After task 3006 or 3008, a query task 3010 determines whether a scale factors 2920, 2922, or 2924 currently being generated for the identified channel 2704 are at a predetermined maximum level. So long as these current scale factors are not at their maximums, a task 3012 increases the scale factors by predetermined amounts, and program control flows back to task 3002. The scale factors for the channel with the poorest EVM are increased while the scale factors for the other channels remain unchanged. This emphasizes the influence of the channel 2704 having the poorest EVM and deemphasizes the influence of the remaining channels 2704. When task 3010 determines that the current scale factors for the worst channel are at or above their maximum permitted level, a programming loop adjusts the scale factors used for all channels. In particular, a task 3014 identifies a first channel during the first iteration of this loop or the next channel in sequence during subsequent iterations. After task 3014, a task 3016 reduces the identified channel's scale factors by predetermined amounts. After task 3014, a query task 3018 determines whether the channel's scale factors are currently at or beneath minimum levels. If the minimum levels are detected, then a task 3020 sets the scale factors at their minimum levels. After task 3020 and when task 3018 determines that the channel's scale factors are not at their minimums, a query task 3022 determines whether the programming loop has adjusted scale factors for the last channel. If the last channel has not been processed, programming control flows back to task 3014. When the last channel is processed, program control flows back to task 3002. As a result of scaling the gains applied to channels 2704 in the feedback used to adapt coefficients for forward equalizer 246, coefficients change in a way that drives the individual EVM's for communication channels 2704 to approximately equal values. Greater reduction in EVM is achieved for channels 2704 having higher EVM's than is achieved for communication channels 2704 having lower EVM's. Distortion introduced by analogtransmitter components 120 is counteracted more in response to communication channels 2704 having higher EVM's than in response to channels having lower EVM's. While the abovepresented discussion specifically details one exemplary algorithm which may be implemented by gain controller 3000, those skilled in the art will be able to devise alternate and equivalent algorithms that will accomplish substantially the same thing. For example, gains for all channels may initially be set to low or minimum values, then gains for channels with higher EVM's may be increased as needed to cause the EVM's of all channels to be maintained at substantially equal levels, which levels are desirably as low as possible. Referring back to Figs. 2728, trace 2714 depicts an additional concern that occurs in the situation when the forwarddata stream conveys a plurality of frequencymultiplexed communication channels and one or more of the channels is significantly stronger than a channel located at an image frequency. In order for a feedback loop to perform satisfactorily, it is desirable that a resultant output track, in a predictable manner, changes in a feedback signal. In the embodiment described above in connection with Figs. 2830, it is therefore desirable that the calculated EVM's for communication channels 2704 bear a predictable relationship to changes in amplifiedRF communication signal 117 that result from changed coefficients in forward equalizer 246. But the quantization that occurs in A/D 304, and particularly in quantizer 2016 of A/D model 2000 (Fig. 20), may jeopardize the EVM calculations. Quantization is a nonlinear operation that generates intermodulation between channels 2704. Some of this intermodulation will fall inband. And, as the resolution of A/D 304 is lowered, the quantization error along with the inband intermodulation becomes worse. Trace 2714 depicts an exemplary situation where the use of a lowresolution A D 304 causes intermodulation 2716 to be even greater than communicationsignal strength 2710 for weak channel B. In such a situation, the abovediscussed EVM measurement performed by spectral management section 2900 for channel B will bear no significant relation to changes that take place in channel B in response to the feedback signal that emphasizes the EVM measured in channel B. Accordingly, quantizationerror compensator 3100 is configured to compensate for quantization error amplitude as well as quantization error dissymmetry. By compensating for quantization error amplitude as well as dissymmetry, the inband intermodulation improves considerably and EVM measurements performed by spectral management section 2900 for weak channels 2704 will track output changes. Fig. 31 shows a block diagram for an exemplary quantizationerror compensator 3100 configured to compensate for quantization error amplitude and dissymmetry introduced by a 2bit A D 304. Those skilled in the art will appreciate that the present invention is not required to use a 2bit A/D 304 and that the principles of exemplary quantizationerror compensator 3100 may be extended to an A/D of any precision. In general, quantizationerror compensator 3100 includes a quantizersimulator 3102 and a differencing circuit 3104. Quantizersimulator 3102 is configured to simulate the