# Patent

## Title
Digital pre-distortion technique using nonlinear filters

## Abstract

A system and method for stabilizing a coefficient set used by a digital predistortion (DPD) engine to apply pre-distortion to a transmit signal and cancel distortion generated by a distorting element or distorting system when transmitting the transmit signal, including obtaining an initial coefficient set; rotating the initial coefficient set to maintain a phase of fundamental components (w10(t), . . . , w1Q(t)) of the initial coefficient set as a constant value; averaging in the time domain the rotated coefficient set to obtain an averaged coefficient set; applying the averaged coefficient set to the DPD engine, the initial coefficient set expressed in a first equation [27]; computing the phase of the fundamental components of the initial coefficient set with a second equation [28]; and computing the rotated coefficient set with a third equation [29].

## Background
CROSS REFERENCE TO RELATED DOCUMENTS
The present invention is a continuation of U.S. patent application Ser. No. 11/951,238 of Cai et al., entitled “DIGITAL PRE-DISTORTION TECHNIQUE USING NONLINEAR FILTERS,” filed on Dec. 5, 2007, now allowed, which is a continuation of U.S. patent application Ser. No. 11/150,445 of Cai et al., entitled “DIGITAL PRE-DISTORTION TECHNIQUE USING NONLINEAR FILTERS,” filed on Jun. 9, 2005, now allowed, which claims benefit of priority to U.S. Provisional Patent Application Ser. No. 60/616,714 of Devendorf et al., entitled “DIGITAL PRE-DISTORTION TECHNIQUE USING NON-LINEAR FILTERS,” filed on Oct. 7, 2004, the entire disclosures of all of which are hereby incorporated by reference herein.


BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to electrical and electronic circuits and systems. More specifically, the present invention relates to power amplifiers for communications systems and predistortion linearizers used in connection therewith.
2. Discussion of the Background
Power amplifiers are used in a variety of communications applications. Power amplifiers not only typically exhibit non-linear distortion but also possess memory effects. While non-linear distortion follows the power amplifier characteristics, the memory effects depend on signal characteristics (e.g., signal bandwidth and also transmit power level.)
Conventional techniques use Lookup Table (LUT) based methods to generate inverse transfer functions in both amplitude and phase to correct for non-linearity in the output of power amplifiers. However these techniques do not effectively handle memory effects and thus provide very moderate linearization improvements.
More importantly, power amplifiers are generally expensive and consume much power. Multiple carrier applications, such as cellular telephone base stations, are particularly problematic inasmuch as a single amplifier is typically used with each carrier signal. Conventional approaches combine separate power amplifiers to transmit multiple carrier signals. However, this approach is also expensive and power intensive.
Further, for maximum efficiency, each power amplifier must be driven close to its saturation point. However, as the power level is increased, intermodulation distortion (IMD) levels increase. Hence, the output power level must be ‘backed-off’ to maintain acceptable ACPR (adjacent channel power ratio) levels. Unfortunately, the required power back-off to meet government (e.g. FCC) specified IMD levels limits the efficiency of the power amplifier to relatively low levels and does not offer a solution that is sufficiently cost effective for certain current requirements.
An alternative approach is to use a predistortion linearizer. This technique allows power amplifiers to operate with better power efficiency, while at the same time maintaining acceptable IMD levels. However, conventional digital predistortion linearizers have, been shown to reduce the IMD levels by only about 10-13 dB for signal bandwidths in excess of 20 MHz.
Hence, a need remains in the art for an efficient, low cost system or method for amplifying multiple carrier signals while maintaining low intermodulation distortion levels.
SUMMARY OF THE INVENTION
The need in the art is addressed by the linearizer and method of the present invention. In a most general embodiment, the inventive linearizer includes a characterizer coupled to an input to and an output from said circuit for generating a set of coefficients and a predistortion engine responsive to said coefficients for predistorting a signal input to said circuit such that said circuit generates a linearized output in response thereto.
As a result, in the best mode, the weights used in the predistortion linearization engine can be computed by solving a matrix equation HW=S for W, where W is a vector of the weights, S is a vector of predistortion linearization engine outputs, and H is a matrix of PA return path inputs.
Accordingly, in exemplary aspects of the present invention there is provided a system and method for stabilizing a coefficient set used by a digital predistortion (DPD) engine to apply pre-distortion to a transmit signal and cancel distortion generated by a distorting element or distorting system when transmitting the transmit signal, including obtaining an initial coefficient set; rotating the initial coefficient set to maintain a phase of fundamental components (w10(t), . . . , w1Q(t)) of the initial coefficient set as a constant value; averaging in the time domain the rotated coefficient set to obtain an averaged coefficient set; applying the averaged coefficient set to the DPD engine, the initial coefficient set expressed in a first equation [27]; computing the phase of the fundamental components of the initial coefficient set with a second equation [28]; and computing the rotated coefficient set with a third equation [29].
In further exemplary aspects of the present invention there is provided a system and method for generating a coefficient set with improved accuracy, the coefficient set used by a digital predistortion (DPD) engine to apply pre-distortion to a transmit signal and cancel distortion generated by a distorting element or distorting system when transmitting the transmit signal, including selecting samples from a pre-distorted transmit signal from the DPD engine exceeding a predetermined threshold; zeroing the selected samples from the transmit signal and the corresponding row of the “H” matrix of the distorting element or distorting system; computing a coefficient set from the transmit signal and the delayed feedback signal with the selected samples removed, the pre-distorted transmit signal having samples S represented as S=[s(0) s(1) s(2) s(3) . . . s(U−1)]T; defining a soft factor vector as G=[g(0) g(1) g(2) g(3) . . . g(U−1)]T where g(i)=1 for |s(i)|<T2, g(i)=0 otherwise, and T2 is the predetermined threshold; and if g(i)=0, zeroing an ith sample of S and zeroing an ith row of the H matrix.
Still other aspects, features, and advantages of the present invention are readily apparent from the following detailed description, by illustrating a number of exemplary embodiments and implementations, including the best mode contemplated for carrying out the present invention. The present invention is also capable of other and different embodiments, and its several details can be modified in various respects, all without departing from the spirit and scope of the present invention. Accordingly, the drawings and descriptions are to be regarded as illustrative in nature, and not as restrictive.



