Analysis of convex adaptive structures and algorithms for smart antennas

In this paper, two different filter structures for smart antennas based on a convex combination of independent transversal adaptive sub-filters are analyzed. The first structure combines the least-mean-squares (LMS) and the augmented complex least-mean-squares (ACLMS) algorithms, whereas the second one uses the recursive least-squares (RLS) and the complex dual least-mean-squares (CDU-LMS) algorithms. The individual sub-filters are independently adapted using their own error signals, while the whole smart system is adapted by means of a convex stochastic gradient algorithm that generates an third independent error signal. The number of iterations required to reach convergence and the effects of the control parameter τ on the learning curve of the whole structure are studied. According to the simulation, these hybrid smart structures turned out to be more robust than a smart antenna that uses an unique adaptive filter. In general, both hybrid smart beamformers show to have a better filtering capacity than the standard LMS and RLS smart antenna systems. General equations for the overall output and the radiation pattern have been developed for both variations.