WO2007060562A1

WO2007060562A1 - Polar modulation system

Info

Publication number: WO2007060562A1
Application number: PCT/IB2006/054069
Authority: WO
Inventors: Gergen W. De Jong; Leonardus J. M. Ruitenburg; Jan Vromans
Original assignee: Nxp B.V.
Priority date: 2005-11-23
Filing date: 2006-11-02
Publication date: 2007-05-31

Abstract

A system and a method for polar modulation achieved via out-phasing two square-wave signals resulting in a pulse width modulated signal. The system in overview comprises a base-band pre-distortion element producing a phase shift control signal, means for producing two radio frequency square waves, which are mutually oppositely phase shifted according to the phase shift control signal, and a logic unit coupled to receive the two radio frequency square waves and adapted to provide a pulse width modulated radio frequency signal carrying the amplitude and the phase of the base-band signal.

Description

POLAR MODULATION SYSTEM

The present invention relates to polar modulation systems, in particular the invention relates to polar modulation systems wherein polar modulation is achieved via out- phasing two square-wave signals resulting in a pulse width modulated signal. The invention further relates to a method for producing polar modulation, moreover the invention relates to software for implementing the method.

Polar modulation has proven an effective method to provide multimode and multi-band operation. Polar modulation is achieved by processing the carrier amplitude and phase signals independently. This approach allows different wireless standards, e.g. CDMA, TDMA, GSM or GPRS, to be implemented using the same modulator architecture and being digitally switched at a transmitter when necessary.

Rather than an RF carrier being modulated using the traditional In-phase, I, and Quadrature, Q, scalar components of the base-band signal, polar modulation explicitly modulates the amplitude of the RF carrier with the magnitude of the complex base-band signal, A, and may explicitly modulate the phase of the RF carrier with the angle, φ, of the complex base-band signal.

A known method of implementing polar modulation consists in modulating the supply voltage of an RF Power amplifier by applying the magnitude of the complex base- band signal, A, directly to the power supply, and wherein the power amplifier amplifies a constant envelope phase modulated signal carrying the phase information of the complex base -band signal. In order to be power efficient the supply voltage modulation should be done via an efficient DC-DC converter. A drawback of such an implementation may be that achieving a high modulation bandwidth and avoiding switching ripples is complicated in an efficient DC-DC converter.

Another known method of implementing polar modulation can be achieved by applying a two level Pulse Width Modulated signal (PWM) to a switching power amplifier. In this method the PWM signal has to be generated by comparing the amplitude and phase- modulated carrier signal with a triangular or a saw-tooth signal. A requirement for the triangular or saw-tooth signal is that its frequency is at least twice the carrier frequency. The method requires a high switching frequency for the power amplifier, inducing an over- sampling, and that the triangular or saw-tooth signal is highly linear. Furthermore the carrier signal needs to be linearly amplitude modulated prior to the pulse width conversion takes place.

The present invention seeks to provide an improved system that enables polar modulation in an effective way, wherein the switching frequency of the power amplifier equals the RF-carrier frequency requiring no over- sampling. Preferably, the invention alleviates, mitigates or eliminates one or more of the above or other disadvantages singly or in any combination.

Accordingly, it is provided a polar modulation system for producing an RF output signal modulated by a base-band signal, the system comprising: - a base-band pre-distortion element for receiving a signal representing an amplitude of the base-band signal and producing a phase shift control signal carrying an information on the amplitude of the base-band signal; means for producing two radio frequency square waves, which are mutually oppositely phase shifted according to the phase shift control signal and having a common-phase component carrying an information on the phase of the baseband signal; and a logic unit receiving the two radio frequency square waves and providing a pulse width modulated radio frequency signal carrying the amplitude and the phase of the base -band signal. The base-band pre-distortion element may include one or more pre-distortion blocks wherein each of the blocks mapping the amplitude of the base-band signal to specific requirements of the RF output signal, e.g. modifications on the duty cycle or modifications on the mutual phase difference. The two radio frequency square waves may be modulated at the frequency of the RF output signal typically locked to one reference RF-oscillator. The phase modulation providing the common-phase component can be either achieved by modulating the reference RF-oscillator with the derivative of the phase or by placing a phase shifter with modulation capabilities behind the RF-oscillator.

