Abstract:
A Wideband Code-Division Multiple Access (WCDMA) transceiver and a method of operating the same. In one embodiment, the transceiver includes: (1) a transmit chain having a lookup table that provides coefficients to a digital predistorter based on power indicators and (2) a predistorter training circuit, coupled to the transmit chain, that employs a receive chain of the WCDMA transceiver to provide a digital compensation signal that is a function of an output of the transmit chain and employs both the power indicators and the digital compensation signal to cause the lookup table to provide alternative coefficients to the digital predistorter thereby to reduce distortion in the output.

Description:
TECHNICAL FIELD OF THE INVENTION 
   The present invention is directed, in general, to wireless communications and, more specifically, to a digital predistortion technique for a Wideband Code-Division Multiple Access (WCDMA) wireless communication system and method of operating the same. 
   BACKGROUND OF THE INVENTION 
   The Wideband Code-Division Multiple Access (WCDMA) standard has been widely adopted in several third generation (3G) mobile communication systems. One major design challenge in the WCDMA transmitter, both for a mobile terminal and a workstation, is to improve the linearity and efficiency of the power amplifier (PA). This can be due to the non-constant envelope modulation and the multi-code scheme used in WCDMA. Nonlinear PA causes spectrum regrowth which results in significant adjacent channel interference (ACI). At present, the state-of-art linear PAs for the wideband applications provide about −40 dB adjacent channel power reduction (ACPR) at 5 MHz and −50 dB at 10 MHz, which fails to fulfill the 3G requirement on the output spectral mask. However, this gap can hardly be solved by PA back-off which will cause severe losses in power efficiency. 
   The third generation wireless systems place much more difficult linearity and efficiency requirements for the RF front-end. The linearity constraint is due to tighter output spectral mask specification, higher signal envelope variations (linear modulation), and, in the case of the PA, the need to keep the operation level near the compression point in order to achieve a high enough efficiency. In addition, when multi-code transmission is applied, more backoff is needed, causing a loss of efficiency. Linearization techniques are considered as one possible solution to overcome the tightened spectral mask requirements with acceptable amplifier efficiency. 
   Linearization techniques can be divided into four main categories: (1) feedforward, (2) feedback, (3) envelope elimination and restoration, and (4) predistortion. Each of these have a set of variants providing different implementation complexity, adjacent channel interference (ACI) improvements, and bandwidth/convergence rates. 
   The first three categories are suited for analog implementation. Feedforward can, in theory, completely eliminate the inter-modulation distortion, but the key problem of this scheme is the need of perfect gain and phase match between the two signal paths. The complexity of this scheme is quite large and the total efficiency is drained due to losses in the main path delay, the couplers and the auxiliary amplifier. Among the various feedback techniques, Cartesian feedback is most prominent and thoroughly studied. It has been proven to work for wideband applications. Polar modulation feedback is most suitable for narrowband systems. The power efficiency of these techniques is low for low input levels. Moreover, the complexity of these schemes is also quite high. 
   In the envelope elimination and restoration scheme, a modulated intermediate frequency (IF) signal is split into its polar components. The constant-envelope IF signal is translated to RF with a mixer and amplified to a level forcing the power amplifier to saturate. The envelope is restored by modulating the supply voltage to the power amplifier with the detected IF envelope. For more information, please see L. Sundstrom, “Digital RF Power Amplifier Linearisers—Analysis and Design,”  Dissertation for the degree of Ph.D , LUTEDX/(TETE-1013)/1–150(1995), Lund university, Sweden, August 1995, which is hereby incorporated by reference in its entirety. 
   Predistortion can be realized at baseband by the DSP techniques or at RF with nonlinear devices. Digital baseband solution is usually preferred, since it is better suited for tracking any possible change in PA parameters. Mapping predistortion has been proposed, using a huge two-dimensional table. The more memory efficient scheme is the complex gain predistortion which has a one-dimensional table and can compensate phase invariant nonlinearities. Adaptive algorithm is frequently used for tracking the variations of the PA parameters. It requires large computing power and a dedicated feedback loop. Available research shows that it is suited for narrowband systems only. 
