Fast robust Quasi-Newton adaptive algorithms for general array processing

This thesis develops a new adaptive algorithm for general array signal-processing. It is a true stochastic Quasi-Newton (QN) Least Mean Squares (LMS) algorithm, as compared to simply an accelerated LMS algorithm. It is inherently faster than LMS but slower than the Recursive Least Squares (RLS) algorithm (which is also QN but optimizes a different performance function). It is unique in that, as LMS, it requires only order-of-N computations per iteration compared to order-of N;Specifically, the new Fast Robust Quasi-Newton (FRQN) algorithm potentially has unique performance advantages over existing algorithms in time-critical digital adaptive antenna arrays, i.e. spatial filtering in a dynamic environment. That is because stable Fast RLS algorithms for general N-element adaptive arrays do not presently exist, only for tapped-delay-line (temporal) adaptive filters (6). The popular, order-of-N LMS algorithm suffers from slow modes of convergence in commonly-encountered ill-conditioned scenarios, and from high misadjustment. It is shown, analytically and via representative computer simulations, that the FRQN algorithm has order-of-N complexity, fast Quasi-Newton convergence and very small misadjustment. Robustness in this thesis refers to the stability of its properties with respect to type of array signal and scenario. The "price" for these desirable features is a larger tracking error, more bits of precision and twice the complexity as the Normalized LMS (NLMS) algorithm.;Background material includes tutorial developments of the LMS and RLS algorithms, a review of competing algorithms in the recent literature and applications which motivate their development. The FRQN algorithm is derived in detail and compared to the NLMS and RLS algorithms. Results demonstrate that in highly ill-conditioned and fast dynamic scenarios, FRQN outperforms the NLMS algorithm, and is only slightly worse than ordinary RLS at low to moderately-high signal-to-noise ratios. Analyses include stability in the mean and mean-square, misadjustment and tracking errors, computational aspects and ways of providing reference signals in possible applications.