A new efficient quadratic filter based on the Chen´s LMS linear algorithm and its performance analysis

In this paper, we propose an efficient approach based on a fast convolution algorithm to reduce the computational complexity of the Least Mean Square (LMS) adaptive algorithm for the quadratic filter, i.e. the quadratic part of the second order Volterra filter (SOVF). The previous works using the fast convolution in the adaptive LMS filtering are limited to the linear case. We show that this approach reduces the multiplications number by close to 25%, at the expense of only 25% more additions. The steady-state performance of this algorithm is studied for gaussian inputs and in stationary setting. The Steady-State Excess Mean-Square-Error is evaluated. The theoretical performance predictions are shown to be in good agreement with simulation results, especially for small step-sizes.