Abstract:
A single or multistage signal predistorter includes an input coupled to receive an information signal comprising input samples and an output coupled to the high power amplifier, the signal predistorter configured to receive an input sample, generate a distortion sample based on an estimate of nonlinearity of the high power amplifier at an operating saturation level, modify the input sample with a correction term to generate a predistortion signal, wherein the correction term is proportional to the distortion sample, and further wherein the predistortion signal comprises the information signal modified to account for nonlinearities in the high power amplifier.

Description:
TECHNICAL FIELD 
       [0001]    The disclosed technology relates generally to communication systems, and more particularly, some embodiments relate to systems and methods for performing signal predistortion. 
       DESCRIPTION OF THE RELATED ART 
       [0002]    A goal of communication system designers is to increase power efficiency in digital communication systems. One conventional technique for increasing efficiency is to operate High Power Amplifiers (HPAs) close to saturation. Examples of these systems are narrowband systems such as those used on the return link in satellite communications systems, or wideband systems such as those employing code-division multiple access (CDMA), orthogonal frequency-division multiple access (FDMA), or multicarrier systems. However, a downside to increasing power efficiency in this way is spectral regrowth caused by operating the HPA close to saturation. Spectral regrowth is energy from the modulated signal that spreads into adjacent channels due to the amplifier&#39;s inherent nonlinearities. This spectral regrowth can cause adjacent channel interference (ACI), and potentially violates out-of-band emission requirements set by regulatory commissions. Furthermore, this can also cause in-band distortion, manifested as clustering in a scatter plot at the receiver and quantified by mean-square error (MSE) relative to nominal constellation. Both effects can severely degrade performance if left unmitigated. 
         [0003]    Accordingly, to avoid or reduce the effects of such issues, designers typically back-off or limit the output power from the maximum level to operate more in the linear range. Other solutions have employed predistortion as a signal processing technique to compensate for nonlinearities in the power amplifier at the transmitter. One conventional approach applies the inverse of the HPA in a single stage in an attempt to undo the effects of the HPA. Another conventional solution is to sample at the symbol rate and modify transmitted symbols, however this generally can only correct for in-band distortion and cannot compensate for spectral regrowth. In fact data predistortion operating at the symbol rate may contribute to spectral regrowth after the HPA. Other conventional predistortion methods require special transmit and receive filters which is not desirable in practical systems. 
       BRIEF SUMMARY OF EMBODIMENTS 
       [0004]    Embodiments of the systems and methods disclosed herein provide an innovative form of signal predistortion to suppress, in some cases significantly, the spectral regrowth as well as in-band distortion simultaneously. This may be done in some embodiments while keeping the HPA operating efficiently near saturation. As a result of the suppression of spectral regrowth, the technology disclosed herein can also allow closer spacing of adjacent carriers in the frequency domain, which can result in higher levels of spectral efficiency. 
         [0005]    The system can be configured to employ successive predistortion and can be further configured to operate at the signal level, or at multiple samples per symbol. Embodiments of the disclosed technology can further include an adjustable memory span that can be selected to account for memory effects associated with the HPA. In some embodiments, it can be memoryless, which is adequate for memoryless HPAs or for conditions in which the symbol rate is much smaller than the bandwidth of the HPA. Other embodiments can be configured to deliberately introduce memory to further suppress mean-square error (MSE) and provide a tuning feature to balance levels of suppressing spectral regrowth versus in-band distortion, measured in terms of ACI and MSE in decibels (dBs). In some embodiments, significant gains can be achieved as compared with systems that do not use the disclosed predistortion techniques. Additionally, embodiments can be implemented allowing tuning the system to trade-off levels of spectral growth suppression and in-band distortion. 
         [0006]    Because configurations can be implemented to reduce spectral regrowth and in band distortion, excellent system performance can be achieved while maintaining high efficiency in both power and bandwidth resources. In various embodiments, the signal predistortion is provided at the transmitter, prior to the HPA, to mitigate the unwanted nonlinear effects caused by operating the HPA at or near saturation. 
         [0007]    According to various embodiments of the disclosed technology a communication system having one or more channels. The channel, or in the case of a multichannel or multicarrier system each addressed channel, may include a corresponding signal input, includes for each channel: a high power amplifier including an input and an output; and a single or multistage signal predistorter including an input coupled to receive an information signal including input samples and an output coupled to the high power amplifier, the signal predistorter configured to receive an input sample, generate a distortion sample based on an estimate of nonlinearity of the high power amplifier at an operating saturation level, modify the input sample with a correction term to generate a predistortion signal, wherein the correction term is proportional to the distortion sample, and further wherein the predistortion signal comprises the information signal modified to account for nonlinearities in the high power amplifier. 
