Approximating Univariate Factored Distributions via Message-Passing Algorithms

Gaussian Mixture Models (GMMs) commonly arise in communication systems, particularly in bilinear joint estimation and detection problems. Although the product of GMMs is still a GMM, as the number of factors increases, the number of components in the resulting product GMM grows exponentially. To obtain a tractable approximation for a univariate factored probability density function (PDF), such as a product of GMMs, we investigate iterative message-passing algorithms. Based on Belief Propagation (BP), we propose a Variable Duplication and Gaussian Belief Propagation (VDBP)-based algorithm. The key idea of VDBP is to construct a multivariate measurement model whose marginal posterior is equal to the given univariate factored PDF. We then apply Gaussian BP (GaBP) to transform the global inference problem into local ones. Expectation propagation (EP) is another branch of message passing algorithms. In addition to converting the global approximation problem into local ones, it features a projection operation that ensures the intermediate functions (messages) belong to a desired family. Due to this projection, EP can be used to approximate the factored PDF directly. However, even if every factor is integrable, the division operation in EP may still cause the algorithm to fail when the mean and variance of a non-integrable belief are required. Therefore, this paper proposes two methods that combine EP with our previously proposed techniques for handling non-integrable beliefs to approximate univariate factored distributions.

Expectations in Expectation Propagation

Expectation Propagation (EP) is a widely used message-passing algorithm that decomposes a global inference problem into multiple local ones. It approximates marginal distributions (beliefs) using intermediate functions (messages). While beliefs must be proper probability distributions that integrate to one, messages may have infinite integral values. In Gaussian-projected EP, such messages take a Gaussian form and appear as if they have "negative" variances. Although allowed within the EP framework, these negative-variance messages can impede algorithmic progress. In this paper, we investigate EP in linear models and analyze the relationship between the corresponding beliefs. Based on the analysis, we propose both non-persistent and persistent approaches that prevent the algorithm from being blocked by messages with infinite integral values. Furthermore, by examining the relationship between the EP messages in linear models, we develop an additional approach that avoids the occurrence of messages with infinite integral values.

Multipath Component Power Delay Profile Based Joint Range and Doppler Estimation for AFDM-ISAC Systems

Integrated Sensing and Communication (ISAC) systems combine sensing and communication functionalities within a unified framework, enhancing spectral efficiency and reducing costs by utilizing shared hardware components. This paper investigates multipath component power delay profile (MPCPDP)-based joint range and Doppler estimation for Affine Frequency Division Multiplexing (AFDM)-ISAC systems. The path resolvability of the equivalent channel in the AFDM system allows the recognition of Line-of-Sight (LoS) and Non-Line-of-Sight (NLoS) paths within a single pilot symbol in fast time-varying channels. We develop a joint estimation model that leverages multipath Doppler shifts and delays information under the AFDM waveform. Utilizing the MPCPDP, we propose a novel ranging method that exploits the range-dependent magnitude of the MPCPDP across its delay spread by constructing a Nakagami-m statistical fading model for MPC channel fading and correlating the distribution parameters with propagation distance in AFDM systems. This method eliminates the need for additional time synchronization or extra hardware. We also transform the nonlinear Doppler estimation problem into a bilinear estimation problem using a First-order Taylor expansion. Moreover, we introduce the Expectation Maximization algorithm to estimate the hyperparameters and leverage the Expectation Consistent algorithm to cope with high-dimensional integration challenges. Extensive numerical simulations demonstrate the effectiveness of our MPCPDP-based joint range and Doppler estimation in ISAC systems.

Decentralized Expectation Propagation for Semi-Blind Channel Estimation in Cell-Free Networks

This paper serves as a correction to the conference version. In this work, we explore uplink communication in cell-free (CF) massive multiple-input multiple-output (MaMIMO) systems, employing semi-blind transmission structures to mitigate pilot contamination. We propose a simplified, decentralized method based on Expectation Propagation (EP) for semi-blind channel estimation. By utilizing orthogonal pilots, we preprocess the received signals to establish a simplified equivalent factorization scheme for the transmission process. Moreover, this study integrates Central Limit Theory (CLT) with EP, eliminating the need to introduce new auxiliary variables in the factorization scheme. We also refine the algorithm by assessing the variable scales involved. Finally, a decentralized approach is proposed to significantly reduce the computational demands on the Central Processing Unit (CPU).

Matched-filter Precoded Rate Splitting Multiple Access: A Simple and Energy-efficient Design

We introduce an energy-efficient downlink rate splitting multiple access (RSMA) scheme, employing a simple matched filter (MF) for precoding. We consider a transmitter equipped with multiple antennas, serving several single-antenna users at the same frequency-time resource, each with distinct message requests. Within the conventional 1-layer RSMA framework, requested messages undergo splitting into common and private streams, which are then precoded separately before transmission. In contrast, we propose a novel strategy where only an MF is employed to precode both the common and private streams in RSMA, promising significantly improved energy efficiency and reduced complexity. We demonstrate that this MF-precoded RSMA achieves the same delivery performance as conventional RSMA, where the common stream is beamformed using maximal ratio transmission (MRT) and the private streams are precoded by MF. Taking into account imperfect channel state information at the transmitter, we proceed to analyze the delivery performance of the MF-precoded RSMA. We derive the ergodic rates for decoding the common and private streams at a target user respectively in the massive MIMO regime. Finally, numerical simulations validate the accuracy of our analytical models, as well as demonstrate the advantages over conventional RSMA.