BRIEF DESCRIPTION OF THE DRAWINGS
The embodiments of the present invention are illustrated by way of example, and not by way of limitation, in the figures of the accompanying drawings and in which like reference numerals refer to similar elements and in which:
FIG. 1 is a block diagram of an illustrative implementation of a transmitter implemented in accordance with the present teachings;
FIG. 2 is a block diagram of an illustrative implementation of a characterizer in accordance with the teachings of the present invention;
FIG. 3 is a series of timing diagrams illustrative of the process of calibration of the receive feedback path in accordance with an illustrative embodiment of the present teachings;
FIG. 4 is a block diagram of an illustrative implementation of the IF to baseband converter;
FIG. 5 is a block diagram of an illustrative implementation of a DPD coefficients estimator in accordance with the present teachings; and
FIG. 6 is a simplified block diagram of a DPD engine implemented in accordance with an illustrative embodiment of the present teachings.



DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
Illustrative embodiments and exemplary applications will now be described with reference to the accompanying drawings to disclose the advantageous teachings of the present invention.
While the present invention is described herein with reference to illustrative embodiments for particular applications, it should be understood that the invention is not limited thereto. Those having ordinary skill in the art and access to the teachings provided herein will recognize additional modifications, applications, and embodiments within the scope thereof and additional fields in which the present invention would be of significant utility.
FIG. 1 is a block diagram of an illustrative implementation of a transmitter implemented in accordance with the present teachings. The inventive transmitter 10 includes a conventional transmitter 12 with a digital upconverter 14, a DAC 16, an analog upconverter (UC) 18 and a power amplifier 20. The digital upconverter 14 converts a baseband input signal y(t) to intermediate frequency (IF) and the analog upconverter 18 converts the analog IF signal to radio frequency (RF) for amplification by the power amplifier 20. The output z(t) of the power amplifier 20 is fed to a conventional RF antenna 22 for transmission.
In accordance with the present teachings, linearization of the performance of the transmitter 12 is effected by a DPD engine 100. The DPD engine performs an inverse filtering of the transmitter 12 using coefficients supplied by a characterizer 30 in a feedback path thereof. As discussed more fully below, the characterizer computes the coefficients of a feedback compensation filter (i.e., using the receive path equalization process) and solves the normal equation during normal operation to compute the weights of the DPD block that are used to provide predistortion. Those skilled in the art will appreciate that the digital processing may be implemented in software using a general purpose microprocessor or other suitable arrangement.
In operation, a complex in-phase and quadrature (I-Q) input signal x(t) is sent to the DPD engine 100 and passes through a set of filters. As discussed more fully below, these filters are non-linear filters with programmable complex weights provided by a characterizer 30. The output of the DPD engine 100 is a predistorted I-Q sample stream.
The transmitter 12 converts the I-Q samples of the DPD output into an RF signal at the desired frequency and power level for transmission. The outputs from the DPD engine 100 are processed by the digital upconverter 14, which converts the I-Q signal into IF digital samples. The IF digital samples are then converted to an analog IF signal by the DAC 16 and are then frequency shifted by the RF upconverter 18 to produce an RF signal. This signal is then amplified using the power amplifier (PA). The linearized output of the transmitter 12 at the desired power level is then sent to the transmit antenna 22.
In accordance with the present teachings, this linearized output is achieved by simultaneously capturing data after the DPD block and at the feedback input in the characterizer 30. The data is correlated/shifted, scaled, combined with noise, and then solved for the predistortion coefficients which are averaged with the previously computed-weights and then applied on the transmit data in the DPD block. This data capture and weight computation is then repeated continuously. Sampling of the PA output is effected by coupling off a signal from the PA output with attenuation of the signal on the line from the PA output to a feedback circuit 24 that includes a down converter 26 and an analog to digital converter (ADC) 28. The down converter 26 converts the signal to intermediate frequency (IF). The ADC 28 converts the IF signal to digital form and feeds the digital samples to the characterizer 30.
The characterizer 30 computes the coefficients of the inverse filter for the transmitter 12 such that the PA output signal z(t) is linearized with respect to the input signal x(t). As discussed more fully below, the samples from the receive feedback path into the characterizer first pass-through a feedback compensation filter whose coefficients were computed by the characterizer to remove the distortion generated in the feedback section, after which the DPD output and the compensated signal are then time aligned and scaled (scaling is not shown in the invention but is a crucial step although a trivial one since the scaling is fixed). Then a DPD coefficient estimator solves a set of normal equations producing weights. Finally these weights are averaged to produce the coefficients for the DPD engine. The more detailed description of these blocks follows below.
From equation 4 of A Robust Digital Baseband Predistorter Constructed Using Memory Polynomials, by Lei Ding, G. Tong Zhou, Zhengriang Ma, Dennis R. Morgan, J. Stevenson Kenney, Jaehyeong Kim, Charles R. Giardina. C. Manuscript submitted to IEEE Trans. On Communication, Mar. 16, 2002, the PA can be modeled as




