Abstract:
Systems and methods are disclosed to adaptively pre-distort a signal prior to being used by a non-linear circuit, such as a higher power amplifier (at transmit) or a low noise amplifier (at receive). The signal is compared with a feedback signal from the non-linear circuit and a metric is calculated and minimized. The input signal is adaptively changed, such as by varying tap coefficients, until the metric is sufficiently minimized, resulting in a pre-distorted signal that is substantially linear upon passing through the non-linear circuit.

Description:
TECHNICAL FIELD  
       [0001]     This invention relates generally to communication systems and, more particularly, to pre-distortion circuitry for use with power amplifiers.  
       BACKGROUND  
       [0002]     Many types of communication systems use a power amplifier as part of the front end of a transmitter for transmitting RF signals. In some systems, a low noise amplifier (LNA) at the front end of a receiver may be used for receiving RF signals. However, a power amplifier has non-linear distorting characteristics that can cause distortion of the information signal being amplified. The non-linear distorting characteristics of the power amplifier can impact the instantaneous amplitude and phase of the signal significantly. Furthermore, non-linearity within the RF components can introduce distortion in the signal and reduced SNR or poorer performance at the receiver. In wireless systems, non-linearity in the power amplifier at transmission can introduce intermodulation distortion which can result in spectral emissions in the adjacent channels. Typically, tight specifications in terms of spectral masks are provided by Standards Committees and/or Government bodies, which put a maximum limit to such spurious, out-of-band emissions for compliant transceivers. Therefore, it is desirable to provide a linear signal out of the power amplifier.  
         [0003]     One type of method to linearize the power amplifier output signal is to “pre-correct” the signal being input to the amplifier, also known as pre-distortion. There are many known techniques are used to pre-correct an information signal in order to linearize the output of the amplifier. One of these techniques involves amplitude correction which produces a linear piece-wise pre-correction function which is correlated to the non-linear characteristics of the amplifier. The result is a piece-wise correction curve which approximates the ideal correction. The correction is then added to the information signal.  
         [0004]     Pre-distortion has been almost exclusively in the baseband domain. The typical approach has been to apply a pre-distortion function at digital baseband. A relatively recent but commonly used approach has been to store the pre-distortion function as a look-up table which stores the gain and phase values as a function of the input signal envelope. The input signal is compared with the feedback signal from the power amplifier and certain metrics, such as ratio of in-band to out-of-band emission power and/or their correlation are used to adaptively map the look-up table with respect to the envelope of the input signal. Thus, the data path is simply a complex multiplication at digital baseband; the adapt-path (or feedback path) consists of a look-up table indexed by the input signal envelope and the adaptation metric is the ratio of in-band to out-of-band emission or the correlation between the feedback and the input signals. These operations are carried out at digital baseband.  
         [0005]     However, increasing the linearity of the power amplifiers can reduce the power efficiency of the amplifiers, make them more-voluminous, require more cooling equipment, and substantially increase the cost and form-factor of the transceivers. To improve the linearity of the transmission without resorting to a higher end and more expensive power amplifier, one method that has been carried out in the prior art is to perform pre-distortion on the transmitted signal before the signal is input into the power amplifier such that the pre-distortion equalizes in some sense the non-linear post-distortion of the amplifier. The pre-distortion may be carried out within an integrated circuit; however, a significant challenge has always been to be able to adaptively obtain the pre-distortion transfer function so as to be optimal in some metric. It is also desirable to have a tracking mechanism with the pre-distortion so that different temperature and aging effects are also compensated for.  
         [0006]     Accordingly, it would be desirable to have systems and methods for performing pre-distortion in power amplifiers that overcome the disadvantages of the prior art as discussed.  
