Complexity reduction of iterative receivers using low-rank equalization

This paper covers the consideration of an iterative or turbo receiver where the nonlinear trellis-based detection of the interleaved and coded data bits is replaced by linear detection using the Wiener filter (WF), i.e., the optimal linear filter based on the mean-square error (MSE) criterion. The equalization of channels with multiple antennas at the receiver as well as frequency-selective transfer functions requires high-dimensional observation vectors which involve computationally intense detectors. We extend an optimal but computationally efficient algorithm, originally derived for single receive antenna systems, to single-input multiple-output (SIMO) channels. To further reduce computational complexity, we apply the suboptimal low-rank multistage WF (MSWF), i.e., the WF approximation in the low-dimensional Krylov subspace, and replace additionally second-order statistics of nonstationary random processes by their time-invariant averages. Complexity investigations reveal the enormous capability of the proposed algorithms to decrease computational effort. Moreover, the analysis based on extrinsic information transfer (EXIT) charts as well as Monte Carlo simulations show that compared with reduced-rank detection methods based on eigensubspaces, the reduced-rank MSWF behaves near optimum although the rank is drastically reduced to two or even one.