   Accordingly, what is needed in the art is a WCDMA transceiver which employs linearization techniques that overcome the limitations of the prior art. 
   SUMMARY OF THE INVENTION 
   To address the above-discussed deficiencies of the prior art, the present invention provides a WCDMA transceiver and a method of operating the same. In one embodiment, the transceiver includes: (1) a transmit chain having a lookup table that provides coefficients to a digital predistorter based on power indicators and (2) a predistorter training circuit, coupled to the transmit chain, that employs a receive chain of the WCDMA transceiver to provide a digital compensation signal that is a function of an output of the transmit chain and employs both the power indicators and the digital compensation signal to cause the lookup table to provide alternative coefficients to the digital predistorter thereby to reduce distortion in the output. 
   The present invention therefore introduces the broad concept of employing the receive chain, instead of dedicated hardware, to create a closed feedback loop designed to reduce distortion in the output of a WCDMA transceiver. 
   In one embodiment of the present invention, the transmit chain includes: (1) an interpolator coupled to an output of the digital predistorter, (2) a digital to analog converter coupled to an output of the interpolator, (3) a low pass filter coupled to an output of the digital to analog converter, (4) a quadrature modulator coupled to an output of the low pass filter and (5) an amplifier coupled to an output of the quadrature modulator. The structure and operation of an exemplary transmit chain will be set forth in detail in the Detailed Description that follows. Those skilled in pertinent art will understand, however, that alternative transmit chain architectures are within the broad scope of the present invention. 
   In one embodiment of the present invention, the receive chain includes: (1) a quadrature de-modulator, (2) a low pass filter coupled to an output of the quadrature de-modulator and (3) an analog to digital converter coupled to an output of the low pass filter. The structure and operation of an exemplary receive chain will be set forth in detail in the Detailed Description that follows. Those skilled in pertinent art will understand, however, that alternative receive chain architectures are within the broad scope of the present invention. 
   In one embodiment of the present invention, the predistorter training circuit comprises a coefficient update circuit to generate alternative power indicators for the lookup table. In a more specific embodiment, the power indicators include both real and quadrature components. Those skilled in the pertinent art will understand that alternative architectures may call for the generation of alternative forms of power indicators. 
   In one embodiment of the present invention, the predistorter training circuit operates only in a training mode. Alternatively, the predistorter training circuit may operate while the transceiver is in its normal transmit mode. 
   In one embodiment of the present invention, a root-raised cosine circuit provides the power indicator. Though the present invention is not so limited, those skilled in the pertinent art are familiar with root-raised cosine circuits and their operation. 
   The foregoing has outlined, rather broadly, preferred and alternative features of the present invention so that those skilled in the art may better understand the detailed description of the invention that follows. Additional features of the invention will be described hereinafter that form the subject of the claims of the invention. Those skilled in the art should appreciate that they can readily use the disclosed conception and specific embodiment as a basis for designing or modifying other structures for carrying out the same purposes of the present invention. Those skilled in the art should also realize that such equivalent constructions do not depart from the spirit and scope of the invention in its broadest form. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     For a more complete understanding of the present invention, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which: 
       FIG. 1  illustrates a transmit channel which is one environment in which the present invention may operate; 
       FIG. 2  illustrates one embodiment of a pre-distortion system which utilizes a receive chain as a feedback loop for altering pre-distortion coefficients; and 
       FIG. 3  illustrates a method of reducing distortion in an output of a WCDMA transceiver employing the principles of the present invention. 
   

