Asymptotic S/N results for an adaptive polyspectral canceller using sample matrix inversion

An adaptive polyspectral canceller configuration is defined, whereby auxiliary canceller channels are formed using distinct monomial expressions of the auxiliary sensor channels. If noises in the auxiliary canceller channels are correlated with the noise in a main channel, then improvement in output signal-to-noise (S/N) power ratio is possible by cancelling in linear fashion the correlated auxiliary canceller channels with the main channel. The convergence performance of the polyspectral canceller is analyzed. A simple expression is derived for the asymptotic S/N efficiency of the adaptive polyspectral canceller as a function of the number of independent input sample vectors used to calculate the adaptive canceller weights and other canceller/noise model parameters. It is shown by simulation for low-order polyspectral cancellers of a specific form with Gaussian inputs that this asymptotic expression is a good approximation of the actual S/N efficiency for a moderate number of input sample vectors. However, for moderate-to-high order polyspectral cancellers, the asymptotic expression is a poor indicator of performance