operation of quantizer 2016 from A/D 304. In particular, quantizersimulator 3102 includes a register 3106 for each switching threshold 2108 (Fig. 21) implemented by A/D 304. For a 2bit A/D, three of registers 3106 are included. Each register 3106 is configured to be loaded by a value provided by controller 286. Desirably, registers 3106 are programmed with actual switching thresholds measured from A/D 304 in accordance with task 2316 of subprocess 2300 or from another process that achieves similar results. The data output from a register 3106', which holds the middle switching threshold 2108, is routed to a negative input of a comparator 3110. Data outputs from the other registers 3106 in this 2bit example are routed to data inputs of a multiplexer (MUX) 3112. The output from comparator 3110 drives a selection input of multiplexer 3112, and a data output from multiplexer 3112 drives a negative input of a comparator 3114. The forwarddata stream, in either a baseband form or an IF form depending upon the state of switch 1820, is routed to positive inputs of comparators 3110 and 3114 and to a positive input of differencing circuit 3104. An output from comparator 3112 provides a mostsignificant bit and an output from comparator 3114 provides a leastsignificant bit to a resolution adjuster 3116. Resolution adjuster 3116 performs a similar operation to that performed by resolution adjuster 2806 located at the output of A/D 304. In some embodiments, no explicit activity needs to occur in resolution adjuster 3116. An output from resolution adjuster 3116 generates a quantizesimulateddata stream 3118, which represents the output from quantizersimulator 3102. Quantizesimulateddata stream 3118 drives a negative input of differencing circuit 3104. A control register 3120 is adapted to receive a control input from controller 286, and has an output that drives one input of an AND functional element 3122. An output from differencing circuit 3104 drives another input of element 3122, and an output of element 3122 provides a quantizationerrordata stream 3124, which represents the output from quantizationerror compensator 3100. Control register 3120 and AND element 3122 provide and enable/disable function for quantizationerror compensator 3100. When disabled, quantizationerror compensator 3100 exerts no influence upon the operation of transmitter 100. When programmed with actual switching thresholds 2108, quantizersimulator 3102 faithfully simulates the operation of quantizer 2016 in A/D model 2000. Quantizersimulator 3102 quantizes the forwarddata stream in either a baseband or IF form, and therefore generates intermodulation which tracks the intermodulation generated by A/D 304. In addition, error in quantization that results from dissymmetry and/or from quantization error amplitude is reflected in quantizesimulateddata stream 3118. The extent to which quantizesimulateddata stream 3118 fails to match the forwarddata stream provides an estimate of the error introduced by quantizer 2016, whether from dissymmetry, quantization error amplitude, or intermodulation. Accordingly, quantizationerrordata stream 3124 characterizes the extent to which quantize simulateddata stream 3118 fails to match the forwarddata stream. As discussed above in connection with the second embodiment of Fig. 18, this A/D error is subtracted, along with other A/D compensation factors, from returnrawdigitizeddata stream 304' at combining circuit 1830 to compensate for A/D 304 errors. Due to the operation of quantizationerror compensator 3100, intermodulation 2716 is reduced to a level beneath communi cationsignal strength 2710 for all communication channels 2704, including weak channel B, as depicted by trace 2718 in Fig. 27. Fig. 32 shows a flowchart of a third embodiment of the transmissiondistortionmanagement process 400 performed by transmitter 100. This third embodiment is referred to below as process 3200. Process 3200 differs from processes 400 and 1900, discussed above, in that a few additional tasks are included to compensate for the abovediscussed image signal and intermodulation concerns. Referring to Figs 28 and 32, process 3200 is assumed to start with a powerup or reset event. Process 3200 first performs several basic initialization tasks which may occur in any order. A task 3202 deactivates HPA 136 so that transmitter 100 will emit no significant transmission. A task 3204 disables quantization error compensator 3100 by programming an appropriate control value in register 3120. A task 3206, locks forward equalizer (EQ_{F}) 246 and return equalizer (EQ_{R}) 260 and insures that equalizers 246 and 260 implement a unity transfer function so that they will exert no influence on the operation of transmitter 100. Locking may be accomplished, for example, by setting convergence factor "μ" (Fig 13) to a value near zero, and the unity transfer function may be accomplished, for example, by setting coefficients to: ...0,1,0.... Likewise, a task 3208 locks all equalizers (EQ_{HPA}) 226 used to compensate for nonlinear distortions introduced by HPA 136, and equalizers (EQ_{A/D}) 226' and 1824 at a zero transfer function so that they will exert no influence on the operation of transmitter 100. The zero transfer function may be accomplished, for example, by setting coefficients to: ...0,0,0.... A task 3210 sets A/D compensation section switch 1820 to pass the baseband form of