Exact SINR Analysis of Matched-filter Precoder

This paper answers a fundamental question about the exact distribution of the signal-to-interference-plus-noise ratio (SINR) under matched-filter (MF) precoding. Specifically, we derive the exact expressions for the cumulative distribution function (CDF) and the probability density function (PDF) of SINR under MF precoding over Rayleigh fading channels. Based on the exact analysis, we then rigorously prove that the SINR converges to some specific distributions separately in high SNR and in massive MIMO. To simplify the exact result in general cases, we develop a good approximation by modelling the interference as a Beta distribution. We then shift to the exact analysis of the transmit rate, and answer the fundamental question: How does the exact rate converge to the well-known asymptotic rate in massive MIMO? After that, we propose a novel approximation for the ergodic rate, which performs better than various existing approximations. Finally, we present some numerical results to demonstrate the accuracy of the derived analytical models.

Full-Duplex-Enabled Joint Communications and Sensing with Reconfigurable Intelligent Surfaces

The full-duplex (FD) technology has the potential to radically evolve wireless systems, facilitating the integration of both communications and radar functionalities into a single device, thus, enabling joint communication and sensing (JCAS). In this paper, we present a novel approach for JCAS that incorporates a reconfigurable intelligent surface (RIS) in the near-field of an FD multiple-input multiple-output (MIMO) node, which is jointly optimized with the digital beamformers to enable JSAC and efficiently handle self-interference (SI). We propose a novel problem formulation for FD MIMO JCAS systems to jointly minimize the total received power at the FD node's radar receiver while maximizing the sum rate of downlink communications subject to a Cram\'{e}r-Rao bound (CRB) constraint. In contrast to the typically used CRB in the relevant literature, we derive a novel, more accurate, target estimation bound that fully takes into account the RIS deployment. The considered problem is solved using alternating optimization, which is guaranteed to converge to a local optimum. The simulation results demonstrate that the proposed scheme achieves significant performance improvement both for communications and sensing. It is showcased that, jointly designing the FD MIMO beamformers and the RIS phase configuration to be SI aware can significantly loosen the requirement for additional SI cancellation.

Near-Field Intelligent Reflecting Surfaces for Millimeter Wave MIMO Full Duplex

Full duplex (FD) systems suffer from very high hardware cost and high power consumption to mitigate the self-interference (SI) in the analog domain. Moreover, in millimeter wave (mmWave) they rely on hybrid beamforming (HYBF) as a signal processing tool to partially deal with the SI, which presents many drawback, e.g., high insertion loss, high power consumption and high computational complexity for its configuration. This article proposes the use of near-field (NF-) IRSs for FD systems with the objective to solve the aforementioned issues cost-efficiently. Namely, we propose to truncate the analog stage of the mmWave FD systems and assist them with an NF-IRS, to simultaneously and smartly control the uplink (DL) and downlink (DL) channels, while assisting in shaping the SI channel: this to obtain very strong passive SI cancellation. A novel joint active and passive beamforming design for the weighted sum-rate (WSR) maximization of a NF-IRS-assisted mmWave point-to-point FD system is presented. Results show that the proposed solution fully reaps the benefits of the IRSs only when they operate in the NF, which leads to considerably higher gains compared to the conventional massive MIMO (mMIMO) mmWave FD and half duplex (HD) systems.

Per-link Parallel and Distributed Hybrid Beamforming for Multi-Cell Massive MIMO Millimeter Wave Full Duplex

This paper presents two novel hybrid beamforming (HYBF) designs for a multi-cell massive multiple-input-multiple-output (mMIMO) millimeter wave (mmWave) full duplex (FD) system under limited dynamic range (LDR). Firstly, we present a novel centralized HYBF (C-HYBF) scheme based on alternating optimization. In general, the complexity of C-HYBF schemes scales quadratically as a function of the number of users and cells, which may limit their scalability. Moreover, they require significant communication overhead to transfer complete channel state information (CSI) to the central node every channel coherence time for optimization. The central node also requires very high computational power to jointly optimize many variables for the uplink (UL) and downlink (DL) users in FD systems. To overcome these drawbacks, we propose a very low-complexity and scalable cooperative per-link parallel and distributed (P$\&$D)-HYBF scheme. It allows each mmWave FD base station (BS) to update the beamformers for its users in a distributed fashion and independently in parallel on different computational processors. The complexity of P$\&$D-HYBF scales only linearly as the network size grows, making it desirable for the next generation of large and dense mmWave FD networks. Simulation results show that both designs significantly outperform the fully digital half duplex (HD) system with only a few radio-frequency (RF) chains, achieve similar performance, and the P$\&$D-HYBF design requires considerably less execution time.

Hybrid Beamforming and Combining for Millimeter Wave Full Duplex Massive MIMO Interference Channel

Full-Duplex (FD) communication can revolutionize wireless communications as it avoids using independent channels for bi-directional communications. In this work, we generalize the point-to-point FD communication in millimeter wave (mmWave) band consisting of K-pair of massive MIMO FD nodes operating simultaneously. To enable the coexistence of massive MIMO FD links cost-efficiently, we present novel joint hybrid beamforming (HYBF) and combining scheme for weighted sum-rate (WSR) maximization. The proposed algorithm is based on alternative optimization based on the minorization-maximization method. Moreover, we present a novel SI and massive MIMO interference channel aware power allocation scheme to include the optimal power control. Simulation results show significant performance improvement compared to a traditional bidirectional half-duplex communication system.