This paper presents a novel turbo-equalizer based on Backward Information Forward Marginals (BIFM) Kalman smoothing. We extend this Kalman smoother with an Expectation Propagation (EP) based message passing strategy to derive an iterative time-domain turbo-equalizer, which exploits a sequential soft decision feedback to improve the detection performance. The application of this receiver to Faster-Than-Nyquist (FTN) signaling demonstrates gains of up to 13 dB compared to existing frequency-domain EP equalizers, at the cost of 12 times higher computational complexity, when operating at a high spectral efficiency of 5 bits/s/Hz.

Kalman smoothers have been successfully used in many digital communication receiver algorithms, including channel equalization. In this paper, we propose low complexity Kalman equalizers based on expectation propagation (EP), and we compare them with state-of-the-art EP-based Kalman equalizers to identify the structure with the most attractive complexity/performance trade-off. In addition, we provide a practical approach for further reducing the computational complexity of Kalman equalizers in time-varying channels. Our analysis show that the Kalman equalizer we derived based on the backward information forward marginals (BIFM) structure is the most efficient in terms of complexity/performance trade-off and numerical results attest its superiority in high-speed vehicle cellular communication scenarios above 50 km/h.

In this paper, a novel category of expectation propagation (EP) based frequency domain (FD) semi-blind receivers are proposed for single-carrier block transmissions. A recently proposed EP-based framework for deriving double-loop turbo detectors is extended to handle joint data-aided channel estimation along with EP-based soft interference cancellation (IC). When addressing this problem in a message passing framework, an unconventional probability density function prevent us from establishing analytical update functions for estimating data and channel estimates. This is solved with variational inference methods, such as mean-field (MF), expectation maximization (EM) or EP, using a three-loop receiver structure with flexible performance-complexity trade-off, thanks to fast Fourier transform (FFT) based processing.

This paper investigates the dynamic behaviour of doubly iterative bit-interleaved coded modulation (BICM) receivers based on expectation propagation (EP). When implemented in the frequency domain, for single-carrier (SC) systems, such receivers achieve attractive performance-complexity trade-offs in quasi-static wideband channels. With this category of receivers, conventional binary extrinsic information transfer (EXIT) functions are subject to a great number of parameters, including channel realizations, constellation and inner iteration parameters. Hence, this paper proposes a novel extrinsic information evolution analysis method which simplifies the receiver's EXIT function into independent inner transfer functions. The core idea is to track state-evolution dynamics of EP through numerically stable extrinsic variance/information transfer (EXVIT) functions. Numerical results attest to the accuracy of this method for tracking the asymptotic receiver behaviour.

This paper analyzes some emerging techniques from the broad area of Bayesian learning for the design of iterative receivers for single-carrier transmissions using bit-interleaved coded-modulation (BICM) in wideband channels. In particular, approximate Bayesian inference methods, such as expectation propagation (EP), and iterative signal-recovery methods, such as approximate message passing (AMP) algorithms are evaluated as frequency domain equalizers (FDE). These algorithms show that decoding performance can be improved by going beyond the established turbo-detection principles, by iterating over inner detection loops before decoding. A comparative analysis is performed for the case of quasistatic wideband communications channels, showing that the EP-based approach is more advantageous. Moreover, recent advances in structured learning are revisited for the iterative EP-based receiver by unfolding the inner detection loop, and obtaining a deep detection network with learnable parameters. To this end, a novel, mutual-information dependent learning cost function is proposed, suited to turbo detectors, and through learning, the detection performance of the deep EP network is optimized.

A novel multiuser multiple-input multiple-output (MU-MIMO) receiver for single-carrier frequency-division multiple-access (SC-FDMA) is proposed within the expectation propagation (EP) framework. Recent advances in iterative receiver design show the ability of low complexity EP-based iterative algorithms to achieve performance close to maximum a posteriori (MAP) detection. In this paper, based on the exact derivation of frequency-domain EP-based turbo receivers, we propose a novel spectrally and computationally efficient soft interference canceller (IC) with a doubly-iterative architecture. Asymptotic and finite-length analysis show that our proposal outperforms existing schemes with comparable complexity, in various spatial-multiplexing configurations.

This paper investigates the design and analysis of minimum mean square error (MMSE) turbo decision feedback equalization (DFE), with expectation propagation (EP), for single carrier modulations. Classical non iterative DFE structures have substantial advantages at high-data rates, even compared with turbo linear equalizers-interference cancellers (LE-IC), hence making turbo DFE-IC schemes an attractive solution. In this paper, we derive an iterative DFE-IC, capitalizing on the use of soft feedback based on expectation propagation, along with the use of prior information for improved filtering and interference cancellation. This turbo iterative DFE-IC significantly outperforms turbo LE-IC, especially at high-spectral efficiency and also exhibits performance improvements over existing DFE-IC variants. The proposed scheme can also be self-iterated, as done in the recent trend on EP-based equalizers, and it is shown to be an attractive alternative to linear self-iterated receivers. For time-varying (TV) filter equalizers, an efficient matrix inversion scheme is also proposed, considerably reducing the computational complexity relative to existing methods. Using finite-length and asymptotic analysis on a severely selective channel, the proposed DFE-IC is shown to achieve higher rates than known alternatives, with better waterfall thresholds and faster convergence, while keeping a similar computational complexity.

An original expectation propagation-based message passing framework is introduced, wherein transmitted symbols are considered to belong to the multivariate white Gaussian distribution family. This approach allows deriving a novel class of single-tap frequency domain (FD) receivers with a quasi-linear computational complexity in block length, thanks to fast-Fourier transform-based implementation. This framework is exposed in detail, through the design of a novel double-loop single-carrier FD equalizer (FDE), where self-iterations of the equalizer with the demapper and turbo iterations with the decoder provide numerous combinations for the performance and complexity tradeoff. Furthermore, the flexibility of this framework is illustrated with the derivation of an overlap FDE, used for time-varying channel equalization, among others, and with the design of an FD multiple-input multiple-output detector, used for spatial multiplexing. Through these different receiver design problems, this framework is shown to improve the mitigation of inter-symbol, inter-block, and multi-antenna interferences, compared to alternative single-tap FD structures of previous works. Thanks to finite-length and asymptotic analysis, supported by numerical results, the improvement brought by the proposed structures is assessed and then completed by also accounting for computational costs.