Method for equalizing digital pre-distortion feedback path

Abstract

A method of optimizing compensation of distortions caused by a feedback path between a transmitter of a wireless system radio and an observation receiver of the wireless system radio, an output signal from the transmitter being amplified by a power amplifier and routed i) via a feedback path to the observation receiver, and ii) to a spectrum analyzer, the method including: deriving, by a computer, a feedback transfer function characterizing a relationship between the output signal from the wireless system radio transmitter and the feedback path, based on the signals received at the observation receiver and the spectrum analyzer; and providing, based on the feedback transfer function, an equalization module to compensate for frequency-dependent distortions caused by feedback path.

Description

METHOD FOR EQUALIZING DIGITAL PRE-DIS TORTION FEEDBACK PATHBACKGROUND OF THE DISCLOSURE1. Field of the Disclosure

[0001] The present disclosure relates to wireless networks, and relates more particularly to radio units which utilize digital pre-distortion (DPD) to improve the efficiency of the amplifiers.2. Description of Related Art

[0002] Conventionally, DPD is used to linearize power amplifiers. DPD allows the amplifiers to be biased to operate in a highly nonlinear mode. This nonlinear bias is desirable as it is much more power efficient than a high linear bias. An amplifier with a nonlinear bias cannot meet emissions and modulation quality requirements. DPD is required to linearize the amplifier system to pass emissions and modulation quality requirements. Without the use of DPD, the amplifiers and radio system would be much less efficient.

[0003] DPD requires a feedback path for the system to sample the output of the radio. DPD processes the feedback samples and calculates coefficients to be applied to the signal before the input of the nonlinear amplifier. For DPD to function optimally, the feedback path must be an amplitude-scaled version of the radio output. Any distortion introduced by the feedback path will have an adverse effect on the ability of DPD to linearize the amplifier system. According to another conventional technique known as Multi-Transmission and Reception Point (mTRP), a 5G nodeB (gNB) uses more than one transmission and reception point to communicate with the user equipment (UE), thereby increasing the robustness of the radio link. However, mTRP technique utilizes radio units (RUs) that are separate and not collocated. In addition, mTRP radios have fixed orientations. These characteristics greatly limit the ability of self-healing (or self-remediation) for 5G mMIMO networks in the event of a radio failure.

[0004] To maximize efficiency, wireless infrastructure radios typically make use of Doherty style power amplifiers, which are highly efficient. The high efficiency comes at the expense oflinearity. The nonlinear nature of a Doherty power amplifier prevents conformance to regulatory emission requirements. The use of digital pre-distortion is required to achieve emission requirements. However, digital pre-distortion requires knowledge of the output signal, which means a feedback loop is required between the output of the power amplifier and the digital predistortion correction engine. For best performance when applying the DPD, the feedback path must provide the DPD engine with an amplitude-scaled version of the power amplifier output. Any frequency-dependent variation in amplitude or phase will introduce calculation errors in the DPD.

[0005] Achieving a feedback path which does not introduce frequency-dependent changes to the amplitude or phase can be quite difficult. Currently, engineers spend extensive time for optimizing the feedback path to minimize frequency-dependent impairments. The problem is more difficult if the feedback path i) must cross a connector or ii) make use of an active component such as an LNA or mixer. Conventional techniques for optimizing the feedback path mainly rely on analog compensation techniques to correct for any frequency -dependent characteristics of the equalization path. For example, attempts have been made to use relatively narrow-band impedance matching or equalizer components to compensate for the frequencydependent characteristics of the feedback path. These techniques include:1) Impedance matching using reactive components to improve the return loss, amplitude and phase ripple across the feedback channel.2) The use of equalizer components to reduce the amplitude slope across the feedback path.3) Impedance matching using passive attenuation pad realized by discrete components or single components to improve the return loss across the feedback channel.4) Impedance matching with etch features such as copper stubs, length matching features, etc.5) A combination of two or more of the techniques listed above.