It is observed that since this polar modulation system provides amplitude modulation in itself no additional linear amplitude modulator is required. As the center positions of the pulses of the pulse width modulated signal are equal to those of the positive peaks of the sinusoidal RF-oscillator signal, no AM to PM conversion is introduced in the out-phasing process. Furthermore the switching frequency required at the logic unit output equals the frequency of the RF output signal avoiding any requirement for over-sampling at the logical unit.

In an embodiment of the invention the polar modulation system further comprises a radio-frequency power amplifier for receiving the pulse width modulated signal and providing an amplified version of the pulse width modulated signal. Hence, the radio- frequency power amplifier provides an amplified version of the pulse width modulated signal with the power level required to ensure a correct transmission of the pulse width modulated signal according to the specific applications, e.g. different power levels may be required if the modulator should be used in a wireless LAN, a Bluetooth application, or a wireless mobile application.

The band-pass filtering stage limits the transmitted signal essentially to its first-harmonic and corresponding sidebands and therefore the band-pass filtering stage provides a filtered version of the amplified pulse width modulated signal reducing its frequency content.

In an embodiment of the invention the pulse width modulated radio frequency signal is a two level signal. In another embodiment of the invention the pulse width modulated radio frequency signal is a three level signal. Advantageously said signal does not contain even-order harmonics, including DC neither contains the corresponding even-order harmonic's side -bands.

In an embodiment of the invention, the fundamental frequencies of the pulse width modulated radio frequency signal contain the RF-carrier frequency. This implies no over-sampling and neither sub-sampling is applied. Alternatively, the fundamental frequencies of the pulse width modulated radio frequency signal are other than the RF-carrier frequency. The fundamental frequencies may be frequencies below or above the RF-carrier frequency providing tunability by control of the pre-distortion element. This situation corresponds to sub-sampling or over-sampling respectively. Sub-sampling is advantageous because in that case the switching frequency of the power amplifier is chosen to be lower than the RF-carrier frequency leading to an easier implementation and a higher efficiency.

In another embodiment of the invention, the two radio frequency square waves are generated by a radio-frequency oscillator. Hence, requirements for the control of the RF- oscillator are simplified. Alternatively, each of the two radio frequency square waves is originated based on an individual radio-frequency oscillator. Therefore, the phase shift control signal may be applied directly to each of the radio-frequency oscillators.

Phase shifters coupled to limiters may generate the two radio frequency square waves. Alternatively, multipliers coupled to limiters generate the two radio frequency square waves. When using multipliers, the phase shift introduced by these multipliers is frequency- independent and another advantage is that there is no upper or lower limit to the phase- shift that can be introduced by the multipliers.

The phase shift control signal produced by the base -band pre-distortion element is related to the duty cycle of the signal amplified by the radio-frequency power amplifier.

Hence, the RF signal may adapt to the intended amplitude provided at the output of the power amplifier.

The logic unit may perform an AND or an OR function on its inputs.

Performing an AND or a NAND function, an OR or a NOR function on two radio frequency square waves with a mutual opposite phase shift component and a common phase component is an effective method to provide a pulse width modulated signal carrying the right phase component.

Preferably, the polar modulation system is included in a transmitter adapted as needed to different transmission standards, e.g. CDMA, TDMA, GSM or GPRS.

The present invention will be now explained, by the way of example only, with reference to the accompanying Figures wherein:

Fig. 1 is a detailed diagram illustrating the elements of a polar modulation system for producing an RF output signal modulated by a base -band signal according to the invention;

Fig. 2a, b, c, d is an example of the application of a polar modulation system showing the characteristics of the different signals involved in the creation of an RF output signal modulated by a base-band signal via polar modulation; Fig. 3a is a detailed diagram of the elements included in an implementation of the logical unit and amplification stage providing a 3-level signal according to one embodiment of the invention.

Fig. 3b depicts a graphical representation of the signals involved in the process within the logical unit and amplification stage are depicted; Fig. 4 depicts a block diagram illustrating the elements of a possible implementation of the local RF-oscillator phase-modulation and the two phase- shifters, comprising multipliers.

Fig. 5 depicts a block diagram illustrating the elements of another possible implementation of the local RF-oscillator phase-modulation and the two phase- shifters, comprising multipliers.

