Information Theory (cs.IT)

Abstract: In this paper, we study the spatial bandwidth for line-of-sight (LOS) channels with linear large-scale antenna arrays (LSAAs) in 3D space. We provide approximations to the spatial bandwidth at the center of the receiving array, of the form $C R^{-B}$, where $R$ is the radial distance, and $C$ and $B$ are directional-dependent and piecewise constant in $R$. The approximations are valid in the entire radiative region, that is, for $R$ greater than a few wavelengths. When the length of the receiving array is small relative to $R$, the product of the array length and the spatial bandwidth provides an estimate of the available spatial degree-of-freedom (DOF) in the channel. In a case study, we apply these approximations to the evaluation of spatial multiplexing regions under random orientation conditions. The goodness-of-fit of the approximations is demonstrated and some interesting findings about the DOF performance of the channel under 3D and 2D orientation restrictions are obtained, e.g., that, under some conditions, it is better to constrain the receiving array orientation to be uniform over the unit circle in the 2D ground plane rather than uniform over the 3D unit sphere.

Abstract: We consider a robust beamforming problem where large amount of downlink (DL) channel state information (CSI) data available at a multiple antenna access point (AP) is used to improve the link quality to a user equipment (UE) for beyond-5G and 6G applications such as environment-specific initial access (IA) or wireless power transfer (WPT). As the DL CSI available at the current instant may be imperfect or outdated, we propose a novel scheme which utilizes the (unknown) correlation between the antenna domain and physical domain to localize the possible future UE positions from the historical CSI database. Then, we develop a codebook design procedure to maximize the minimum sum beamforming gain to that localized CSI neighborhood. We also incorporate a UE specific parameter to enlarge the neighborhood to robustify the link further. We adopt an indoor channel model to demonstrate the performance of our solution, and benchmark against a usually optimal (but now sub-optimal due to outdated CSI) maximum ratio transmission (MRT) and a subspace based method.We numerically show that our algorithm outperforms the other methods by a large margin. This shows that customized environment-specific solutions are important to solve many future wireless applications, and we have paved the way to develop further data-driven approaches.

Abstract: The nonnegative rank of nonnegative matrices is an important quantity that appears in many fields, such as combinatorial optimization, communication complexity, and information theory. In this paper, we study the asymptotic growth of the nonnegative rank of a fixed nonnegative matrix under Kronecker product. This quantity is called the asymptotic nonnegative rank, which is already studied in information theory. By applying the theory of asymptotic spectra of V. Strassen (J. Reine Angew. Math. 1988), we introduce the asymptotic spectrum of nonnegative matrices and give a dual characterization of the asymptotic nonnegative rank. As the opposite of nonnegative rank, we introduce the notion of the subrank of a nonnegative matrix and show that it is exactly equal to the size of the maximum induced matching of the bipartite graph defined on the support of the matrix (therefore, independent of the value of entries). Finally, we show that two matrix parameters, namely rank and fractional cover number, belong to the asymptotic spectrum of nonnegative matrices.

Abstract: We study the successive refinement setting of Shannon cipher system (SCS) under the maximal leakage constraint for discrete memoryless sources under bounded distortion measures. Specifically, we generalize the threat model for the point-to-point rate-distortion setting of Issa, Wagner and Kamath (T-IT 2020) to the multiterminal successive refinement setting. Under mild conditions that correspond to partial secrecy, we characterize the asymptotically optimal normalized maximal leakage region for both the joint excess-distortion probability (JEP) and the expected distortion reliability constraints. Under JEP, in the achievability part, we propose a type-based coding scheme, analyze the reliability guarantee for JEP and bound the leakage of the information source through compressed versions. In the converse part, by analyzing a guessing scheme of the eavesdropper, we prove the optimality of our achievability result. Under expected distortion, the achievability part is established similarly to the JEP counterpart. The converse proof proceeds by generalizing the corresponding results for the rate-distortion setting of SCS by Schieler and Cuff (T-IT 2014) to the successive refinement setting. Somewhat surprisingly, the normalized maximal leakage regions under both JEP and expected distortion constraints are identical under certain conditions, although JEP appears to be a stronger reliability constraint.

Abstract: The paradigm of joint communications and sensing (JCAS) envisions a revolutionary integration of communication and radar functionalities within a unified hardware platform. This novel concept not only opens up unprecedented possibilities, but also presents unique challenges. Its success is highly dependent on efficient full-duplex (FD) operation, which has the potential to enable simultaneous transmission and reception within the same frequency band. While ongoing research explores the potential of JCAS, there are related avenues of investigation that hold tremendous potential to profoundly transform the sixth generation (6G) and beyond cellular networks. This article sheds light on the new opportunities and challenges presented by JCAS by taking into account the key technical challenges of FD systems. Unlike simplified JCAS scenarios, we delve into the most comprehensive configuration, encompassing uplink (UL) and downlink (DL) users, as well as monostatic and bistatic radars, all harmoniously coexisting to jointly push the boundaries of both the communications and sensing performance. The performance improvements introduced by this advancement bring forth numerous new challenges, each meticulously examined and expounded upon.