[0006] These conventional compensation techniques have their limitations and often cannot fully compensate for the channel effects of the feedback path. The result is a DPD system which does not function to its full potential. The problem is exacerbated when wideband amplifiers are used(which is increasingly the case in modem radios), because wideband amplifiers require wider band feedback paths which are more suspectable to frequency-dependent degradation.

[0007] Accordingly, there is a need for a system and a method of equalizing the feedback path with respect to the output of the radio, such that the equalization will yield a feedback path which is a true amplitude-scaled version of the output of the radio.SUMMARY

[0008] Accordingly, what is desired is a system and a method of equalizing the feedback path with respect to the output of the radio, such that the equalization will yield a feedback path which is a true amplitude-scaled version of the output of the radio.

[0009] According to an example system and method of the present disclosure, compensation techniques provided in the digital domain are incorporated, in contrast to the conventional techniques utilizing solely the analog domain compensation techniques, which digital domain compensation can provide nearly perfect compensation for any impairments in the feedback path.

[0010] According to an example system and method of the present disclosure, a first component of the digital compensation technique comprises deriving a relationship between the input of the transceiver’s DPD feedback path and the output of the radio prior to the filter unit, which derived relationship can be used to understand the impairments of the feedback signal added by the feedback path.

[0011] According to an example system and method of the present disclosure, a second component of the digital compensation technique comprises providing digital equalization technique(s) to compensate for the impairments introduced by the feedback path.

[0012] According to an example system and method of the present disclosure, an equalization block is introduced between the input of the feedback path and a calculation block for the calculation of the DPD correction parameters.

[0013] According to an example method of optimizing compensation of distortions caused by a feedback path between a wireless system radio transmitter and an observation receiver of thewireless system radio, wherein an output signal from the wireless system radio transmitter is amplified by a power amplifier and routed i) via a feedback path to the observation receiver, and ii) to a spectrum analyzer, the method comprises the following:deriving, by a computer, a transfer function characterizing a relationship between the output signal from the wireless system radio transmitter and the feedback path, based on the signals received at the observation receiver and the spectrum analyzer; andproviding, based on the transfer function, an equalization module to compensate for frequency-dependent distortions caused by the feedback path, wherein the equalization module comprises equalization coefficients calculated based on the feedback transfer function.

[0014] For this application, the following terms and definitions shall apply:

[0015] The term “computer” as used herein refers to a device having one or more general or special purpose processors, memory, storage, and networking components (either wired or wireless), which device can execute an operating system, e.g., a Microsoft® Windows®-compatible operating system (OS), Apple® OS X or iOS, a Linux® distribution, or Google® Android OS.

[0016] The term “network” as used herein includes both networks and internetworks of all kinds, including the Internet, and is not limited to any particular type of network or inter-network.

[0017] The terms “first” and “second” are used to distinguish one element, set, data, object or thing from another, and are not used to designate relative position or arrangement in time.

[0018] The terms “coupled”, “coupled to”, “coupled with”, “connected”, “connected to”, and “connected with” as used herein each mean a relationship between or among two or more devices, apparatus, files, programs, applications, media, components, networks, systems, subsystems, and / or means, constituting any one or more of (a) a connection, whether direct or through one or more other devices, apparatus, files, programs, applications, media, components, networks, systems, subsystems, or means, (b) a communications relationship, whether direct or through one or more other devices, apparatus, files, programs, applications, media, components, networks, systems, subsystems, or means, and / or (c) a functional relationship in which theoperation of any one or more devices, apparatus, files, programs, applications, media, components, networks, systems, subsystems, or means depends, in whole or in part, on the operation of any one or more others thereof.

[0019] The above-described and other features and advantages of the present disclosure will be appreciated and understood by those skilled in the art from the following detailed description, drawings, and appended claims.BRIEF DESCRIPTION OF THE DRAWINGS

[0020] FIG. 1 is a block diagram illustrating an example embodiment of the system according of the present disclosure.

