Some Tricks of Calculations in MIL RLS Algorithm

This paper presents two optimized computational procedures of the Recursive Least Squares (RLS) adaptive filtering algorithm based on the Matrix Inversion Lemma (MIL). The traditional MIL RLS algorithm might be unstable due to the accumulation of the errors of the computations. These errors are the reasons of the loss of the Hermitian structure of the adaptive filter input signal correlation matrix. As a result, the matrix becomes noninvertible and this leads to the wrong calculation of the weighs and the unstable behavior of the adaptive filter. In this paper it is suggested to compute the main diagonal and only the upper or the lower diagonal part of the correlation matrix. The rest of the computations, required at each iteration, are executed assuming the Hermitian structure of the whole matrix. In this case, no loss of the matrix symmetry appears. This ensures the optimized MIL RLS algorithm stability that is demonstrated via the simulation of an adaptive antenna array. The optimization also decreases the MIL RLS algorithm complexity. This is demonstrated via the estimates of the number of the arithmetical operations per iteration of the traditional MIL RLS algorithm, its optimized versions and RLS algorithms based on the QR decomposition and Householder transform.