       SUMMARY  
       [0007]     According to one aspect of the present invention, adaptive pre-distortion is performed using a least-mean square (LMS) method to adaptively obtain an optimal pre-distortion transfer function in the mean square error sense. In one embodiment, a LMS-based adaptive pre-distortion circuit coupled between an input signal to be transmitted and a non-linear power amplifier compares the input signal to a feedback signal from the power amplifier. The circuit adaptively reduces the least-mean square error between the two signals using both linear and non-linear filters and various feedback signals within the circuit. The result is an approximately linear output from the power amplifier. This technique can be used with single and multi-carrier transceivers, as well as with either a power amplifier (at the transmitter) or low noise amplifier (LNA) (at the receiver). The adaptive pre-distortion can be performed in the baseband domain or purely in the RF domain, using analog continuous-time or discrete-time signal processing.  
         [0008]     According to one embodiment, an LMS-based adaptive pre-distortion (LAPD) circuit receives an input signal to be transmitted, such as from a baseband processor and RF circuitry, and a feedback signal from a power amplifier. The LAPD circuit adaptively minimizes a metric, such as an error signal, formed by the difference between the two signals. The LAPD circuit receives the input signal through an adaptive AGC circuit. The LAPD circuit further includes a feedforward filter, an adaptive coefficient generator, a slicer, timing control circuit, and slicer output time-align circuit. An error timing align circuit within the adaptive coefficient generator may be used to time align the input signal from the adaptive AGC circuit with the error signal e(t). The error timing align circuit may receive as an input signal a feedback tap coefficient vector c or the error signal e(t). The timing control circuit time aligns the input signal and the feedback signal from the power amplifier to compute an error signal, which is the time difference between the two signals. This error signal is iteratively reduced until a desired signal is obtained. The output signal is then input to the non-linear power amplifier, which amplifies the signal for transmission, resulting in a linearized output signal.  
         [0009]     The scope of the invention is defined by the claims, which are incorporated into this section by reference. A more complete understanding of embodiments of the present invention will be afforded to those skilled in the art, as well as a realization of additional advantages thereof, by a consideration of the following detailed description of one or more embodiments. Reference will be made to the appended sheets of drawings that will first be described briefly. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0010]      FIG. 1  shows a block diagram of a portion of a single-carrier transceiver with adaptive pre-distortion according to one aspect of the present invention;  
         [0011]      FIG. 2  shows a block diagram of a pre-distortion circuit for use in the transceiver of  FIG. 2  according to one embodiment;  
         [0012]      FIG. 3  shows a more detailed block diagram of the pre-distortion circuit of  FIG. 2  according to one embodiment;  
         [0013]      FIG. 3A  shows one embodiment of the pre-distortion circuit of  FIG. 3  with a more detailed feedforward filter and adaptive coefficient generator;  
         [0014]      FIG. 4  shows one embodiment of a feedforward filter in  FIG. 3 ;  
         [0015]      FIG. 5  shows one embodiment of an adaptive coefficient generator of  FIG. 3 ;  
         [0016]      FIG. 5A  shows one embodiment of a controllable delay in  FIG. 5 ;  
         [0017]      FIG. 5B  shows one embodiment of an interpolation control circuit of  FIG. 5A ;  
         [0018]      FIG. 5C  shows one embodiment of an interpolation delay circuit of  FIG. 5A ;  
         [0019]      FIG. 6  shows one embodiment of a low pass filter block suitable for use in the system of  FIG. 5 ;  
         [0020]      FIG. 7  shows one embodiment of a slicer input time align circuit for use in the system of  FIG. 3 ;  
         [0021]      FIG. 7A  shows one embodiment of an interpolating mixer circuit of  FIG. 7 ;  
         [0022]      FIG. 7B  shows one embodiment of a phase detector circuit of  FIG. 7 ;  
         [0023]      FIG. 8  shows one embodiment of a slicer output time align circuit for use in the system of  FIG. 3 ;  
         [0024]      FIG. 8A  shows one embodiment of a coefficient generator circuit of  FIG. 8 ;  
         [0025]      FIG. 8B  shows one embodiment of a timing interpolation parameter signal generator circuit of  FIG. 8 ;  
         [0026]      FIG. 9  shows a block diagram of a multi-carrier transceiver with adaptive pre-distortion according to one embodiment; and  
         [0027]      FIG. 10  show a block diagram of a multi-carrier pre-distortion circuit of  FIG. 9  according to one embodiment.  
