Nonlinear signal filtering

Abstract

In a nonlinear signal filtering system, a signal having a series of signal samples is filtered. The signal samples are affected by interactions with adjacent signal samples and nonlinear distortions. The system contains a series of alternating linear system elements and nonlinear system elements that are used for mitigation of distortion resulting from the nonlinear distortions with memory effects. The linear system elements can scale each signal sample in the series of signal samples by scaling parameters and sums a plurality of consecutive scaled signal samples, and the nonlinear system elements can transform the output of the linear system elements according to instantaneous nonlinear functions.

What is claimed is: 
     
         1 . A nonlinear signal filtering system comprising:
 a series of one or more filtering stages that filter a signal comprising a series of signal samples, each filtering stage comprising alternating linear system elements and nonlinear system elements;   wherein the linear system elements and nonlinear system elements correct 1) sample interactions between a plurality of consecutive signal samples in the signal, and 2) nonlinear distortions in a value of each signal sample.   
     
     
         2 . The nonlinear signal filtering system of  claim 1 , wherein the linear system elements and the nonlinear system elements process multiple input signals to produce multiple output signals. 
     
     
         3 . The nonlinear signal filtering system of  claim 1 , wherein the linear system elements comprise tapped delay lines. 
     
     
         4 . The nonlinear signal filtering system of  claim 1 , wherein the signal comprises:
 a first signal sample in the series of signal samples affected by an interaction with N consecutive signal samples adjacent to the first signal sample; and   the value of each signal sample in the series of signal samples is subject to nonlinear distortions.   
     
     
         5 . The nonlinear signal filtering system of  claim 4 , wherein:
 the linear system elements in each filtering stage comprise linear filtering functions each comprising from 1 to N parameters;   the nonlinear system elements in each filtering stage comprise nonlinear filtering functions each comprising from 1 to M parameters; and   the total number of parameters used in each filtering stage to correct 1) the sample interactions between the plurality of consecutive signal samples in the signal, and 2) the nonlinear distortions in the value of each signal sample, is equal to, or less than the sum of N and M.   
     
     
         6 . The nonlinear signal filtering system of  claim 5 , wherein M is from 1 to 10. 
     
     
         7 . The nonlinear signal filtering system of  claim 5 , wherein the nonlinear filtering functions are instantaneous functions selected from the group consisting of: piece-wise linear functions, nonlinear functions, or piece-wise nonlinear functions. 
     
     
         8 . The nonlinear signal filtering system of  claim 1 , comprising from 2 to 10 filtering stages connected sequentially in series to receive and filter the series of signal samples. 
     
     
         9 . The nonlinear signal filtering system of  claim 8 , wherein:
 a first filtering stage comprises a first linear system element and a first nonlinear system element;   each subsequent filtering stage comprises a subsequent linear system element and a subsequent nonlinear system element;   the first linear system element in the first filtering stage produces a linear combination of the series of signal samples by means of scaling each signal sample in the series of signal samples by first scaling parameters, sums a first number of consecutive scaled signal samples, and produces a first series of linearly transformed signal samples;   the first nonlinear system element in the first filtering stage transforms each of the samples in the first series of linearly transformed signal samples according to a first instantaneous nonlinear function, and produces a first series of nonlinearly transformed signal samples;   the subsequent linear system elements in the subsequent stages scale each transformed signal sample in the series of nonlinearly transformed signal samples produced by a preceding stage by subsequent scaling parameters, sums a subsequent number of consecutive scaled signal samples, and produces a subsequent series of linearly transformed signal samples;   the subsequent nonlinear system elements in the subsequent stages transform the subsequent series of linearly transformed signal samples according to a subsequent instantaneous nonlinear function, and produces a subsequent series of nonlinearly transformed signal samples; and   the first scaling parameters, the subsequent scaling parameters, the first instantaneous nonlinear function, and the subsequent instantaneous nonlinear functions correct for the sample interactions and the nonlinear distortions.   
     
     
         10 . The nonlinear signal filtering system of  claim 8 , wherein:
 each filtering stage comprises one of the linear system elements and one of the nonlinear system elements;   a first one of the linear system elements in a first one of the filtering stages receives as its input each signal sample in the series of signal samples;   each subsequent linear system element receives as its input an output of a preceding nonlinear system element;   each nonlinear system element receives as its input an output of a preceding linear system element;   each linear system element produces an output of linearly transformed signal samples;   each nonlinear system element produces an output of nonlinearly transformed signal samples;   each linear system element scales its input by scaling parameters and sums a plurality of consecutive scaled signal samples for each linearly transformed signal sample;   each nonlinear system element transforms its input according to an instantaneous nonlinear function for each nonlinearly transformed signal sample.   
     