         [0008]    For a first stage of a multistage signal predistorter, the input sample includes the input samples prior to amplification by the high power amplifier and the predistortion signal is a first predistortion signal output by the first stage. For each s th  stage of the multistage signal predistorter after the first stage, the input to this stage is the signal generated by the (s−1) th  stage of the multistage signal predistorter. 
         [0009]    The communication system in some embodiments further include a second single or multistage signal predistorter to account for nonlinearities caused by the power amplifier as experienced by a receiver in communication with the transmitter, the second signal predistorter including an input coupled to receive a received information signal and an output, the second multistage signal predistorter configured to receive a received sample from the received information signal, generate a receiver distortion sample based on an estimate of nonlinearity of the receiver, modify the received sample with a second correction term to generate a receiver predistortion signal, wherein the second correction term is proportional to the receiver distortion sample, and further wherein the receiver predistortion signal includes the received information signal modified to account for nonlinearities in the receiver. In some embodiments, the first and second signal predistorters are applied in the communication system as a weighted combination. 
         [0010]    In some embodiments, a single or multistage signal predistorter includes an input coupled to receive an input sample; a nonlinear estimator configured to estimate a nonlinearity of the high power amplifier at an operating saturation level; a plurality of stages, each s th  stage including: a first adder configured to subtract the determined estimate from an input information signal at the s th  stage to generate an s th  distortion sample; a multiplier configured to multiply the s th  distortion sample by an s th  convergence factor to generate an s th  correction term; a second adder configured to add the s th  correction term to the input information signal at the s th  stage to generate an s th  predistortion signal; and an output coupled to the high power amplifier and configured to output the s th  predistortion signal from the last stage of the plurality of stages. 
         [0011]    For a first stage of a multistage signal predistorter, the input information signal includes an undistorted information signal, and for each s th  stage of the multistage signal predistorter after the first stage, the input information signal includes the predistortion signal generated by the (s−1) th  stage of the multistage signal predistorter. 
         [0012]    Other features and aspects of the disclosed technology will become apparent from the following detailed description, taken in conjunction with the accompanying drawings, which illustrate, by way of example, the features in accordance with embodiments of the disclosed technology. The summary is not intended to limit the scope of any inventions described herein, which are defined solely by the claims attached hereto. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0013]    The technology disclosed herein, in accordance with one or more various embodiments, is described in detail with reference to the following figures. The drawings are provided for purposes of illustration only and merely depict typical or example embodiments of the disclosed technology. These drawings are provided to facilitate the reader&#39;s understanding of the disclosed technology and shall not be considered limiting of the breadth, scope, or applicability thereof. It should be noted that for clarity and ease of illustration these drawings are not necessarily made to scale. 
           [0014]      FIG. 1  illustrates an example communication transmitter in accordance with one embodiment of the technology described herein. 
           [0015]      FIG. 2  is an operational flow diagram illustrating an example process for signal predistortion in accordance with one embodiment of the technology described herein. 
           [0016]      FIG. 3  is a block diagram displaying an example implementation of an embodiment of an s th  stage of a signal predistorter. 
           [0017]      FIG. 4  is a diagram illustrating an example signal model for implementing signal predistortion at a HPA in accordance with one embodiment of the technology described herein. 
           [0018]      FIG. 5  is a diagram illustrating Power Spectral Density (PSD) for an original signal  422  without distortion, for an amplified signal without signal predistortion, and for the amplified signal with signal predistortion at the HPA output when operated at OBO level of 1.5 dB in accordance with one embodiment of the technology described herein. 
           [0019]      FIG. 6  shows Adjacent Channel Interference (ACI) with and without signal predistortion at the receive filter output for varying levels of OBO. 
           [0020]      FIG. 7  shows the mean-square error (MSE) at the best-sampled output of the receive filter with embodiments of the disclosed signal predistortion and without signal predistortion. 
           [0021]      FIG. 8  shows simulation results for ACI with embodiments of the disclosed signal predistortion and without signal predistortion at receive filter output for varying levels of OBO with adjacent carrier spacing of 1.25×symbol rate. 
           [0022]      FIG. 9  is similar to  FIG. 8  but shows the simulation results for MSE, instead of ACI, with embodiments of the disclosed signal predistortion and without signal predistortion at receive filter output for varying levels of OBO with adjacent carrier spacing of 1.25×symbol rate. 
           [0023]      FIG. 10  displays noiseless scatter plots at the best-sampled output of receive filter for a system without predistortion (left) and with proposed signal predistortion (right) at OBO level of 1.5 dB when no adjacent carriers are present. 
           [0024]      FIG. 11  displays Power Spectral Density (PSD) as would be measured at the gateway when three equal-power carriers are transmitted at adjacent carrier spacing of 1.25×symbol rate. 
           [0025]      FIG. 12  quantifies performance using an LDPC code having a code rate 2/3 and codeblock length of 5760 bits at a target packet-error rate of 10 −3 . 
       
