A Triple Cross-correlation Approach For Enhancing Noisy Signals

Noise cancelers are traditionally designed based on secondorder statistics of the available observation. The design assumes availability of a reference signal in the secondwy input, which is highly correlated with the noise, while being independent of the zero-mean information signal in the primary input. In this paper triple correlation based cancelers are derived for enhancing noisy signrds. It is shown that cancelers based on second- and higher-order statistics are equivalent when the additive noise and the reference signal are related by a linear time-invariant transformation. The triple correlation based noise canceler outperforms the classical design when the reference signal is corrupted by additive Gaussian noise of unknown covariance. Simulations illustrate the performance of the proposed design.