the forwarddata stream, and a task 3212 sets spectral management switch 2814 to pass forwarddata stream 272 and error stream 276 for use in adapting coefficients in forward equalizer 246. In other words, the operation of task 3212 prevents spectral management section 2900 from exerting an influence over the operation of transmitter 100. A task 3214 disables delay and phase estimators 2810 and 2808 so that no differential delay or phase adjustments will be automatically made. And, a task 3216 switches multiplexer 250 to route baseband signal 123 to the input of A/D 304. Following task 3216, the basic initialization is complete. Following the basic initialization, process 3200 performs a task 3218 to adjust common mode time alignment section 700 using subprocess 600 or another function that produces a similar result. Task 3218 generally brings forwarddata stream 272 and returndata stream 262 into temporal alignment with one another at subtraction circuit 274. Next, a task 3220 compensates for A/D quantization error and dissymmetry. Task 3220 desirably performs subprocess 2300 or another function that produces a similar result. Subprocess 2300 evaluates A/D 304 to measure actual switching thresholds 2108 and programs those actual switching thresholds 2108 into quantizersimulator 3102. Task 3220 may take place by passing a swept test signal through the forward path of transmitter 100. Following task 3220, a task 3222 causes transmitter 100 to process a frequencymultiplexed communication signal in which one channel may be much stronger than a channel located at its image frequency. In other words, transmitter 100 may begin to produce a communication signal, although that signal may not be emitted from transmitter 100 because HPA 136 has not yet been enabled. Next, a task 3224 activates linear A/D equalizer (EQ_{&D}) 1824 to compensate for linear A/D distortions. Task 3224 may perform subprocess 2400 or another function that produces a similar result. Then, a task 3226 locks or greatly restricts the bandwidth of linear A/D equalizer 1824 so that the coefficients in equalizer 1824 will not undergo significant further adaptation. After task 3226, a task 3228 switches multiplexer 250 to route RFanalog signal 134 to the input of A/D 304, which further delays returndata stream 262 relative to forwarddata stream 272. So, a task 3230 realigns timing between forwarddata stream 272 and returndata stream 262. Task 3230 may again perform subprocess 600 or another function that produces a similar result to restore the desired temporal alignment. Bandpass filter 132 (Fig. 1) inserts a significant phase rotation in the returnanalog signal now input to A/D 304. So, a task 3232 activates phase estimator 2808 to close the feedback loop and maintain phase alignment between the forwarddata stream and the returndata stream originating from A/D 304. And, a task 3234 activates differential delay estimator 2810 to close the feedback loop and maintain differential timing alignment between the inphase (I) and quadrature (Q) components of the complexforwarddata stream processed through analogtransmitter components 120. Following task 3234, a task 3236 sets A/D compensation switch 1820 to pass the IF version of forwarddata stream 272. At this point, quantizationerror compensator 3100 and A/D linear equalizer 1824 begin to operate on an IF version of the communication signal, as characterized in the forwarddata stream, much like the subsampled version of the RF signal upon which A/D 304 operates. Quantization and linear distortion errors introduced by A/D 304 are now being compensated. Intermodulation 2716 is being reduced, but image signals may still remain and deteriorate EVM in weak channels 2704. A task 3238 then activates forward equalizer (EQ_{F}) 246, causing forward equalizer 246 to perform estimation and convergence algorithm subprocess 1100, or another function that produces a similar result, and causing coefficients for forward equalizer 246 to adapt to values that minimize correlation between forwarddata stream 272 and error stream 276. This reduces distortions that further reduce error in the returndata stream, which further reduces intermodulation 2716. Next, a task 3240 sets spectral management switch 2814 to pass mergedcommunication signal 272" and mergederror signals 276" to forward equalizer 246 for use in adapting coefficients. Spectral management section 2900 now begins to influence the operation of transmitter 100. Forward equalizer 246 continues to adapt its coefficients, but now in response to spectrallyaltered versions of the forwarddata and error streams. The spectrallyaltered versions emphasize the weaker channels. As depicted, in trace 2718 of Fig. 27, errorsignal strength 2712 may increase in the stronger channels, but errorsignal strength 2712 decreases in the weaker channels. Collectively, all channels 2704 are better able to meet EVM specifications, and equilibrium is achieved when EVM is substantially equal across all channels 2704. After a period of time sufficient in duration to allow coefficients to adapt to the point where this equilibrium is achieved, a task 3242 locks forward equalizer 246 to prevent further coefficient adaptation. Next, a task 3244 performs nonlinear A/D compensation subprocess 2600, or another function that achieves a similar result, to compensate for nonlinear distortions introduced by A/D 304. A task 