Robust adaptive beamforming using least mean mixed norm algorithm

This paper proposes an accurate and rapidlyconvergent algorithm for enhanced adaptive beamforming based on the combination of the least mean mixed norm (LMMN) algorithm with initialization using sample matrix inversion (SMI). The algorithm uses a mixing parameter δ which controls the proportions of the error norms and offers an extra degree of freedom within the adaptation. Monte Carlo simulations show that the misadjustment curve has a minimum at δ = 0.40 which means that the proposed algorithm has an optimum steady-state performance at this mixing parameter value. The convergence of the algorithm is further improved by employing SMI to initialize the weights vector in the LMMN update equation. This makes the proposed SMI-initialized LMMN algorithm have a better steady state performance when compared to the least mean squares (LMS) algorithm and better stability properties when compared to the least mean fourth (LMF) algorithm. Simulation results obtained show that the developed SMI-initialized LMMN algorithm outperforms other algorithms in terms of computational efficiency, numerical accuracy, and cosnvergence rate.