[0021] FIG. 2 is a block diagram illustrating an example embodiment of lower physical layer (LoPHY) blocks including specific example location where the equalization is applied.DETAILED DESCRIPTION

[0022] According to an example system and method of the present disclosure, compensation techniques provided in the digital domain are incorporated, in contrast to the conventional techniques utilizing solely the analog domain compensation techniques, which digital domain compensation can provide ideal compensation for any impairments in the feedback path.According to an example system and method of the present disclosure, the digital compensation technique comprises: i) deriving a relationship between the input of the transceiver’s DPD feedback path and the output of the radio prior to the filter unit, which derived relationship can be used to understand the impairments of the feedback signal added by the feedback path; and ii) providing digital equalization technique(s) to compensate for the impairments introduced by the feedback path. According to an example embodiment, an equalization block is introduced between the input of the feedback path and a calculation block for the calculation of the DPD correction parameters.

[0023] This section describes the technique(s) used to derive the relationship between the feedback path and the output of the radio. In an example embodiment, the relationship between the feedback path and the output of the radio can be established at the product level bycharacterizing several radios (e.g., in the lab) and applying a generic transfer function to each radio. Alternatively, the characterization can also be done at the unit level by characterizing each individual radio during production test and using a unique transfer function on each radio.

[0024] An example method of deriving a transfer function which captures the relationship between the feedback path and the output of the radio involves transmitting a large bandwidth carrier with a Zadoff-Chu function as its baseband input. This transmitter output needs to be recorded by the feedback receiver (also referred to as observation receiver (ORx)) as well as a spectrum analyzer (also referred to as a vector signal analyzer). The spectrum analyzer needs to be connected to measure the Zadoff-Chu signal at the output of the power amplifier. The spectrum analyzer and the device under test, e.g., radio frequency system on chip (RFSoC) (also referred to as printed circuit board assembly (PCBA)), are used to capture the in-phase / quadrature (IQ) samples of the transmit output and the signal received at the feedback receiver, respectively. A transfer function which relates the feedback path to the output of the radio must be calculated based on the Zadoff-Chu signal. The transfer function will be an amplitude and phase response of the feedback receiver (ORx) over the bandwidth of the feedback receiver. The Zadoff-Chu function has the advantage of providing i) a constant amplitude vs. frequency and ii) good auto-correlation properties to facilitate time alignment between the transmitted signal and the feedback receiver signal.

[0025] FIG. l is a block diagram illustrating an example embodiment of the system according of the present disclosure, which block diagram illustrates the connection of the spectrum analyzer 107 to the device under test, e.g., radio frequency system on chip (RFSoC) 10 (also referred to as PCBA), for the purposes of explaining the method of deriving the relationship (e.g., as represented by a transfer function) between the feedback path 11 and the output of the radio, e.g., output of the transmitter (Tx) 101 in the RF SoC 10. As shown in FIG. 1, the output of the RF SoC 10 is amplified by an amplifier 103 and a high power amplifier 104, and then sent to a coupler 105. From the coupler 105, the amplified signal is routed to: i) ORx 102 via feedback path 11; and ii) to spectrum analyzer 107 via a RF connector 106. Normally a filter is placed on top of the RF SoC (PCBA) 10, and the RF connection between the filter unit and the RFSoC (PCBA) 10 is made via an RF connector (e g., RF connector 106 shown in FIG. 1). However, in the case of the present embodiment, the transfer function needs to be determined without thefilter unit in place, i.e., the spectrum analyzer 107 is connected to the RF connector 106 on the RF SoC (PCBA) 10 to implement the characterization of the feedback path. Once the characterization of the feedback path is completed, the spectrum analyzer 107 can be disconnected and the filter unit can be reconnected to the RF SoC (PCBA) 10.