    
    
       [0026]    The figures are not intended to be exhaustive or to limit the invention to the precise form disclosed. It should be understood that the invention can be practiced with modification and alteration, and that the disclosed technology be limited only by the claims and the equivalents thereof. 
       DETAILED DESCRIPTION OF THE EMBODIMENTS 
       [0027]    Embodiments of the technology disclosed herein is directed toward a devices and methods for providing signal predistortion to suppress spectral regrowth and limit in-band distortion in communication systems. More particularly, some embodiments of the technology disclosed herein provide successive predistortion for RF communication systems that can operate at the signal level (e.g., at multiple samples per symbol) to suppress spectral regrowth while simultaneously limiting in-band distortion, while operating at or near saturation of the HPA. 
         [0028]    Before describing the technology in further detail, it is useful to describe an example communication system with which the disclosed technology can be implemented. One such example is a multicarrier communication transmitter such as, for example, a transmitter included in a satellite communication transceiver.  FIG. 1  illustrates an example communication transmitter. With reference now to  FIG. 1 , it is assumed that there are Mc independent carriers for transmitting binary data. This example communication transmitter includes, for each carrier, a bit source  102 , a forward error correction (FEC) encoder  104 , an interleaver  106 , a modulator  108 , a transmit filter  110 , an HPA  112  and a mixer  114 . Although these components are shown in a particular order in this example, one of ordinary skill in the art reading this description will understand that the order of components can be varied (e.g., in some cases the HPA may be included after the mixer to amplify the mixed signal, etc.) and some components may be excluded. One of ordinary skill in the art will understand how other transmitter configurations can be implemented, and that one or more of these components can be implemented in either digital form (e.g., as software running on a DSP or other processing device, with the addition of a DAC) or as analog components. 
         [0029]    Bit source  102  provides information bits to be transmitted to FEC encoder  104 . The information can include, for example, images, video, audio, information and other data. FEC encoder  104  provides forward error correction by adding redundancy to information data bits signal  152 . Forward error correction improves the capacity of a channel by adding redundant information to the data being transmitted through the channel. 
         [0030]    Interleaver  106  is scrambles the encoded data bits by rearranging the bit sequence order to make distortion at the receiver more independent from bit to bit. In other words, interleaver  106  rearranges the ordering of the data sequence in a one to one deterministic format. Interleaving may be used to enhance the error correcting capability of coding. 
         [0031]    Modulator  108  modulates the interleaved bits to form complex-valued data symbols. Examples of modulation include Amplitude Phase Shift Keying (APSK), Quadrature Phase Shift Keying (QPSK), n/M-MPSK, other orders of Multiple Phase Shift Keying MPSK, Quadrature Amplitude Modulation (QAM), and so on. 
         [0032]    Pulse shaping filter  110  converts complex-valued data symbols to a waveform signal using a pulse shaping function with an impulse response p(t). High Power Amplifier (HPA)  112  amplifies the waveform for transmission. As discussed herein, embodiments of the signal predistortion can be implemented such that the HPA can be driven at or near saturation, with little or no backoff. 
         [0033]    Mixer  114  mixes the waveform signal  160  with a carrier signal from a local oscillator (not shown) to modulate it onto an appropriate carrier for transmission. For a given transmitting source, the local oscillator signal may be represented as a function of e j(2πƒ     x     t) , where ƒ x  is the carrier for the respective source, ƒ 1  . . . ƒ Mc . Adder  116  adds output signals from the plurality of transmitting sources to provide a composite signal. 
         [0034]    Having thus described an example application, the technology disclosed herein may from time to time be described herein in terms of this example application. Description in terms of this environment is provided to allow the various features and embodiments of the invention to be portrayed in the context of an exemplary application. After reading this description, it will become apparent to one of ordinary skill in the art how the invention can be implemented in different and alternative environments and applications. By way of example, one of ordinary skill in the art will understand how the technology disclosed herein can also be implemented in a single-channel system. 
         [0035]    As noted above, in various embodiments the signal predistortion described herein can be implemented to cancel distortion in one or more stages and to operate at the sample (as opposed to symbol) level. Before describing a few more specific example embodiments, the technique is more generally described.  FIG. 2  is an operational flow diagram illustrating an example process for signal predistortion in accordance with one embodiment of the technology described herein. With reference to  FIG. 2 , at operation  144  input samples are received at the predistorter. For example, the input of the predistorter can be a vector of complex-valued samples at the each stage. For the first stage or application of signal predistortion, the input signal is not predistorted by a prior stage and the input is therefore composed of undistorted input samples. 
         [0036]    At operation  146 , a scaling parameter is determined. In other embodiments, the scaling parameter is a real-valued scaling parameter that can be included and used to scale to the correct input back-off (IBO) level. The scaling parameter can be chosen based on the operating point of the amplifier, and can be determined based on the desired operating range of the HPA. It can be chosen, for example, to provide a determined balance between power loss and distortion. In some embodiments, it can be modeled in advance based on known operating characteristics of the amplifier. 
         [0037]    At operation  148 , the operating characteristics of the HPA operating at a determined level of saturation (which may be, for example, at or near saturation) are determined and a distorted sample estimate at the HPA output is determined. The distorted sample estimate can be based on modeled HPA characteristics for static cases in some embodiments, while in other embodiments it can be adaptively estimated. Adaptive estimation can be performed, for example, using standard estimation techniques such as, for example, stochastic gradient methods, which can track slowly-varying effects due to ageing and temperature variations experienced by the HPA. Accordingly, a model of the specified HPA can be generated based on known amplifier characteristics, such as its nonlinearity at high saturation levels. 
         [0038]    At operation  150 , a distortion sample is generated based on the determined estimate. At operation  152 , the predistortion output is generated. This can be accomplished, for example by modifying the predistorted sample from the previous stage (for stages other than stage 1) with a correction term. The correction term applied may be proportional to the distortion sample. In some embodiments, the correction term may be the distortion sample multiplied by a sequence factor to provide convergence in successive stages. The process can be repeated for multiple stages where the input for a given stage is the predistored sample from the previous stage. 
         [0039]    A few example embodiments of the above-described process are now provided. The first example embodiment cancels distortion at the HPA output and can provide control in suppressing the spectral regrowth typically encountered when operating the HPA efficiently. It also provides benefit in reducing mean-square error (MSE) at the receiver. In this embodiment, let the input to of the predistorter,  x   PD   (s) [k;L], be the vector of complex-valued samples at the s-th stage. This input can be given by 
         [0000]    
       
