Canonical piecewise linear network for nonlinear filtering and its application to blind equalization

Figure 1: Comparison of CMA and CPL blind equalizer performance (nonlinear channel) Figure 2: Comparison of CMA and CPL blind equalizer performance (linear channel) Abstract Canonical piecewise linear structures provide a desirable compromise between the approximation ability of nonlinear models and the eeciency and theoretical accessibility of the linear domain, and they reduce the parameter storage requirement of piecewise linear models considerably by employing a global linear representation. We rst study the representation and approximation ability of CPL network and show that we can always construct a partition for which a CPL representation exists, and that we can approximate any given continuous nonlinear mapping with a CPL network. We then present application of CPL network to blind equalization, show the ability of CPL equalizer to achieve blind equalization of a nonlinear channel, speciically, we show that if the distribution of the equalizer output is the same as that of the input to the channel, then the channel and equalizer combination is identity except for a sign and a delay factor. We also present experimental results to show the successful application of CPL lter to blind equalization.