Fast and Robust Adaptation of DFT-Domain Volterra Filters in Diagonal Coordinates Using Iterated Coefficient Updates

This paper presents a novel data-reusing technique for implementing adaptive discrete Fourier transform (DFT) domain Volterra filters in diagonal coordinates having arbitrary nonlinear order. In general, a major drawback of such nonlinear filters is the large number of parameters. Thus, a weak excitation of higher-order kernels results in a slow convergence for system identification tasks. In order to exploit the available innovation of the signals more effectively, each data frame is processed for a specified number of iterations in an overlap-save scheme, thereby enhancing the convergence performance. Due to inherent recursions of the repeated filtering and updating steps, this concept also lends itself to a fast algorithm, requiring only a moderate increase in algorithmic complexity over a baseline implementation. A detailed comparison of the required number of multiplications is given for several different algorithm versions. Despite the relatively simple concept, the outlined iteration algorithm exhibits significant gains in both adaptation speed and steady-state convergence. This is demonstrated by various experiments for both stationary noise and speech input considering an application of nonlinear acoustic echo cancellation. Finally, investigations on the tracking behavior for time-variant nonlinearities and robustness against misdetection of double-talk situations confirm the promising benefits and good trade-off of the proposed iterated coefficient updates Volterra filters approach.