CA2103215A1 - Modulation signal detection and determination by statistical estimation - Google Patents

Abstract

MODULATION SIGNAL DETECTION AND DETERMINATION
BY STATISTICAL ESTIMATION
Abstract of the Disclosure A method and apparatus for the demodulation of received frequency modulated (FM) electromagnetic signals.
The desired output is estimated from the input by a special mathematical computation performed in the device. A zero-crossing detector is used to provide the information necessary to estimate the output from the input. The method will result in the superior performance of frequency modulated receivers using this device. Phase reversals, missing parts of the transmissions due to shadow effects, and ordinary noise will not affect the receiver using this device. The device consists of an integrated circuit designed to perform this specific task.

Description

~ ~ J ~"~

Descri~tion 2~ODULATION SIGN~L DETBCTION AND DETERMINATION
BY STP.TISTICAI, ESTIl~ATIO~

Technical Field This invention relates to a method and apparatus for detecting the modulation used in a communication system by statistical estimation of modulation parameters based on samples of the signals produced by the communication system.

Backqround of the Invention Radio waves can be made to transmit information by imposing a modulation representing the information on the radio waves. For example, an amplitude modulation (AM) signal modulates the amplitude of a carrier signal which typically contains frequencies much higher than the modulation signal contains. An important aspect of communication system design is to provide an effective way of reconstituting the information from radio waves which are received after being exposed to different kinds of disruption such as additive noise.
Angle modulation of radio waves is a widely used method of communication in which the radio waves can be received and processed in very effective ways to retrieve the modulation information. Frequency modulation (FM), which is one form of angle modulation, is used in commercial broadcast, mobile radio, cellular telephone and 1 fixed site communication syst~ms. Demodulation of FM
i waves is somewhat more complicated than the demodulation of AM waves. Despite the greater complexity in demodulation, a hisher quality audio output is generally produced from an angle-modulation receiver than an AM
receiver, since angle modulated signals are more immune to ij .,~ , 2 ~ 3 2 ~. ~

noise and less susceptible to interfering signals at nearby carrier frequencies than are AM signals.
Present methods of demodulating angle modulated signals depend on measurement of the input signals in the 5 corrupted radio waves carrying the signals. The methods , produce an audio output directly from these measured input ~ i~
I signals, regardless of the amount of corruption to which ; the signals and/or radio waves are subjected. However, this practice can result in a grèater susceptibility to 10 interference than is necessary.
As an example, FM mobile radio signals are often subjected to multiple propagation paths (including ;1 reflection paths) because the transmitter and/or receiver is moving through the landscape while it is operating.
15 The waves propagated over multiple paths often produce phase reversals at the receiver. In an FM receiver equipped with a widely used phase locked loop (PLL) for demodulation, this situation results in a "drop out of -~
lockl' condition. This causes the FM receiver to produce a l 20 noisy output signal until the PLL regains loc~. The ;~. motion of a FM mobile radio transmitter or receiver also produces some loss o~ the received signal for short periods of time. These periods may be only milliseconds or even microseconds long, but they result in a disruption 25 of the recPiver's output audio signal that is much longer 3 in duration than the disruption that caused it.
Other methods of transmitting a modulation signal are subject to the same sorts of disruption as FM
~o~ile radio signals if the detection and determination of 1 30 modulation signal depends upon an accurate measurement of the time of occurrence of a featuxe in the modulation signal. For example, just as FM modulation signal detection and determination depends upon a measurement of the deviation of the carrier frequency caused by the 3S modulation signal, pulse would then pulse position ~J modulation systems similarly depend upon properly . ~ ,.

2 't , ~

ascertaining the time of occurrence of a feature, such as the time when the modulation signal or modulated carrier signal crosses a given voltage threshold while increasing or decreasing. T~e method and apparatus of the present 5 invention operate to predict the time of occurrence of a predetermined feature of the modulation signal based upon the statistics of previous times of occurrence of the same feature. In this way, if the modulation signal is obliterated or corrupted by noise, the past statistical 10 behavior of the modulation signal can ~e used to predict its actual value.
. -; :
::
Summarv of_the Invention It is an object of the present invention to 15 provide a method and apparatus of estimating a modulation I signal from measurements of angle modulated radio waves.
¦ It is another object of the present invention to provide a method and apparatus for estimating a modulation signal from digital signals that result from a conversion 20 from angle modulated radio waves to a digital signal by use o~ the zero crossings of the angle modulation.
According to one aspect, the present invention is an apparatus for producing an output signal from a signal that is received in response to the transmission of 25 a transmitted signal which is a ~unction of a modula ion ; signal containing information. The apparatus comprises a sampler, an estimator and a controller. The sampler produces samples of the received signal. The estimator receives the samples of the received signal and produces 30 an estimated output signal from ~he samples of the received signal. The controller receives the estimated output signal and the samples of the received signal and 9 produces the output signal as a function of the estimated output signal and the statistics of the samples of the t 35 received signal.

