The operation of multichannel feedforward adaptive systems

A generalized formulation describing the operation of multichannel feedforward adaptive systems is developed that is applicable to random as well as to deterministic signals. Expressions for the optimum multichannel adaptive-filter transfer functions and the resulting minimized cost function are derived. The cost function is a generalized, nondiagonal, quadratic function of the error signal and the expended power. Spectral shaping of the cost function is also considered, which enables varying the emphasis between error and power reduction as a function of frequency. The maximum achievable error-reduction performance of multichannel feedforward adaptive systems is derived. Results of computer experiments are presented, validating all analytical results.