Stability and convergence behaviour of second-order LMS Volterra filter

The stability and convergence characteristics of a second-order LMS Volterra filter subjected to stationary random inputs are reported. Conditions are obtained for convergence in the mean and in the mean square. It is also shown that the stability depends on the eigenvalues associated with input signal moments to order four, and that the second-order Volterra undergoes nonuniform convergence even with white inputs. These results contrast sharply with the usual LMS, and with previously published results for second-order systems.