Spectrum Sensing will play a pivotal role in 6G Cognitive Radio Networks, in which unlicensed users could dynamically use the spectrum and perform opportunistic transmission. In this paper, we focus on a multiple-antenna data-aided Spectrum Sensing algorithm and we compute the exact Moment Generating Function and probability density function under the null hypothesis of such test statistic, by resorting to tools from finite-dimensional random matrix theory. The test at hand is formulated in terms of a quadratic form with unit-norm random vector and random kernel matrix with determinantal joint probability distribution of its eigenvalues. The algorithm exploits the availability of a set of auxiliary data, collected under the assumption of primary signal presence. Results, presented in terms of Receiver Operating Characteristic curve and detection probability vs. the Signal-to-Noise Ratio, show that the presented test outperforms some well-established sensing schemes, such as the Generalized Likelihood Ratio Test and the Roy's Largest Root Test. Furthermore, we compare the outcomes of our analytical derivation with corresponding Monte Carlo simulated data in scenarios with both spatio-temporally uncorrelated and correlated samples.

Due to their low complexity, Minimum Mean Squared Error (MMSE) and Zero-Forcing (ZF) emerge as two appealing MIMO receivers. Although they provide asymptotically the same achievable rate as the signal-to-noise ratio (SNR) grows large, a non-vanishing gap between the signal to interference and noise ratio (SINR) obtained through the two receivers exists, affecting the error and outage probability, and the multiuser efficiency. Interestingly, both the SINR and the multiuser efficiency gaps can be compactly expressed as quadratic forms of random matrices, with a kernel that depends solely on the statistics of the interfering streams. By leveraging, we derive the closed-form distribution of such indefinite quadratic forms with random kernel matrix, which turns out to be proportional to the determinant of a matrix containing the system parameters. Then, specializing our result to different fading conditions, we obtain the closed-form statistics of both the SINR gap and the multiuser efficiency gap. Although the focus of this work is on the finite-size statistics, for completeness we also provide some results on the doubly-massive MIMO case. We validate all our derivations through extensive Monte Carlo simulations.

We present an information-theoretic analysis of a point-to-point multiple-input multiple-output (MIMO) link affected by Rayleigh fading and multiple scattering, under perfect channel state information at the receiver. Unlike previous work addressing this setting, we investigate the random coding error exponent, its associated cutoff rate and the expurgated error exponent, and derive closed-form expressions for them. Moreover, leveraging the average mutual information expression presented by Akemann et al., we derive another important metric, namely, the sum rate, under linear receive processing and independent stream decoding. In particular, we characterize the performance of the minimum mean squared error receiver in closed form, and that of the zero forcing receiver by resorting to bounding techniques. The bulk of the work relies on results about finite-dimensional random matrix products, a number of which are novel and detailed in the Appendices. The analysis, validated through numerical results, highlights the severe degradation in the performance of linear receivers due to multi-fold scattering. It also unveils the performance trend of multiple scattering MIMO channels as a function of the number of antennas and the number of scattering stages.

A one-sided spatially-correlated multi-cluster scattering Rayleigh MIMO channel is considered in this work and its outage probability is derived in an analytic form based on Meijer function determinants. First, the spatially-uncorrelated case is addressed and the Moment Generating Function (MGF) of the information rate is expressed in an analytic closed-form. The MGF is then used to obtain the outage probability. A few special cases are addressed to provide a confirmation of the analytic results. Next, the MGF in the one-sided spatially correlated case is derived with the constraint of distinct positive spatial correlation eigenvalues. Numerical results are included to provide confirming evidence of the analytic results. These results are then used to assess the outage probability degradation due to spatial correlation in a selected example.

This paper presents a statistical characterization of the SNR gap between MIMO Zero-Forcing (ZF) and Minimum Mean Squared Error (MMSE) equalizers, beyond the Rayleigh assumption for the interfering streams amplitude fading. Results are valid for arbitrary transmit SNR values and number of transmit/receive antennas. Specifically, we provide the exact closed-form distribution of the random variable representing the difference between the output SNR on a generic receive filter branch, under MMSE and ZF equalization. Analytical results turn particularly useful for the study of heterogeneous cellular networks.

