This paper analyzes the impact of spatially correlated additive noise on the minimum mean-square error (MMSE) estimation of multiple-input multiple-output (MIMO) channels from one-bit quantized observations. Although additive noise can be correlated in practical scenarios, e.g., due to jamming, clutter, or other external disturbances, the effect of such correlation on the MMSE channel estimator in this setting remains unexplored in prior work. Against this backdrop, we derive a novel analytical expression for the general MIMO MMSE channel estimator, which is inherently nonlinear in one-bit observations, and accommodates arbitrary channel and noise correlation structures. To further characterize the impact of noise correlation, we subsequently specialize the general MMSE expression to certain tractable multi antenna configurations in which both the channel and the noise assume single-parameter constant correlation structures. Our analyses reveal nontrivial, noise-correlation-induced scenarios in which the estimator remains linear despite non-zero channel and noise correlation parameters. Moreover, the results indicate that, at low-to-medium signal-to-noise ratio, noise correlation improves the MMSE performance when channels are uncorrelated, but degrades performance when channels are strongly correlated.

Robust signal detection in colored noise with unknown covariance is essential in radar, cognitive radio, integrated sensing and communication (ISAC), and quantum sensing applications. This paper develops a unified analytical framework for the Standard Condition Number (SCN) detector, which employs the ratio of the largest to smallest eigenvalues of the whitened sample covariance matrix. The framework jointly covers both ideal conditions in which the training and sensing noise statistics are identical and disturbed conditions in which interference or jamming alters the sensing covariance. Despite the SCN's practical relevance, its finite-sample false-alarm and detection behavior has not been analytically characterized. Using random matrix theory (RMT), we derive general expressions for these probabilities, provide closed-form results for special cases, and show that the SCN preserves the Constant False Alarm Rate (CFAR) property under covariance mismatch. Analytical and simulation results confirm that the proposed unified framework delivers consistent detection performance and greater robustness than conventional eigenvalue- and LRT-based detectors.

Cooperative spectrum sensing (CSS) is essential for improving the spectrum efficiency and reliability of cognitive radio applications. Next-generation wireless communication networks increasingly employ uniform planar arrays (UPA) due to their ability to steer beamformers towards desired directions, mitigating interference and eavesdropping. However, the application of UPA-based CSS in cognitive radio remains largely unexplored. This paper proposes a multi-beam UPA-based weighted CSS (WCSS) framework to enhance detection reliability, applicable to various cognitive radio networks, including cellular, vehicular, and satellite communications. We first propose a weighting factor for commonly used energy detection (ED) and eigenvalue detection (EVD) techniques, based on the spatial variation of signal strengths resulting from UPA antenna beamforming. We then analytically characterize the performance of both weighted ED and weighted EVD by deriving closed-form expressions for false alarm and detection probabilities. Our numerical results, considering both static and dynamic user behaviors, demonstrate the superiority of WCSS in enhancing sensing performance compared to uniformly weighted detectors.

This paper considers a MIMO Integrated Sensing and Communication (ISAC) system, where a base station simultaneously serves a MIMO communication user and a remote MIMO sensing receiver, without channel state information (CSI) at the transmitter. Existing MIMO ISAC literature often prioritizes communication rate or detection probability, typically under constant false-alarm rate (CFAR) assumptions, without jointly analyzing detection reliability and communication constraints. To address this gap, we adopt an eigenvalue-based detector for robust sensing and use a performance metric—the total detection error—that jointly captures false-alarm and missed-detection probabilities. We derive novel closed-form expressions for both probabilities under the eigenvalue detector, enabling rigorous sensing analysis. Using these expressions, we formulate and solve a —joint power allocation and threshold optimization— problem that minimizes total detection error while meeting a minimum communication rate requirement. Simulation results demonstrate that the proposed joint design substantially outperforms conventional CFAR-based schemes, highlighting the benefits of power-and threshold-aware optimization in MIMO ISAC systems.

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.

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.$F- \mathbf{matrix}$) 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$F-\mathbf{matrix}$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.

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.