         [0028]     Embodiments of the present invention and their advantages are best understood by referring to the detailed description that follows. It should be appreciated that like reference numerals are used to identify like elements illustrated in one or more of the figures. 
     
    
     DETAILED DESCRIPTION  
       [0029]      FIG. 1  is a block diagram of a portion of an RF communication system  100  for transmitting RF signals. System  100  includes a baseband processor  102  as part of a single carrier transceiver that generates signals in baseband to be transmitted. These signals are input to one or more RF circuits  104  that translate the signals to the RF domain. A least-mean square (LMS) based adaptive pre-distortion (LAPD) circuit  106  processes the desired signal (x 1 ) to be transmitted from RF circuits  104  and feedback signals (x 2 ) from a single carrier power amplifier  108  to generate a pre-distorted signal to power amplifier  108 . LAPD circuit  106  adaptively pre-distorts the input signal such that after traveling through power amplifier circuit  108 , the signal is linear. Note that with conventional systems, LAPD circuit  106  is replace by a look-up table that compares the two input signals and assigns specific values to the signal for pre-distortion.  
         [0030]     System  100  further includes a power coupler  110  that receives the output signal from power amplifier  108  and splits a portion of the input RF signal into the feedback path and passes the rest of the signal through to the antenna for transmission. The output signal from power coupler  110  is received by an amplitude control or controllable gain circuit  112 , which then scales the signal so that the signal input into LAPD circuit  106  is within an admissible range for operation of the LAPD circuit. Controllable gain circuit  112  feeds the signal back to LAPD circuit  106  for comparing with the desired signal to be transmitted. Power coupler  110 , after receiving the signal from power amplifier circuit  108 , sends the signal to an antenna  114  for transmission. After adaptive pre-distortion by LAPD circuit  106 , the signal from power amplifier circuit  108  is essentially linear.  
         [0031]      FIG. 2  is a block diagram of LAPD circuit  106  according to one embodiment of the invention. LAPD circuit  106  includes an adder  200  that calculates the difference between the input signal (x 1 ) from RF circuits  104  and the feedback signal (x 2 ) from power amplifier circuit  108 . Signal x 2  will sometimes be referred to as the feedback signal from power amplifier  108 . However, it is recognized that feedback signal x 2  may actually pass from power amplifier  108  through power coupler  110  and amplitude control circuit  112 . Thus, a feedback signal from the power amplifier or a low noise amplifier (or other non-linear element) can be any signal that passes through one or more circuit elements before entering LAPD circuit  106  and does not require a direct signal from the power amplifier to the LAPD circuit. The output signal e(t) of adder  200  (i.e., the difference or error signal) is input to an LAPD adaptpath circuit  202 , which provides adaptive tap coefficients or vector c from the error signal e(t) and the input signal x 1 . Note that as used herein, adaptpath indicates circuitry that adaptively changes a signal. The tap coefficients c, along with input signal x 1 , are then input to an LAPD datapath circuit  204 , which generates an pre-distorted signal z(t). LAPD datapath-circuit  204  pre-distorts the signal based on a set of configuration parameters (or tap weights) which are controlled by LAPD adaptpath circuit  202  based on minimizing a certain metric, such as mean squared amplitude of the input signal into the LAPD and the amplitude control circuit output. The signal is then filtered through a bandpass filter  206  for transmission to the power amplifier. In one embodiment, bandpass filter  206  is part of LAPD circuit  106 , while in another embodiment, bandpass filter  206  is external to LAPD circuit  106 .  