   DETAILED DESCRIPTION 
   Referring initially to  FIG. 1 , illustrated is a transmit channel  100  of a transceiver which embodies one environment in which the present invention may operate. Briefly, the transmit channel  100  may have a channel multiplexer  110 , which multiplexes, or combines, various output signals. The channel multiplexer is connected to a spreader  120 , which performs such functionality as preparing the output signal for a spread-spectrum transmission. Coupled to the spreader  120  is a pulse shaper  130 . The pulse shaper  130  may be a filter, such as a raised root cosine (RRC) filter, although those skilled in the art should understand that any appropriate filter may be used. 
   After the pulse shaper  130 , a connected digital predistorter  140  (“predistorter  140 ”) is then employed. Predistortion can be realized at baseband by using DSP techniques, or alternatively at radio frequency by using the non-linear characteristics of an analog predistorter. The predistorter  140  is generally responsible for compensating for non-linearities which may be introduced into the system, such as by a power amplifier (PA)  180 . In the present embodiment, digital base-band solution is preferred, since it is better suited for tracking any possible change in the PA parameters. The predistorter  140  will be described in more detail at a later point. 
   After the output signal has been processed by the predistorter  140 , it is then transformed into the analog output signal in a digital to analog converter (DAC)  150 . Uses and applications of DACs are well known to those skilled in the art, and will therefore not be described in more detail. 
   Once the output signal has been converted into analog form by the DAC  150 , the output signal is then filtered by an analog low pass filter (LPF)  160 . The analog LPF  160  may be a Butterworth filter. After being filtered by the analog low pass filter  160 , the output signal is then modulated by an RF modulator  170 . The RF modulator  170  may perform such functionality as QAM modulation. 
   After the RF modulator  170  has performed, the PA  180  is employed for such purposes as to increase the power of the transmitted signal. The PA  180  may be typically operated at close to saturation to help ensure effective utilization of the PA  180 . However, operation in such as the above manner may lead to various non-linearities within the transmit channel  100 . Finally, after the PA  180  has been employed, the amplified output signal may be broadcasted by the antenna  190 . 
   Turning now to  FIG. 2 , illustrated is one embodiment of a predistortion system  200  which utilizes a receive chain as a feedback loop for altering pre-distortion coefficients. One goal of the predistortion system  200  is to provide a simple but efficient digital baseband linearization method suited for the WCDMA transmit channel  100 . A concern in implementing the predistortion system  200  is how to implement a feedback loop needed for tracking the change in the PA parameters. A dedicated feedback loop would be nice for this purpose, but it will substantially increase the overall complexity. 
   In the illustrated embodiment of the predistortion system  200 , one around the dilemma of a dedicated feedback loop is to take advantage of a compressed mode of protocol, such as a Universal Mobile Telecommunications System (UMTS) protocol. In UTMS, a transmission gap (TG) may be inserted periodically or upon a request basis during the normal traffic mode upon a transmit chain  205 . This TG may then be employed by a receive chain  207  and the receive chain  207  will serve as the feedback loop temporarily. 
   In a “normal transmission” mode the transmit train  205  works alone, separate from the receive chain  207 . The transmit chain  205  has an RRC filter  210 , a digital predistorter  220  (“predistorter  220 ”), a lookup table which forms a basis for the digital predistortion functionality of the predistorter  220 , an interpolator  230 , a DAC  240 , a LPF  250 , a quadrature modulator  255 , and a power amplifier  260 . A list of complex numbers is stored in the lookup table  225 , addressed by the power of the input signal. 
   More specifically, in the predistortion system  200 , the output of the DAC  240  is fed into the LPF  250  which may generally act as an anti-aliasing filter to remove the images at integer multiples of sampling frequency. As addressed in J. Yiin, “CPS4: GSM/UMTS Baseband Mixed-Signal chip”, Lucent Technologies internal document, V0.9, Apr. 27, 2000, (which is hereby incorporated by reference in its entirety) the LPF  250  with cutoff frequency around 3.0 MHz would be desirable for this purpose and also for limiting the out-of-band noise. 
   The adoption of the predistorter  220  calls for the LPF  250  with much larger cut-off frequency than normally used in configurations without predistortion. Since the predistorter  220  is basically a nonlinear component, the baseband signal at the predistorter  220  output will have much larger bandwidth than the incoming signal. In order to achieve the best effects on reducing ACI, the LPF  250  must leave the desired harmonics in the distorter  220  output intact for the next stage, which requires the cut-off frequency be as large as possible. (On the other hand, the LPF  250  still needs to fulfil the task of removing the images at integer multiples of sampling frequency, which makes a smaller cutoff frequency more desirable.) 
