Detection of Signals in Colored Noise: Roy's Largest Root Test for Non-central $F$-matrices

This paper investigates the signal detection problem in colored noise with an unknown covariance matrix. In particular, we focus on detecting a non-random signal by capitalizing on the leading eigenvalue (a.k.a. Roy's largest root) of the whitened sample covariance matrix as the test statistic. To this end, the whitened sample covariance matrix is constructed via \(m\)-dimensional \(p \) plausible signal-bearing samples and \(m\)-dimensional \(n \) noise-only samples. Since the signal is non-random, the whitened sample covariance matrix turns out to have a {\it non-central} \(F\)-distribution with a rank-one non-centrality parameter. Therefore, the performance of the test entails the statistical characterization of the leading eigenvalue of the non-central \(F\)-matrix, which we address by deriving its cumulative distribution function (c.d.f.) in closed-form by leveraging the powerful orthogonal polynomial approach in random matrix theory. This new c.d.f. has been instrumental in analyzing the receiver operating characteristic (ROC) of the detector. We also extend our analysis into the high dimensional regime in which \(m,n\), and \(p\) diverge such that \(m/n\) and \(m/p\) remain fixed. It turns out that, when \(m=n\) and fixed, the power of the test improves if the signal-to-noise ratio (SNR) is of at least \(O(p)\), whereas the corresponding SNR in the high dimensional regime is of at least \(O(p^2)\). Nevertheless, more intriguingly, for \(m<n\) with the SNR of order \(O(p)\), the leading eigenvalue does not have power to detect {\it weak} signals in the high dimensional regime.

Signal Detection in Colored Noise Using the Condition Number of $F$-Matrices

Signal detection in colored noise with an unknown covariance matrix has numerous applications across various scientific and engineering disciplines. The analysis focuses on the square of the condition number \(\kappa^2(\cdot)\), defined as the ratio of the largest to smallest eigenvalue \((\lambda_{\text{max}}/\lambda_{\text{min}})\) of the whitened sample covariance matrix \(\bm{\widehat{\Psi}}\), constructed from \(p\) signal-plus-noise samples and \(n\) noise-only samples, both \(m\)-dimensional. This statistic is denoted as \(\kappa^2(\bm{\widehat{\Psi}})\). A finite-dimensional characterization of the false alarm probability for this statistic under the null and alternative hypotheses has been an open problem. Therefore, in this work, we address this by deriving the cumulative distribution function (c.d.f.) of \(\kappa^2(\bm{\widehat{\Psi}})\) using the powerful orthogonal polynomial approach in random matrix theory. These c.d.f. expressions have been used to statistically characterize the performance of \(\kappa^2(\bm{\widehat{\Psi}})\).

Throughput Optimization in Cache-aided Networks: An Opportunistic Probing and Scheduling Approach

This paper addresses the challenges of throughput optimization in wireless cache-aided cooperative networks. We propose an opportunistic cooperative probing and scheduling strategy for efficient content delivery. The strategy involves the base station probing the relaying channels and cache states of multiple cooperative nodes, thereby enabling opportunistic user scheduling for content delivery. Leveraging the theory of Sequentially Planned Decision (SPD) optimization, we dynamically formulate decisions on cooperative probing and stopping time. Our proposed Reward Expected Thresholds (RET)-based strategy optimizes opportunistic probing and scheduling. This approach significantly enhances system throughput by exploiting gains from local caching, cooperative transmission and time diversity. Simulations confirm the effectiveness and practicality of the proposed Media Access Control (MAC) strategy.

Interference Mitigation in LEO Constellations with Limited Radio Environment Information

This research paper delves into interference mitigation within Low Earth Orbit (LEO) satellite constellations, particularly when operating under constraints of limited radio environment information. Leveraging cognitive capabilities facilitated by the Radio Environment Map (REM), we explore strategies to mitigate the impact of both intentional and unintentional interference using planar antenna array (PAA) beamforming techniques. We address the complexities encountered in the design of beamforming weights, a challenge exacerbated by the array size and the increasing number of directions of interest and avoidance. Furthermore, we conduct an extensive analysis of beamforming performance from various perspectives associated with limited REM information: static versus dynamic, partial versus full, and perfect versus imperfect. To substantiate our findings, we provide simulation results and offer conclusions based on the outcomes of our investigation.

Dynamic Cooperative MAC Optimization in RSU-Enhanced VANETs: A Distributed Approach

This paper presents an optimization approach for cooperative Medium Access Control (MAC) techniques in Vehicular Ad Hoc Networks (VANETs) equipped with Roadside Unit (RSU) to enhance network throughput. Our method employs a distributed cooperative MAC scheme based on Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) protocol, featuring selective RSU probing and adaptive transmission. It utilizes a dual timescale channel access framework, with a ``large-scale'' phase accounting for gradual changes in vehicle locations and a ``small-scale'' phase adapting to rapid channel fluctuations. We propose the RSU Probing and Cooperative Access (RPCA) strategy, a two-stage approach based on dynamic inter-vehicle distances from the RSU. Using optimal sequential planned decision theory, we rigorously prove its optimality in maximizing average system throughput per large-scale phase. For practical implementation in VANETs, we develop a distributed MAC algorithm with periodic location updates. It adjusts thresholds based on inter-vehicle and vehicle-RSU distances during the large-scale phase and accesses channels following the RPCA strategy with updated thresholds during the small-scale phase. Simulation results confirm the effectiveness and efficiency of our algorithm.

