Information Theory (cs.IT)

Abstract: This paper proposes an energy-efficient scheme for multicell multiple-input, multiple-output (MIMO) simultaneous transmit and reflect (STAR) reconfigurable intelligent surfaces (RIS)-assisted broadcast channels by employing rate splitting (RS) and improper Gaussian signaling (IGS). Regular RISs can only reflect signals. Thus, a regular RIS can assist only when the transmitter and receiver are in the reflection space of the RIS. However, a STAR-RIS can simultaneously transmit and reflect, thus providing a 360-degrees coverage. In this paper, we assume that transceivers may suffer from I/Q imbalance (IQI). To compensate for IQI, we employ IGS. Moreover, we employ RS to manage intracell interference. We show that RIS can significantly improve the energy efficiency (EE) of the system when RIS components are carefully optimized. Additionally, we show that STAR-RIS can significantly outperform a regular RIS when the regular RIS cannot cover all the users. We also show that RS can highly increase the EE comparing to treating interference as noise.

Abstract: By exploiting the connection between scattered $\mathbb{F}_q$-subspaces of $\mathbb{F}_{q^m}^3$ and minimal non degenerate $3$-dimensional rank metric codes of $\mathbb{F}_{q^m}^{n}$, $n \geq m+2$, described in \cite{AlfaranoBorelloNeriRavagnani2022JCTA}, we will exhibit a new class of codes with parameters $[m+2,3,m-2]_{q^m/q}$ for infinite values of $q$ and $m \geq 5$ odd. Moreover, by studying the geometric structures of these scattered subspaces, we determine the rank weight distribution of the associated codes.

Abstract: End-to-end routing in Low Earth Orbit (LEO) satellite constellations (LSatCs) is a complex and dynamic problem. The topology, of finite size, is dynamic and predictable, the traffic from/to Earth and transiting the space segment is highly imbalanced, and the delay is dominated by the propagation time in non-congested routes and by the queueing time at Inter-Satellite Links (ISLs) in congested routes. Traditional routing algorithms depend on excessive communication with ground or other satellites, and oversimplify the characterization of the path links towards the destination. We model the problem as a multi-agent Partially Observable Markov Decision Problem (POMDP) where the nodes (i.e., the satellites) interact only with nearby nodes. We propose a distributed Q-learning solution that leverages on the knowledge of the neighbours and the correlation of the routing decisions of each node. We compare our results to two centralized algorithms based on the shortest path: one aiming at using the highest data rate links and a second genie algorithm that knows the instantaneous queueing delays at all satellites. The results of our proposal are positive on every front: (1) it experiences delays that are comparable to the benchmarks in steady-state conditions; (2) it increases the supported traffic load without congestion; and (3) it can be easily implemented in a LSatC as it does not depend on the ground segment and minimizes the signaling overhead among satellites.

Abstract: The inference of a large symmetric signal-matrix $\mathbf{S} \in \mathbb{R}^{N\times N}$ corrupted by additive Gaussian noise, is considered for two regimes of growth of the rank $M$ as a function of $N$. For sub-linear ranks $M=\Theta(N^\alpha)$ with $\alpha\in(0,1)$ the mutual information and minimum mean-square error (MMSE) are derived for two classes of signal-matrices: (a) $\mathbf{S}=\mathbf{X}\mathbf{X}^\intercal$ with entries of $\mathbf{X}\in\mathbb{R}^{N\times M}$ independent identically distributed; (b) $\mathbf{S}$ sampled from a rotationally invariant distribution. Surprisingly, the formulas match the rank-one case. Two efficient algorithms are explored and conjectured to saturate the MMSE when no statistical-to-computational gap is present: (1) Decimation Approximate Message Passing; (2) a spectral algorithm based on a Rotation Invariant Estimator. For linear ranks $M=\Theta(N)$ the mutual information is rigorously derived for signal-matrices from a rotationally invariant distribution. Close connections with scalar inference in free probability are uncovered, which allow to deduce a simple formula for the MMSE as an integral involving the limiting spectral measure of the data matrix only. An interesting issue is whether the known information theoretic phase transitions for rank-one, and hence also sub-linear-rank, still persist in linear-rank. Our analysis suggests that only a smoothed-out trace of the transitions persists. Furthermore, the change of behavior between low and truly high-rank regimes only happens at the linear scale $\alpha=1$.

Abstract: Extremely large-scale Array (ELAA) promises to deliver ultra-high data rates with more antenna elements. Meanwhile, the increase of antenna elements leads to a wider realm of near-field, which challenges the traditional design of codebooks. In this paper, we propose novel codebook design schemes which provide better quantized correlation with limited overhead. First, we analyze the correlation between codewords and channel vectors uniform linear array (ULA) and uniform planar array (UPA). The correlation formula for the ULA channel can be expressed as an elliptic function, and the correlation formula for the UPA channel can be represented as an ellipsoid formula. Based on the analysis, we design a uniform sampling codebook to maximize the minimum quantized correlation and a dislocation ULA codebook to reduce the number of quantized bits further. Besides, we give a better sampling interval for the codebook of the UPA channel. Numerical results demonstrate the appealing advantages of the proposed codebook over existing methods in quantization bit number and quantization accuracy.

Abstract: Millimeter-waves' propagation characteristics create prospects for spatial and temporal spectrum sharing in a variety of contexts, including cognitive spectrum sharing (CSS). However, CSS along with omnidirectional sensing, is not efficient at mmWave frequencies due to their directional nature of transmission, as this limits secondary networks' ability to access the spectrum. This inspired us to create an analytical approach using stochastic geometry to examine the implications of directional cognitive sensing in mmWave networks. We explore a scenario where multiple secondary transmitter-receiver pairs coexist with a primary transmitter-receiver pair, forming a cognitive network. The positions of the secondary transmitters are modelled using a homogeneous Poisson point process (PPP) with corresponding secondary receivers located around them. A threshold on directional transmission is imposed on each secondary transmitter in order to limit its interference at the primary receiver. We derive the medium-access-probability of a secondary user along with the fraction of the secondary transmitters active at a time-instant. To understand cognition's feasibility, we derive the coverage probabilities of primary and secondary links. We provide various design insights via numerical results. For example, we investigate the interference-threshold's optimal value while ensuring coverage for both links and its dependence on various parameters. We find that directionality improves both links' performance as a key factor. Further, allowing location-aware secondary directionality can help achieve similar coverage for all secondary links.