   The transmit chain  205  is then coupled to a coupler  265  which may be coupled to an antenna  267 . Where appropriate, the various elements of the transmit train  205 , such as the predistorter  220  and the lookup table  225 , will be described in more detail below. 
   During a “training” mode of operation, however, (to be described in more detail below) for the predistorter  220 , the transmit chain  205  and the receive chain  207  cooperate through the use of the coupler  265  to form a loop through the receive train  207 , and the antenna  267  is disconnected from the transmit chain  205 . 
   The receive train  207  has a quadrature demodulator  270 , which extracts incoming information and demodulates the signal into a single one-dimensional analog value. This demodulated analog signal then passes through an LPF  275 , perhaps a Butterworth filter, and then is converted into digital form by an analog to digital converter (ADC)  280 . Finally, the now digital coefficients corresponding to the demodulated signal are received by a training circuit  290 , which may then update the lookup table  225  with appropriate and/or alternative coefficients, as a function of the output of the transmit train  205 , through a digital compensation signal to reduce distortion in the output of the PA  260 , in a manner also to be described in more detail below. The training circuit  290  would generally operate only when the predistortion system  200  is in training mode. The training circuit  290  employs both the “in phase I” and “quadrature Q” (i.e. the “power indicators” have a real and quadrature component) information of the signal input to calculate the proper alternative coefficients for the lookup table  225 . 
   However, since the measured PA  260  transfer function is actually an approximation of the entire feedback loop (and the transfer function expresses any nonlinearities), all of the nonlinearity in the transmit train  205  can be compensated, in theory, by the predistorter  220 , while the nonideality in the receive channel will be emphasized by the predistorter  220  due to the estimation error. This may suggest that the linearity requirements for the receive chain  207  should be more stringent for the sake of accurate PA  260  estimation. Adaptation is achieved by the recurrence of the training interval, considering the fact that the temperature and time variations of the PA parameters are generally very slow. 
   Predistortion of the predistortion system  200  is generally performed by multiplying a source signal for transmission by complex gain factors obtained from the lookup table  225  (which is pre-calculated during the training period) within the predistorter  220 . In one embodiment of the present invention, a “training sequence” (to be described later on in more detail) is injected into the transmit chain  105  between the spreader  120  and the pulse shaper  130  (perhaps employing the RRC filter  210 ), during the training interval. The output of the RRC filter  210  is then stored in RAM and will be referred to as the input signal. The input signal is then predistorted by the predistorter  220  using predistortion coefficients stored in the lookup table  225  which were obtained during last training period before transmission. For the first training period, the coefficients within the lookup table  225  can be set to “1” or any reasonable number for use by the predistorter  220 . 
   In other words, after the entire training sequence has been transmitted and detected, the nonlinear characteristics of the PA  260  can be calculated by the training circuit  290 , using methods to be revealed below. The training circuit  290  is then employed to update the alternative predistortion coefficients through the digital compensation signal to cause the lookup table  225  to provide alternative coefficients to the predistorter  220 . The lookup table  225  employs the power indicators I 2  plus Q 2 . Interpolation by the interpolator  230  is used to lessen the requirements for the LPF  250 . 
   More specifically, an output of the RRC filter  210  is stored in RAM and will be used as the reference signal for the PA  260  signal distortion estimation when comparing the output training signal of the RRC filter  210  to the input of the training circuit  290 . For simplicity, the training sequence is injected into the transmit chain  100  between the spreader  120  and the pulse shaper  130 , perhaps employing the RRC filter  210 . 
   The training chip sequence should be designed such that the output of RRC sweeps the entire dynamic range of the PA  180  in magnitude. Such sequences are obtained by a random search. Each of the sequence in Table I is selected from 100,000 randomly generated sequences. Each time a random sequence is generated, the corresponding RRC filter  210  output and the power density function (PDF) of the output signal power are calculated by the transmit channel  100 . Only the sequence which minimizes the variance of the PDF is chosen. After generation, a window function is also applied by the training circuit  290  to smooth the coefficients. The window function [¼ ½ ¼] may be used for the first half of the table where the coefficients are typically very close to each other and the window function [−⅛ ⅜ ½ ⅜ −⅛] may be used for the rest where rapid changes may be present. The boundary points are adjusted so that the first entry has zero phase and the last one has a magnitude of 1. One such table of random training sequences is given below: 
   