  
    
      
        
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where x is the input to the PA, akq=ckqejφkq. Similarly, if we want to predistort the signal, we implement a structure equivalent to the PA model,




  
    
      
        
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where wkq=akqejφkq, and x(t) and y(t) are DPD input and output respectively. A practitioner may use only the odd k terms in the first summation since the even terms correspond to out-of-band harmonics which are not of interest in the illustrative application. However, performance can be enhanced by using these terms. Equation 2 can be realized with a structure based on the following manipulation thereof:




  
    
      
        
          
            
              
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The inner summation in parenthesis can be viewed as a filter for a fixed ‘k’. This feature is exploited in the hardware implementation.
The processing sequence of the data input to the DPD is as follows:
Select the parameters K (K is odd) and Q for the DPD engine.
1. Compute the signal amplitude |x(n)|, and subsequently compute the powers |x(n)|2, |x(n)|3, |x(n)|4, . . . , |x(n)|K−1.
2. The signals |x(n)|k, k=1, 2, 3, . . . , K−1 are sent to a tapped delay line to generate |x(n−q)|k, k=1, 2, 3, . . . , K−1, q=0, 1, . . . , Q.
3. The signals |x(n−q)|k are multiplied with the coefficients wkq and the results are summed to produce the combined weights:




  
    
      
        
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4. The combined weights are then used as coefficients for filtering the signal x(t) to produce the signal:




  
    
      
        
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The coefficients, wkq, used in the data path implementation of the DPD engine are generated by the characterizer 30 as discussed more fully below and illustrated in FIG. 2.
FIG. 2 is a block diagram of an illustrative implementation of a characterizer 30 in accordance with the teachings of the present invention. The transmit data and the PA feedback data are stored in random access memory (RAM) 32 and 34 respectively for signal processing in batch mode. While the transmit data phase is known, the PA feedback data is an IF signal and its phase is dependent on the time interval during which the data is collected. Thus it is necessary to capture the data at the time of known phase in relation to the phase of the transmit data phase at the DPD output so that the computed DPD coefficients can be averaged to increase accuracy.
FIG. 3 is a series of timing diagrams illustrative of the process of initialization and compensation filter coefficient calculation in accordance with an illustrative embodiment of the present teachings. As illustrated in FIG. 3a, during the initialization process a stream of impulses are transmitted using a signal generator or DAC at the input to the feedback path just after the coupling means.
As illustrated in FIG. 3b, samples output by the ADC 28 are collected and samples surrounding the peaks that exceed a threshold are stored. These samples are represented as:




  
    
      
        
          
            
              
                
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The impulse responses are averaged to improve the signal-to-noise ratio to produce the mean impulse response as:




  
    
      
        
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As illustrated in FIG. 3c, a processor (not shown) in the characterizer 30 then computes the Fast Fourier Transform (FFT) of this impulse response to produce the spectral response of RF down converter 26 and the ADC 28. Hence, the processor and associated software implement a PA feedback inverse filter estimator 36. Note that zeros are padded to produce the desired number of samples that the PA Feedback correction filter will use.

C(f)=FFT(c(t))=FFT([c1 c2 c3 . . . cN 0 0 0 . . . 0])  [8]

The spectral response of the PA Feedback path filter is then computed as follows:

D(f)=1/C(f)  [9]

and the inverse FFT is used to determine the coefficients for the PA Feedback compensation filter d(t):

d(t)=IFFT(D(f))  [10]