We develop a gradient-like algorithm to minimize a sum of peer objective functions based on coordination through a peer interconnection network. The coordination admits two stages: the first is to constitute a gradient, possibly with errors, for updating locally replicated decision variables at each peer and the second is used for error-free averaging for synchronizing local replicas. Unlike many related algorithms, the errors permitted in our algorithm can cover a wide range of inexactnesses, as long as they are bounded. Moreover, we do not impose any gradient boundedness conditions for the objective functions. Furthermore, the second stage is not conducted in a periodic manner, like many related algorithms. Instead, a locally verifiable criterion is devised to dynamically trigger the peer-to-peer coordination at the second stage, so that expensive communication overhead for error-free averaging can significantly be reduced. Finally, the convergence of the algorithm is established under mild conditions.

Let$\mathrm {W}\in \mathbb {C}^{n\times n}$be a single-spiked Wishart matrix in the class$\mathrm {W}\sim \mathcal {CW}_{n}(m,\mathrm {I}_{n}+ \theta \mathrm {v}\mathrm {v}^{\dagger}) $with$m\geq n$, where${\mathrm {I}}_{n}$is the$n\times n$identity matrix,$\mathrm {v}\in \mathbb {C}^{n\times 1}$is an arbitrary vector with unit Euclidean norm,$\theta \geq 0$is a non-random parameter, and$(\cdot)^{\dagger} $represents the conjugate-transpose operator. Let u1 and${\mathrm {u}}_{n}$denote the eigenvectors corresponding to the smallest and the largest eigenvalues of W, respectively. This paper investigates the probability density function (p.d.f.) of the random quantity$Z_{\ell }^{(n)}=\left |{\mathrm {v}^{\dagger} \mathrm {u}_\ell }\right |^{2}\in (0,1)$for$\ell =1,n$. In particular, we derive a finite dimensional closed-form p.d.f. for$Z_{1}^{(n)}$which is amenable to asymptotic analysis as$m,n$diverges with$m-n$fixed. It turns out that, in this asymptotic regime, the scaled random variable$nZ_{1}^{(n)}$converges in distribution to$\chi ^{2}_{2}/2(1+\theta)$, where$\chi _{2}^{2}$denotes a chi-squared random variable with two degrees of freedom. This reveals that u1 can be used to infer information about the spike. On the other hand, the finite dimensional p.d.f. of$Z_{n}^{(n)}$is expressed as a double integral in which the integrand contains a determinant of a square matrix of dimension$(n-2)$. Although a simple solution to this double integral seems intractable, for special configurations of$n=2,3$, and 4, we obtain closed-form expressions.

Let$\mathbf {X}\in \mathbb {C}^{n\times m}$($m\geq n$) be a random matrix with independent columns each distributed as complex multivariate Gaussian with zero mean andsingle-spikedcovariance matrix$\mathbf {I}_{n}+ \eta \mathbf {u}\mathbf {u}^{*}$, where$\mathbf {I}_{n}$is the$n\times n$identity matrix,$\mathbf {u}\in \mathbb {C}^{n\times 1}$is an arbitrary vector with unit Euclidean norm,$\eta \geq 0$is a non-random parameter, and$(\cdot)^{*}$represents the conjugate-transpose. This paper investigates the distribution of the random quantity$\kappa _{\text {SC}}^{2}(\mathbf {X})=\sum _{k=1}^{n} \lambda _{k}/\lambda _{1}$, where$0\le \lambda _{1}\le \lambda _{2}\le \ldots \leq \lambda _{n} < \infty $are the ordered eigenvalues of$\mathbf {X}\mathbf {X}^{*}$(i.e., single-spiked Wishart matrix). This random quantity is intimately related to the so calledscaled condition numberor the Demmel condition number (i.e.,$\kappa _{\text {SC}}(\mathbf {X})$) and the minimum eigenvalue of the fixed trace Wishart-Laguerre ensemble (i.e.,$\kappa _{\text {SC}}^{-2}(\mathbf {X})$). In particular, we use an orthogonal polynomial approach to derive an exact expression for the probability density function of$\kappa _{\text {SC}}^{2}(\mathbf {X})$which is amenable to asymptotic analysis as matrix dimensions grow large. Our asymptotic results reveal that, as$m,n\to \infty $such that$m-n$is fixed and when$\eta $scales on the order of$1/n$,$\kappa _{\text {SC}}^{2}(\mathbf {X})$scales on the order of$n^{3}$. In this respect we establish simple closed-form expressions for the limiting distributions. It turns out that, as$m,n\to \infty $such that$n/m\to c\in (0,1)$, properly centered$\kappa _{\text {SC}}^{2}(\mathbf {X})$fluctuates on the scale$m^{\frac {1}{3}}$.