This paper considers the problem of coherent (in the sense that both amplitudes and relative phases of the polarimetric returns are used to construct the decision statistic) multipolarization synthetic aperture radar change detection starting from the availability of image pairs exhibiting possible power mismatches/miscalibrations. The principle of invariance is used to characterize the class of scale-invariant decision rules which are insensitive to power mismatches and ensure the constant false alarm rate property. A maximal invariant statistic is derived together with the induced maximal invariant in the parameter space which significantly compresses the data/parameter domain. A generalized likelihood ratio test is synthesized both for the cases of two- and three-polarimetric channels. Interestingly, for the two-channel case, it is based on the comparison of the condition number of a data-dependent matrix with a suitable threshold. Some additional invariant decision rules are also proposed. The performance of the considered scale-invariant structures is compared to those from two noninvariant counterparts using both simulated and real radar data. The results highlight the robustness of the proposed method and the performance tradeoff involved.

We analyze throughput-delay scaling laws of mobile ad hoc networks under a content-centric traffic scenario, where users are mainly interested in retrieving contents cached by other nodes. We assume limited buffer size available at each node and Zipf-like content popularity. We consider nodes uniformly visiting the network area according to a random-walk mobility model, whose flight size varies from the typical distance among the nodes (quasi-static case) up to the edge length of the network area (reshuffling mobility model). Our main findings are: (1) the best throughput-delay tradeoffs are achieved in the quasi-static case: increasing the mobility degree of nodes leads to worse and worse performance; (ii) the best throughput-delay tradeoffs can be recovered by power control (i.e., by adapting the transmission range to the content) even in the complete reshuffling case.

The information that can be transmitted through a wireless channel, with multiple-antenna-equipped transmitter and receiver, is crucially influenced by the channel behavior as well as by the structure of the input signal. We characterize in closed form, the probability density function (pdf) of the output of multiple-input and multiple-output block-fading channels, for an arbitrary signal-to-noise ratio value. Our results provide compact expressions for such output statistics, paving the way to a more detailed analytical information-theoretic exploration of communications in presence of block fading. The analysis is carried out assuming two different structures for the input signal: 1) the independent identically distributed (i.i.d.) Gaussian distribution and 2) a product form that has been proved to be optimal for noncoherent communication, i.e., in absence of any channel state information. When the channel is fed by an i.i.d. Gaussian input, we assume the Gramian of the channel matrix to be unitarily invariant and derive the output statistics in both the noise- and interference-limited scenario, considering different fading distributions. When the product-form input is adopted, we provide the expressions of the output pdf as the relationship between the overall number of antennas and fading coherence length varies. We also highlight the relation between our newly derived expressions and the results already available in the literature, and, for some cases, we numerically compute the mutual information based on the proposed expression of the output statistics.

We consider extended wireless networks characterized by a random topology of access points (APs) contending for medium access over the same wireless channel. Recently, stochastic geometry has emerged as a powerful tool to analyze random networks adopting MAC protocols such as ALOHA and CSMA. The main strength of this methodology lies in its ability to account for the randomness in the nodes' location jointly with an accurate description at the physical layer, based on the SINR, that allows considering also random fading on each link. In this paper, we extend previous stochastic geometry models of CSMA networks, developing computationally efficient techniques to obtain throughput distributions, in addition to spatial averages, which permit us to get interesting insights into the impact of protocol parameters and channel variability on the spatial fairness among the nodes. Moreover, we extend the analysis to a significant class of topologies in which APs are not placed according to a Poisson process.

We analyze throughput-delay scaling laws of mobile ad-hoc networks under a content-centric traffic scenario, where users are mainly interested in retrieving contents cached by other nodes. We assume limited buffer size available at each node and Zipf-like content popularity. We consider nodes uniformly visiting the network area according to a random-walk mobility model, whose flight size is varied from the typical distance among the nodes (quasi-static case) up to the edge length of the network area (reshuffling mobility model). Our main findings are i) the best throughput-delay trade-offs are achieved in the quasi-static case: increasing the mobility degree of nodes leads to worse and worse performance; ii) the best throughput-delay trade-offs can be recovered by power control (i.e., by adapting the transmission range to the content) even in the complete reshuffling case.

