Kernel-Based Nonlinear Beamforming Construction Using Orthogonal Forward Selection With the Fisher Ratio Class Separability Measure

Abstract

Abstract-This letter shows that the wireless communication system capacity is greatly enhanced by employing nonlinear beamforming and that the optimal Bayesian beamformer outperforms the standard linear beamformer significantly in terms of a reduced bit error rate, at a cost of increased complexity. A block-data adaptive implementation of the Bayesian beamformer is realized based on an orthogonal forward selection procedure with the Fisher ratio for class separability measure.Index Terms-Bayesian classification, Fisher ratio for class separability measure, nonlinear beamforming, orthogonal least squares.

Adaptive minimum error-rate filtering design: A review

“…Otherwise, nonlinear filtering is required in order to achieve an adequate performance. Examples of such nonlinear filtering include nonlinear single-user channel equalisation [89][90][91][92][93][94][95][96][97][98][99][100][101], nonlinear CDMA multiuser detection [102], nonlinear beamforming assisted detection [103][104][105][106], and nonlinear space-time equalisation [107]. Let us consider the generic nonlinear filter of the form y R ðkÞ ¼ f ðxðkÞ; wÞ,…”

“…3, as an example to illustrate the above NLBER filtering. The optimal nonlinear filtering for beamforming detection is known to be the Bayesian detector [103][104][105][106], which requires the complete knowledge of the underlying system (1). The Bayesian beamforming detector has an inherently odd symmetry property [105,106].…”

Adaptive Radial Basis Function Detector for Beamforming

“…The L-MMSE technique requires that the number of users M is no higher than the number of antenna array elements L. The optimal weight vector designed for the linear beamformer is known to be the L-MBER solution [12], [13] which directly minimises the BER of the linear beamformer and is capable of operating in rank-deficient scenarios. However, the optimal multiple antenna aided beamforming detector is nonlinear [16], [25]. Let us denote the…”

“…However, digital communication signal detection can be viewed as a classification problem [14]- [16], where the receiver detector simply classifies the received multidimensional channel-impaired signal into the most-likely transmitted symbol constellation point or class. Both the radial basis function (RBF) network [17]- [19] and other kernel models [20]- [25] have been applied to solve this nonlinear detection problem. All these nonlinear detectors attempt to approximate the underlying optimal Bayesian solution.…”

“…This symmetric property is difficult to infer from noisy training data using a standard RBF model. In fact, previous studies [16]- [25] have shown that a standard RBF detector typically requires significantly more RBF centres than the number of channel output states in order to approximate the Bayesian detector using noisy training data, and often there is a performance difference between such a RBF detector and the optimal Baysian solution. In contrast to the standard RBF model, the proposed symmetric RBF model is capable of approaching the optimal Bayesian performance accurately, despite using channel-impaired training data and despite using no more RBF centres than the number of channel output states.…”