It is noted that this process is only performed only during system initialization, or per request.
The feedback compensation filter coefficients output by the estimator 36 are input to a feedback correction filter 38. The feedback correction filter 38 is a finite impulse response filter with N taps. The coefficients of this filter are extracted as set forth above. This filter removes any distortion caused by the RF down converter 26 and ADC 28.
The output of the PA feedback correction filter 38 is an IF signal and it is necessary to convert it into a baseband signal in I-Q form for subsequent signal processing.
FIG. 4 is a block diagram of an illustrative implementation of the IF to baseband converter 40. The output of the feedback correction filter 40 is first multiplied by cos(2πfIFn/fs) and sin(2πfIFn/fs) via multipliers 44 and 46 respectively. These outputs are fed through low-pass filters 48 and 50 to extract a baseband signal centered at DC. Since the ADC 28 (FIG. 1) may have an output sample rate different than the sample rate in the DPD engine 100, assume that the ratio between the DPD rate and the ADC sample rate is P/Q. Then the outputs of the low pass filters are up-sampled by a factor of P (by up-sampling circuits (US) 52 and 54) and filtered by filters 55 and 57. Following a time shift via shifters 56 and 58, these signals are then filtered and down-sampled (DS) by a factor of Q by down-sampling circuits 60 and 62. The output signals are baseband I-Q signals having the same sampling rate as the DPD engine.
The shifters 56 and 58 placed between the up-samplers 52, 54 and down-samplers 60, 62 refine the time t2 during the time synchronization. After the synchronization, this time shift t2 is kept constant.
As mentioned above, the time synchronization is required to align the DPD output signal and the output of the PA Feedback Correction Filter. The time offset error is deterministic and is due to the latency delay in the transmit and receive paths. After synchronization, the time shift will maintain a constant value since the time drift is insignificant.
The correlation process to align the signal is as follows:
Coarse Correlation
(a) First, note that there are multiple possible values of n2 in FIG. 4 that will give different results for r. Since r is a function of n2, we will so indicate only during the correlation discussion by writing the output as r(n, n2). After finding the optimal value for n2, we apply it as in FIG. 4 and drop the n2 from the r notation. We compute the correlation between input y(n) and output r(n, n2) signals over +/−L sample shift with n2=0 as follows:




  
    
      
        
          
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(b) Search for the shift l that yields maximum correlation R(l). n1=lmax is the coarse shift; and
(c) Output the time shift n1.
Since the correlation R(l) has the sampling rate of fs, the time correlation is accurate to ±1/(2fs)
Fine Correlation
(a) After the coarse time sync, compute correlation between shifted input y(n−n1) and output r(n, n2) signals over n2{−2, −1, 0, 1, 2} sample in time shift where n2 functions as shown in FIG. 4;




  
    
      
        
          
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(b) Search for the shift g that yields maximum correlation R(g)·n2=gmax is the fine shift;
(c) Output the time shift n2; and
(d) Since the correlation R(g) has the sampling rate of Qfs, the time correlation is accurate to ±1/(2Qfs).
DPD Coefficients Estimator
After the signals s(n) and r(n) are aligned in time by a time shift estimator 42 and time shifters 56, 58 and 64, the DPD weights are estimated by a DPD coefficients estimator 70. The objective is to solve the DPD equation as defined in [3]:




  
    
      
        
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        13
        ]
      
    
  




where s(n) is derived from the DPD output and r(n) is derived from the PA Feedback output.
FIG. 5 is a block diagram of an illustrative implementation of a DPD coefficients estimator in accordance with the present teachings. The inputs S1 is s(n) and R1 is r(n) from the above discussion. The process for weight estimation is described below.
High Pass Noise Generation
Because both the signal s(n) and r(n) have narrow bandwidths relative to the DPD sampling frequency, the estimation of the weights may exhibit undesirable behavior at high frequencies where little signal content exists. To prevent this from happening, either a properly scaled all-pass or high-pass signal (pre-stored in a RAM 72 or generated using a random noise generator such as a pn linear feedback shift register), is added to both signals s(n) and r(n) at steps 74 and 76. This added all-pass or high-pass signal ensures bounded, stable weights and also greatly improves weight averaging.
The new signals with the added signal are expressed as:

S2=S1+N  [14]

R2=R1+N  [15]

where S1 and R1 are the processed DPD samples and the processed IF to BB converter output, respectively.
Soft Factor
When operating near saturation of the PA, the peak amplitude of the DPD output s(n) will increase as the DPD loop progresses, but the amplitude of the ADC output will be remain saturated due to PA compression. This is always the case for a PA with an input versus output amplitude profile which curves very flat very quickly, i.e. it becomes highly saturated, and the user has selected a low K and small Q which will not provide an accurate solution for W. A perfect PA has a linear transfer function, output=100*input, i.e., a straight line. A real PA will start to tail off from linear as the input power is increased eventually hitting a maximum output power no matter how much the input power is increased (it becomes a flat line at this time), so the transfer function ends up looking like a hockey stick. The soft factor is used to remove the samples s(n) with very strong amplitude from consideration in solving for the weights in equation [5]. Let

S=[s(0) s(1) s(2) s(3) . . . s(U−1)]T  [16]

be the processed DPD signal samples, the soft factor vector is expressed as:

G=[g(0) g(1) g(2) g(3) . . . g(U−1)]T  [17]

where

    
    
        g(i)=1 for |s(i)|<T2 
        g(i)=0 otherwise, and
    
    


T2 is the user chosen threshold that controls how large the samples are that will be processed. This soft factor vector will be used to help solve for the weights with high accuracy.
Sampling Shift n3 
The distribution of the weight W between [0-Q] impacts the accuracy of the DPD engine. In order to maximize the accuracy of the DPD=PA−1 estimation process, it is necessary to place the weight distribution correctly, by shifting the delay n3 between from 0 to Q and checking for the residue error E as defined in Equation 26. The output of the sample Shift is expressed as:

R3(n)=R2(n−n3)  [18]

DPD Weight Estimator
The DPD equation can be expressed as:




  
    