. :

:

4 2 ~ JJ3 ~1 rj According to another aspect, the present invention is an apparatus for producing an output signal from a signal that is received in response to the transmission of a sinusoidal carrier signal. The 5 sinusoidal carrier signal has an instantaneous amplitude -and is modulated by an angle modulation signal containiny information. The apparatus comprises a receiver, a sampler, a processing circuit, an estimator and a controller. The receiver receives the transmitted constant amplitude sinusoidal carrier signal that is modulated by the angle modulation signal and produces an intermediate analog signal from the angle-~odulated sinus~idal carrier signal. The base frequency of the modulated sinusoidal carrier signal is substantially equal to the frequency of the sinusoidal carrier signal. The sampler produces samples of the intermediate analog signal. The processing circuit processes the samples of the intermediate analog signal and produces a first signal indicative of at least some of the relative times when the instantaneous amplitude of the intermediate analog signal has a zero crossing. The estimator receives the samples o~ the intermediate anal~g signal and produces an estimated output signal from the samples. The controller receives the estimated output signal and the samples of the received signal. The controller then produces the output signal as a function of the estimated output signal ~ and the statistics of the samples of the received i transmitted constant amplitude sinusoidal carrier signal.
,, ~, :- -~ ::
Brief Description of the Drawinqs ~! ' Figure 1 is a bloc~ diagram o~ a general ~;
i co~munication system. I
.
Figure 2 is a timing diagram of a typical pulse duration modulation signal. ~ -Figure 3 is a timing diagram of a typical pulse position modulation signal.

, ~: -. .
J :
.:: : :: :::' 5 ~'J~_33;'`

Figure 4 is a timing diagram showing a typical phase modulation signal.
Figure 5 is a timing diagram showing a typical frequency modulation signal.
Figure 6 is a schematic diagram of a typical situation producing a multipath signal at the receiver of a mobile communication system.
Figure 7 is a timing diagram of a typical received multipath signal.
j 10 Figure 8 is a block diagram of a receiver according to the present invention.
~ Figure 9 is flow chart showing the operation of i a receiver operating in accordance with the present invention.
Figure 10 is a block diagram of a preferred embodiment of the apparatus of the present invention.

Detailed Description of th~ Invention Figure 1 is a block diagram of a general communication system. The general communication system 20 includes a transmitter 22 and a receiver 24. The j transmitter 22 transmits signals to the receiver 24 through the channel 26. The transmitter 22 receives information to be transmitted in the form of a modulation signal m(t) and produces the transmitted signal s(t). The channel 26, which is subject to noise (represented by the signal n(t)), modifies the transmitted signal s(t) to produce a received signal r(t). The receiver 24 proc~sses the received signal r(t) to produce a demodulated signal m~t). Th~ demodulated signal m(t) is generally an ~ approximation to the modulation signal m(t) and represents '-~ the in~ormation contained in the modulation signal m(t).
, ......... .
The transmitter 22 generally contains a transmitter signal processor 28 which receives the ~,3S modulation signal m(t) which represents the input ~,in~ormation and produces a processed modulation signal.

i ~

3'~

The processed modulation signal is then further processed by transmitter carrier circuits 30 to generate the transmitted signal s(t). In a passband communication system, the processed modulation signal i5 at an intermediate frequency above the frequency of the modulation signal. Also, the transmitted signal s(t) in a passband communication system is based on a carrier signal generally having a frequency content higher than the intermediate fre~uency. In a baseband communication system, the carrier circuits 30 are unnecessary and the signal produced by the transmitter signal processor 28 is the transmitted signal s(t).
The receiver 24 generally includes receiver carrier circuits 32 and a receiver signal processor 34.
In the case of a passband communication system, the receiver carrier circuits 32 are designed to remove the carrier signal, which is imposed on the processed j modulation signal in the receiver 22. If the 'I communication system is a base~and communication system, 1 20 the receiver carrier circuits 32 are unnecessary. The j resulting signal is then transmitted to the receiver ¦ signal processor 34 to generate m(t), the approximation to the modulation signal m(t).
Fiqure 2 is a timing diagram of a typical analog modulation signal m(t) and the resulting pulse duration modulated transmitted signal s(t). At certain times, indicated by the vertical lines passing through both the upper and lower portions of Figure 2, the modulation signal m(t) is sampled and used to determine the form of the output signal s(t). The general form of the output signal is a train of pulses having two levels - a low level (here shown as a baseline) and a high level (here ' shown as a level above the baseline). The relative durations of the low and high levels for each pulse are determined by the value of the corresponding sample of the modulation signal m(t). Typically, the greater the value .,.

7 ~ ~ u3~1~
.,~ . `
of the modulation signal m(t), the longer the duration of the high level portion of the corresponding pulse. In a baseband communication system, the modulation signal m(t) is the transmitted signal s(t). However, in a pass~and communication system, the modulation signal m(t) is used to modulate a carrier signal as will be understood by those sXilled in the radio communication systems art.
Figure 3 is a timing diagram of a typical pulse Iposition modulation signal. As descri~ed in connection !lo with Figure 2, a pulse position modulation signal can be used as the transmitted signal in a baseband communication system, or as a modulation signal in a passband communication system. In this form of output signal, the samples of the modulation signal are used to determine the relative position of a corresponding fixed duration pulse in the time period between consecutive sample times (the ~intersample time periodn). Generally, the greater the value of the sampled modulation signal m(t), the greater the delay of the pulse 50 within the intersample time period~
A significant point to be made in connection ¦with the output signals s~t) shown in Figures 2 and 3 is ~that the information they contain can be determined by `~locating the times of occurrence of some significant features in the output signal s(t). In the case of the pulse width modulation output signal (~igure 2), the significant features are the relative times at which the levei of the output signal falls from its high level to its low level. In the case of the pulse position ~30 modulation output signal tFigure 3), the significant -;features could be either of two classes of features, or possibly both. One class of features includes the lrelative times at which the level of the output signal `~'falls from its high level to its low level. The other ~l3S class of featur@s includes the relative times at which the ,~ .
' ~
: :
,~ ~