     
       
             
           
             
             
             
           
         
             
               TABLE 1 
             
           
           
             
                 
             
             
               TRAINING SEQUENCES OF DIFFERENT LENGTHS 
             
           
        
         
             
               Number 
                 
                 
             
             
               of 
                 
                 
             
             
               Chips 
               I channel 
               Q channel 
             
             
                 
             
             
               10 
               0 19 32 −19 18 92 
               0 96 −32 −69 15 
             
             
                 
               −51 22 −72 0 
               1 100 −78 −69 0 
             
             
               20 
               0 92 21 39 37 −58 
               0 54 28 −18 −44 
             
             
                 
               −57 −57 −58 −93 
               59 79 −43 90 7 
             
             
                 
               87 −47 54 54 28 5 
               30 2 −91 −43 24 
             
             
                 
               95 −79 50 0 
               −79 −38 −78 −59 0 
             
             
               30 
               0 87 26 17 −27 50 
               0 −67 −15 −84 85 
             
             
                 
               91 20 −69 1 −82 82 
               −21 81 −56 78 −47 
             
             
                 
               88 −16 −48 −14 −72 
               86 −40 52 3 29 −65 
             
             
                 
               −20 29 96 −36 10 −8 
               −99 −52 68 50 −47 
             
             
                 
               49 77 −49 76 −59 
               −35 8 12 −8 76 −61 
             
             
                 
               −30 0 
               21 32 0 
             
             
               40 
               0 19 32 −19 18 92 
               0 96 −32 −96 15 1 
             
             
                 
               −51 22 −72 0 0 87 
               100 −78 −69 0 0 
             
             
                 
               26 17 −17 50 91 
               −67 −15 −84 85 −21 
             
             
                 
               26 17 −82 82 88 
               81 −56 78 −47 86 
             
             
                 
               −16 −48 −14 −72 
               −40 52 37 29 −65 
             
             
                 
               −20 96 −36 10 −8 
               −99 31 52 68 50 −47 
             
             
                 
               49 77 −49 76 −59 
               −35 8 12 −8 76 
             
             
                 
               −30 0 
               −61 −21 32 0 
             
             
                 
             
           
        
       
     
   
   Now the characteristics, functionality and interplay between and among the transmit chain  205  and the training circuit  290  shall be described in more detail. As a prerequisite to this discussion, let the input signal to the PA  260  be described by:
 
 x ( t )= r ( t )cos( w   0   t +φ( t ))
 
where w 0  is the carrier frequency, and r(t) and φ(t) are a modulated envelope and phase, respectively.
 
   In an amplitude-phase model, the corresponding output is written as:
 
 y ( t )= A ( r ( t ))cos{ w   0   t +φ( t )+Φ( r ( t ))},
 
where A(r(t)) is an odd function of r, with a linear leading term representing amplitude-to-amplitude (AM-AM) conversion, and Φ(R) is an even function of r, with a quadratic leading term representing amplitude-to-phase (AM-PM) conversion. In literature (A. Saleh, “Frequency-Independent and Frequency-Dependent Nonlinear Models of TWT Amplifiers,”  IEEE Trans. On Commun ., Vol. 29, No. 11, pp 1715–1720, November, 1981, (which is hereby incorporated by reference in its entirety), two-parameter formulas are frequently used to model power amplifier characteristics:
 
 A ( r )=α a   r /(1+β α   r   2 ), Φ( r )=α φ   r   2 /(1+β φ   r   2 ).
 
   The parameters are determined by the specific PA  260  to be modelled. The time varying nature is not accounted for here because the variation is assumed to be very slow as compared to the updating period. 
   To further elaborate upon the above, the predistorter  220  compensates for the nonlinearity of the PA  260 , but the predistorter  220  should be supplied with the proper predistortion coefficients. The overall performance gain achieved by predistortion of the predistorter  220  is determined by the accuracy of PA  260  distortion estimation by the training circuit  290 . One goal of the present invention is to obtain the coefficients for predistortion for use of the predistorter  220 , which requires the inverse of the PA  260  transfer function, calculated by the training circuit  290  and the results thereof stored in the lookup table  225 . One of the following two procedures may be used, that is, that of estimating the PA  260  transfer function first followed by computing the PA  260  inverse, or estimating the PA  260  inverse directly. 
   AM-AM and AM-PM conversions directly obtained from the input and output signal are distorted because of errors caused by quantization and other nonidealities. A curve-fitting method has to be used to reconstruct the PA  260  characteristics more accurately and smoothly. 
   In this two-step procedure of estimating the PA  260  characteristics, the characteristics are first reconstructed by using a polynomial model, then the inverse of the PA  260  transfer function is solved by the training circuit  290  for filling up the lookup table  225 . 
   The curve-fitting method from H. Lai and Y Bar-Ness, “Minimum Distortion Power Polynomial Model (MDP-PM) of Nonlinear Power Amplifiers and Its Application to Analog Predistorters,” VTC &#39;99 Fall, Amsterdam, The Netherland, pp. 1501–1505, September 1999 (which is incorporated by reference in its entirety] where a polynomial model is used. In this model, the relationship between the input and output signal for any given time t is given by
 
