Linear and non-linear adaptive noise cancelers

Viewing noise cancellation as an input/output identification problem, designs are developed using third-order statistics which are insensitive to corruption of the reference signal by adaptive Gaussian noise of unknown covariance. As a by-product of designing linear noise cancelers, a parametric time-delay estimation approach is readily available. Higher-order statistics can also be employed to design nonlinear cancelers of the discrete Volterra type, which maximize the output signal-to-noise ratio. Both the linear only and the linear-quadratic designs are derived in batch and adaptive form, the latter being implemented using recursive least-squares approaches. Simulation examples are given to illustrate the new cancelers and to compare them with conventional approaches.