Channel Equalization With Expectation Propagation at Smoothing Level

Abstract

In this paper we propose a smoothing turbo equalizer based on the expectation propagation (EP) algorithm with quite improved performance compared to the Kalman smoother, at similar complexity. In scenarios where high-order modulations or/and large memory channels are employed, the optimal BCJR algorithm is computationally unfeasible. In this situation, lowcost but suboptimal solutions, such as the linear minimum mean square error (LMMSE), are commonly used. Recently, EP has been proposed as a tool to improve the Kalman smoothing performance. In this paper we review these solutions to apply the EP at the smoothing level, rather than at the forward and backwards stages. Also, we better exploit the information coming from the channel decoder in the turbo equalization schemes. With these improvements we reduce the computational complexity, speed up convergence and outperform previous approaches. We included some simulation results to show the robust behavior of the proposed method regardless of the scenario, and its improvement in terms of performance in comparison with other EP-based solutions in the literature.

A Double EP-Based Proposal for Turbo Equalization

“…This novel approach can be exploited in block, WF and KS implementations of the equalizer. The experimental results included show that the proposed equalizer improves or achieves the same performance of FEP, BEP and KSEP equalizers [10], [12] with half their computational complexity. It also outperforms the LMMSE, with just twice its complexity, and other EP-based solutions, such as the BP-EP [13].…”

“…Since the information provided by the channel decoder, ppu k q, is discrete, the first step of the equalizer is to find an initial Gaussian approximation, t r1s k pu k q. In [9]- [12], this Gaussian approximation is obtained by projecting ppu k q into the family of Gaussians, as the turbo LMMSE does, i.e.,…”

“…Recently research works successfully apply this tool to develop a turbo equalizer [9]- [14]. In [9]- [12], the EP is used to better approximate the posterior (or extrinsic) distribution at the output of the equalizer. To that end, the non Gaussian factors in (2) are replaced by Gaussians, denoted as…”

“…However, this equalizer does not improve the equalization step by itself since it boils down to the LMMSE for standalone equalization, i.e., if no turbo equalization is carried out. In contrast, in [9]- [12], [14] the output of the decoder is directly projected into the family of Gaussians, as the turbo LMMSE does, i.e., the EP is not applied at the output of the decoder. Instead, the EP is used to obtain a better Gaussian approximation for the extrinsic distribution at the output of the equalizer, before sending it to the channel decoder.…”

“…This equalizer improves the performance of the LMMSE and the EP in [13], either as standalone or turbo equalization. In other words, in [9]- [12], [14] the EP is used at an inner loop while in [13] it is used at an outer loop, as will be explained in Section III.…”