         
           
             
               
                 
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         [0000]    where the parameter L is the double-sided memory span of the predistorter and s=0, 1, . . . , S−1. 
         [0040]    For the first stage or application of signal predistortion, the input signal is input samples undistorted by a prior stage and the input is therefore composed of undistorted samples. In this special case, the input is given by: 
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         [0041]    The distorted sample at the HPA output is estimated. This estimation can be performed, for example, based on known operating characteristics of the specified HPA when it is operating at or near saturation. A sample {circumflex over (x)} PA [k] can be defined as the estimate of the distorted sample at the HPA output or 
         [0000]        {circumflex over (x)}   PA   [k]=ƒ   NL (   x     PD   (s)   [k;L];γ   IBO ) 
         [0000]    where ƒ NL (•) represents the nonlinearity of the HPA at a given level of saturation, and γ IBO  is a real-valued scaling parameter that can be included and used to scale to the correct input back-off (IBO) level. In practical application, and depending on the signal input, it may not be possible to completely eliminate the need for some input backoff. However, successive applications may allow the system designer to get as close to the saturation point as possible while avoiding unwanted levels of spectral regrowth. 
         [0042]    In some embodiments, the function ƒ NL (•) can be an estimate of the nonlinearity of the HPA. The function ƒ NL (•) can use the modeled HPA characteristics for static cases, or it can be adaptively estimated using standard estimation techniques such as stochastic gradient methods, to track slowly-varying effects due to ageing and temperature variations experienced by the HPA. Accordingly, ƒ NL (•) can be thought of as a model of the specified HPA that can be generated based on known amplifier characteristics, such as its nonlinearity at high saturation levels. In various embodiments, ƒ NL (•) can be approximated using, for example, polynomial approximation and can therefore be developed and trained off-line. 
         [0043]    The scaling parameter can be used to match the operating point of the amplifier. The scaling parameter can be determined based on where the system designer desires to operate the HPA. It can be chosen, for example, to provide the best balance between power loss and distortion, and it can be modeled in advance based on known operating characteristics of the amplifier. 
         [0044]    In the various stages, the determined estimate {circumflex over (x)} PA [k] may be utilized to generate a distortion sample e PA [k] relative to the undistorted sample. For example, in one embodiment, the estimate of the distortion introduced by the HPA can be subtracted out from the input signal to the HPA by the predistorter such that when the HPA distorts incoming signal that actually returns the incoming signal to, or closer to, its original form. Accordingly, distortion sample e PA [k] can be given by: 
         [0000]    
       
      
       e 
       PA 
       [k]=x[k]−{circumflex over (x)} 
       PA 
       [k] 
      
     
         [0045]    As noted above, various embodiments use a successive application of the predistortion to drive the distortion sample e PA [k] toward zero. For this, the predistortion output is generated by modifying the predistorted sample from the previous stage with a correction term that is proportional to the distortion sample. More particularly, the output of the predistorter at the s-th stage, x PD   (s+1) [k], is mathematically expressed as 
         [0000]    
       
      
       x 
       PD 
       (s+1) 
       [k]=x 
       PD 
       (s) 
       [k]+μ 
       1 
       (s) 
       ·e 
       PA 
       [k] 
      