[0026] According to an example embodiment of the present disclosure, calculating the transfer function (e.g., by the computer 108 shown in FIG. 1, based on signals transmitted from the Tx 101) can be implemented as follows:1) Download (e.g., by the computer 108 shown in FIG. 1) the in-phase / quadrature (IQ) data samples (of received signals) from both the spectrum analyzer 107 and the feedback receiver (e.g., ORx 102).2) Resample at least one of the two signals to a common sample rate.3) Perform an auto-correlation between the two signals to time align the two signals.4) Perform a Fast Fourier transform (FFT) on the two signals.5) Calculate the amplitude and phase difference between the two signals at selected frequency points of interest.a) In an example embodiment, the frequency points of interest can be spaced by the frequency resolution desired for characterizing the response of the feedback receiver.b) Several frequency points from the FFT can be used around each frequency point of interest to provide averaging.6) The above-described process (i.e., transmit, receive, download and analyze) to calculate the transfer function (e.g., by the computer 108) can be repeated at different transmit frequencies if the instantaneous bandwidth of the feedback receiver is larger than the individual Zadoff-Chu bandwidth being transmitted.

[0027] This section discusses a second aspect of the example embodiment of the present disclosure, i.e., providing a digital equalization module to compensate for any impairmentsintroduced by the feedback path. The equalization coefficients are calculated based on the feedback transfer function previously described above, and the equalization removes the impairments to the feedback data introduced by the feedback path. FIG. 2 is a block diagram illustrating an example embodiment of lower physical layer (LoPHY) blocks including specific example location where the equalization is applied. The component blocks shown in FIG. 2 include: digital up converter (DUC) / mixer / carrier aggregation module 201, which performs digital up conversion and allocates the carriers as needed in the frequency domain; crest factor reduction (CFR) module 202, which provides crest factor reduction of the time domain waveform; re-sampler module 203, which adjusts the sampling rate prior to the next module (i.e., DPD); digital pre-distortion (DPD) module 204, which provides digital pre-distortion of the time domain signal to linearize the effects of non-linear components (e.g., by calculating the DPD correction coefficients); radio frequency digital-to-analog converter (RF DAC) module 205, the output of which is sent to the power amplifier(s) (e.g., high power amplifier 104); radio frequency observation receiver analog-to-digital (RF ORx ADC) module 206, which converts the feedback path’s analog signal to the digital domain samples; and equalizer (EQ) module 207, which removes the frequency-dependent properties of the feedback path data which were characterized in the transfer function.

[0028] When looking at the component blocks shown in FIG. 1 in connection with the lower physical layer (LoPHY) blocks shown in FIG. 2, the digital pre-distortion (DPD) module 204 (which can be implemented, e.g., in the RF SoC 10 shown in FIG. 1, but it can also be implemented outside of the RF SoC 10) pre-distorts the digital data such that the output signal transmitted through the RF DAC 205 (which can be implemented, e.g., in the RF SoC 10 shown in FIG. 1) and the power amplifier (e.g., high power amplifier 104 shown in FIG. 1) is then corrected for any distortion effects introduced by the power amplifier. The feedback path 11 (shown in FIG. 1), which is coupled off of the power amplifier, is fed through the RF ORx ADC 206 shown in FIG. 2 (RF ORx ADC 206 can be implemented within the RF SoC 10 shown in FIG. 1, e.g., interfacing ORx 102). The EQ module 207 (which can be implemented, e.g., in the RF SoC 10 shown in FIG. 1) then corrects the feedback path data fed through the RF ORx ADC 206 (and the ORx 102) to remove the amplitude and phase impairments of the feedback path, so that the DPD algorithm has an accurate representation of the signal originally coupled off the power amplifier.

