Online estimation of the optimum quadratic kernel size of second-order Volterra filters using a convex combination scheme

This paper presents a method for estimating the optimum memory size for identification of an unknown second-order Volterra kernel. As these structures may imply considerable computational demands, it is highly desirable to design adaptive realizations with a minimum number of coefficients. Therefore, we propose a combination scheme comprising two Volterra filters with time-variant sizes of the actually used quadratic kernels. By following some simple rules, the number of diagonals in the quadratic kernels is increased or decreased in order to find the optimum memory configuration in parallel to the coefficient adaptation. Thus, the arbitrary choice of the nonlinear system size is overcome by a dynamically growing/shrinking system. Experimental results for various signals and nonlinear scenarios demonstrate the effectiveness of the proposed method.