3246 then switches multiplexer 250 to route amplifiedRFanalog signal 117 to the input of A/D 304, and predistortion circuit 2800 can now begin compensating for distortions introduced by HPA 136. A task 3248 activates HPA 136 so that HPA 136 will begin to produce signal. Since the returnanalog signal now input to A/D 304 takes a different path, additional delay has been introduced and has disturbed the temporal and phase alignment between the forwarddata and returndata streams. After a suitable warmup period, a task 3250 realigns timing and phase by repeating tasks 3230, 3232, and 3234. Then, a task 3252 activates return equalizer (EQ ) 260 to compensate for linear distortion introduced in the returnanalog signal by HPA 136, and a task 3254 locks return equalizer 260 to prevent any significant readjustment of its coefficients. At this point, a signal with very low distortion should be presented to the memoryless nonlinearity labeled amp 142 in Fig. 1 because of the previous tasks performed in distortion management process 3200. Consequently, predistortion circuit 2800 is now ready to compensate for nonlinear distortions introduced by HPA 136 and process 3200 performs a task 3256. Task 3256 performs nonlinear HPA compensation by performing task 402, which calls subprocess 1500, or another function that achieves a similar result. As a result, nonlinear distortions introduced by HPA 136 are compensated. Then, forward equalizer 246 is again activated in a task 3258 to track relative changes in the signal strengths of channels 2704. After task 3258, a task 3260 is performed to repeat some or all of the previouslyperformed tasks in process 3200 from timeto time to track heat and/or aging effects. In addition, task 3260 may include tasks which manage peak reduction in response to EVM calculations, as discussed above. In summary, the present invention provides an improved transmission predistortion circuit and method. A quantizationerror compensator is provided to compensate for quantization errors introduced by an analogtodigital circuit (A/D) that monitors a feedback signal generated by analogtransmitter components. A process is provided that compensates for distortions introduced in a feedback signal path prior to using that feedback signal path to counteract distortions introduced by analogtransmitter components. And, distortions introduced by analogtransmitter components are counteracted in a manner responsive to the relative strengths of frequencymultiplexed communication channels. Although the preferred embodiments of the invention have been illustrated and described in detail, it will be readily apparent to those skilled in the art that various modifications may be made therein without departing from the spirit of the invention or from the scope of the appended claims. For example, differentialmodetimealignment section 800 or phaserotate section 1000 may be omitted, particularly when forward equalizer 246 has a generous number of taps. Or, section 800 may be implemented differently, such as through the generation of clock signals for I and Q legs using independent phaselocked loops. Adaptation engine 1300 could be configured as an adaptation engine that simultaneously operates on all paths of a complex equalizer rather than just two paths as described above, as an entire adaptive equalizer switched into and out from the respective data streams to determine filter coefficients, or individual adaptive equalizers could replace all nonadaptive equalizers even though power and chip area would increase as a result. Many of the various delay sections and elements that are shown herein as being in series may be combined. In one embodiment, the equalizer that provides linear distortion compensation for the A/D may be placed in series with the returndata stream, rather than as shown herein. A gainslope equalizer may be inserted at the output of the A/D to allow the full authority of the equalizer that provides linear distortion compensation for the A/D to be applied to other distortion components. And, while the abovepresented discussion only mentions using the spectral management section in the adaptation of coefficients in the forward equalizer, the spectral management section may be used in the adaptation of other adaptive equalizer coefficients as well. These and other modifications and adaptations which are obvious to those skilled in the art are to be included within the scope of the present invention.
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US10766801 US7099399B2 (en)  20040127  20040127  Distortionmanaged digital RF communications transmitter and method therefor 
US10766779 US7430248B2 (en)  20040127  20040127  Predistortion circuit and method for compensating nonlinear distortion in a digital RF communications transmitter 
US10766768 US20050163249A1 (en)  20040127  20040127  Predistortion circuit and method for compensating linear distortion in a digital RF communications transmitter 
US10840735 US7342976B2 (en)  20040127  20040506  Predistortion circuit and method for compensating A/D and other distortion in a digital RF communications transmitter 
US11012427 US7469491B2 (en)  20040127  20041214  Transmitter predistortion circuit and method therefor 
PCT/US2005/002316 WO2005074121A1 (en)  20040127  20050124  Transmitter predistortion circuit and method therefor 
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