The novel reconfigurable intelligent surface (RIS) is an emerging technology which facilitates high spectrum and energy efficiencies in Beyond 5G and 6G wireless communication applications. Against this backdrop, this paper investigates two-way communications via reconfigurable intelligent surfaces (RISs) where two users communicate through a common RIS. We assume that uplink and downlink communication channels between two users and the RIS can be reciprocal. We first obtain the optimal phase adjustment at the RIS. We then derive the exact outage probability and the average throughput in closed-forms for single-element RIS. To evaluate multiple-element RIS, we first introduce a gamma approximation to model a product of Rayleigh random variables, and then derive approximations for the outage probability and the average throughput. For large average signal-to-interference-plus-noise ratio (SINR) $\rho$, asymptotic analXsis also shows that the outage decreases at the rate $(\log(\rho)/\rho)$ where L is the number of elements, whereas the throughput increases with the rate $\log(\rho)$.

This paper addresses a classical problem in random matrix theory-finding the distribution of the maximum eigen-value of the correlated Wishart unitary ensemble. In particular, we derive a new exact expression for the cumulative distribution function (c.d. f.) of the maximum eigen-value of a 2 × 2 correlated non-central Wishart matrix with rank-l mean. By using this new result, we derive the exact outage probability of 2 × 2 multiple-input multiple-output maximum-ratio-combining (MIMO-MRC) in Rician fading with transmit correlation and a strong line-of-sight (LoS) component (rank-l channel mean). We also show that the outage performance is affected by the relative alignment of the eigen-spaces of the mean and correlation matrices. In general, when the LoS path aligns with the least eigenvector of the correlation matrix, in the high transmit signal-to-noise ratio (SNR) regime, the outage gradually improves with the increasing correlation. Moreover, we show that as K (Rician factor) grows large, the outage event can be approximately characterized by the c.d.f. of a certain Gaussian random variable.

In this paper, we investigate the two-way communication between two users assisted by a reconfigurable intelligent surface (RIS). The scheme that two users communicate simultaneously over Rayleigh fading channels is considered. The channels between the two users and RIS can either be reciprocal or non-reciprocal. For reciprocal channels, we determine the optimal phases at the RIS to maximize the signal-to-interference-plus-noise ratio (SINR). We then derive exact closed-form expressions for the outage probability and spectral efficiency for single-element RIS. By capitalizing the insights obtained from the single-element analysis, we introduce a gamma approximation to model the product of Rayleigh random variables which is useful for the evaluation of the performance metrics in multiple-element RIS. Asymptotic analysis shows that the outage decreases at (log(ρ)/ρ)Lrate where L is the number of elements, whereas the spectral efficiency increases at log(ρ) rate at large average SINR p. For non-reciprocal channels, the minimum user SINR is targeted to be maximized. For single-element RIS, closed-form solution is derived whereas for multiple-element RIS the problem turns out to be non-convex. The latter one is solved through semidefinite programming relaxation and a proposed greedy-iterative method, which can achieve higher performance and lower computational complexity, respectively.

