Low Complexity Equalization for Doubly Selective Channels Modeled by a Basis Expansion

We propose a novel equalization method for doubly selective wireless channels, whose taps are represented by an arbitrary Basis Expansion Model (BEM). We view such a channel in the time domain as a sum of product-convolution operators created from the basis functions and the BEM coefficients. Equivalently, a frequency-domain channel can be represented as a sum of convolution-products. The product-convolution representation provides a low-complexity, memory efficient way to apply the channel matrix to a vector. We compute a regularized solution of a linear system involving the channel matrix by means of the GMRES and the LSQR algorithms, which utilize the product-convolution structure without ever explicitly creating the channel matrix. Our method applies to all cyclic-prefix transmissions. In an OFDM transmission with K subcarriers, each iteration of GMRES or LSQR requires only O(K K) flops and O(K) memory. Additionally, we further accelerate convergence of both GMRES and LSQR by using the single-tap equalizer as a preconditioner. We validate our method with numerical simulations of a WiMAX-like system (IEEE 802.16e) in channels with significant delay and Doppler spreads. The proposed equalizer achieves BERs comparable to those of MMSE equalization, and noticeably outperforms low-complexity equalizers using an approximation by a banded matrix in the frequency domain. With preconditioning, the lowest BERs are obtained within 3-16 iterations. Our approach does not use any statistical information about the wireless channel.