Adaptive Radial Basis Function Detector for Beamforming

We consider nonlinear detection in rank-deficient multiple-antenna assisted beamforming systems. By exploiting the inherent symmetry of the underlying optimal Bayesian detection solution, a symmetric radial basis function (RBF) detector is proposed and two adaptive algorithms are developed for training the proposed RBF detector. The first adaptive algorithm, referred to as the nonlinear least bit error, is a stochastic approximation to the Parzen window estimation of the detector output's probability density function while the second algorithm is based on a clustering. The proposed adaptive solutions are capable of providing a signal to noise ratio gain in excess of 8 dB against the theoretical linear minimum bit error rate benchmarker, when supporting four users with the aid of two receive antennas or five users employing three antenna elements.