     
         [0000]    where μ 1   (s)  is a step-size sequence satisfying certain conditions, including being positive and decreasing, to ensure progress toward a solution. 
         [0046]    The factor, μ, can be adjusted to control the speed of convergence. This factor can be determined and optimized using simulation techniques. In various embodiments, the μ factor is a positive value decreasing with each successive stage. 
         [0047]    The greater the convergence factor, μ, the quicker the solution converges. However, if the factor is not decreased in successive stages the system may overcompensate. Accordingly, the convergence factor starts at a large value for quicker convergence and as stages progress it gets increasingly smaller. 
         [0048]      FIG. 3  is a block diagram displaying an example implementation of this embodiment of the s-th stage of the signal predistorter. With reference now to  FIG. 3 , in this example the vector of complex-valued samples at the s-th stage,  x   PD   (s) [k;L], is input to a nonlinear estimator  204 . The subscript ‘PD’ indicates that these are pre-distorted symbols being input into nonlinear estimator  204  at this stage. The superscript ‘(s)’ indicates the number of the stage. 
         [0049]    In this example, non-linear estimator estimates the effect of the HPA on the input signal and outputs that estimation as {circumflex over (x)} PA [k]. Adder  206  determines the difference between this output estimate and the input signal x[k], to determine the distortion sample, e PA [k]=x[k]−{circumflex over (x)} PA [k]. 
         [0050]    The distortion sample is multiplied by the scaling factor μ 1   (s)  at signal multiplier  208 . μ 1   (s) ·e PA [k]. This is then added to the pre-distorted sample for that stage in adder  210 , resulting in the pre-distorted sample for the next stage, (s+1): x PD   (s+1) [k]=x PD   (s) [k]+μ 1   (s) ·e PA [k]. 
         [0051]    As noted above, L represents the memory span of the predistorter. In various applications, the high power amplifier can be memoryless or it can have a memory. Therefore, the memory span of the predistortion can be as large as the memory of the amplifier with which it is implemented. In various embodiments, predistortion can be implemented with an adjustable memory span L. 
         [0052]      FIG. 4  is a diagram illustrating an example signal model for implementing signal predistortion at the HPA in accordance with one embodiment of the technology described herein. Although the systems and methods disclosed herein can be implemented in a single-channel system, the example illustrated in  FIG. 4  is a multicarrier communication system having Mc carriers. Each carrier includes a bit source  302 , an FEC encoder/interlever  304 , a bit-to-symbol mapper  306 , a pulse shaper  310 , a successive signal predistorter  312  and HPA  314  and a mixer  316 . The adders  318  represent the communication channel which can introduce noise, n(t), into the system. 
         [0053]    In operation, data received at bit source  302  can be encoded using forward error correction (FEC) coding for error control purposes. Bit-to-symbol mapper  306  maps the incoming bits to samples in a constellation to create the M-ary constellation of samples  308 . Pulse shaper  310 , also referred to as a pulse shaping filter, transfers the resultant waveform for transmission by limiting its effective bandwidth. 
         [0054]    Signal pre-distort or  312  applies predistortion, such as that described above, to the signal before it is supplied to the HPA  314 . Because of the predistortion, HPA  314  can be configured to operate at or near saturation to amplify the wave form for transmission across the communication channel. 
         [0055]    At the receiver, the received signal is down converted at mixer  322 , applied it to a conjugate pulse shaper  324 , and sampled by sampler  326 . The inter-lever  328  and FEC decoder  330  reproduce estimates of the transmitted data. 
         [0056]    A second example embodiment is now described. While the above example focuses on spectral regrowth and may be applied at the HPA, this example focuses on in-band distortion (IBD). Particularly, this example embodiment may use a model of the receive filter, which has a band limited output. Because the receive filter filters out the effects spectral regrowth, there is little or no need to address this component of distortion at this point in the communication system. 
         [0057]    This example embodiment can be used to cancel in-band distortion experienced at the receive filter output and suppress MSE at the receiver, as manifested by clustering in a scatter plot typically encountered when operating the HPA at or near saturation. This example embodiment is now described. 
         [0058]    As in the first embodiment, the input to the second embodiment of the predistorter can be given by  x   PD   (s) [k;L], which in one example is a vector of complex-valued samples at the s-th stage: 
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         [0000]    where the parameter L is the double-sided memory span of the predistorter and s=0, 1, . . . , S−1. In some applications, the vector can be collapsed into a sample. A special case of the above is the first application of the predistortion for which the input is composed of the undistorted samples or 
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         [0059]    The sample {circumflex over (x)} RCVR [k] at the output of the receive filter can be estimated. This estimate of the distorted sample at the receive filter output can be stated as: 
         [0000]        x   RCVR   [k]=g   NL (   x     PD   (s)   [k;L];γ   IBO ) 
         [0000]    where g NL (•) represents the nonlinear system, including the receive filter, and γ IBO  is a real-valued parameter used to scale to the correct IBO level. 
         [0060]    The estimate {circumflex over (x)} RCVR [k] may be utilized to generate a receiver distortion sample e RCVR [k] relative to the sample as it would appear at the receive filter output without distortion, x RCVR,Ideal [k] or 
         [0000]    
       
      
       e 
       RCVR 
       [k]=x 
       RCVR,Ideal 
       [k]−{circumflex over (x)} 
       RCVR 
       [k] 
      
