Nonlinear channel identification and performance analysis with PSK inputs

Many real life systems are nonlinear. We focus on the so-called Volterra models and the input-output aspect of the identification problem. To this date, closed form solutions for the Volterra kernels exist only for Gaussian inputs and they are usually in rather complicated forms. In this paper, we adopt a class of non-Gaussian inputs, namely the PSK (phase shift keying) sequences, which are common in digital communications systems. Such signals allow for simple closed form solutions of the Volterra kernels of any order. Kernels are estimated separately thus preventing error propagation. Signal independent zero-mean additive noise can also be tolerated even when its color and distribution are unknown. Because closed form solutions for the kernels are available, explicit variance expressions for their estimates can also be derived. Simulation results verify our theoretical findings.