A Novel Circulant Approximation Method for Frequency Domain LMMSE Equalization

The coefficients of a Linear Minimum Mean Square Error (LMMSE) equalizer for a stationary random signal are defined by a Toeplitz system. The Toeplitz structure can be exploited to reduce computational complexity. In this paper we investigate the Levinson and Schur algorithm, as well as circulant embedding and circulant approximation methods applied to the Preconditioned Conjugate Gradient (PCG) method and Frequency Domain Equalization (FDE). We develop a novel circulant approximation method which improves the performance/complexity tradeoff. We show that the optimal choice of algorithms largely depends on the antenna configuration. Investigated configurations are Single Input Single Output (SISO), Single Input Multiple Output (SIMO) and Multiple Input Multiple Output (MIMO). All considered algorithms are benchmarked in terms of implementation complexity and capacity achieved by a High Speed Downlink Packet Access (HSDPA) receiver in a multipath fading scenario.