Information Theory (cs.IT)

Abstract: Signal processing over hypercomplex numbers arises in many optical imaging applications. In particular, spectral image or color stereo data are often processed using octonion algebra. Recently, the eight-band multispectral image phase recovery has gained salience, wherein it is desired to recover the eight bands from the phaseless measurements. In this paper, we tackle this hitherto unaddressed hypercomplex variant of the popular phase retrieval (PR) problem. We propose octonion Wirtinger flow (OWF) to recover an octonion signal from its intensity-only observation. However, contrary to the complex-valued Wirtinger flow, the non-associative nature of octonion algebra and the consequent lack of octonion derivatives make the extension to OWF non-trivial. We resolve this using the pseudo-real-matrix representation of octonion to perform the derivatives in each OWF update. We demonstrate that our approach recovers the octonion signal up to a right-octonion phase factor. Numerical experiments validate OWF-based PR with high accuracy under both noiseless and noisy measurements.

Abstract: The far-field channel model has historically been used in wireless communications due to the simplicity of mathematical modeling and convenience for algorithm design, and its validity for relatively small array apertures. With the need for high data rates, low latency, and ubiquitous connectivity in the sixth generation (6G) of communication systems, new technology enablers such as extremely large antenna arrays (ELAA), reconfigurable intelligent surfaces (RISs), and distributed multiple-input-multiple-output (D-MIMO) systems will be adopted. These enablers not only aim to improve communication services but also have an impact on localization and sensing (L\&S), which are expected to be integrated into future wireless systems. Despite appearing in different scenarios and supporting different frequency bands, these enablers share the so-called near-field (NF) features, which will provide extra geometric information. In this work, starting from a brief description of NF channel features, we highlight the opportunities and challenges for 6G NF L\&S.

Abstract: We establish several convexity properties for the entropy and Fisher information of mixtures of centered Gaussian distributions. First, we prove that if $X_1, X_2$ are independent scalar Gaussian mixtures, then the entropy of $\sqrt{t}X_1 + \sqrt{1-t}X_2$ is concave in $t \in [0,1]$, thus confirming a conjecture of Ball, Nayar and Tkocz (2016) for this class of random variables. In fact, we prove a generalisation of this assertion which also strengthens a result of Eskenazis, Nayar and Tkocz (2018). For the Fisher information, we extend a convexity result of Bobkov (2022) by showing that the Fisher information matrix is operator convex as a matrix-valued function acting on densities of mixtures in $\mathbb{R}^d$. As an application, we establish rates for the convergence of the Fisher information matrix of the sum of weighted i.i.d. Gaussian mixtures in the operator norm along the central limit theorem under mild moment assumptions.

Abstract: With the rapid advancement of the Internet of Things (IoT) and mobile communication technologies, a multitude of devices are becoming interconnected, marking the onset of an era where all things are connected. While this growth opens opportunities for novel products and applications, it also leads to increased energy demand and battery reliance in IoT devices, creating a significant bottleneck that hinders sustainable progress. Traditional energy harvesting (EH) techniques, although promising, face limitations such as insufficient efficiency, high costs, and practical constraints that impede widespread adoption. Backscatter communication (BackCom), a low-power and passive method, emerges as a promising solution to these challenges, directly addressing stranded energy impasse by reducing manufacturing costs and energy consumption in IoT devices. We perform an in-depth analysis of three primary BackCom architectures: Monostatic, Bistatic, and Ambient BackComs. In our exploration, we identify fundamental challenges, such as complex interference environments (including the direct-link interference and the mutual interference among tags) and double-path fading, which contribute to suboptimal performance in BackCom systems. This review aims to furnish a comprehensive examination of existing solutions designed to combat complex interference environments and double-path fading, offering insightful analysis and comparison to select effective strategies to address these challenges. We also delve into emerging trends and challenges in BackCom, forecasting potential paths for technological advancement and providing insights into navigating the intricate landscape of future communication needs. Our work provides researchers and engineers with a clear and comprehensive perspective, enabling them to better understand and creatively tackle the ongoing challenges in BackCom systems.

