Expectation Propagation as Turbo Equalizer in ISI Channels

Santos, Irene; Murillo-Fuentes, Juan José; Boloix-Tortosa, Rafael; Arias-de-Reyna, Eva; Olmos, Pablo M.

doi:10.1109/tcomm.2016.2616141

Cited by 32 publications

(81 citation statements)

References 36 publications

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“…In a simpler scenario, i.e. channel equalization for single-user intersymbolinterference (ISI) channels, different heuristics have been recently proposed in [37] to improve the EP probabilistic output, but it is shown that ultimately a turbo-like receiver, where the LDPC decoder output is fed back to the EP equalizer, is required to obtain a robust solution that is not tailored to a particular modulation or channel instance.…”

mentioning

confidence: 99%

Probabilistic MIMO Symbol Detection With Expectation Consistency Approximate Inference

Cespedes

Olmos

Sanchez-Fernandez

et al. 2018

IEEE Trans. Veh. Technol.

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In this paper we explore low-complexity probabilistic algorithms for soft symbol detection in high-dimensional multiple-input multiple-output (MIMO) systems. We present a novel algorithm based on the Expectation Consistency (EC) framework, which describes the approximate inference problem as an optimization over a non-convex function. EC generalizes algorithms such as Belief Propagation and Expectation Propagation. For the MIMO symbol detection problem, we discuss feasible methods to find stationary points of the EC function and explore their tradeoffs between accuracy and speed of convergence. The accuracy is studied, first in terms of input-output mutual information and show that the proposed EC MIMO detector greatly improves state-of-the-art methods, with a complexity order cubic in the number of transmitting antennas. Second, these gains are corroborated by combining the probabilistic output of the EC detector with a low-density parity-check (LDPC) channel code.

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confidence: 99%

Probabilistic MIMO Symbol Detection With Expectation Consistency Approximate Inference

Cespedes

Olmos

Sanchez-Fernandez

et al. 2018

IEEE Trans. Veh. Technol.

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“…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.,…”

Section: Double Ep Turbo Equalizermentioning

confidence: 99%

“…At this point, it is important to remark the difference with previous proposals, where the EP is applied just once. In [9]- [12], the EP 2 block is replaced by a projection into a Gaussian distribution, as described in (15). On the other hand, in the proposal in [13], named BP-EP, the block EP 1 does not appear, i.e., BP-EP can be viewed as a particularization of the scheme in Fig.…”

Section: Double Ep Turbo Equalizermentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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A Double EP-Based Proposal for Turbo Equalization

Santos

Murillo-Fuentes

Arias-de-Reyna

2020

IEEE Signal Process. Lett.

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This letter deals with the application of the expectation propagation (EP) algorithm to turbo equalization. The EP has been successfully applied to obtain either a better approximation at the output of the equalizer or at the output of the channel decoder to better initialize the Gaussian prior used by the equalizer. In this letter we combine both trends to propose a novel double EP-based equalizer that is able to decrease the number of iterations needed, reducing the computational complexity to twice that of the linear MMSE. This novel equalizer is developed in three different implementations: a block design that exploits the whole vector of observations, a Wiener filter-type approach that just uses the observations within a predefined window and a Kalman smoothing filter-type approach that emulates the BCJR behavior. Finally, we include some experimental results to compare the three different implementations and to detail their improvements with respect to other EP-based proposals in the literature.

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“…In [10], a block implementation of an EP-based equalizer is proposed, whose complexity is quadratic in the frame length. This implementation is revised in [23] to propose an optimized version for turbo equalization.…”

Section: Introductionmentioning

confidence: 99%

Channel Equalization With Expectation Propagation at Smoothing Level

Santos

Murillo-Fuentes

Aradillas

et al. 2020

IEEE Trans. Commun.

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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.

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Expectation Propagation as Turbo Equalizer in ISI Channels

Cited by 32 publications

References 36 publications

Probabilistic MIMO Symbol Detection With Expectation Consistency Approximate Inference

Probabilistic MIMO Symbol Detection With Expectation Consistency Approximate Inference

A Double EP-Based Proposal for Turbo Equalization

Channel Equalization With Expectation Propagation at Smoothing Level

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