The present invention provides polar modulation systems wherein polar modulation is achieved via a pulse width modulated signal generated by means of out- phasing. A block diagram illustrating elements required for achieving polar modulation via out-phasing a pulse width modulated signal using a base-band pre-distortion element is shown in Fig. 1 according to one embodiment of the invention. A system for achieving polar modulation via out-phasing a pulse width modulated signal using a base-band pre-distortion element 100 comprises a base -band pre-distortion element 115, a signal generation stage 105, a logical unit 170 and a transmission stage 195. The signal generation stage comprises in this embodiment a radio-frequency (RF) oscillator 125, an inverting linear amplifier with unity gain 135, a first phase shifter 130, a second phase shifter 140, a first limiter 150 and a second limiter 160. The transmission stage comprises in this embodiment a power amplifier 180, a band-pass filter 185 and an antenna 190. The band-pass pre-distortion element 115 may consist of a plurality of pre-distortion blocks 116-119.

The base-band pre-distortion element 115 receives a signal 110 representing the amplitude information of a base-band signal and provides a phase shift control signal carrying the amplitude information of the base-band signal to the inverter 135 and the second phase shifter 140. The inverting linear amplifier with unity gain 135 provides an opposite version of the phase shift control signal to the first phase shifter 130. An RF sinusoidal signal is generated by the RF-oscillator 125 and modulated in phase by the phase information 120 of the base-band signal. The phase modulation can be achieved either by modulating the RF sinusoidal signal with the derivative of the phase or by placing a phase shifter with modulation capabilities behind the RF-Oscillator. The RF phase modulated sinusoidal signal is inputted to the first phase shifter 130 wherein a phase shift is applied according to the opposite version of the phase shift control signal, providing a first phase-shifted signal. The RF phase modulated sinusoidal signal is also inputted to the second phase shifter 140 wherein a phase shift is applied according to the phase shift control signal providing a second phase- shifted signal. The first phase- shifted signal and second phase- shifted signal share a common phase component carrying the phase information of the base-band signal. The first phase- shifted signal and second phase- shifted signal are also characterized in that they have been mutually oppositely phase shifted according to the phase shift control signal provided by the base -band pre-distortion element 115. The first phase- shifted signal is provided as input to a first limiter 150 that generates a first RF square-wave phase-shifted signal, A. The second phase-shifted signal is provided as input to a second limiter 160 that generates a second RF square-wave phase-shifted signal, B. The logical unit 170 receives the first and second RF square- wave phase-shifted signals and provides a two level pulse width modulated radio frequency signal carrying the amplitude and the phase of the base -band signal. In one specific embodiment of the invention the logical unit used may be an AND gate. In another specific embodiment of the invention the logical unit used may be an OR gate, however other specific embodiments of the invention can be envisaged using other logical units such as EXOR, NAND, NOR or NEXOR or specific combinations of two or more logical gates. The pulse width modulated radio frequency signal is inputted to the power amplifier 180 that generates an amplified version of the pulse width modulated signal. The amplified version of the pulse width modulated signal is filtered at the band-pass filter 185 and the filtered signal is sent via an antenna 190. The band-pass filter may reduce the bandwidth of the pulse width modulated signal so that the RF signal at the output of the band-pass filter mainly contains its first harmonic and the corresponding sidebands, having significantly suppressed the higher harmonics and the low frequency spurious content of the amplified pulse width modulated signal.

In alternative implementations of the embodiment described above the bandpass filter may also be included in the power amplifier as an LC-tank. The power amplifier, the band-pass filter and/or the antenna may be physically separated from the signal generation stage and/or the base-band pre-distortion element. The base -band pre-distortion element may be implemented in the analogue or in the digital domain.

In one other embodiment of the invention, the power amplifier is not required as the power of the signal obtained at the output of the logical unit is sufficient to ensure a correct communication within a receiver receiving the pulse width modulated radio frequency signal or its band-pass filtered version.

In another embodiment of the invention two separate RF-oscillators are used in order to eliminate the need of the two phase- shifters 130,140. The first RF-oscillator is modulated in phase providing a first phase- shifted signal that contains a common-phase component carrying the phase information of the base -band signal and a differential phase component according to the opposite version of the phase shift control signal generated in the base -band pre-distortion element 115. The second RF-oscillator is modulated in phase providing a second phase-shifted signal that contains a common-phase component carrying the phase information of the base-band signal and a differential phase component according to the phase shift control signal generated in the base-band pre-distortion element 115. The first phase-shifted signal is provided as input to a first limiter 150 and the second phase- shifted signal is provided as input to a second limiter 160.