      
        
          s
          ⁡
          
            (
            n
            )
          
        
        =
        
          
            ∑
            
              q
              =
              0
            
            Q
          
          ⁢
          
            
              ∑
              
                k
                =
                1
              
              K
            
            ⁢
            
              
                w
                kq
              
              ⁢
              
                
                  
                  
                    r
                    ⁡
                    
                      (
                      
                        n
                        -
                        q
                      
                      )
                    
                  
                  
                
                
                  k
                  -
                  1
                
              
              ⁢
              
                r
                ⁡
                
                  (
                  
                    n
                    -
                    q
                  
                  )
                
              
            
          
        
      
    
    
      
        [
        19
        ]
      
    
  




Let U be the number of observation samples. The above equation can be expressed in this form:

SUx1=HUxTWTx1  [20]

where

T=1⁄2(N+1)(Q+1)  [21]

S=[s(0)·g(0) s(1)·g(1) s(2)·g(2) s(3)·g(3) . . . s(U−1)·g(U−1)]T  [22]

H=[h10 h30 . . . hK0|h11 h31 . . . hK1| . . . |h1Q h3Q . . . hKQ]  [23]

hij=[sij(0)·g(0) sij(1)·g(1) sij(2)·g(1) sij(3)·g(3) . . . sij(U−1)·g(U−1)]T  [24]

and

W=[w10 w30 . . . wK0|w11 w31 . . . wK1| . . . |w1Q w3Q . . . wKQ]T  [25]

Note that the equation SUx1=HUxTWTx1 was modified to take into account the soft factor G. The normal equation [20] can be solved with QR method or Matrix inversion technique to estimate the coefficient set W.
The residue error for this estimation is:

E=∥SUx1−HUxT·ŴTx1∥2  [26]

where ŴTx1 is the computed weight vector.
Coefficient Averaging
After solving for the coefficients W(t) using samples taken at discrete times t (t=0, 1, 2, . . . ), the coefficient set can be expressed as:




  
    
      
        
          W
          ⁡
          
            (
            t
            )
          
        
        =
        
          [
          
            
              
                
                  
                    w
                    10
                  
                  ⁡
                  
                    (
                    t
                    )
                  
                
              
              
                
                  
                    w
                    11
                  
                  ⁡
                  
                    (
                    t
                    )
                  
                
              
              
                ...
              
              
                
                  
                    w
                    
                      1
                      ⁢
                      Q
                    
                  
                  ⁡
                  
                    (
                    t
                    )
                  
                
              
            
            
              
                
                  
                    w
                    20
                  
                  ⁡
                  
                    (
                    t
                    )
                  
                
              
              
                
                  
                    w
                    21
                  
                  ⁡
                  
                    (
                    t
                    )
                  
                
              
              
                ...
              
              
                
                  
                    w
                    
                      2
                      ⁢
                      Q
                    
                  
                  ⁡
                  
                    (
                    t
                    )
                  
                
              
            
            
              
                ...
              
              
                ...
              
              
                ...
              
              
                ...
              
            
            
              
                
                  
                    w
                    
                      K
                      ⁢
                      
                        
                      
                      ⁢
                      0
                    
                  
                  ⁡
                  
                    (
                    t
                    )
                  
                
              
              
                
                  
                    w
                    
                      K
                      ⁢
                      
                        
                      
                      ⁢
                      1
                    
                  
                  ⁡
                  
                    (
                    t
                    )
                  
                
              
              
                ...
              
              
                
                  
                    w
                    KQ
                  
                  ⁡
                  
                    (
                    t
                    )
                  
                
              
            
          
          ]
        
      
    
    
      
        [
        27
        ]
      
    
  




The phase of the fundamental component at DC is expressed as:




  
    
      
        
          
            θ
            1
          
          ⁡
          
            (
            t
            )
          
        
        =
        
          angle
          ⁡
          
            (
            
              
                ∑
                
                  q
                  =
                  0
                
                Q
              
              ⁢
              
                
                  w
                  
                    1
                    ⁢
                    q
                  
                
                ⁡
                
                  (
                  t
                  )
                
              
            
            )
          
        
      
    
    
      
        [
        28
        ]
      
    
  




It is necessary to maintain this fundamental component phase as zero to ensure that the DPD block does not provide phase rotation of the desired signal. Thus, the new coefficient set W2(t) is expressed as:




  
    
      
        
          
            W
            2
          
          ⁡
          
            (
            t
            )
          
        
        =
        
          
            [
            
              
                
                  
                    
                      w
                      10
                    
                    ⁡
                    
                      (
                      t
                      )
                    
                  
                
                
                  
                    
                      w
                      11
                    
                    ⁡
                    
                      (
                      t
                      )
                    
                  
                
                
                  ...
                
                
                  
                    
                      w
                      
                        1
                        ⁢
                        Q
                      
                    
                    ⁡
                    
                      (
                      t
                      )
                    
                  
                
              
              
                
                  
                    
                      w
                      20
                    
                    ⁡
                    
                      (
                      t
                      )
                    
                  
                
                
                  
                    
                      w
                      21
                    
                    ⁡
                    
                      (
                      t
                      )
                    
                  
                
                
                  ...
                