[0029] An equalizer (e g., the EQ module 207) with complex coefficients is required to remove both amplitude and phase impairments. Calculating the equalizer coefficients from the feedback receiver transfer function can be implemented with the following steps:1) Determine the sample rate (Fs) to be used for the equalizer such that i) Nyquist sampling rate is satisfied for the bandwidth of the feedback receiver transfer function (FRTFbw), and ii) Fs is an integer multiple of the frequency of the DSP processing clock being used (Fclk) and the sample rate being used for the feedback receiver’s sample rate within the digital predistortion (DPD) processing (Ffbr). Typically, Fs and Ffbr will be equal, and Ffbr will already be an integer multiple of Fclk.2) Interpolate the feedback receiver transfer function to Fs with N sample points, where N is a power of 2 and Fs / N provides the desired frequency resolution of the equalizer.3) Calculate the inverse feedback receiver transfer function as (1 / feedback receiver transfer function), as this will be the compensation required.3) Multiply the inverse feedback receiver transfer function by a window function vs. frequency, such as a Tukey window that has a center lobe that covers the bandwidth of the feedback receiver. The Tukey window will provide a flat response over the bandwidth of interest and taper the edges of the bandwidth.4) Perform an Inverse Fast Fourier Transform (IFFT) to convert the windowed inverse feedback receiver transfer function from frequency domain to time domain.5) Extract the selected first M outputs of the IFFT to be the complex coefficients of the equalizer and scale them appropriately so that the equalizer has unity gain. The time domain values of the IFFT output will become insignificant after M outputs depending on the perturbations in the windowed inverse feedback receiver transfer function.

[0030] The equalizer implements the multiplication of M complex equalizer coefficients against K samples of the feedback receiver signal at the Fs sample rate. The feedback receiver data will contain K samples per clock in parallel, where K = (Fs / Fclk). This will be the input to the equalizer and the output will also contain K samples per clock in parallel. Running at Fclk, theequalizer will require an array of complex multiplier-accumulators, K by M, that can calculate K outputs of the equalizer in parallel on each Fclk period.

[0031] While the present disclosure has been described with reference to one or more exemplary embodiments, it will be understood by those skilled in the art that various changes can be made and equivalents can be substituted for elements thereof without departing from the scope of the present disclosure. Although the example methods have been described in the context of wireless cellular networks, the example methods are equally applicable to the satcom radios, high power radar systems and broadband optical communication systems. In addition, many modifications can be made to adapt a particular situation or material to the teachings of the disclosure without departing from the scope thereof. Therefore, it is intended that the present disclosure not be limited to the particular embodiment(s) disclosed as the best mode contemplated, but that the disclosure will include all embodiments falling within the scope of the appended claims.

Claims

CLAIMS:

1. A method of optimizing compensation of distortions caused by a feedback path between a wireless system radio transmitter and an observation receiver of the wireless system radio, wherein an output signal from the wireless system radio transmitter is amplified by a power amplifier and routed i) via a feedback path to the observation receiver, and ii) to a spectrum analyzer, the method comprising:deriving, by a computer, a feedback transfer function characterizing a relationship between the output signal from the wireless system radio transmitter and the feedback path, based on the signals received at the observation receiver and the spectrum analyzer; and providing, based on the feedback transfer function, an equalization module to compensate for frequency-dependent distortions caused by the feedback path, wherein the equalization module comprises equalization coefficients calculated based on the feedback transfer function.

2. The method of claim 1, wherein the deriving of the feedback transfer function by the computer comprises:downloading in-phase / quadrature (IQ) data samples of the signals received at the observation receiver and the spectrum analyzer;performing a Fast Fourier transform (FFT) on the I / Q data samples of the signals received at the observation receiver and the spectrum analyzer; andcalculating amplitude and phase differences between the signals received at the observation receiver and the spectrum analyzer, at selected frequency points of interest.

3. The method of claim 2, wherein:the feedback path is fed through the the observation receiver to the equalization module to remove amplitude and phase distortions caused by the feedback path.

4. The method of claim 3, further comprising:providing a digital pre-distortion (DPD) module coupled to an output of the equalization module, wherein an output of the DPD is pre-distorted by the DPD, and wherein the pre-distorted output of the DPD is fed through the power amplifier, whereby the pre-distorted output of the DPD compensates for distortion effects introduced by the power amplifier.

