Recursive inverse algorithm: Mean-square-error analysis

The recently proposed recursive inverse (RI) adaptive algorithm has shown improved performance compared to some well-known adaptive algorithms [1]. However, there has been no detailed study of its performance. In this paper, we provide an analytical treatment of the ensemble-average learning curve of the RI algorithm. A novel analytical result which describes the learning behavior of the RI algorithm is obtained. It is shown that within limits of approximation, the excess mean-square-error (MSE) of the algorithm approaches zero and the RI algorithm converges to a lower steady-state MSE than the LMS algorithm. The results show that the theoretical and experimental MSE curves of the RI algorithm are in agreement. Also, the MSE analysis of the RI algorithm in a nonstationary environment, where the optimum weight is assumed to be randomly changing about a fixed vector, is derived.