In another embodiment of the invention the amplitude 110, A, and the phase information 120, φ, of the base-band signal are obtained from the in-phase, /, and quadrature, Q, components of the base-band signal. The relation between the amplitude and the in-phase and quadrature components of the base -band signal being provided by equation (1).

The relation between the phase and the in-phase and quadrature components of the base-bans signal being provided by equation (2).

φ = arctan(Q / 1) (2)

where all the variables, /, Q, A, and φ, are (in general) a function of time t.

In another embodiment of the invention the phase shift control signal produced by the base -band pre-distortion element is related to the duty cycle of the signal amplified by the radio-frequency power amplifier. The band-pass filtering ensures that only the first harmonic content of the binary signal is transmitted by the antenna. In general the amplitude, A_g of the first-harmonic content of a binary signal having a duty cycle, dc_g is given by equation (3)

A₀ = dc - sinc^ - dcj = l/^ - sin(^ - dC- ) (3)

In the described embodiment the system requires the transmission of an RF signal with an amplitude A, therefore the power amplifier should be driven with a binary signal having a duty cycle, dc, as indicated in equation (4). dc = 1/π • arcsin(;r • A) (4)

A first pre-distortion block 116 of the pre-distortion element 115 carries out the conversion from the required amplitude, A, of the RF signal generated to a required duty cycle, dc, at the input of the power amplifier.

In general the and-operation carried out on two symmetric square-wave signals with mutual phase shift of 2Δφ_g results in a third binary signal with a duty cycle, dc_g, provided by equation (5)

In the described embodiment the system requires that the power amplifier should be driven with a binary signal having a duty cycle, dc, as indicated in equation (4), therefore the final phase shift control signal generated by the pre-distortion element, Δφ, should follow equation (6)

Aφ = π - \ dc = π • arcsin(;r • A) I (6)

9 9 π TT

A second pre-distortion block 117 of the pre-distortion element 115 carries out the conversion from required duty-cycle, dc, of the pulse width modulated signal at the input of the power amplifier to a required phase-shift control signal Δφ.

In Fig. 2a three signals are depicted as a function of time; the amplitude A of the base band signal 220, the duty cycle signal dc generated by the first pre-distortion block 210 and the phase shift control signal 230, Δφ, expressed in radians and generated by the second pre-distortion block 117. In Figs. 2b and 2c the first 240 and second 260 phase shifted sinusoidal signals as well as the first 250 and second 270 RF square- wave phase-shifted signal are depicted when the phase shift signal 230 is applied to the phase shifters 130,140. A time dependent phase difference can be observed between the first and second phase shifted sinusoidal signals (240 and 260) or their hard-limited counterparts (250 and 270). The pulse width modulated radio frequency signal 280, output from an AND gate 170 fed at its inputs by the first and second square-wave phase-shifted signals is shown in Fig. 2d. Fig. 2d also presents the sinusoidal radio frequency signal 290 obtained at the output of a band-pass filtering stage 185 characterized by in essence allowing only transmission of the first- harmonic content.

In Fig. 3a depicts the elements included in a possible implementation of the logical unit and amplification stage providing a 3-level signal according to another embodiment of the invention. For illustration purpose examples of waveforms involved in the process within the logical unit and the amplification stage are depicted in Fig. 3b. The logical unit 170 consists of an AND gate 330 and an OR gate 340. The AND gate receives a first 310 and second 320 RF square- wave phase-shifted signals and provides a first two-level pulse width modulated signal 370. The OR gate receives a first 310 and second 320 RF square- wave phase-shifted signals and provides a second two-level pulse width modulated signal 375. The power amplifier 350 receives the first 370 and the second 375 two-level pulse width modulated signals and provides a three-level pulse width modulated signal 360. The power amplifier may contain a decoder and a three-level switching output stage in order to perform the two-level to three-level conversion. Systems generating pulse width modulated signals with more than 3 levels are also envisaged.