5. The method of claim 3, wherein the equalization coefficients are complex coefficients for correcting amplitude and phase distortions, and wherein the calculation of the equalization coefficients based on the feedback transfer function comprises:1) determining a sample rate Fs to be used for the equalization module such that i) Nyquist sampling rate is satisfied for a bandwidth FRTFbw of the feedback transfer function, and ii) Fs is an integer multiple of a frequency Fclk of a digital signal processing (DSP) clock being used and a sample rate Ffbr for the observation receiver;2) interpolating the feedback transfer function to Fs with N sample points, where N is a power of 2 and Fs / N provides a desired frequency resolution of the equalization module;3) calculating an inverse feedback transfer function as 1 / feedback transfer function; 3) multiplying the inverse feedback transfer function by a window function versus frequency;4) performing an inverse Fast Fourier Transform (IFFT) to convert the windowed inverse feedback transfer function from frequency domain to time domain; and5) extracting selected first M outputs of the IFFT to be the complex coefficients.

6. The method of claim 5, wherein:the equalization module implements multiplication of M complex equalizer coefficients against K samples of the observation receiver signal at the Fs sample rate, and K = (Fs / Fclk), whereby the equalization module, running at Fclk and utilizing an array of complex multiplieraccumulators of K by M dimensions, calculates K outputs in parallel for each Fclk period.

7. The method of claim 1, wherein:the feedback path is fed through the the observation receiver to the equalization module to remove amplitude and phase distortions caused by the feedback path.

8. The method of claim 7, further comprising:providing a digital pre-distortion (DPD) module coupled to an output of the equalization module, wherein an output of the DPD is pre-distorted by the DPD, and wherein the predistorted output of the DPD is fed through the power amplifier, whereby the pre-distorted output of the DPD compensates for distortion effects introduced by the power amplifier.

9. The method of claim 8, wherein the equalization coefficients are complex coefficients for correcting amplitude and phase distortions, and wherein the calculation of the equalization coefficients based on the feedback transfer function comprises:1) determining a sample rate Fs to be used for the equalization module such that i) Nyquist sampling rate is satisfied for a bandwidth FRTFbw of the feedback transfer function, and ii) Fs is an integer multiple of a frequency Fclk of a digital signal processing (DSP) clock being used and a sample rate Ffbr for the observation receiver;2) interpolating the feedback transfer function to Fs with N sample points, where N is a power of 2 and Fs / N provides a desired frequency resolution of the equalization module;3) calculating an inverse feedback transfer function as 1 / feedback transfer function; 3) multiplying the inverse feedback transfer function by a window function versus frequency;4) performing an inverse Fast Fourier Transform (IFFT) to convert the windowed inverse feedback transfer function from frequency domain to time domain; and5) extracting selected first M outputs of the IFFT to be the complex coefficients.

10. The method of claim 9, wherein:the equalization module implements multiplication of M complex equalizer coefficients against K samples of the observation receiver signal at the Fs sample rate, and K = (Fs / Fclk), whereby the equalization module, running at Fclk and utilizing an array of complex multiplieraccumulators of K by M dimensions, calculates K outputs in parallel for each Fclk period.

11. A system for optimizing compensation of distortions caused by a feedback path between a wireless system radio transmitter and an observation receiver of the wireless system radio, wherein an output signal from the wireless system radio transmitter is amplified by a power amplifier and routed i) via a feedback path to the observation receiver, and ii) to a spectrumanalyzer, the system comprising:a computer system configured to derive a feedback transfer function characterizing a relationship between the output signal from the wireless system radio transmitter and the feedback path, based on the signals received at the observation receiver and the spectrum analyzer; andan equalization module configured to compensate for frequency-dependent distortions caused by the feedback path, wherein the equalization module comprises equalization coefficients calculated based on the feedback transfer function.