         [0032]      FIG. 3A  is a more detailed block diagram of LAPD circuit  106  of  FIGS. 1 and 2  according to one embodiment. LAPD circuit  106  includes an adaptive automatic gain control (AGC) circuit  300  within LAPD adaptpath circuit  202 , which provides the necessary gain for small signals. Thus, after a signal is output from AGC circuit  300 , the signal is within a suitable range that allows the signal to be properly used throughout the rest of the circuit. Adaptive AGCs are known and any such suitable one can be used with the present invention to adaptively provide the proper gain. LAPD circuit  106  also includes a feedforward filter  302 , an adaptive coefficient generator  304 , an output signal slicer  306 , a timing control or time-align circuit  308 , and a slicer output time-align circuit  310 . Within LAPD circuit  106  is LAPD adaptpath circuit  202 , which includes adaptive coefficient generator  304 , an adder  318 , and an integrator, such as a low pass filter block  316 , and LAPD datapath circuit  204 , which includes adaptive AGC circuit  300 , feedforward filter  302 , timing control circuit  308 , output signal slicer  306 , slicer output time-align circuit  310 , an adder  312 , and a multiplier  314 .  
         [0033]     Input signal x 1  is received by adaptive AGC circuit  300 . Feedforward filter  302  receives the output signal x 1  from adaptive AGC circuit  300  and tap coefficients from adaptive coefficient generator  304  and generates a pre-distorted signal, which is input to adder  312 . The other input to adder  312  is the product  314  of the output of low pass filter block  316 , and slicer output time-align circuit  310 .  
         [0034]     The feedback signal (from product  314 ) into adder  312  provides an iterative correction to an error signal e(t) for use by adaptive coefficient generator  304  to generate adaptive tap coefficients. The error signal, processing through adder  318 , is the difference between the output of timing control circuit  308  and input signal x 2  (the feedback signal from the power amplifier). As time passes, the error signal converges until a sufficiently small error signal is obtained through adaptively changing the tap coefficients.  
         [0035]      FIG. 3B  is a more detailed block diagram of LAPD circuit  106  according to one embodiment, in which adaptive coefficient generator  304  and feedforward filter  302  are shown in greater detail. Details will be discussed further below.  
         [0036]      FIG. 4  shows one embodiment of a feedforward filter suitable for use as feedforward filter  302  of  FIG. 3 . The feedforward filter includes a series of signal delay elements  402 - 1  to  402 -N. Each delay element  402  delays the incoming signal by a fixed amount τ, e.g., x 1 ′(t−τ), x 1 ′(t− 2 τ), . . . x 1 ′(t−Nτ). The delay τis typically selected to be less than a symbol period, and in one embodiment, is based on the symbol period τ, and the number of feedforward taps N as follows:  
       τ   =       T   s       N   -   1             
 The input data signal x 1 ′( t ) and each successive delayed signal from delay elements  402 - 1  to  402 -N are multiplied by multipliers  404 - 1  to  404 -N with its respective adaptive coefficient signals from adaptive coefficient generator  304 . The product signals are then summed by an adder circuit  406  to form the pre-distorted signal. 
 
         [0037]      FIG. 5  shows one embodiment of an adaptive coefficient generator for use as adaptive coefficient generator  304  of  FIG. 3 . The generator includes a controllable delay  500 , which receives input data signal x 1 ′( t ) and the error signal e(t), and introduces a fixed delay into the signal. One type of controllable delay suitable for the present invention is an error timing control (ETC) and precursor/postcursor control (PPC) circuit, such as described in commonly-owned U.S. patent application Ser. No. 10/290,993, filed Nov. 8, 2002, entitled “Adaptive Signal Equalizer with Adaptive Error Timing and Precursor/Postcursor Configuration Control”, which is incorporated herein by reference in its entirety. The controllable delay in the present invention is used to align the error signal e(t) with the input signal x 1 ′( t ). In one embodiment, the ETC/PPC circuit of the above referenced application is used to adaptively set the delay by using the error signal e(t) as a control input signal.  
         [0038]      FIG. 5A  shows one embodiment of controllable delay  500 . Controllable delay  500  includes an interpolation control stage  552  and an interpolation delay stage  554 . Interpolation control  552  processes the error signal coefficients to produce a set of delay interpolation control signals for interpolation stage  554 . In response to these delay interpolation control signals, interpolation delay stage  554  processes its input signal x 1 ′( t ) to produce the corresponding delayed signal for processing by delay elements  502 .  
