Blind equalizers of multichannel linear-quadratic FIR Volterra channels

Blind equalization of general Volterra models has not been addressed, despite its practical value in communications, acoustics, and physiological modeling. Relying upon diversity (sufficient number of multiple outputs), we establish existence and uniqueness conditions which guarantee that single-input, FIR nonlinear Volterra channels can be perfectly but blindly equalized using linear FIR equalizers. Apart from a minimal order persistence-of-excitation condition (also present with input-output approaches), the inaccessible input is allowed to be deterministic or random and of unknown color or distribution. With the kernels also satisfying a certain co-primeness condition, we develop direct blind equalizers which by-pass the channel estimation step. Preliminary simulations corroborate our analytical results.