                
                  
                    
                      w
                      
                        2
                        ⁢
                        Q
                      
                    
                    ⁡
                    
                      (
                      t
                      )
                    
                  
                
              
              
                
                  ...
                
                
                  ...
                
                
                  ...
                
                
                  ...
                
              
              
                
                  
                    
                      w
                      
                        K
                        ⁢
                        
                          
                        
                        ⁢
                        0
                      
                    
                    ⁡
                    
                      (
                      t
                      )
                    
                  
                
                
                  
                    
                      w
                      
                        K
                        ⁢
                        
                          
                        
                        ⁢
                        1
                      
                    
                    ⁡
                    
                      (
                      t
                      )
                    
                  
                
                
                  ...
                
                
                  
                    
                      w
                      KQ
                    
                    ⁡
                    
                      (
                      t
                      )
                    
                  
                
              
            
            ]
          
          ⁢
          
            e
            
              
                -
                j
              
              ⁢
              
                
              
              ⁢
              
                
                  θ
                  1
                
                ⁡
                
                  (
                  t
                  )
                
              
            
          
        
      
    
    
      
        [
        29
        ]
      
    
  




Now, since all of the weights have the same fundamental component phase and are also highly correlated, the coefficients can be filtered to improve the signal to noise ratio. The filter coefficient set is expressed as:

W3(t+1)=(1−α)W3(t)+αW2(t+1)  [30]

where W2(t) is the coefficient set per data taken and W3(t) is the filtered coefficient set.
As noted above, the transmitter 12 (FIG. 1) can be modeled as a combination of multiple filters, where each filter is associated with an intermodulation order with its own amplitude, phase and delay, linearization may be achieved using multiple filters with weights designed to effect an inverse or reciprocal operation. Such that when the signal output by the DPD engine is processed by the power amplifier 20 of the transmitter 12 the performance of the transmitter 12 is improved with respect to the efficiency thereof. As the generation of the DPD coefficients is set forth above, these coefficients are utilized in the manner depicted in FIG. 6 to implement the DPD engine 100.
FIG. 6 is a simplified block diagram of a DPD engine implemented in accordance with an illustrative embodiment of the present teachings. As shown in FIG. 6, the engine 100 includes a complex finite impulse response (FIR) filter 110 with ‘Q’ taps. The amplitude of the input signal ‘x’ is computed at 108 by an absolute value operation. This signal is fed forward to a series of multipliers 160 . . . 180, each of which multiply the input signal by the output of the previous multiplier. As a result, a number of products are available each of which being a sample of the input signal raised to consecutive powers. Each of these products is fed to one of K tapped delay lines 140, 142, . . . 144. Each delay line has a Q+1 multipliers e.g., 146, 150, 154, . . . 158 and Q delay elements e.g., 148, 152, . . . 156. A plurality (Q) of summers or summation operations 132, 134, 136 . . . 138 are included. Those skilled in the art will appreciate that the engine 100 depicted in FIG. 6 utilizes the coefficients generated above in accordance with equations [1]-[30] above to provide predistorted input signals to effect linearization of the operation of the transmitter 12 as discussed herein.
The devices and subsystems of the exemplary embodiments of FIGS. 1-6 can include computer readable medium or memories for holding instructions programmed according to the teachings of the present invention and for holding data structures, tables, records, and/or other data described herein. Computer readable medium can include any suitable medium that participates in providing instructions to a processor for execution. Such a medium can take many forms, including but not limited to, non-volatile media, volatile media, etc. Non-volatile media can include, for example, optical or magnetic disks, magneto-optical disks, and the like. Volatile media can include dynamic memories, and the like. Transmission media can include coaxial cables, copper wire, fiber optics, and the like. Common forms of computer-readable media can include, for example, a floppy disk, a flexible disk, hard disk, magnetic tape, any other suitable magnetic medium, a CD-ROM, CDRW, DVD, any other suitable optical medium, a RAM, a PROM, an EPROM, a FLASH-EPROM, any other suitable memory chip or cartridge, or any other suitable medium from which a computer can read.
While the present inventions have been described in connection with a number of exemplary embodiments, and implementations, the present inventions are not so limited, but rather cover various modifications, and equivalent arrangements, which fall within the purview of the appended claims.

## Claims

1. A method for stabilizing a coefficient set used by a digital predistortion (DPD) engine to apply pre-distortion to a transmit signal and cancel distortion generated by a distorting element or distorting system when transmitting the transmit signal, the method comprising:
obtaining an initial coefficient set;
rotating the initial coefficient set to maintain a phase of fundamental components (w10(t), . . . , w1Q(t)) of the initial coefficient set as a constant value;
averaging in the time domain the rotated coefficient set to obtain an averaged coefficient set;
applying the averaged coefficient set to the DPD engine,
the initial coefficient set expressed as





  
    
      W
      ⁡
      
        (
        t
        )
      
    
    =
    
      [
      
        
          
            
              
                w
                10
              
              ⁡
              
                (
                t
                )
              
            
          
          
            
              
                w
                11
              
              ⁡
              
                (
                t
                )
              
            
          
          
            ...
          
