Fast robust quasi-Newton algorithm for adaptive arrays

A stable, fast (order-of-N) quasi-Newton (QN) algorithm (FRQN) applicable to arbitrary array signals is presented. Its complexity is only twice that of the normalised least mean squares (NLMS) algorithm, yet its convergence is faster and smoother, proceeding along the optimal QN path as that of the order N² recursive least squares (RLS) algorithm, albeit more slowly. The development of its recursive update equation is outlined and compared to those of the NLMS and RLS algorithms, as well as variations of the conjugate gradient (CG) algorithm. Analytic expressions for its excess mean squared error in stationary and non-stationary scenarios are presented and compared with those of the LMS algorithm. Simulations of an adaptive array in a mobile wireless base-station show that the FRQN performance falls between that of the NLMS and RLS algorithms for a wide range of signal scenarios