2 ~

level of the output signal rises from its low level ~o its high level.
~he significant features discussed above can be detected by processing the modulation output signal s(t) 5 to determine the time when the signal crosses a threshold in a predetermined direction (e.g., a falling direction from the signal's high level to its low level, or vice ~
versa). The threshold can be established as a function of ~ i ~a time average of the modulation output signal s(t) 310 (either a long-term time average or a short-term time average). In the case of the pulse duration modulation - ~-~
output signal shown in Figure 2, the predetermined ~ -direction will be a falling direction. In the case of the 7pulse position modulation output signal shown in Figure 3, 15 the predetermined direction could be either a rising or a falling direction, as long as the choice is used ~3 consistently.
i~Figure 4 is a timing diagram showing a typical phase modulation signal and Figure 5 is a timing diagram 20 showing a typical frequency modulation signal. Both of ¦these signals are examples of a more general form, the angle modulation signal. Angle modulation signals ~generally are applied to a passband communication system .~having a constant amplitude sinusoidal carrier signal.
25 However, other forms of carrier signal, such as a pulsed carrier signal, are also possible.
In the typical phase modulation signal shown in Figure 4, the sinusoidal carrier 60 in the output signal -~
s(t) is modulated by changing its instantaneous phase in l~
30 accordance with the value of the modulation signal m(t).
This change in instantaneous phase is shown as the irelative time between the occurrence of two types of ;Jevents in each cycle of the output signal. One type of ~ i~
.. 3~ event is indicated by the uniformly spaced times occurring ;~35 at the frequency of the unmodulated carrier frequency and ',indicated by the long vertical lines above the signal , ~ :.. ~

~- 2 i ~

s(t). The other type of event is indicated by the time of occurrence of a predetermined feature ln each cycle of the sinusoidal carrier. One such feature is the time when the sinusoidal carrier reaches its maximum. These times are represented by the short vertical lines above the signal s(t). As shown, when the value of the modulation signal m(t) is positive, the phase of the modulated carrier signal is positive relative to the phase of the unmodulated carrier signal. On the other hand, when the value of the modulation signal m(t) is negative, the phase of the modulated carrier signal is negative relative to the phase of the unmodulated carrier signal.
In the typical frequency modulation signal shown in Figure S, the sinusoidal carrier in the output signal s(t) is modulated by changing its instantaneous frequency in i~ccordance with the value of the modulation signal m(t~. This modulated frequency is apparent from the lower portion of Figure 5. As shown, when the value of the modulation signal m(t) is positive, the frequency of the modulated carrier signal is greater than the frequency of ~he unmodulated carrier signaI. On the other hand, when the value of the modulation signal m(t) is negative, the fre~uency of the modulated carrier signal is lower than the frequency of the unmodulated carrier signal.
The modulation of both of the modulated signals shown in Figures 4 and 5 can be determined by measuring the relative times of occurrence of co~secutive zero crossings of the modulated carrier signals 60 and 70, respectively. While measuring the times of occurrence of I
all zero crossings is useful, it is only necessary to measure the relative times of occurrence of the zero-crossings in a predetermined direction, e.g., from a positive amplitude to a negative amplitude. These times ~ u~
of occurrence will determine either the relative phase shift, or relative freque~cy of the modulated carrier signal.

3 ~ -' ~

lo ~ ~ ~3 3.~

Figure 6 is a schematic diagram of a typical situation producing a multipath signal at the receiver o~
a mobile communication system. In this case, a transmitter 80 is placed at a fixed location, and the transmitted signal produced by the transmitter 80 is being received by a mobile receiver 82 along a first transmission path 84. In the absence of any other transmission paths or interfering signals, and assuming su~icient received signal strength, the signal received !~ 10 by the mobile receiver 82 along the transmission path 84 should be processed without error. Xowever, the situation is complicated if there is another transmission path, such as secondary transmission path 86, which results from reflection of the signal transmitted by the transmitter 80 l 15 from an object 88 to the mobile receiver 82. In this 3 case, the two signals interfere with each other and ,~ produce undesirable results, as shown in Figure 7.
Undesirable results are even more likely if the transmitter 80 is also mobile, as is generally the case in ~-~ 20 mobile communication systems applications.
Figure ~ is a timing diagram of a typical l received mul~ipath signal. It can ~e related to Figure 6.
The primary received signal rl(t) is received along the first transmission path 84 and the secondary received 25 signal r2(t) is received along the secondary path 86 (see ~3; Figure 6)- Although the two received si~nals are modulated similarly, the modulation of the secondary received signal r2(t) is delayed relative to the .~ modulation of the primary received signal r1(t). The 30 reason is that the path 86 is lon~er than the path 84.
For the present position of the transmitter ~0 relative to the mobile receiver 82 and the object 88, the amount of the delay is T seconds. The value of T will vary as the -~ mobile receiver 82 moves. However, for the present 35 situation, the time difference between the occurrence of a given feature in primary received signal r1(t~ and the 11 2 ~