          
            
              
                w
                
                  1
                  ⁢
                  Q
                
              
              ⁡
              
                (
                t
                )
              
            
          
        
        
          
            
              
                w
                20
              
              ⁡
              
                (
                t
                )
              
            
          
          
            
              
                w
                21
              
              ⁡
              
                (
                t
                )
              
            
          
          
            ...
          
          
            
              
                w
                
                  2
                  ⁢
                  Q
                
              
              ⁡
              
                (
                t
                )
              
            
          
        
        
          
            ...
          
          
            ...
          
          
            ...
          
          
            ...
          
        
        
          
            
              
                w
                
                  K
                  ⁢
                  
                    
                  
                  ⁢
                  0
                
              
              ⁡
              
                (
                t
                )
              
            
          
          
            
              
                w
                
                  K
                  ⁢
                  
                    
                  
                  ⁢
                  1
                
              
              ⁡
              
                (
                t
                )
              
            
          
          
            ...
          
          
            
              
                w
                KQ
              
              ⁡
              
                (
                t
                )
              
            
          
        
      
      ]
    
  
  ;



computing the phase of the fundamental components of the initial coefficient set as





  
    
      
        θ
        1
      
      ⁡
      
        (
        t
        )
      
    
    =
    
      angle
      ⁡
      
        (
        
          
            ∑
            
              q
              =
              0
            
            Q
          
          ⁢
          
            
              w
              
                1
                ⁢
                q
              
            
            ⁡
            
              (
              t
              )
            
          
        
        )
      
    
  
  ;
  and



computing the rotated coefficient set as





  
    
      W
      2
    
    ⁡
    
      (
      t
      )
    
  
  =
  
    
      [
      
        
          
            
              
                w
                10
              
              ⁡
              
                (
                t
                )
              
            
          
          
            
              
                w
                11
              
              ⁡
              
                (
                t
                )
              
            
          
          
            ...
          
          
            
              
                w
                
                  1
                  ⁢
                  Q
                
              
              ⁡
              
                (
                t
                )
              
            
          
        
        
          
            
              
                w
                20
              
              ⁡
              
                (
                t
                )
              
            
          
          
            
              
                w
                21
              
              ⁡
              
                (
                t
                )
              
            
          
          
            ...
          
          
            
              
                w
                
                  2
                  ⁢
                  Q
                
              
              ⁡
              
                (
                t
                )
              
            
          
        
        
          
            ...
          
          
            ...
          
          
            ...
          
          
            ...
          
        
        
          
            
              
                w
                
                  K
                  ⁢
                  
                    
                  
                  ⁢
                  0
                
              
              ⁡
              
                (
                t
                )
              
            
          
          
            
              
                w
                
                  K
                  ⁢
                  
                    
                  
                  ⁢
                  1
                
              
              ⁡
              
                (
                t
                )
              
            
          
          
            ...
          
          
            
              
                w
                KQ
              
              ⁡
              
                (
                t
                )
              
            
          
        
      
      ]
    
    ⁢
    
      
        e
        
          -
          
            
              jθ
              1
            
            ⁡
            
              (
              t
              )
            
          
        
      
      .

2. The method of claim 1, further comprising averaging the rotated coefficient set by computing an average of a current rotated coefficient set and a previous rotated coefficient set.

3. The method of claim 1, further comprising computing a current weighted averaged rotated coefficient set W3(t+1) from the current rotated coefficient set and the previous weighted averaged rotated coefficient set according to the equation


W3(t+1)=(1−α)W3(t)+αW2(t+1),

wherein W2(t+1) is the current rotated coefficient set, W3(t) is the previous weighted averaged rotated coefficient set, and α is a weighting factor, 0≦α≦1.

4. A system for stabilizing a coefficient set used by a digital predistortion (DPD) engine to apply pre-distortion to a transmit signal and cancel distortion generated by a distorting element or distorting system when transmitting the transmit signal, the system comprising:
means for obtaining an initial coefficient set;
means for rotating the initial coefficient set to maintain a phase of fundamental components (w10(t), . . . , w1Q(t)) of the initial coefficient set as a constant value;
means for averaging in the time domain the rotated coefficient set to obtain an averaged coefficient set;
means for applying the averaged coefficient set to the DPD engine,
the initial coefficient set expressed as





  
    
      W
      ⁡
      
        (
        t
        )
      
    
    =
    
      [
      
        
          
            
              
                w
                10
              
              ⁡
              
                (
                t
                )
              
            
          
          
            
              
                w
                11
              
              ⁡
              
                (
                t
                )
              
            
          
          
            ...
          
          
            
              
                w
                
                  1
                  ⁢
                  Q
                
              
              ⁡
              
                (
                t
                )
              
            
          
        
        
          
            
              
                w
                20
              
              ⁡
              
                (
                t
                )
              
            
          
          
            
              
                w
                21
              
              ⁡
              
                (
                t
                )
              
            
          
          
            ...
          
          
            
              
                w
                
                  2
                  ⁢
                  Q
                
              
              ⁡
              
                (
                t
                )
              
            
          
        
        
          
            ...
          
          
            ...
          
          
            ...
          
          
            ...
          