Abstract: The first linear programming bound of McEliece, Rodemich, Rumsey, and Welch is the best known asymptotic upper bound for binary codes, for a certain subrange of distances. Starting from the work of Friedman and Tillich, there are, by now, some arguably easier and more direct arguments for this bound. We show that this more recent line of argument runs into certain difficulties if one tries to go beyond this bound (say, towards the second linear programming bound of McEliece, Rodemich, Rumsey, and Welch).

Abstract: This article examines the problem of state estimation over multi-terminal channels in an unreliable regime. More specifically, we consider two canonical settings. In the first setting, measurements of a common stochastic source need to be transmitted to two distinct remote monitors over a packet-erasure broadcast channel. In the second setting, measurements of two distinct stochastic sources need to be transmitted to a common remote monitor over a packet-erasure multi-access channel. For these networked systems, we uncover the fundamental performance limits in the sense of a causal tradeoff between the estimation error and the communication cost by identifying optimal encoding and decoding strategies. In the course of our analysis, we introduce two novel semantic metrics that play essential roles in state estimation over broadcast and multi-access channels. The first metric arising in the context of broadcast channels is the dissemination value of information, which quantifies the valuation of provisioning a piece of information to multiple receivers simultaneously. The second metric arising in the context of multi-access channels is the prioritization value of information, which quantifies the valuation of provisioning a piece of information chosen from one out of multiple transmitters. Our findings certify that the optimal encoding and decoding strategies hinge on these semantic metrics.

Abstract: The cell-free (CF) massive multiple-input multiple-output (MIMO) system is considered a cutting-edge technology in next-generation mobile communication due to its ability to provide high-performance coverage seamlessly and uniformly. This paper aims to mitigate the negative impact of channel aging due to the movement of user equipment in CF massive MIMO systems by utilizing rate-splitting (RS) technology. Taking into account the outdated channel state information, we obtain the achievable sum spectral efficiency (SE) of the RS-assisted CF massive MIMO system, where the private messages can directly adopt conventional maximum ratio, local minimum mean square error (MMSE), and centralized MMSE precoding schemes. Moreover, we propose a bisection-based precoding scheme that maximizes the minimum SE of common messages, which outperforms the superposition-based and random precoding schemes and exhibits strong robustness in complex mobile scenarios. Furthermore, we derive a novel closed-form sum SE expression for the considered system. The results demonstrate that RS technology can mitigate interference in mobile CF massive MIMO systems, improving overall system performance.

Abstract: This paper studies a near-field multiple-input multiple-output (MIMO) radar sensing system, in which the transceivers with massive antennas aim to localize multiple near-field targets in the three-dimensional (3D) space over unknown cluttered environments. We consider a spherical wavefront propagation with both channel phase and amplitude variations over different antennas. Under this setup, the unknown parameters include the 3D coordinates and complex reflection coefficients of the targets, as well as the noise and interference covariance matrix. First, by considering general transmit signal waveforms, we derive the Fisher information matrix (FIM) corresponding to the 3D coordinates and the complex reflection coefficients of the targets and accordingly obtain the Cram\'er-Rao bound (CRB) for the 3D coordinates. This provides a performance bound for 3D near-field target localization. For the special single-target case, we obtain the CRB in an analytical form, and analyze its asymptotic scaling behaviors with respect to the target distance and antenna size of the transceiver. Next, to facilitate practical localization, we propose two estimators to localize targets based on the maximum likelihood (ML) criterion, namely the 3D approximate cyclic optimization (3D-ACO) and the 3D cyclic optimization with white Gaussian noise (3D-CO-WGN), respectively. Numerical results validate the asymptotic CRB analysis and show that the consideration of varying channel amplitudes is vital to achieve accurate CRB and localization when the targets are close to the transceivers. It is also shown that the proposed estimators achieve localization performance close to the derived CRB under various cluttered environments, thus validating their effectiveness in practical implementation. Furthermore, it is shown that transmit waveforms have a significant impact on CRB and the localization performance.