         [0039]      FIG. 5B  shows one embodiment of interpolation controller  552 . Interpolation controller  552  includes a set of signal multipliers  556 - 1  to  556 -N, a signal combining circuit  558 , a signal integration circuit (e.g., a low pass filter)  560 , and a signal complement circuit  562 , interconnected substantially as shown. Each of the error signal coefficient signals e 1  to e N  is multiplied in a respective multiplier  556 - 1  to  556 -N with a corresponding weighted or scaled signal K 1  to K N . In one embodiment, K 1  to K N/2  are equal to +1, while K (N/2)+1  to K N  are equal to −1. The resulting product signals are summed in signal combiner  558 . The sum signal is integrated by signal integrator  560  to produce the primary delay interpolation control signal representing the timing control ratio parameter r. This delay interpolation control signal is also complemented by signal complement circuit  562  to provide the complement delay interpolation control signal. Signal complement circuit  562  processes the delay interpolation control signal by subtracting it from a normalized value (e.g., unity) to produce the complement signal. The uncomplemented and complemented signals are then processed by interpolation delay  554 .  
         [0040]      FIG. 5C  shows one embodiment of interpolation delay  554 . Interpolation delay  554  includes three signal delay elements  572 - 1 ,  572 - 2 , and  572 - 3 . The incoming signal, i.e., the input signal x 1 ′( t ), and the corresponding successively time-delayed versions are multiplied in signal multipliers  574 - 1 ,  574 - 2 ,  574 - 3 , and  574 - 4  with corresponding interpolation control signals. The resulting product signals are summed in a signal combiner  576  to produce the delayed version of the incoming signal.  
         [0041]     Referring to  FIG. 5 , the aligned output signal of controllable delay  500  is processed through a series of delay elements  502 - 1  through  502 -N. Delay elements  502  introduce a delay of τ′ to its input signal. In one embodiment, τ′ is greater than the delay τ of delay elements  402  of  FIG. 4 , although it may also be suitable for τ′ to be approximately equal to τ in other embodiments. Having τ′&gt;τ results in a generally more robust system. The delayed signals (by multiples of τ′) are input to respective low pass filter blocks  504 - 1  to  504 -N, along with the error signal e(t) from adder  318  of  FIG. 3 . Low pass filter blocks  504  multiply each delayed signal with a corresponding error signal and integrate the result to generate individual tap coefficient signals for use by multipliers  404 - 1  to  404 -N of  FIG. 4 .  FIG. 6  shows one embodiment of low pass filter block  504 , which includes a multiplier circuit  600  and an integrator circuit, such as a low pass filter  602 .  
         [0042]     In one embodiment, low pass filters  602  are analog (or continuous-time) first-order low-pass filters having a transfer function  
         H   ⁡     (   s   )       =     G     1   +     s   ·     T   l               
 
 where G is the gain of the low pass filter and T 1  is the leakage time constant. The filter parameters gain G and time constant T 1  can be chosen to meet system and component requirements. For example, the time constant T 1  is selected as a non-zero positive number for more robust performance with a fractionally-spaced feedforward filter at the front-end. The gain G should be large enough so that the mismatch of the tap coefficient with the least-mean square value at convergence is sufficiently small. Further, T 1 &gt;0 and G need to be moderate enough to minimize the effects of “tap coefficient drift”. Another factor in selecting gain G and time constant T 1  is to achieve a convergence time that is sufficiently small for the system. 
 
         [0043]     Selecting values for G and T 1  depend on system requirements and include factors such as the maximum steady state mismatch of signals, time variability of the channel, amount of noise within the channel, and parasitic effects of the circuit. In one embodiment, the gain G may be set to 10 to 50 which will result in small mismatch and possibly stable operation. The time constant T 1  is typically set to about 10,000 to 100,000 symbol times, in one embodiment. For very fast varying channels, T 1  is much smaller. T 1  is larger for channels having less temporal variations and more noise. Higher order low pass filters are also suitable for use with the present invention.  