same feature in secondary received signal r2(t) is T
seconds, as indicated in Figure 7. aecause of the reflection from the object 88 over the secondary transmission path 86, the secondary received signal r2(t) will also generally have a lower amplitude than the primary received signal r1(t). The features or the secondary received signal r2(t) may also be phase shifted relative to, the same features of the primary received signal r1(t).
The voltages induced in the mobile receiver 82 (shown in Figure 6) by the primary and secondary received signals rl(t) and r2(t) add together to produce the resultant received signal r(t). The resultant received signal r(t) will not generally have the desirable relatively continuous behavior of each of the received signals r1(t) and r2(t), however.
As shown in Figure 7, the resultant received signal r(t) may have sudden reversals in the received voltage. These reversals can be so fast that they cause the circuitry in a conventional receiver to perform erratically and produce a false detected modulation signal m'(t)- This is shown as the bot:tom trace in Figure 7.
The sudden drop-outs in the modulation signal m'(t) are due to the ~ailure of the circuitry in the conventional receiver to follow the sudden changes in the resultant received signal r(t). As also shown in the ~ttom trace of Figure 7, this failure generally lasts longer than the disturbance in the resultant received signal r(t) because ~; ~he circuitry in the receiver must reestablish its proper ~i 30 operation.
~ailures of the sort illustrated in Fiqure 7 and just described can occur for each of the types of modulation signals shown in Figures 2-6, although hereinafter the discussion will describe the performance of a frequency-modulated communication system. The reason thesP failures can occur for each of the types of signals 3 : ~

21~3.~

shown in Figures 2-6 is that their proper reception is equivalent to the proper detection of the times of occurrence of predetermined features that can be used to ~ i characterize each of the types of signal.
Multipath propagation will affect the time of occurrence or even the existence of a predetermined feature needed to detect a modulation signal. For example, in the case of a frequency-modulated communication system, the presence of a secondary transmission path can give rise to signals that momentarily do not cross zero when they would be expected to in the absence of the secondary transmission path. If the receiver depends on detecting zero-crossings, the disappearance of a single zero-crossing would cause the instant modulation frequency to decrease by a factor of two. The disappearance of two consecutive zero-crossings ~;~
would cause the instantaneous modulation frequency to ,decrease by a factor of three.
¦When an FM receiver that has a PLL loses track j20 of the instantaneous frequency, its output is generally a "hiss," which is generated as the PLL works to regain its ,loc~ on the phase of the frequency modulation signal.
IThis can be undesirable. Under certain circumstances, !when the frequency of the modulation signal i5 unknown and Z5 no reliable prediction of the fre~uency can be made, it is preferable to cause the receiver to produce no output at Iall. ~owever, under certain other circumstances, when the ~requency of the modulation signal is also unXnown, but reliable predictions of the ~requency can be made, it is l~
preferable to cause the receiver to produce an output corresponding to a predicted modulation frequency rather than a "hiss," or no signal at all.
For example, if the FM system is being modulated ;'2 by a signal that contains important information, but which 35 is not protected by error-detection or -correction codes, -~
it is possible that it is preferable to receive no signal ., , ~:

2 i `~ ~ 2 iL ~i rather than risk receiving incorrect information. On the other hand, if the FM system is being modulated by a music signal for mobile entertainment purposes or by a common voice signal in a cellular phone system, it is likely that it is preferable to receive an estimate of the modulation signal rather than no signal. A preferred embodiment of ~, the invention, as applied to an FM communication system, ', will be described in the following. Those s~illed in the ' art will appreciate how the concepts illustrated in connection with a frequency-modulated communication system , can be applied to communication systems using the other modulation signals illustrated, as well as further modulation signals.
Figure 8 is a bloc~ diagram of a receiver according to the present invention. The receiver 100 contains a signal processor 102 and an estimator 104. In some embodiments, the output signal produced by the ~stimator 104 can be further processed by an output stage 106 to produce an information signal that represents an ~ 20 even better approximation to t:he information in the j modulation signal of the transmitted signal s(t) than the output signal produced by the esl:imator 104. The signal processor 102 includes a ~eature detector 108, a counter (or clock) 11~, a memory 112 and a signal processor controller 114. The feature detector 108, the counter 110 and the signal processor controller 114 all receive the received signal r(t). The feature detector 108 analyzes the received signal r(t) to detect the presence of a predetermined feature (such as passage o~ the signal r(t) through a zero ~oltage in a predetermined direction~
Thus, the feature detector 108 for one type of modulation scheme can be a conventional zero crossing detector. Upon detection of such an occurrence, the feature detector 108 produces a feature detect signal which it transmits to the counter 110 and the signal processor controller 114. The `~ signal processor controller 114 periodically samples the .. j~ .: .

