Nonlinear channel equalization for wireless communication systems using Legendre neural networks

In this paper, we present a computationally efficient neural network (NN) for equalization of nonlinear communication channels with 4-QAM signal constellation. The functional link NN (FLANN) for nonlinear channel equalization which we had proposed earlier, offers faster mean square error (MSE) convergence and better bit error rate (BER) performance compared to multilayer perceptron (MLP). Here, we propose a Legendre NN (LeNN) model whose performance is better than the FLANN due to simple polynomial expansion of the input in contrast to the trigonometric expansion in the latter. We have compared the performance of LeNN-, FLANN- and MLP-based equalizers using several performance criteria and shown that the performance of LeNN is superior to that of MLP-based equalizer, in terms of MSE convergence rate, BER and computational complexity, especially, in case of highly nonlinear channels. LeNN-based equalizer has similar performance as FLANN in terms of BER and convergence rate but it provides significant computational advantage over the FLANN since the evaluation of Legendre functions involves less computation compared to trigonometric functions.