In another embodiment of the invention the base-band pre-distortion element is adjusted in order to provide a pulse width modulated signal at the output of the logical unit with fundamental frequencies other than the RF-carrier frequency. This characteristic can be achieved by applying a proper amplitude to duty cycle conversion within the first block of the base-band pre-distortion element. Two different cases can be envisioned in this particular embodiment. The first case relates to the situation where the fundamental frequencies of the pulse width modulated signal at the output of the power amplifier are lower than the RF- carrier frequency, this case can be considered as a sub-sampling case. The second case relates to the situation where the fundamental frequencies of the pulse width modulated signal at the output of the power amplifier are higher than the RF-carrier frequency, this case can be considered as an over-sampling case.

The relation presented in equation (3) relating the amplitude, A_g of the first- harmonic content of a binary with the duty cycle, dc_g, of a given binary signal can be generalized to the integer sub-sampling or integer over-sampling cases as shown in equation (7) ) A A_vσ == ddcc -- -- TNV -- ddec J) == ^■ (7)

wherein N e {2,3,4...} in the integer sub-sampling case

N e \Xζ, J/, %, ,■■■) ^{m me} i^nteger over-sampling case.

In the described embodiment the system requires the transmission of an RF signal with an amplitude A, therefore the power amplifier should be driven with a binary signal having a duty cycle, dc, as indicated in equation (8).

aicsJnfr - ΛT - Λ) π - N

In another embodiment of the invention, the two radio frequency square waves are originated using multipliers and limiters. In Fig. 4 a block diagram illustrates the elements of the signal generator stage according to this embodiment comprising three full-complex multipliers 430,450,460. In this embodiment the phase modulation is generated based on the complex signal, S, resulting from the division of the original complex base -band signal (I+j-Q) by the magnitude, A, of the base -band signal. The complex signal S is depicted in equation (8), wherein A is related to / and Q by equation (1). The complex signal S always has a unity magnitude and preserves the phase information of the base-band signal.

S = i + j - Q (9)

Ψ² + Q²

The first full-complex multiplier 430 up-mixes the complex signal S to the frequency of the local oscillator, inducing a phase modulation on the local oscillator signal corresponding to the phase of the base-band signal. The first full-complex multiplier 430 multiplies S, with real part 420 and imaginary part 425, by in phase 414 and quadrature 418 signals obtained from a local RF-oscillator 410. The cosine 440 and sine 445 of the phase shift control signal provided by the base-band pre-distortion element 400 are multiplied in the second full-complex multiplier 450 to the Real and Imaginary components obtained from the first full-complex multiplier 430, providing a first phase shifted signal 480 i.e. the Real content of the result obtained from the multiplier. The phase shift control signal provided by the base-band pre-distortion element 400 is negated in 405. The cosine 470 and sine 475 of the negated phase shift control signal provided by the inverting linear amplifier with unity gain 405 are multiplied in the third full-complex multiplier 460 to the real and imaginary components obtained from the first full-complex multiplier 430 providing a second phase shifted signal 490 (real content of the result obtained from the multiplier). The first phase- shifted signal 480 and second phase-shifted signal 490 share a common phase component carrying the phase information of the base-band signal. The first phase-shifted signal and second phase-shifted signal are also characterized in that they have been mutually oppositely phase shifted according to the phase shift control signal 400 provided by the base-band pre- distortion element 115. The first phase- shifted signal and second phase- shifted signal are input signals to the limiters 150,160 of the modulation system. The imaginary components 485,495 of the multiplication functions implemented in the second and third full-complex multipliers may not be used further in the modulation system, resulting in a simplification of the implementation of the second and third multipliers and therefore reducing the amount of hardware needed in the implementation of the signal generator according to this embodiment. In another embodiment of the invention, the two radio frequency square waves are originated using a reduced number of multipliers. Fig. 5 depicts the elements of the signal generator stage according to this embodiment comprising two half-complex multipliers 550,560. A half-complex multiplier contains only 2 real multipliers as opposed to a full- complex multiplier (used in the previously described embodiment) which contains 4 real multipliers. In this embodiment the phase shift control signal generated by the pre-distortion element 500, Δφ, is added to the phase of the base-band signal 530, φ, in a first adder 520, providing a first composed signal, (φ+Aφ). The phase shift control signal provided by the base -band pre-distortion element 500 is negated in 505. The negated phase shift signal generated, -Δφ, is added to the phase of the base-band signal 530, φ, in a second adder 525 providing a second composed signal, (φ-Δφ). The in-phase component 514 of the RF-signal generated by the local oscillator 510 is directly phase-shifted with the resulting first composed signal, (φ+Δφ),by means of the first half-complex multiplier 550, a first cosine generator 540, and a first sine generator 545, providing the first phase-shifted signal 580 (real part of the result obtained from the multiplier). The in-phase component 514 of the RF-signal generated by the local oscillator 510 is directly phase-shifted with the resulting second composed signal, (φ-Δφ), m by means of the second half-complex multiplier 560, a second cosine generator 570, and a second sine generator 575, providing the second phase-shifted signal 590 (real part of the result obtained from the multiplier). The first phase-shifted signal 580 and second phase-shifted signal 590 share a common phase component carrying the phase information of the base-band signal. The first phase-shifted signal and second phase- shifted signal are also characterized in that they have been mutually oppositely phase shifted according to the phase shift control signal 500 provided by the base-band pre-distortion element 115. The first phase-shifted signal and second phase-shifted signal are input signals to the limiters 150,160 of the modulation system. The invention can be implemented in any suitable form including hardware, software, firmware or any combination of these. The invention can be implemented as computer software running on one or more data processors and/or digital signal processors. The elements and components of an embodiment of the invention may be physically, functionally and logically implemented in any suitable way. Indeed, the functionality may be implemented in a single unit, in a plurality of units or as part of other functional units. As such, the invention may be implemented in a single unit, or may be physically and functionally distributed between different units and processors.