         [0044]     Referring back to  FIG. 3 , similarly, low pass filter block  316  receives error signal e(t) from adder  318  and the output of slicer output time-align circuit  310 . These two signals are then multiplied and integrated by low pass filter block  316 .  
         [0045]      FIG. 7  shows one embodiment of a timing control circuit for use as timing control circuit  308  of  FIG. 3 . The circuit includes a controllable delay, which receives the input data signal x 1 ( t ) and introduces a delay Δ into the signal. One type of controllable delay suitable for the present invention is an adaptive least mean square-based timing interpolation (ALTI) circuit, such as described in commonly-owned U.S. patent application Ser. No. 10/321,893, filed Dec. 17, 2002, entitled “Adaptive Signal Latency Control for Communications Systems Signals”, which is incorporated herein by reference in its entirety.  
         [0046]     The controllable delay in the present invention is used to time align the input signal x 1  with the feedback signal x 2  from the power amplifier. In one embodiment, the ALTI circuit of the above referenced application is used to adaptively set the delay to align the signals by using the feedback signal x 2 ( t ) from the power amplifier. The ALTI block may be used to time-align the input signal to compute the distortion error signal which is the difference between the power amplifier output signal and the input signal, i.e., the time-align circuit  308  delays its output signal to compensate for delays introduced by processing of the input signal by the circuit.  
         [0047]      FIG. 7  shows one embodiment of timing control circuit  308 , which includes an interpolating mixer  702 , a phase detector  704 , and a signal integrator  706 , interconnected substantially as shown. The feedback signal x 2 ( t ) is compared in signal phase by phase detector  704  with the delayed signal from interpolating mixer  702 . The resulting detection signal is integrated by signal integrator  706  (e.g., a low pass filter) to produce an interpolation control signal r(t) for interpolating mixer  702 .  
         [0048]      FIG. 7A  shows one embodiment of interpolating mixer  702 , which is implemented as a tapped delay line with correlated tap coefficients. The input signal x 1 ( t ) is delayed by a signal delay element  712  which is a fractional delay element introducing a delay which is less than one data symbol period in duration. The resulting fractionally delayed signal and the original input signal x 1 ( t ) are mixed (e.g., multiplied) in respective signal mixers  714 - 1 ,  714 - 2  with respective interpolation control signals representing timing interpolation parameters. The first timing interpolation parameter signal is the feedback signal from signal integrator  706  ( FIG. 7 ). This signal is also complemented by a signal complement circuit  718  in which the input signal is subtracted from a normalized value (e.g., unity) to produce the second timing interpolation parameter signal. The resultant mixed signals are combined (e.g., summed) in a signal combining circuit  716  to produce the delayed signal x 1 (t−Δ).  
         [0049]      FIG. 7B  shows one embodiment of phase detector  704  of  FIG. 7 , which can be implemented using a fractional delay element  722 , a signal combining circuit  724 , and a signal mixer  726 , interconnected substantially as shown. The delayed signal x 1 (t−Δ) is further delayed by fractional delay element  722 , after which it is combined with delayed signal x 1 (t−Δ) in signal combiner  724  such that the further delayed signal is subtracted from the input delayed signal x 1 (t−Δ). The resulting combined signal is mixed (e.g., multiplied) in signal mixer  726  with the feedback signal x 2 ( t ) (and a gain constant G r , if desired) to produce the phase detection signal for signal integrator  706  ( FIG. 7A ).  
         [0050]      FIG. 8  shows one embodiment of a slicer output time-align circuit for use as slicer output time-align circuit  310  of  FIG. 3 . The circuit includes a controllable delay, which receives the data signal y(t) from slicer  306  of  FIG. 3  and introduces a delay into the signal. One type of circuit suitable for the present invention is a fat tap adaptation (FTA) circuit, such as described in commonly-owned U.S. patent application Ser. No. 10/322,024, filed Dec. 17, 2002, entitled “Adaptive Coefficient Signal Generator for Adaptive Signal Equalizers with Fractionally-Spaced Feedback”, which is incorporated herein by reference in its entirety.  
