Reduced-rank BEACON algorithm based on joint iterative optimization of adaptive filters

This paper presents a novel reduced-rank implementation of the set-membership (SM) Bounding Ellipsoid Adaptive Constrained Least Squares (BEACON) algorithm using the method of joint iterative optimization (JIO) of adaptive filters. The sparsely updating estimation error SM framework is applied to the adaption of the rank reduction matrix and the symbol estimation filter that operates in the reduced-rank signal subspace. A derivation of the scheme, based on least squares (LS) optimization, is given along with an intuitive geometric interpretation of the update procedure. The proposed JIO-BEACON algorithm along with other established reduced-rank algorithms are applied to interference suppression in a multiuser DS-CDMA system. The JIO-BEACON algorithm is shown to exceed the performance of the standard LS JIO and other existing algorithms in terms of convergence and steady state error whilst achieving significant complexity savings.