     
         11 . The nonlinear signal filtering system of  claim 8 , wherein:
 a first filtering stage comprises:
 a first linear system element that scales each signal sample in the series of signal samples by scaling parameters and sums a plurality of consecutive scaled signal samples; and 
 a first stage nonlinear system element that transforms an output of the first linear system element according to an instantaneous nonlinear function; 
   each subsequent filtering stage comprises:
 a subsequent linear system element that scales the output of a preceding stage by scaling parameters and sums a plurality of consecutive scaled signal samples; and 
 a subsequent nonlinear system element, wherein the nonlinear system element transforms an output of the preceding linear system element according to an instantaneous nonlinear function; and 
   the scaling parameters in the linear system elements and the instantaneous nonlinear functions of the nonlinear system elements correct for the sample interactions and the nonlinear distortions in the value of each signal sample.   
     
     
         12 . The nonlinear signal filtering system of  claim 8 , wherein:
 a first filtering stage comprises a first linear system element and a first nonlinear system element;   a second filtering stage comprises a second linear system element and a second nonlinear system element;   the first linear system element scales each signal sample in the series of signal samples by first scaling parameters, sums a first number of consecutive scaled signal samples, and produces a first series of linearly transformed signal samples;   the first nonlinear system element transforms the first series of linearly transformed signal samples according to a first instantaneous nonlinear function, and produces a first series of nonlinearly transformed signal samples;   the second linear system element scales each transformed signal sample in the first series of nonlinearly transformed signal samples by second scaling parameters, sums a second number of consecutive scaled signal samples, and produces a second series of linearly transformed signal samples;   the second nonlinear system element transforms the second series of linearly transformed signal samples according to a second instantaneous nonlinear function, and produces a second series of nonlinearly transformed signal samples; and   the first and second scaling parameters and the first and second instantaneous nonlinear functions correct for the sample interactions and the nonlinear distortions.   
     
     
         13 . A nonlinear signal filtering system comprising:
 a first linear system element that receives a signal comprising a series of signal samples;   a first nonlinear system element connected to receive an output of the first linear system element; and   a second linear system element connected to receive an output of the first nonlinear system element;   and wherein:   a first signal sample in the series of signal samples is affected by an interaction with one or more consecutive signal samples adjacent to the first signal sample;   a value of each signal sample in the series of signal samples is subject to nonlinear distortions;   the first linear system element scales each signal sample in the series of signal samples using scaling parameters and sums a plurality of consecutive scaled signal samples;   the first nonlinear system element transforms the output of the first linear system element according to an instantaneous nonlinear function;   the second linear system element scales the output of the first nonlinear system element by scaling parameters and sums a plurality of consecutive scaled outputs of the first nonlinear system element; and   the scaling parameters in the first linear system element and the second linear system element and the instantaneous nonlinear function of the first nonlinear system element correct for the signal sample interactions and the nonlinear distortions in the value of each signal sample.   
     
     
         14 . The nonlinear signal filtering system of  claim 13 , wherein
 the consecutive signal samples are one of: before the first signal sample, after the first signal sample, or both before and after the first signal sample; and   the number of consecutive scaled signal samples that are summed by the first linear system element is from 1 to 200.   
     
     
         15 . The nonlinear signal filtering system of  claim 13 , wherein
 the nonlinear distortions in the value of each signal sample are described by functions selected from the group consisting of: piece-wise linear functions, nonlinear functions, or piece-wise nonlinear functions.   
     
     
         16 . The nonlinear signal filtering system of  claim 13 , wherein
 the first linear system element is a tapped delay line.   
     
     
         17 . The nonlinear signal filtering system of  claim 13 , wherein
 the instantaneous nonlinear function of the first nonlinear system element is a function selected from the group consisting of: piece-wise linear functions, nonlinear functions, or piece-wise nonlinear functions.   
     
     
         18 . The nonlinear signal filtering system of  claim 13 , wherein
 the second linear system element is a tapped delay line.   
     
     
         19 . A method for filtering a signal comprising:
 providing a signal comprising a series of signal samples, wherein a first signal sample in the series of signal samples is affected by an interaction with one or more consecutive signal samples adjacent to the first signal sample, and a value of each signal sample is subject to nonlinear distortions;   filtering the signal through a first linear system element, wherein the first linear system element scales each signal sample by a scaling parameter and sums a plurality of consecutive scaled signal samples; and   filtering an output of the first linear system element using a first nonlinear system element, wherein the first nonlinear system element transforms the output of the first linear system element according to an instantaneous nonlinear function;   wherein the scaling parameters in the first linear system element and the instantaneous nonlinear function of the first nonlinear system element correct for the signal sample interactions and the nonlinear distortions in the value of each signal sample in the signal.   
     
     
         20 . The method of  claim 19 , wherein
 the consecutive signal samples are selected from the group consisting of: a set of signal samples before the first signal sample, a set of signal samples after the first signal sample, or a set of signal samples both before and after the first signal sample, and   the number of consecutive scaled signal samples that are summed by the first linear system element is from 1 to 200.