         [0051]     The controllable delay in the present invention is used to time align the decision feedback signal, which is the signal from slicer  306 , to be a symbol period delay with respect to the slicer input signal from which it is cancelled. A method of obtaining this delay in an adaptive manner is by using the FTA block, as described in the above-referenced application, which uses the tap coefficients or error signal e(t) as a control input signal.  
         [0052]      FIG. 8  shows one embodiment of slicer output time-align circuit  310 , which includes multiplier circuits  802 - 1 ,  802 - 2  and control signal generator circuitry implemented as a coefficient signal generator  804  and a timing interpolation parameter signal generator  806 , all interconnected as substantially shown. The adjacent time-delayed feedback signals, the output signal y(t) of slicer  306  ( FIG. 3 ) and the signal y(t−δ) delayed by a symbol period δ, are multiplied in their respective multiplier circuits  802 - 1 ,  802 - 2  with the error signal e(t). The resulting product signals e(t)y(t) and e(t)y(t−δ) are processed by signal generator circuits  804 ,  806 . Coefficient signal generator circuit  804  provides an adaptation control signal d(t) to timing interpolation parameter signal generator circuit  806 , which in return, provides two other adaptation control signals r(t) and  1 −r(t) back to coefficient signal generator  804 . As a result of processing these input signals e(t)y(t), e(t)y(t−δ), r(t), and  1 −r(t), coefficient signal generator  804  provides the adaptive coefficient signals d(t)r(t) and d(t)[ 1 −r(t)], where signal element d(t) is the weighting factor and signal element r(t) is the factor indicative of the degree of correlation between the adjacent time-delayed feedback signals y(t) and y(t−δ).  
         [0053]      FIG. 8A  shows one embodiment of coefficient signal generator  804 . Initial product signals y(t) and y(t−δ) are further multiplied in multiplier circuits  812 - 1 ,  812 - 2  with the adaptation control signals r(t) and  1 −r(t), respectively, from timing interpolation parameter signal generator  806 . An additional constant signal μ c  can also be multiplied as part of the product operations or implemented as a constant scaling factor within the multiplier circuits  812 - 1 ,  812 - 2 .  
         [0054]     The resulting product signals are summed in a signal summing circuit  814 . The resulting sum signal is integrated in an integration circuit  816  (e.g., a low pass filter) to produce the first adaptation control signal d(t). This adaptation control signal d(t), in addition to being provided to timing interpolation parameter signal generator  806 , is multiplied within multiplier circuits  818 - 1 ,  818 - 2  with the other adaptation control signals r(t) and  1 −r(t), respectively, provided by timing interpolation parameter signal generator  806 . The product signals resulting from these multiplication operations are the adaptive coefficient signals d(t)r(t) and d(t)[ 1 −r(t)].  
         [0055]      FIG. 8B  shows one embodiment of timing interpolation parameter signal generator  806 . The initial product signals e(t)y(t) and e(t)y(t−δ) are differentially summed in a signal summing circuit  822 , where the second product signal e(t)y(t−δ) is subtracted from the first product signal e(t)y(t). The resulting difference signal is multiplied in a multiplier circuit  824  with the adaptation control signal d(t) provided by coefficient signal generator  804 . As with the multiplier circuits  812 - 1 ,  812 - 2  of coefficient signal generator  604 , an additional constant signal μ r  can also be used in this multiplication operation or implemented as a constant scaling factor within multiplier circuit  824  operation.  
         [0056]     The resulting product signal is integrated by a signal integration circuit  826  (e.g., a low pass filter) to produce one of the adaptation control signals r(t) used by coefficient signal generator  804 . This adaptation control signal r(t) is further processed by a signal complement circuit  828 , in which the input signal r(t) is subtracted from a reference signal having a normalized value, with the resulting difference signal  1 −r(t) serving as the other adaptation control signal used by coefficient signal generator  804 . For example, if the value of the incoming signal r(t) were considered to have a normalized signal value range bounded by the values of zero and one, signal complement circuit  828  subtracts the incoming signal r(t) from the value of one to produce the output signal  1 −r(t).  