2 ~

received signal r(t~ on a continuous basis. Receipt of the feature detect signal causes the counter 110 to transfer its present count to the memory 112, to which the counter 110 is connected. The memory 112 stores the sampled count for possible later use by the signal processor controller 114 and the estimator 104. At the same time, the feature detect si~nal also causes the signal processor controller 114 to receive the present count.
The processed signal always includes digital representations of the periodic samples of the received signal r(t). When the feature detector 108 stops sending the feature detect signal periodically to the signal processor contxoller 114, the signal processor controller 114 also causes the processed signal to include the data and the sample count stored digitally in the memory 112. -~
~he digital representations in the processed signal are sent serially.
The estimator 104 lncludes an estimator 2~ controller 122, a Bayesian statistics microprocessor 124, ;~
and a random-access memory (RAM) 126. The estimator controller 122 and the Bayesian statistics microprocessor 124 both receive the processed signal from the signal processor controller 114 in the signal processor 102. In addition, the estimator controller 122 communicates with the signal processor controller 114 over a bi-directional ~ bus 128. The estimator controller 122 also communicates ¦ with the Bayesian statistics microprocessor 124 over a bi~
', directional bus 130. Further, the RAM }26 communicates l~
with the Bayesian statistics microprocessor 124 over a bi-directional bus 132. ~ ~;
The Bayesian statistics microprocessor 124conditions the samples of the received signal r(t) by compiling histograms of a predetermined number of the last ~I35 samples. The histograms, as approximations to the !probability density ~unction of the distribution of the ., :

2 i ~

samples of the received signal r(t), are used by the Bayesian statistics microprocessor 124 to develop estimates of the probability that a particular sample of the received signal r(t) will be the next to be received.
This pro~ability is conditioned on the distribution of the values of the samples of the received signal r(t) in the recent past. The ~ayesian statistics microprocessor 124 i also develops histograms of the recent times of occurrence of the predetermined feature in the received signal r(t).
. 10 These times of occurrencP are determined by the outputs o~
the counter 110 in the signal processor 102.
The estimator controller 122 and the Bayesian statistics microprocPssor 124 operate in accordance with a - program to be described subsequently to mair~tain and update statistics concerning the recent times of occurrence of the predetermined features and the samples . o~ the received signal r(t). The Bayesian statistics ¦ microprocessor 124 stores the updated statistics in the RAM 126.
When the estimator controller 122 receives a communication from the signal processor controller 114 in the signal processor 102, the estimator controller 122 determines whether to transmit the most rec~nt sample of the received signal r(t), to trcmsmit no signal, or to 2S transmit an estimated output signal in accordance with the statistics maintained by the Bayesian statistics microprocessor 124 and stored in the RAM 126. Xf the estimator controller 122 determines that the output siynal should be the most recent sample of the received signal r(t), which is represented in the processed signal produced by the signal processor controller 114. If the estimator controller 122 determines that no signal should be transmitted, then it transmits no signal. Otherwise, the controller 122 produces the most likely signal based on the statistics of previously received signal samples ;~ and the statistics of times of occurrence of the ~ '' .; :
.~,, .

2 ~ ~

predetermined features. The controller 122 is programmed in accordance with the application, as described abave.
The estimator 104 then produces the desired output signal.
The output signal may be in an inappropriate form for use as an information signal. For example, the output signal may be digital, ~hile it is most useful as an analog signal. In this case, it may be necessary to further process the output signal in order for it to be most useful. The output stage 106 can perform the necessary transformation of the output signal to its most useful form.
Figure 9 is flow chart showing the operation of a rec~iver operating in accordance with the present invention. This flow chart describes the combined operations of the estimator controller 122 and the Baye~ian statistics microprocessor 124, both of which can i be implemented with a conventional microprocessor. The flow chart is entered at bloc~ 140. At bloc~ 142 the estimator controller 122 determines whether th~re has been a loss o~ signal from an analysis of the processed signal which it receives from the signal processor 102 If the processed signal has not conta:ined data describing a ~l recent occurrence of the predetermined feature, then the i~ controller 122 determines that the signal has been lost.
As described previously, the estimator controller 122 also causes the Bayesian statistics microprocessor 124 to ~ procass the received signal and time of occurrence ¦ statistics data computed from the data forwarded from the `3 ' Signal processor 102 to the Bayesian statistics ;~ 30 microprocessor 124 (block 144). In bloc~ 146 the Bayesian statistics microprocessor 124 also updates the data stored in the statiistics RAM 126. The Bayesian statistics microprocessor 124 further maintains and updates conditional probability density functions of the times of ¦ 35 occurrence of the features detected by the feature detector 102 and, if necessary, computes the mast likely ., ~
:.
'. ~