Signal detection in colored noise with an unknown covariance matrix has a myriad of applications in diverse scientific/engineering fields. The test statistic is the largest generalized eigenvalue (l.g.e.) of the whitened sample covariance matrix, which is constructed via m-dimensional p signal-plusnoise samples and m-dimensional n noise-only samples. A finite dimensional characterization of this statistic under the alternative hypothesis has hitherto been an open problem. We answer this problem by deriving cumulative distribution function (c.d.f.) of this l.g.e. via the powerful orthogonal polynomial approach, exploiting the deformed Jacobi unitary ensemble (JUE). Two special cases and an asymptotic version of the c.d.f. are also derived. With this new c.d.f., we comprehensively analyze the receiver operating characteristics (ROC) of the detector. Importantly, when the noise-only covariance matrix is nearly rank deficient (i.e., m = n), we show that (a) when m and p increase such that m/p is fixed, at each fixed signal-to-noise ratio (SNR), there exists an optimal ROC profile. We also establish a tight approximation of it; and (b) asymptotically, reliable signal detection is always possible if SNR scales with m.

This paper investigates the classical statistical signal processing problem of detecting a signal in the presence of colored noise with an unknown covariance matrix. In particular, we consider a scenario wherem-dimensionalppossible signal-plus-noise samples andm-dimensionalnnoise-only samples are available at the detector. Then the presence of a signal can be detected using the largest generalized eigenvalue (l.g.e.) of the so called whitened sample covariance matrix. This amounts to statistically characterizing the maximum eigenvalue of the deformed Jacobi unitary ensemble (JUE). To do this, we employ the powerful orthogonal polynomial approach to determine a new finite dimensional expression for the cumulative distribution function (c.d.f.) of the l.g.e. of the deformed JUE. This new c.d.f. expression facilitates the further analysis of the receiver operating characteristics (ROC) of the detector. It turns out that, form=n, when m andpincrease such thatm/pis fixed, there exists an optimal ROC profile for each fixed signal-to-noise ratio (SNR). In this respect, we have established a tight approximation for the corresponding optimal ROC profile.

This paper investigates a user-fairness relay selection (RS) problem for decode-and-forward (DF) full-duplex (FD) relay networks, where multiple users cooperate with multiple relays in each coherence time. We consider two residual self-interference (RSI) models with or without direct links. We propose a sub-optimal relay selection (SRS) scheme which requires only the instantaneous channel state information (CSI) of source-to-relay and relay-to-destination links. To evaluate the performance, the outage probability of SRS is derived for different scenarios depending on RSI models and the availability of direct links. To further investigate, asymptotic expressions are derived for the high-transmit power regime. For comparison purposes, 1) the average throughputs of the FD and half-duplex (HD) modes are derived; 2) non-orthogonal transmission is considered and its performance is discussed with approximations; and 3) the impact of imperfect CSI is investigated with the aid of analysis. While simulation results are provided to verify the analytical results, they reveal interesting fundamental trends. It turns out that a significant throughput degradation occurs with FD mode over HD mode when self-interference is fully proportional to the transmit power. Since all users can communicate in the same coherence time with the FD mode, these joint RS schemes are useful for user-fairness low-latency applications.

This paper investigates the relay selection (RS) problem in full-duplex (FD) wireless networks with multiple users and multiple common relays. We consider three self-interference models at FD relays. For amplify-and-forward (AF) and decode- and-forward (DF) relaying, the exact and asymptotic expressions for the outage probability are derived over Rayleigh fading channels with distance-dependent path loss for three RS schemes: i) optimal RS (ORS); ii) naive RS; and iii) random RS. Simulation results are provided to verify the analytical results.

In this paper, we investigate the classical problem of finding the probability density function (pdf) of the sum of Nakagami-mrandom variables. Exact infinite series representations are derived for the sum of three and four identically and independently distributed (i.i.d.) Nakagami-mrandom variables, and subsequently, it is extended to the sum of general number of random variables. A useful pattern emerged as a result of these extensions, and a new Fourier transform pair that involves parabolic cylinder function and Gauss hypergeometric function is obtained. Bounds on the error resulting from truncation of the infinite series of pdfs are also presented. These pdfs are used to analyze the performance of dual, triple, and quadruple branch predetection equal gain combining (EGC) receivers over Nakagami-mfading environment. Furthermore, a hypergeometric relation is derived as a result of those derivations. Subsequently, the analysis is extended to the case of L branch EGC receiver performance as well. Selected simulation plots are provided to compare the results with the approximate results available in the literature and to illustrate the validity of the formulation.