         [0057]     The above described embodiment utilizes an adaptive pre-distortion circuit with feedback circuitry and both linear and non-linear elements. By selecting the appropriate parameters for the low pass filters, the convergence of the least mean square value can be controlled to prevent coefficient drift of the adaptive tap coefficients. The continuous time iterative process results in the ability to adaptively change the tap coefficients for error minimization and provide a linear signal out of a non-linear power amplifier.  
         [0058]     While the above description is for a single-carrier transceiver, the present invention can also be used with multi-carrier transceivers.  FIG. 9  shows a block diagram of a transceiver  900 , in which multi-carrier adaptive pre-distortion is performed by a multi-carrier LAPD circuit  910 . In this example, there are two carriers. Transceiver  900  includes two baseband processors  102 - 1  and  102 - 2 , each followed by two RF circuits  104 - 1  and  104 - 2 , LAPD circuit  910  that receives the outputs x 11  and x 12  from RF circuits  104 - 1  and  104 - 2 , respectively, and a feedback signal x 2  from a multi-carrier power amplifier  912  via power coupler  110 . Amplitude control circuit  112  (not shown) may be coupled between power coupler  110  and LAPD circuit  910  in some embodiments. A linearized signal out of power amplifier  912  can be transmitted through antenna  114 .  
         [0059]      FIG. 10  is a block diagram of multi-carrier LAPD circuit  910  of  FIG. 9 , according to one embodiment. LAPD circuit  910  includes two “branches”, one for each signal at a different carrier. The input signal x 11  from the first carrier is utilized by a first branch, which includes LAPD adaptpath circuit  202 - 1  and LAPD datapath circuit  204 - 1 , such as described above with respect to a single carrier LAPD circuit. The input signal x 12  from the second carrier is utilized by a second branch, which includes LAPD adaptpath circuit  202 - 2  and LAPD datapath circuit  204 - 2 , again as described above with respect to  FIGS. 3A and 3B  according to one embodiment. The error signal e(t) is input to LAPD adaptpath circuits  202 - 1  and  202 - 2  for adaptive processing, as described above. However, a difference with the single-carrier LAPD circuit is that the error signal for multi-carrier LAPD  160  is the difference between power amplifier feedback signal x 2  and all the different input signals (x 11  and x 12  in this example), instead of just a single carrier input signal x 1 . This difference or error signal is determined by an arithmetic circuit  1002 , such as a multi-input adder.  
         [0060]     After adaptively generating a pre-distortion signal for each carrier, the output signals from LAPD datapath  204 - 1  and from LAPD datapath  204 - 2  are passed through bandpass filters  206 - 1  and  206 - 2 , respectively. As with the single-carrier embodiment, bandpass filters  206  may be internal to or external of multi-carrier LAPD circuit  910 . The output signals from bandpass filters  206 - 1  and  206 - 2  are then summed by an adder  1004  to generate a pre-distorted signal z for power amplifier  912 . Due to adaptively pre-distorting input signals according to the present invention, the output of a non-linear power amplifier can be made linear with a wider range of factors, as well as at lower cost and size.  
         [0061]     In some applications and systems, the power amplifier and/or other RF components may introduce inter-symbol interference (ISI) in addition to non-linearity. To compensate for both ISI and non-linearity effects jointly, the present invention can be modified, in part, by using a larger number of taps N′ such that N′*τ&gt;T s .  
         [0062]     The above-described embodiments of the present invention are merely meant to be illustrative and not limiting. It will thus be obvious to those skilled in the art that various changes and modifications may be made without departing from this invention in its broader aspects. For example, although the multi-carrier mode is shown with two carriers, the invention can also be used with a multi-carrier transceiver having more than two carriers by modifying the above descriptions accordingly. Further, the above description has focused on continuous-time, RF domain signal processing; however, the present invention can be extended or modified for use with discrete-time signal processing architectures as well. Therefore, the appended claims encompass all such changes and modifications as fall within the true spirit and scope of this invention.