., 17 2 1 ~ 2 1rj value of the received signal at a point ~here the received signal r(t) was disrupted based on the statistics of the most recently previous times of occurrence of the detected feature. The program in the flow chart then repeats by return to the block 142.
In some circumstancPs, simplifying assumptions ca~ be made which greatly simplify the structure of the receiver as discussed in connection with Figures 8 and 9.
For example, Figure lO is a bloc~ diagram of a preferred embodiment of the apparatus of the present invention that is useful in the special case when the communication system is based on passband FM signals that are subject to multipath propagation. As is conventional in FM
communication systems, the incoming FM signal is heterodyned with a local oscillator to produ~e a signal at a fixed intermediate frequency. This intermediate fre~uency signal is fed into a zero crossing detector, which produces a series of pulses that are unevenly spaced in time, depending on the instantaneous frequency at the zero crossing detector. The modulation signal information I is contained in the spacing of th~se pulses. If there is ¦ a loss of information for only a reasonably short period ¦ of time the estimator portion of the apparatus can I estimate what the received signal should be. For example, ¦ 25 if the infor~ation in the spacing of the pulses indicates a large spike in the audio signal, the estimator portion o~ the apparatus will not estimate a large spike in the audio ou~put, but rather will estimate an output signal based on past statistics. l~
There are a num~er of ways of accomplishing the estimation of the desired output signal, one of the ii techniques being shown in block diagram form in Figure 10.
;' In this technique, the apparatus takes advantage of the highly repetitive nature of F~ signals to simplify the computation of the estimated parameters of the FM signal.

.,, ,: '.

3 ~ ~ 5 The measured times of consecutive zero crossings (tn) can be used to determine the parameters k, ~, ~ that respectively characterize the modulation index, instantaneous modulation frequency, and fixed phase shift of the modulation signal. The measured times can al50 be u~ed to characterize the reflection parameters r and T
that characterize the multipath propagation, where r is the reflection coefficient and T is the time delay due to multipath propagation.
For simplicity, first consider the case of no reflected wave, i.e., r = 0. The signal with which this apparatus is concerned is the instantaneous phase of the modulated carrier signal with respect to an unmodulated carrier. Samples of the instantaneous phase, Sn, can be taken by comparing the time of occurrence of a zero crossing of the modulated carrier with the time of ! occurrence of the corresponding zero crossing of the unmodulated carrier. When there is no reflected wave, the values of Sn are given by Sn = k sint~tn + ~
where k, ~, and ~ are the parameters defined above.
If there were no noise or measurement error, this equation would determine the parameters exactly, and it would only be necessary to have three values of Sn (i.e., as many values of n as there are para~eters to determine). However, the presence of both noise and measurement error means that a fitting procPdure is necessary to determine the best ~it of the parameteriæed signal to the data.
Three consecutive values of the received signal are used to produce initial estimates of the amplitude k, the frequency ~ and the phase ~. This is performed by the initial estimator 160 in accordance with equation (1) above, and the results are stored in the memory 162.
3S According to the prasent invention, the way to determine the estimated values of the parameters is to ., .

2 ~ ~ 3 ~ 1 ~

choose the values of the parameters that minimize the mean squared error (MSE) between the sampled signals and the parameterized signal. The MS~ is given by MSE = ~ [k sin (w~D + ~) - s,.]
To analytically determine the values of the parameters k, ~ and ~ that minimize the MSE, the partial derivatives of the MSE with respect to each of the parameters must be set equal to zero. In other words ~M~kS = 2~ [ksin (~A+~-S~] sin(~+ ~ = O (2) = 2~ [ksin (~t.+~)-S.J. cos(~t.+~) = O (3) ~MSE = 2~ [ks~ (~t.+~)-S.] . cos(~t.+~).t. = O (4) The optimum value of k is given, from eguation ~2), in terms of the other two parameters by the formula k = ~ n SD sln (a~ t~l +
ill(a~ tn +~i)] ~ -n 1~ ~:

Equations (3) and ~4), respectively, lead to : :.:
k~sin(~t.+~)cos(~ S.cos(~t. +~) ~5) n n ~ '" ~ ' ':
k~toSill(~to+~) COS (~t.+~ S.t.cos (~t. +~) (6) ~ ~"

~''J~ ~ ~

.. Referring to the block diagram in Figure 10, the resulting values of the initial estimates are then used . with computations 164, 166 and 168 to produce multiplier terms produced by computations 170, 172, 174, 176, 178 and 180. These terms are respectively designated Ss, Sc, Sct, sc, sct and ss. The terms sct and Ss are multiplied to :1 produce the term from computation 182. The values of sct ~ and ss are multiplied to produce the term from computation `, 184. The terms ss and Sc are multiplied to produce the ;~ 10 term fxom computation 186. Also, the terms Sc and sc are ~ multiplied to produce the term from computation 187.
.. One condition for the minimization of the MS~ is that the result of the computation 18~ be nearly equal to ~,, the term from computation 186 (see equation (5)). Another condition for the minimization of the MSE is that the result of the computation 182 ~e nearly equal to the result of the computation 184 (see equation (6)). In the present em~odiment, these equalities are enforced only approximately (within a predetermined error, ~
The values computed in the computations 182, ~' 184, 186 and 187 are used to update the statistical ~ estimates of the amplitude, frequency and phase shit .i parameters originally estimated in computation 160. They are also used to produc~ optimal estimates of the current .31 25 vall-e of the omitted received signal. Whether these data are updated or used as estimates is dependent upon the .l results of the comparisons shown in the comparison : computation 188 and the comparison computation 190. If the values of the computations 182 and 184 are ; 30 sufficiently close (signified in Figure 10 by the symbol ~ ~Y0l'), the current estimated signal, determined by the :~, estimates from the computation 160, is used as an estimate of the present omitted value of the received signal. If, i howe~er, the result of the comparison computation 188 i5:~3 35 not sufficiently close to zero or the result of the ' comparison computation 190 is not sufficiently close to .