     
         [0061]    Successive application of the predistortion is then used to drive the distortion sample e RCVR [k] toward zero. For this, the predistortion output is generated by modifying the predistorted sample from the previous stage with a correction term that is proportional to the distortion sample. Namely, the output of the predistorter at the s-th stage, x PD   (s+1) [k], is mathematically expressed as 
         [0000]    
       
      
       x 
       PD 
       (s+1) 
       [k]=x 
       PD 
       (s) 
       [k]+μ 
       2 
       (s) 
       ·e 
       RCVR 
       [k] 
      
     
         [0000]    where μ 2   (s)  is a step-size sequence satisfying certain conditions, including being positive and decreasing, to ensure progress toward a solution. 
         [0062]    The third example embodiment combines predistortion to compensate for the HPA with predistortion to compensate for the receive filter to allow scaling of the two error signals relative to each other. The compensation applied to cancel distortion at the HPA or the receive filter can be weighted to adjust the amount of predistortion applied for each source of distortion. 
         [0063]    The output of this combined predistorter at the s-th stage, x PD   (s+1) [k], allows a weighted combination of the HPA predistortion signal correction and the receiver predistortion correction, such that two adjustments are made. This may be mathematically expressed as 
         [0000]        x   PD   (s+1)   [k]=x   PD   (s)   [k ]+(α·μ 1   (s)   ·e   PA   [k]+β·μ   2   (s)   ·e   RCVR   [k ])
 
