Legendre Based Equalization For Nonlinear Wireless Communication Channels

A nonlinear adaptive channel equalizer in a wireless digital communication system is presented. The proposed Legendre equalizer (LE) employs Legendre functional expansion as in the single-layer functional-link ANN (FLANN) to expand the input space into a higher dimension. Unlike the conventional FLANN, the LE employs linear transfer functions at the output neurons rather than the nonlinear sigmoid or hyperbolic tangent transfer functions. This provides the proposed LE with the advantage of providing explicit formula relating the input and target patterns. It also removes back propagation needed in the adaptation of the conventional FLANN and consequently speeds up convergence and reduces the computational requirements. Training the proposed LE is performed using the fast gradient based LMS signed algorithm. A comparison between the proposed LE, linear FIR and FLANN based equalizers is demonstrated. The performance indicator is the bit error rate at different channel and nonlinearity models with additive white Gaussian noise.