21 2 -~ ~J ~;~ 1 r zero, the estimates of the parameters must be updated by the most recsntly received data. If the data are needed to make further estimates, then the output signal is zero.
It is important to note that, in general, the points tn do not need to be consecutive. Since the number of points tn is much larger than the number of parameters to be fit, it is permissible to s~ip selected points, thereby reducing the computing load and, by judicious choice of the points retained, increase the accuracy of the determination of the parameters.
It must be noted that the particular mathematics used to estimate the audio output from the input of zero crossing data is not necessarily crucial. Other I predictions could be used and the resulting output would be much better than with existing demodulators. The predictions can be limited to desired outputs so that, for instance, there would be no "hiss" heard when there was no input signal. Phase reversals that cause a PLL to unloc would not disturb the output o~ the present in~ention.

;~ -' :~

;J :::
.~ . .

Claims (28)

1. Apparatus for producing an output signal from a received signal that is received in response to the transmission of a transmitted signal, the transmitted signal being a function of a modulation signal containing information, the apparatus comprising:
a sampler that produces samples of the received signal;
an estimator to receive the samples of the received signal and to produce an estimated output signal from the samples of the received signal; and a controller that receives the estimated output signal and the samples of the received signal and produces the output signal as a function of the estimated output signal and the statistics of the samples of the received signal.

2. The apparatus of claim 1 wherein the estimator comprises a storage device and detects at least some of the relative times of occurrence of at least one predetermined feature of the received signal, the estimator storing the relative times in the storage device.

3. The apparatus of claim 2 wherein the received signal has an amplitude and the at least one predetermined feature is the passage of the amplitude of the received signal through a predetermined threshold, and the estimator further comprises a signal processor to produce an estimate of a relative time of the occurrence of the passage of the amplitude of the received signal through a predetermined threshold based on the relative times stored in the storage device.

4. The apparatus of claim 3 wherein the predetermined threshold is an average of the amplitude of the received signal.

5. The apparatus of claim 3 wherein the estimator analyzes the statistical distribution of the relative times stored in the storage device and produces a Bayesian estimate of a relative time at which the amplitude of the received signal passes through the predetermined threshold.

6. Apparatus for producing an output signal from a received signal that is received in response to the transmission of a carrier signal that is modulated by a modulation signal containing information, the apparatus comprising:
a demodulator that demodulates the received signal with respect to the carrier signal to produce a demodulated received signal;
a sampler that produces samples of the demodulated received signal;
an estimator to receive the samples of the demodulated received signal and to produce an estimated output signal from the samples of the demodulated received signal;
and a controller that receives the estimated output signal and the samples of the demodulated received signal and produces the output signal as a function of the estimated output signal and the statistics of the samples of the demodulated received signal.

7. The apparatus of claim 6 wherein the estimator comprises a storage device and detects at least some of the relative times of occurrence of at least one predetermined feature of the demodulated received signal, the estimator storing the relative times in the storage device.

8. The apparatus of claim 7 wherein the at least one predetermined feature is the passage of the amplitude of the demodulated received signal through a predetermined threshold, and the estimator further comprises a signal processor to produce an estimate of a relative time of the occurrence of the passage of the amplitude of the demodulated received signal through a predetermined threshold based on the relative times stored in the storage device.

9. The apparatus of claim 8 wherein the predetermined threshold is an average of the amplitude of the demodulated received signal.

10. The apparatus of claim 8 wherein the estimator analyzes the statistical distribution of the relative times stored in the storage device and produces a Bayesian estimate of a relative time at which the amplitude of the demodulated received signal passes through the predetermined threshold.

11. Apparatus for producing an output signal from a received signal that is received in response to the transmission of a sinusoidal carrier signal that is modulated by an angle modulation signal containing information, the sinusoidal carrier signal having an instantaneous amplitude, the apparatus comprising:
a receiver to receive the transmitted constant amplitude sinusoidal carrier signal that is modulated by the angle modulation signal and to produce therefrom an intermediate analog signal having a time-varying instantaneous amplitude and a base frequency substantially equal to the frequency of the sinusoidal carrier signal;
a sampler that produces samples of the intermediate analog signal;
a processing circuit to process the samples of the intermediate analog signal and to produce a first signal indicative of at least some of the relative times when the instantaneous amplitude of the intermediate analog signal has a zero crossing;

an estimator to receive the samples of the intermediate analog signal and to produce an estimated output signal from the samples of the intermediate analog signal; and a controller that receives the estimated output signal and the samples of the received signal and produces the output signal as a function of the estimated output signal and the statistics of the samples o f the received transmitted constant amplitude sinusoidal carrier signal.

12. The apparatus of claim 11 wherein the estimator comprises a storage device and detects at least some of the relative times when the instantaneous amplitude of the intermediate analog signal has a zero crossing, the estimator storing the relative times in the storage device.