Graph Neural Networks for Physical-Layer Security in Multi-User Flexible-Duplex Networks

This paper explores Physical-Layer Security (PLS) in Flexible Duplex (FlexD) networks, considering scenarios involving eavesdroppers. Our investigation revolves around the intricacies of the sum secrecy rate maximization problem, particularly when faced with coordinated and distributed eavesdroppers employing a Minimum Mean Square Error (MMSE) receiver. Our contributions include an iterative classical optimization solution and an unsupervised learning strategy based on Graph Neural Networks (GNNs). To the best of our knowledge, this work marks the initial exploration of GNNs for PLS applications. Additionally, we extend the GNN approach to address the absence of eavesdroppers' channel knowledge. Extensive numerical simulations highlight FlexD's superiority over Half-Duplex (HD) communications and the GNN approach's superiority over the classical method in both performance and time complexity.

Detection of Signals in Colored Noise: Leading Eigenvalue Test for Non-central $F$-matrices

This paper investigates the signal detection problem in colored noise with an unknown covariance matrix. In particular, we focus on detecting an unknown non-random signal by capitalizing on the leading eigenvalue of the whitened sample covariance matrix as the test statistic (a.k.a. Roy's largest root test). Since the unknown signal is non-random, the whitened sample covariance matrix turns out to have a non-central $F$-distribution. This distribution assumes a singular or non-singular form depending on whether the number of observations $p\lessgtr$ the system dimensionality $m$. Therefore, we statistically characterize the leading eigenvalue of the singular and non-singular $F$-matrices by deriving their cumulative distribution functions (c.d.f.). Subsequently, they have been utilized in deriving the corresponding receiver operating characteristic (ROC) profiles. We also extend our analysis into the high dimensional domain. It turns out that, when the signal is sufficiently strong, the maximum eigenvalue can reliably detect it in this regime. Nevertheless, weak signals cannot be detected in the high dimensional regime with the leading eigenvalue.

Distributed CSMA/CA MAC Protocol for RIS-Assisted Networks

This paper focuses on achieving optimal multi-user channel access in distributed networks using a reconfigurable intelligent surface (RIS). The network includes wireless channels with direct links between users and RIS links connecting users to the RIS. To maximize average system throughput, an optimal channel access strategy is proposed, considering the trade-off between exploiting spatial diversity gain with RIS assistance and the overhead of channel probing. The paper proposes an optimal distributed Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) strategy with opportunistic RIS assistance, based on statistics theory of optimal sequential observation planned decision. Each source-destination pair makes decisions regarding the use of direct links and/or probing source-RIS-destination links. Channel access occurs in a distributed manner after successful channel contention. The optimality of the strategy is rigorously derived using multiple-level pure thresholds. A distributed algorithm, which achieves significantly lower online complexity at $O(1)$, is developed to implement the proposed strategy. Numerical simulations verify the theoretical results and demonstrate the superior performance compared to existing approaches.

Generalized Eigenvalue Based Detection of Signals in Colored Noise: A Sample Deficient Analysis

This paper investigates the signal detection problem in colored noise with an unknown covariance matrix. To be specific, we consider a scenario in which the number of signal bearing samples ($n$) is strictly smaller than the dimensionality of the signal space ($m$). Our test statistic is the leading generalized eigenvalue of the whitened sample covariance matrix (a.k.a. $F$-matrix) which is constructed by whitening the signal bearing sample covariance matrix with noise-only sample covariance matrix. The sample deficiency (i.e., $m>n$) in turn makes this $F$-matrix rank deficient, thereby singular. Therefore, an exact statistical characterization of the leading generalized eigenvalue (l.g.e.) of a singular $F$-matrix is of paramount importance to assess the performance of the detector (i.e., the receiver operating characteristics (ROC)). To this end, we employ the powerful orthogonal polynomial approach to derive a new finite dimensional c.d.f. expression for the l.g.e. of a singular $F$-matrix. It turns out that when the noise only sample covariance matrix is nearly rank deficient and the signal-to-noise ratio is $O(m)$, the ROC profile converges to a limit.

Flex-Net: A Graph Neural Network Approach to Resource Management in Flexible Duplex Networks

Flexible duplex networks allow users to dynamically employ uplink and downlink channels without static time scheduling, thereby utilizing the network resources efficiently. This work investigates the sum-rate maximization of flexible duplex networks. In particular, we consider a network with pairwise-fixed communication links. Corresponding combinatorial optimization is a non-deterministic polynomial (NP)-hard without a closed-form solution. In this respect, the existing heuristics entail high computational complexity, raising a scalability issue in large networks. Motivated by the recent success of Graph Neural Networks (GNNs) in solving NP-hard wireless resource management problems, we propose a novel GNN architecture, named Flex-Net, to jointly optimize the communication direction and transmission power. The proposed GNN produces near-optimal performance meanwhile maintaining a low computational complexity compared to the most commonly used techniques. Furthermore, our numerical results shed light on the advantages of using GNNs in terms of sample complexity, scalability, and generalization capability.