In this paper, we present the result of our study on the application of artificial neural networks (ANNs) for adaptive channel equalization in a digital communication system using 4-quadrature amplitude modulation (QAM) signal constellation. We propose a novel single-layer Legendre functional-link ANN (L-FLANN) by using Legendre polynomials to expand the input space into a higher dimension. A performance comparison was carried out with extensive computer simulations between different ANN-based equalizers, such as, radial basis function (RBF), Chebyshev neural network (ChNN) and the proposed L-FLANN along with a linear least mean square (LMS) finite impulse response (FIR) adaptive filter-based equalizer. The performance indicators include the mean square error (MSE), bit error rate (BER), and computational complexities of the different architectures as well as the eye patterns of the various equalizers. It is shown that the L-FLANN exhibited excellent results in terms of the MSE, BER and the computational complexity of the networks.