         [0000]    which shows HPA predistortion, μ 1   (s) ·e PA [k], weighted by α, and receiver predistortion, μ 2   (s) ·e RCVR [k], weighted by β. In various embodiments, α,β are positive parameters that can be included for tunability to scale one factor relative to the other, and, μ 1   (s) , μ 2   (s)  are step-size sequences satisfying certain conditions, including being positive and decreasing, to ensure convergence toward a solution. Note that in this example, a weighted sum is taken of the distortion samples at the HPA output e PA [k] and the distortion sample at the receive filter output e RCVR [k], defined previously. Successive application of the predistortion here is used to drive the weighted sum of the distortion samples toward zero. 
         [0064]    The memory span of the predistorter, or parameter L above, may be selected by the designer to achieve good performance while meeting computational complexity requirements. The memory of the first embodiment is dictated by the memory of the HPA. For narrowband applications, typical of satellite return link communications, the HPA is memoryless, so it would be sufficient to use memoryless successive predistorter, or L=0. For wider bandwidth applications, such as wideband CDMA or wideband OFDM or multicarrier communications, HPA memory effect needs to be taken into consideration. Selecting L to match the memory span of the HPA provides good performance. Using memoryless predistortion for HPA with memory yields degraded performance. Moreover, the second and third example embodiments disclosed above introduce more memory into the predistortion to further suppress in-band distortion and provide significant tuning capability to balance levels of ACI and MSE. 
         [0065]    Results achieved by embodiments of the systems and methods disclosed herein have been modeled by simulation, and those results are now described. The simulations were configured using a simulation set up as depicted in  FIG. 4 , which as described above includes up to M c  data sources that transmit information bits through binary encoders. Code bits are interleaved and processed through bit-to-symbol mapping  306  onto the signal constellation  308 . A transmit filter p(t)  310  is used to provide bandwidth-efficient pulse shaping. At its output, the proposed successive signal predistorter  312  is placed, followed by the HPA  314 . Each HPA output is frequency translated to its respective frequency slot by mixers  316 . For simulation, Additive White Gaussian Noise (AWGN) n(t) is added to the sum of the frequency-translated outputs of the HPA devices. The noisy signal is then translated in frequency back to baseband and is processed by the receive filter which forms a matched pair with the transmit pulse, or p*(−t). This matched filter rejects noise in non-signal band. The sampled output is used to generate log-likelihood ratios (LLR) for the FEC decoders. 
         [0066]    As an example, in the simulation, a root-raised cosine (RRC) with a rolloff factor of 0.25 is used for pulse shaping, and 16-ary Amplitude and Phase Shift Keying (APSK) constellation is employed. Also, the HPA used in the testing is considered to be memoryless that introduces amplitude and phase distortions in terms of amplitude modulation (AM)/AM and AM/phase modulation (PM) conversions that can be modeled. The placement of transmit and receive filters before and after the memoryless HPA introduces nonlinear distortion with memory. 
         [0067]    Results are reported at various levels of output back-off (OBO), which is defined as the loss in power, relative to saturation, of the modulated signal and is measured at the HPA output.  FIG. 5  shows the Power Spectral Density (PSD) for the original signal  422  wihout distortion, for the amplified signal  426  without signal predistortion, for the amplified signal  424  with signal predistortion at the HPA output when operated at OBO level of 1.5 dB. This simulation illustrates the suppression of spectral regrowth due to nonlinear distortion by an amount that exceeds 8 dB as a result of signal predistortion. 
         [0068]      FIG. 6  shows Adjacent Channel Interference (ACI) with and without signal predistortion at the receive filter output for varying levels of OBO. For these measurements, adjacent carrier spacing of 1.25×symbol rate is used. This illustrates levels of ACI with successive signal predistortion  476  as compared with the levels of ACI without predistortion  478 . As this illustrates, the levels of ACI are drastically reduced by embodiments of the disclosed techniques, indicating the ability to suppress the spectral regrowth or out-of-band emission due to nonlinear distortion, while keeping the HPA operating efficiently at the same, or about the same, OBO level. 
         [0069]      FIG. 7  shows the mean-square error (MSE) at the best-sampled output of the receive filter with embodiments of the disclosed successive signal predistortion  512  and without signal predistortion  514 . As can be seen from the results of this simulation, the proposed signal predistortion effectively mitigates in-band distortion due to the nonlinear HPA behavior, while keeping the HPA operating efficiently at or near the same OBO level. 
         [0070]    As noted above in the third example embodiment, scaling can be applied to each of the two error signals to adjust their relative levels.  FIGS. 8 and 9  illustrate this tunability feature of embodiments of the disclosed technology. The results of this simulation illustrate that combinations of the first two example embodiments of signal predistortion offer a balance to trade-off levels of suppression of out-of-band distortion versus in-band distortion generated when nonlinear HPA is included in the system. 
         [0071]      FIG. 8  shows simulation results for ACI with embodiments of the disclosed successive signal predistortion  518  and without signal predistortion  520  at receive filter output for varying levels of OBO with adjacent carrier spacing of 1.25×symbol rate. Curve  523  illustrates an example in which the weighting coefficient for predistortion at the amplifier, α, is set at 1.0, and the weighting coefficient for predistortion at the receiver, β, is set at 0.0. Curve  525  illustrates an example in which the weighting coefficients for predistortion at the amplifier and at the receiver are each set at 0.5. Curve  527  illustrates an example in which the weighting coefficient for predistortion at the amplifier, α, is set at 0.3, and the weighting coefficient for predistortion at the receiver, β, is set at 0.7. 
         [0072]      FIG. 9  is similar to  FIG. 8  but shows the simulation results for MSE, instead of ACI, with successive signal predistortion  534  and without any signal predistortion  536  at the receive filter output for varying levels of OBO with an adjacent carrier spacing of 1.25×symbol rate. Curve  538  illustrates an example in which the weighting coefficient for predistortion at the amplifier, α, is set at 0.3, and the weighting coefficient for predistortion at the receiver, β, is set at 0.7. Curve  539  illustrates an example in which the weighting coefficients for predistortion at the amplifier and at the receiver are each set at 0.5. Curve  540  illustrates an example in which the weighting coefficient for predistortion at the amplifier, α, is set at 1.0, and the weighting coefficient for predistortion at the receiver, β, is set at 0.0. 
         [0073]    As these examples in  FIGS. 8 and 9  illustrate, with embodiments such as that in example embodiments three, the weighting coefficients for predistortion to cancel distortion at the amplifier and to cancel distortion at the receive filter can be adjusted to attack ACI, MSE, or a combination of both. 
