Equalization for OFDM with Multiple Delay-Doppler Paths using Conjugate Gradients with Chebyshev Preconditioning

In this paper we consider the performance of iterative solution techniques when applied to equalization for orthogonal frequency division multiplexing (OFDM) with multiple delay-doppler paths. The use of a minimum mean-squared error (MMSE) equalizer in this problem yields satisfactory bit error rate (BER) performance, but requires the inversion of a high-dimensional matrix. Reduced complexity is achieved by applying the method of conjugate gradients (CG). Proper use of preconditioning is used to accelerate convergence of CG in terms of reducing the number of steps required for good performance. We analyze the performance and efficiency of a polynomial-based preconditioner wherein an approximate inverse of the MMSE equalizer is formed from a linear combination of matrix-valued Chebyshev polynomials. The results of a simulation study are presented, demonstrating that Chebyshev-preconditioning substantially reduces the number of CG steps required to achieve performance close to that obtained with the MMSE estimator using the full inverse.