 V   0 ( t )= V   i ( t ){Σ k=1   K α 2k−1   |V   i ( t )| 2k−2   }+V   e ( t )
 
(2) where V i (t) and V O (t) are the input and output signal at time t, respectively, and V e (t) is the error signal. The value of K defines the order of the polynomial used for reconstruction, i.e., 2K−1. Normally, K=3 is enough, which corresponds to a 5th order polynomial. The coefficients α&#39;s will be determined by curve-fitting, using the minimum distortion power criterion of H. Lai and Y. Bar-Ness, where the power of the error signal V e  is minimized.
 
Define
 
             α   =         [           α   1                 α   3     ,             ⋯             α       2   ⁢   K     -   1             ]     ⁢           ⁢     V   i       =     [             V   i     ⁡     (     t   1     )                   V   i     ⁡     (     t   2     )               ⋯               V   i     ⁡     (     t   n     )             ]         ,       V   o     =     [             V   o     ⁡     (     t   1     )                   V   o     ⁡     (     t   2     )               ⋯               V   o     ⁡     (     t   n     )             ]       ,     
     ⁢       V   I     =     [                 V   i     ⁡     (     t   1     )       ⁢       V   i     ⁡     (     t   1     )       ⁢              V   i     ⁡     (     t   1     )            2     ⁢           ⁢   ⋯   ⁢           ⁢       V   i     ⁡     (     t   1     )       ⁢              V   i     ⁡     (     t   1     )                2   ⁢   K     -   2         ⁢                           V   i     ⁡     (     t   2     )       ⁢       V   i     ⁡     (     t   2     )       ⁢              V   i     ⁡     (     t   2     )            2     ⁢           ⁢   ⋯   ⁢           ⁢       V   i     ⁡     (     t   2     )       ⁢              V   i     ⁡     (     t   2     )                2   ⁢   K     -   2                 ⋯                 V   i     ⁡     (     t   n     )       ⁢       V   i     ⁡     (     t   n     )       ⁢              V   i     ⁡     (     t   n     )            2     ⁢           ⁢   ⋯   ⁢           ⁢       V   i     ⁡     (     t   n     )       ⁢              V   i     ⁡     (     t   n     )                2   ⁢   K     -   2               ]             
where n is the number of samples in the input/output signals. It is proved that the solution
 α=( V   I   H   V   I ) −1 ( V   I   H   V   O ) 
minimizes the distortion power.
 
   To realize the predistorter  220 , it is necessary to know what is the appropriate predistorted signal for the desired output. In other words, the inverse of the estimated PA transfer function which is a polynomial must be derived. This is not easy because there is no general way of solving high-order (the order is 5 in our case for K=3) polynomial equations efficiently. Typically, an iterative method can be used to solve this problem:
 
 V   i   (l) ( t )= V   O ( t )/{Σ k=1   K α 2k−1   |V   i   (l−1) ( t )| 2k−2 } at iteration l.
 