         [0074]      FIG. 10  displays noiseless scatter plots at the best-sampled output of receive filter for a system without predistortion (left) and with proposed signal predistortion (right) at OBO level of 1.5 dB when no adjacent carriers are present. As the results of this simulation illustrate, in embodiments disclosed herein proposed scheme offer a significant reduction in the clustering with close to 11.5 dB improvement in MSE, while keeping the HPA operating efficiently at the same OBO level for both cases. 
         [0075]      FIG. 11  displays Power Spectral Density (PSD) as would be measured at the gateway when three equal-power carriers are transmitted at adjacent carrier spacing of 1.25×symbol rate. Particularly the shows the PSD without signal predistortion (left) and with signal predistortion (right) at OBO level of 1.5 dB, for the three carriers, each process through its own HPA, with adjacent carrier spacing of 1.25×symbol rate. As these simulation results illustrate, there is better separation between the adjacent frequency bands where signal predistortion is implemented. This might best be seen by the deeper valley between the carriers where signal predistortion is applied (right-hand side) as compared to the carriers for which there is no signal predistortion (left-hand side). 
         [0076]      FIG. 12  quantifies performance using an LDPC code having a code rate 2/3 and codeblock length of 5760 bits. The number of internal LDPC iterations in this simulation was set at 50. This figure shows the total degradation (TD) in dB relative to the ideal case of AWGN-only impairment at target coded packet error rate (PER) of 10 −3 . 
         [0077]      FIG. 12  also includes a comparison with existing signal predistortion technique reported in the open literature. In particular, a signal predistortion technique was chosen for comparison that predistorts the signal by applying memory polynomial (MP) inverse in a single-stage. Three curves are shown in the results of  FIG. 12 , one for a system employing the successive signal predistortion  575  described in embodiments herein, a second curve for a system employing single-stage signal predistortion using memory polynomial-based inverse  576 , and a third is for a system without predistortion  577 . The system that uses a memory polynomial-based inverse assumes a nonlinearity of the seventh order with odd and even terms, whose coefficients are obtained using least-mean-square (LMS) adaptation based on indirect learning, with a training sequence spanning 5000 symbols. Again, adjacent carrier spacing of 1.25×symbol rate is used. 
         [0078]    This shows that for lower levels of backoff, the successive signal predistortion according to embodiments disclosed herein provides lower levels of degradation as measured in dB as compared to applying a single-stage signal predistortion using memory polynomial-based inverse, or with no predistortion at all. This simulation indicates that the amplifier with successive signal predistortion can be pushed harder than it could otherwise be pushed without successive signal predistortion. As can be seen in the figure, the single-stage inverse-based signal predistortion performs better than the system without predistortion, yielding close to 0.3 dB improvement in TD. The proposed successive signal predistortion offers additional benefit over state-of-the-art signal predistortion using nonlinearity inverse, providing 0.9 further improvement in TD. 
         [0079]    While various embodiments of the disclosed technology have been described above, it should be understood that they have been presented by way of example only, and not of limitation. Likewise, the various diagrams may depict an example architectural or other configuration for the disclosed technology, which is done to aid in understanding the features and functionality that can be included in the disclosed technology. The disclosed technology is not restricted to the illustrated example architectures or configurations, but the desired features can be implemented using a variety of alternative architectures and configurations. Indeed, it will be apparent to one of skill in the art how alternative functional, logical or physical partitioning and configurations can be implemented to implement the desired features of the technology disclosed herein. Also, a multitude of different constituent module names other than those depicted herein can be applied to the various partitions. Additionally, with regard to flow diagrams, operational descriptions and method claims, the order in which the steps are presented herein shall not mandate that various embodiments be implemented to perform the recited functionality in the same order unless the context dictates otherwise. 
         [0080]    Although the disclosed technology is described above in terms of various exemplary embodiments and implementations, it should be understood that the various features, aspects and functionality described in one or more of the individual embodiments are not limited in their applicability to the particular embodiment with which they are described, but instead can be applied, alone or in various combinations, to one or more of the other embodiments of the disclosed technology, whether or not such embodiments are described and whether or not such features are presented as being a part of a described embodiment. Thus, the breadth and scope of the technology disclosed herein should not be limited by any of the above-described exemplary embodiments. 
         [0081]    Terms and phrases used in this document, and variations thereof, unless otherwise expressly stated, should be construed as open ended as opposed to limiting. As examples of the foregoing: the term “including” should be read as meaning “including, without limitation” or the like; the term “example” is used to provide exemplary instances of the item in discussion, not an exhaustive or limiting list thereof; the terms “a” or “an” should be read as meaning “at least one,” “one or more” or the like; and adjectives such as “conventional,” “traditional,” “normal,” “standard,” “known” and terms of similar meaning should not be construed as limiting the item described to a given time period or to an item available as of a given time, but instead should be read to encompass conventional, traditional, normal, or standard technologies that may be available or known now or at any time in the future. Likewise, where this document refers to technologies that would be apparent or known to one of ordinary skill in the art, such technologies encompass those apparent or known to the skilled artisan now or at any time in the future. 
         [0082]    The presence of broadening words and phrases such as “one or more,” “at least,” “but not limited to” or other like phrases in some instances shall not be read to mean that the narrower case is intended or required in instances where such broadening phrases may be absent. The use of the term “module” does not imply that the components or functionality described or claimed as part of the module are all configured in a common package. Indeed, any or all of the various components of a module, whether control logic or other components, can be combined in a single package or separately maintained and can further be distributed in multiple groupings or packages or across multiple locations. 
         [0083]    Additionally, the various embodiments set forth herein are described in terms of exemplary block diagrams, flow charts and other illustrations. As will become apparent to one of ordinary skill in the art after reading this document, the illustrated embodiments and their various alternatives can be implemented without confinement to the illustrated examples. For example, block diagrams and their accompanying description should not be construed as mandating a particular architecture or configuration.