Adaptive nonlinear least bit error-rate detection for symmetrical RBF beamforming

A powerful symmetrical radial basis function (RBF) aided detector is proposed for nonlinear detection in so-called rank-deficient multiple-antenna assisted beamforming systems. By exploiting the inherent symmetry of the optimal Bayesian detection solution, the proposed RBF detector becomes capable of approaching the optimal Bayesian detection performance using channel-impaired training data. A novel nonlinear least bit error algorithm is derived for adaptive training of the symmetrical RBF detector based on a stochastic approximation to the Parzen window estimation of the detector output’s probability density function. The proposed adaptive solution is capable of providing a signal-to-noise ratio gain in excess of 8 dB against the theoretical linear minimum bit error rate benchmark, when supporting four users with the aid of two receive antennas or seven users employing four receive antenna elements.