12. The system of claim 11, wherein the computer system is configured to derive the feedback transfer function by:downloading in-phase / quadrature (IQ) data samples of the signals received at the observation receiver and the spectrum analyzer;performing a Fast Fourier transform (FFT) on the I / Q data samples of the signals received at the observation receiver and the spectrum analyzer; andcalculating amplitude and phase differences between the signals received at the observation receiver and the spectrum analyzer, at selected frequency points of interest.

13. The system of claim 12, wherein:the feedback path is fed through the the observation receiver to the equalization module to remove amplitude and phase distortions caused by the feedback path.

14. The system of claim 13, further comprising:a digital pre-distortion (DPD) module coupled to an output of the equalization module, wherein an output of the DPD is pre-distorted by the DPD, and wherein the pre-distorted output of the DPD is fed through the power amplifier, whereby the pre-distorted output of the DPD compensates for distortion effects introduced by the power amplifier.

15. The system of claim 13, wherein the equalization coefficients are complex coefficients for correcting amplitude and phase distortions, and wherein the calculation of the equalization coefficients based on the feedback transfer function comprises:1) determining a sample rate Fs to be used for the equalization module such that i) Nyquist sampling rate is satisfied for a bandwidth FRTFbw of the feedback transfer function, and ii) Fs is an integer multiple of a frequency Fclk of a digital signal processing (DSP) clock being used and a sample rate Ffbr for the observation receiver;2) interpolating the feedback transfer function to Fs with N sample points, where N is a power of 2 and Fs / N provides a desired frequency resolution of the equalization module;3) calculating an inverse feedback transfer function as 1 / feedback transfer function; 3) multiplying the inverse feedback transfer function by a window function versus frequency;4) performing an inverse Fast Fourier Transform (IFFT) to convert the windowed inverse feedback transfer function from frequency domain to time domain; and5) extracting selected first M outputs of the IFFT to be the complex coefficients.

16. The system of claim 15, wherein:the equalization module is configured to implement multiplication of M complex equalizer coefficients against K samples of the observation receiver signal at the Fs sample rate, and K = (Fs / Fclk), whereby the equalization module, running at Fclk and utilizing an array of complex multiplier-accumulators of K by M dimensions, calculates K outputs in parallel for each Fclk period.

17. The system of claim 11, wherein:the feedback path is fed through the the observation receiver to the equalization module to remove amplitude and phase distortions caused by the feedback path.

18. The system of claim 17, further comprising:a digital pre-distortion (DPD) module coupled to an output of the equalization module, wherein an output of the DPD is pre-distorted by the DPD, and wherein the pre-distorted outputof the DPD is fed through the power amplifier, whereby the pre-distorted output of the DPD compensates for distortion effects introduced by the power amplifier.

19. The system of claim 18, wherein the equalization coefficients are complex coefficients for correcting amplitude and phase distortions, and wherein the calculation of the equalization coefficients based on the feedback transfer function comprises:1) determining a sample rate Fs to be used for the equalization module such that i) Nyquist sampling rate is satisfied for a bandwidth FRTFbw of the feedback transfer function, and ii) Fs is an integer multiple of a frequency Fclk of a digital signal processing (DSP) clock being used and a sample rate Ffbr for the observation receiver;2) interpolating the feedback transfer function to Fs with N sample points, where N is a power of 2 and Fs / N provides a desired frequency resolution of the equalization module;3) calculating an inverse feedback transfer function as 1 / feedback transfer function; 3) multiplying the inverse feedback transfer function by a window function versus frequency;4) performing an inverse Fast Fourier Transform (IFFT) to convert the windowed inverse feedback transfer function from frequency domain to time domain; and5) extracting selected first M outputs of the IFFT to be the complex coefficients.

20. The system of claim 19, wherein:the equalization module is configured to implement multiplication of M complex equalizer coefficients against K samples of the observation receiver signal at the Fs sample rate, and K = (Fs / Fclk), whereby the equalization module, running at Fclk and utilizing an array of complex multiplier-accumulators of K by M dimensions, calculates K outputs in parallel for each Fclk period.

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