   The number of iterations needed is dependent on the slope of the AM-AM curve at the operation point. For the operation point near saturation, the slope is flat, which leads to a relatively large number of iterations (about 6). Of course, if the initial value is close enough to the correct solution, two or three iterations are enough. The initial value can be pre-calculated and stored. Another possible way is to use the value obtained in the last training period and, therefore, only one or two iterations may be needed assuming the variation of the PA parameters is slow compared with the updating period. These calculations would be typically performed within the training circuit  290 , and the training circuit  290  then uses the above values to further determine the coefficients stored within the lookup table  225  for use by the predistorter  220 . 
   However, The two-step solution discussed above is computationally power consuming since we need to repeat this process for each of the table entries. To save computation power, a one-step solution may also be used. Actually, the inverse of PA  260  transfer function can be estimated directly by the same curve-fitting method. One needs only to exchange the input and output in the above equations. Assume the polynomial model
 
 V   i ( t )= V   o ( t ){Σ k=1   K β 2k−1   |V   o ( t )| 2k−2   }+V   e ( t )
         define       

             β   =         [           β   1               β   ,             ⋯             β       2   ⁢   K     -   1             ]     ⁢           ⁢     V   i       =     [             V   i     ⁡     (     t   1     )                   V   i     ⁡     (     t   2     )               ⋯               V   i     ⁡     (     t   n     )             ]         ,     
     ⁢       V   o     =     [                 V   o     ⁡     (     t   1     )       ⁢       V   o     ⁡     (     t   1     )       ⁢              V   o     ⁡     (     t   1     )            2     ⁢           ⁢   ⋯   ⁢           ⁢       V   o     ⁡     (     t   1     )       ⁢              V   o     ⁡     (     t   1     )                2   ⁢   K     -   2         ⁢                           V   o     ⁡     (     t   2     )       ⁢       V   o     ⁡     (     t   2     )       ⁢              V   o     ⁡     (     t   2     )            2     ⁢           ⁢   ⋯   ⁢           ⁢       V   o     ⁡     (     t   2     )       ⁢              V   o     ⁡     (     t   2     )                2   ⁢   K     -   2                 ⋯                 V   o     ⁡     (     t   n     )       ⁢       V   o     ⁡     (     t   n     )       ⁢              V   o     ⁡     (     t   n     )            2     ⁢           ⁢   ⋯   ⁢           ⁢       V   o     ⁡     (     t   n     )       ⁢              V   o     ⁡     (     t   n     )                2   ⁢   K     -   2               ]             
the polynomial coefficients given by:
 β=( V   O   H   V   O ) −1 ( V   O   H   V   i ) 
will minimize the power of the error signal V e (t). In this way, the training circuit  290  can directly compute the predistorted signal for a given output by the following equation:
   V   i ( t )= V   O ( t ){Σ k=1   K β 2k−1   |V   o ( t )| 2k−2 } 
   Again, these calculations would be typically performed within the training circuit  290 , and the training circuit  290  then uses the above values to further determine the coefficients stored within the lookup table  225  for use by the predistorter  220 . 
   Both of the above methods should work well. In the following discussion the one-step method is further detailed, since the one-step method saves computation power. To compute the polynomial coefficients, about (4K 2 +4K+11) M multiplications and (2K 2 +2K+1) M additions are needed, where M is 4 times the number of chips and K is 3 for a 5th degree polynomial model. Computing the table entries requires 8T real multiplications and 4T real additions for a T-entry table. All of the operations are for real numbers. 
   Turning now to  FIG. 3 , illustrated is a method  300  of reducing distortion in an output of a WCDMA transceiver employing the principles of the present invention. After the start  310 , the method  300  then executes both a power indicator in a step  320  and a digital compensation signal in a step  330 . The power indicator in the step  320  provides power coefficients to a lookup table in a step  340 , which in turns provides coefficients in a predistorter step  350 . 
   The digital compensation signal step  330  employs a receive chain of the WCDMA transceiver to create the digital compensation signal as a function of an output (e.g. the transfer characteristics) of the transmit train. Also, the digital compensation signal also employs the output of the power indicator of the step  320 . 
   In the lookup table step  340 , both the power indicators of the step  320  and the digital compensation signal are employed by the lookup table step  340  to cause the lookup table to provide alternative coefficients in the step predistorter  350 . The output of the step  350  is input into the step  330  to be processed by the step  330  as a basis for the digital compensation signal. Finally, the method  300  stops at the step stop  360 . 
   Although the present invention has been described in detail, those skilled in the art should understand that they can make various changes, substitutions and alterations herein without departing from the spirit and scope of the invention in its broadest form.