        
        
          
            
              
                w
                
                  K
                  ⁢
                  
                    
                  
                  ⁢
                  0
                
              
              ⁡
              
                (
                t
                )
              
            
          
          
            
              
                w
                
                  K
                  ⁢
                  
                    
                  
                  ⁢
                  1
                
              
              ⁢
              
                
              
              ⁢
              
                (
                t
                )
              
            
          
          
            ...
          
          
            
              
                w
                KQ
              
              ⁢
              
                
              
              ⁢
              
                (
                t
                )
              
            
          
        
      
      ]
    
  
  ;



means for computing the phase of the fundamental components of the initial coefficient set as





  
    
      
        θ
        1
      
      ⁡
      
        (
        t
        )
      
    
    =
    
      angle
      ⁡
      
        (
        
          
            ∑
            
              q
              =
              0
            
            
              Q
              ⁢
              
                
              
            
          
          ⁢
          
            
              w
              
                1
                ⁢
                q
              
            
            ⁡
            
              (
              t
              )
            
          
        
        )
      
    
  
  ;
  and



means for computing the rotated coefficient set as





  
    
      W
      2
    
    ⁡
    
      (
      t
      )
    
  
  =
  
    
      [
      
        
          
            
              
                w
                10
              
              ⁡
              
                (
                t
                )
              
            
          
          
            
              
                w
                11
              
              ⁡
              
                (
                t
                )
              
            
          
          
            ...
          
          
            
              
                w
                
                  1
                  ⁢
                  Q
                
              
              ⁡
              
                (
                t
                )
              
            
          
        
        
          
            
              
                w
                20
              
              ⁡
              
                (
                t
                )
              
            
          
          
            
              
                w
                21
              
              ⁡
              
                (
                t
                )
              
            
          
          
            ...
          
          
            
              
                w
                
                  2
                  ⁢
                  Q
                
              
              ⁡
              
                (
                t
                )
              
            
          
        
        
          
            ...
          
          
            ...
          
          
            ...
          
          
            ...
          
        
        
          
            
              
                w
                
                  K
                  ⁢
                  
                    
                  
                  ⁢
                  0
                
              
              ⁡
              
                (
                t
                )
              
            
          
          
            
              
                w
                
                  K
                  ⁢
                  
                    
                  
                  ⁢
                  1
                
              
              ⁡
              
                (
                t
                )
              
            
          
          
            ...
          
          
            
              
                w
                KQ
              
              ⁢
              
                
              
              ⁢
              
                (
                t
                )
              
            
          
        
      
      ]
    
    ⁢
    
      
        e
        
          
            -
            j
          
          ⁢
          
            
          
          ⁢
          
            
              θ
              1
            
            ⁡
            
              (
              t
              )
            
          
        
      
      .

5. The system of claim 4, further comprising means for averaging the rotated coefficient set by computing an average of a current rotated coefficient set and a previous rotated coefficient set.

6. The system of claim 4, further comprising means for computing a current weighted averaged rotated coefficient set W3(t+1) from the current rotated coefficient set and the previous weighted averaged rotated coefficient set according to the equation


W3(t+1)=(1−α)W3(t)+αW2(t+1),

wherein W2(t+1) is the current rotated coefficient set, W3(t) is the previous weighted averaged rotated coefficient set, and α is a weighting factor, 0≦α≦1.

7. A method for generating a coefficient set with improved accuracy, the coefficient set used by a digital predistortion (DPD) engine to apply pre-distortion to a transmit signal and cancel distortion generated by a distorting element or distorting system when transmitting the transmit signal, the method comprising:
selecting samples from a pre-distorted transmit signal from the DPD engine exceeding a predetermined threshold;
zeroing the selected samples from the transmit signal and the corresponding row of the “H” matrix of the distorting element or distorting system;
computing a coefficient set from the transmit signal and the delayed feedback signal with the selected samples removed,
the pre-distorted transmit signal having samples S represented as


S=[s(0) s(1) s(2) s(3) . . . s(U−1)]T;


defining a soft factor vector as


G=[g(0) g(1) g(2) g(3) . . . g(U−1)]T 


where
g(i)=1 for |s(i)|<T2, g(i)=0 otherwise, and T2 is the predetermined threshold; and
if g(i)=0, zeroing an ith sample of S and zeroing an ith row of the H matrix.

8. A system for generating a coefficient set with improved accuracy, the coefficient set used by a digital predistortion (DPD) engine to apply pre-distortion to a transmit signal and cancel distortion generated by a distorting element or distorting system when transmitting the transmit signal, the system comprising:
means for selecting samples from a pre-distorted transmit signal from the DPD engine exceeding a predetermined threshold;
means for zeroing the selected samples from the transmit signal and the corresponding row of the “H” matrix of the distorting element or distorting system;
means for computing a coefficient set from the transmit signal and the delayed feedback signal with the selected samples removed,
the pre-distorted transmit signal having samples S represented as


S=[s(0) s(1) s(2) s(3) . . . s(U−1)]T;


means for defining a soft factor vector as


G=[g(0) g(1) g(2) g(3) . . . g(U−1)]T 


where
g(i)=1 for |s(i)|<T2, g(i)=0 otherwise, and T2 is the predetermined threshold; and
if g(i)=0, zeroing an ith sample of S and zeroing an ith row of the H matrix.