It is noted that the term "comprises" or "comprising" when used in the specification including the claims is intended to specify the presence of stated features, means, steps or components, but does not exclude the presence or addition of one or more other features, means, steps, components or group thereof. Further, the word "a" or "an" preceding an element in a claim does not exclude the presence of a plurality of such elements.

Claims

CLAIMS:

1. A polar modulation system for producing an RF output signal, containing an

RF carrier and modulated by a base -band signal, the system comprising: a base-band pre-distortion element (115) for receiving a signal (110) representing - an amplitude of the base-band signal and producing a phase shift control signal carrying an information on the amplitude of the base-band signal; means for producing (150, 160) two radio frequency square waves, which are mutually oppositely phase shifted according to the phase shift control signal and having a common-phase component carrying an information on the phase (120) of the base-band signal; and a logic unit (170) receiving the two radio frequency square waves and providing a pulse width modulated radio frequency signal carrying the amplitude and the phase of the base -band signal.

2. A polar modulation system as claimed in claim 1, further comprising a radio- frequency power amplifier (180) for receiving the pulse width modulated signal and providing an amplified version of the pulse width modulated signal.

3. A polar modulation system as claimed in claim 2, further comprising a band- pass filtering stage (185) for filtering the amplified version of the pulse width modulated signal.

4. A polar modulation system as claimed in claim 3, wherein the band-pass filtering stage (185) limits the transmitted signal essentially to its first-harmonic and corresponding sidebands.

5. A polar modulation system as claimed in claim 1, wherein the pulse width modulated radio frequency signal is a two level signal.

6. A polar modulation system as claimed in claim 1, wherein the pulse width modulated radio frequency signal is a three level signal.

7. A polar modulation system as claimed in claim 1, wherein the fundamental frequencies of the pulse width modulated radio frequency signal contain the RF-carrier frequency.

8. A polar modulation system as claimed in claim 1, wherein the fundamental frequencies of the pulse width modulated radio frequency signal are other than the RF-carrier frequency.

9. A polar modulation system as claimed in claim 1, wherein the two radio frequency square waves are generated by a radio-frequency oscillator (125).

10. A polar modulation system as claimed in claim 1, wherein each of the two radio frequency square waves is originated based on an individual radio-frequency oscillator.

11. A polar modulation system as claimed in claim 1, wherein the two radio frequency square waves are generated by phase shifters (130,140) coupled to limiters (150,160).

12. A polar modulation system as claimed in claim 1, wherein the two radio frequency square waves are generated by multipliers (430, 450, 460) coupled to limiters.

13. A polar modulation system as claimed in claim 1, wherein the phase shift control signal produced by the base-band pre-distortion element is related to the duty cycle of the signal amplified by the radio-frequency power amplifier.

14. A polar modulation system as claimed in claim 1, wherein the logic unit performs an AND function on its inputs.

15. A polar modulation system as claimed in claim 1, wherein the logic unit performs an OR function on its inputs.

6. A transmitter comprising A polar modulation system as claimed in claim 1.