Development of a low complexity RLS based adaptive Filter

Abstract

The classical RLS algorithm is known to have fast convergence but a high computational complexity. It is based on the technique of using the well known matrix inversion lemma to build recursive equations from least squares technique. In this thesis we propose a di erent approach towards developing a RLS algorithm that is based on the iterative techniques for solution of the linear system of equations. Iterative techniques have the advantage of using a number of less computationally complex iterations to solve a linear system of equa- tions. Two such fundamental methods namely the Steepest Descent and the Gauss-Seidel algorithms are applied in developing low com- plexity RLS algorithms. Simple optimization is presented to reduce the overall complexity of the algorithm and not compromising on the performance. Simulation results are compared with those of the classical RLS algorithm and it is shown that the proposed algorithm gives convergence results similar to those of Classical RLS with the added advantage of reduced computational complexity.