Multi-level Radial Basis Function Network Based Equalisers for Rayleigh Channel

Radial Basis Function (RBF) network based channel equalisers have a close relationship with Bayesian schemes. Decision feedback is introduced in the design of the RBF equaliser in order to reduce its computational complexity. The RBF Decision Feedback Equaliser (DFE) was found to give similar performance to the conventional mean square error (MSE) DFE over Gaussian channels using various Quadrature Amplitude Modulation (QAM) schemes, while requiring a lower feedforward and feedback order. Over Rayleigh-fading channels similar ndings were valid for binary modulation, while for higher order modems the RBF based DFE requires increased feedforward and feedback orders in order to outperform the conventional MSE DFE scheme. I. RADIAL BASIS FUNCTION NETWORK EQUALISER WITH DECISION FEEDBACK Background and Formalism The background to neural networks has been documented for example by Haykin [1] and Bishop [2]. Various so-called Radial Basis Function (RBF) based equalisers were studied by Chen, McLaughlin, Mulgrew and Grant [3, 4] and the reader is referred to the above references for background reading. Below we introduce our basic formalism in the context of the RBF Decision Feedback Equaliser (DFE) following the approach of Chen, Mulgrew and McLaughlin [3, 5], while extending it to M-ary modems. The characteristics of the transmitted sequence can be exploited by capitalising on the nite state nature of the channel and by considering equalisation as a geometric classi cation problem related to the complex signal constellation. We assume that the transmitted symbols are selected from the set of M complex values, Ii; i = 1; 2; : : : ;M, with equal probability. The symbol-spaced channel output can be de ned by