Linear multichannel blind equalizers of nonlinear FIR Volterra channels

Truncated Volterra expansions model nonlinear systems encountered with satellite communications, magnetic recording channels, and physiological processes. A general approach for blind deconvolution of single-input multiple-output Volterra finite impulse response (FIR) systems is presented. It is shown that such nonlinear systems can be blindly equalized using only linear FIR filters. The approach requires that the Volterra kernels satisfy a certain coprimeness condition and that the input possesses a minimal persistence-of-excitation order. No other special conditions are imposed on the kernel transfer functions or on the input signal, which may be deterministic or random with unknown statistics. The proposed algorithms are corroborated with simulation examples.