13. The apparatus of claim 12, further comprising means for receiving the output signal corresponding to the angle modulation signal and producing a first analog signal representing the information contained in the angle modulation signal.

14. The apparatus of claim 13, further comprising a local oscillator that produces a local oscillator analog signal, and wherein the receiver includes a mixer that mixes the local oscillator analog signal with the carrier signal having the modulation signal imposed thereon to produce the intermediate analog signal.

15. The apparatus of claim 12 wherein the estimator further comprises a signal processor to produce an estimate of a relative time at which the instantaneous amplitude of the carrier signal having the modulation signal imposed thereon has a zero crossing at substantially the same relative times as the modulated carrier frequency.

16. The apparatus of claim 15 wherein the signal processor analyzes the statistical distribution of the relative times stored in the storage device and produces a Bayesian estimate of a relative time at which the amplitude of the carrier signal having the modulation signal imposed thereon passes through zero.

17. Apparatus for producing an output signal from a received signal that is received in response to the transmission of a frequency modulation signal imposed on a sinusoidal carrier signal having a substantially constant time-averaged amplitude, the frequency modulated sinusoidal carrier signal being transmitted to the apparatus under conditions wherein the time-averaged amplitude of the frequency modulated sinusoidal carrier signal received at the apparatus may be substantially equal to zero for a period of time equal in duration to at least two cycles of the carrier signal, the apparatus comprising:
a receiver to receive the transmitted constant amplitude sinusoidal carrier signal with the frequency modulation signal imposed thereon and to produce therefrom a received signal having a time-varying instantaneous amplitude and a base frequency substantially equal to the frequency of the sinusoidal carrier signal;
a sampler that produces samples of the received signal;
an estimator to receive the samples of the received signal and to produce an estimated output signal from the samples of the received signal; and a controller that receives the estimated output signal and the samples of the received signal and produces the output signal as a function of the estimated output signal and the statistics of the samples of the received signal.

18. The apparatus of claim 17 wherein the estimator comprises a storage device and detects at least some of the relative times when the instantaneous amplitude of the received signal changes sign, the estimator storing the relative times in the storage device.

19. The apparatus of claim 18, further comprising means for receiving the output signal corresponding to the frequency modulation signal and producing a first analog signal representing the information contained in the frequency modulation signal.

20. The apparatus of claim 19, further comprising a local oscillator that produces a local oscillator analog signal at a local oscillator signal frequency that is substantially lower than the frequency of the carrier signal, and wherein the receiver includes a mixer that mixes the local oscillator analog signal with the carrier signal having the frequency modulation signal imposed thereon to produce the received signal.

21. The apparatus of claim 18 wherein the estimator further comprises a signal processor to produce an estimate of a relative time at which the instantaneous amplitude of the carrier signal having the modulation signal imposed thereon changes sign at substantially the same relative times as the frequency modulated carrier frequency.

22. The apparatus of claim 21 wherein the signal processor analyzes the statistical distribution of the relative times stored in the storage device and produces a Bayesian estimate of a relative time at which the amplitude of the carrier signal having the modulation signal imposed thereon changes sign.

23. Apparatus for producing an output signal from a received signal that is received in response to the transmission of a phase modulation signal imposed on a sinusoidal carrier signal having a substantially constant time-averaged amplitude, the phase modulated sinusoidal carrier signal being transmitted to the apparatus under conditions wherein the time-averaged amplitude of the phase modulated sinusoidal carrier signal received at the apparatus may be substantially equal to zero for a period of time equal in duration to at least two cycles of the carrier signal, the apparatus comprising:
a receiver to receive the transmitted constant amplitude sinusoidal carrier signal with the phase modulated signal imposed thereon and to produce therefrom a received signal having a time-varying instantaneous amplitude and a base frequency substantially equal to the frequency of the carrier signal;
a sampler that produces samples of the received signal;
an estimator to receive the samples of the received signal and to produce an estimated output signal from the samples of the received signal; and a controller that receives the estimated output signal and the samples of the received signal and produces the output signal as a function of the estimated output signal and the statistics of the samples of the received signal.

24. The apparatus of claim 23 wherein the estimator comprises a storage device and detects at least some of the relative times when the instantaneous amplitude of the intermediate analog signal changes sign, the estimator storing the relative times in the storage device.

25. The apparatus of claim 24, further comprising means for receiving the output signal corresponding to the phase modulation signal and producing a first analog signal representing the information contained in the phase modulation signal.

26. The apparatus of claim 24, further comprising a local oscillator that produces a local oscillator analog signal at a local oscillator signal frequency that is substantially lower than the frequency of the carrier signal, and wherein the receiver includes a mixer that mixes the local oscillator analog signal with the carrier signal having the phase modulation signal imposed thereon to produce the intermediate analog signal.

27. The apparatus of claim 24 wherein the estimator further comprises a signal processor to produce an estimate of a relative time at which the instantaneous amplitude of the carrier signal having the modulation signal imposed thereon changes sign at substantially the same relative times as the phase modulated carrier frequency.

28. The apparatus of claim 27 wherein the signal processor analyzes the statistical distribution of the relative times stored in the storage device and produces a Bayesian estimate of a relative time at which the amplitude of the carrier signal having the modulation signal imposed thereon changes sign.