The information that can be conveyed through a wireless channel, with multiple-antenna equipped transmitter and receiver, crucially depends on the channel behavior as well as on the input structure. In this paper, we derive analytical results, concerning the probability density function (pdf) of the output of a single-user, multiple-antenna communication. The analysis is carried out under the assumption of an optimized input structure, and assuming Gaussian noise and a Rayleigh block-fading channel. Our analysis therefore provides a quite general and compact expression for the conditional output pdf. We also highlight the relation between such an expression and the results already available in the literature for some specific input structures.

Wireless networks are fundamentally limited by the intensity of the received signals and the mutual interference caused by many concurrent transmissions. We consider large wireless ad hoc networks whose underlying node distribution is a Poisson cluster process. Under the assumption that multiple antennas are available at each node, we evaluate the performance of interference alignment (IA) inside each cluster. We extend our previous analysis of the outage probability achieved by this technique by generalizing it to IA with receive diversity. Furthermore, we provide a simplified expression applicable at high Signal-to-Interference Ratio, along the lines of the analysis recently proposed by Ganti, Andrews and Haenggi.

Stochastic geometry proves to be a powerful tool for modeling dense wireless networks adopting random MAC protocols such as ALOHA and CSMA. The main strength of this methodology lies in its ability to account for the randomness in the nodes' location jointly with an accurate description at the physical layer, based on the SINR, that allows to consider also random fading on each link. Existing models of CSMA networks adopting the stochastic geometry approach suffer from two important weaknesses: 1) they permit to evaluate only spatial averages of the main performance measures, thus hiding possibly huge discrepancies in the performance achieved by individual nodes; 2) they are analytically tractable only when nodes are distributed over the area according to simple spatial processes (e.g., the Poisson point process). In this paper we show how the stochastic geometry approach can be extended to overcome the above limitations, allowing to obtain node throughput distributions as well as to analyze a significant class of topologies in which nodes are not independently placed.

In this paper we study the optimal placement and optimal number of active relay nodes through the traffic density in mobile sensor ad hoc networks. We consider a setting in which a set of mobile sensor sources is creating data and a set of mobile sensor destinations is receiving that data through multihop wireless paths. We make the assumption that the network is massively dense, i.e., there are so many sources, destinations, and relay nodes, that it is best to describe the network in terms of macroscopic parameters rather than in terms of microscopic parameters. A simple one-dimensional scenario is used to introduce the problem. We solve the two-dimensional scenario where the mobility of the nodes is deterministic and when it follows the brownian mobility model.

Information-theoretic performance analysis of a MIMO communication over Land Mobile Satellite (LMS) channels, under ergodic and non-ergodic regimes, is performed. The capacity-achieving input covariance matrix, and the corresponding ergodic capacity, assuming perfect receive-side information but making different assumptions on the amount of channel knowledge at the transmitter, are derived. We obtain exact results, but for the case when perfect channel knowledge is assumed at both ends of the link, for which we provide an upper bound to the ergodic capacity. In the non-ergodic scenario, we compute the outage capacity in absence of power-control, and discuss the asymptotic Gaussianity of the mutual information, which strongly depends on the overall number of degrees of freedom available on the channel. Design guidelines for multiantenna LMS channels are gained studying the low Signal-to-Noise Ratio (SNR) behavior of the capacity, still under the assumption of absence of knowledge of the channel matrix (or its statistics) at the transmitter. The results are illustrated through several examples, aimed at assessing the impact on the performance of the diversity order and/or the Line-of-Sight (LOS) fluctuations.

A statistical model for Land Mobile Satellite (LMS) channels, where transmitters and receivers are equipped with multiple antennas, is introduced. Several spectral statistics are given, which allow the theoretical performance analysis of the newly proposed channel model from both a communication and an information-theoretic point of view. Specifically, joint and marginal statistics of the squared singular-values of the channel matrix are evaluated, paving the way for the performance analysis under ergodic and nonergodic assumptions on the channel behavior. The capacity-achieving input covariance matrix, and the corresponding ergodic capacity, assuming perfect receive-side information but making different assumptions on the amount of channel knowledge at the transmitter, are derived. We obtain exact results, but for the case when perfect channel knowledge is assumed at both ends of the link, for which we provide an upper bound to the ergodic capacity. In the nonergodic scenario, we compute the outage probability in absence of power-control, and discuss the asymptotic Gaussianity of the mutual information, which strongly depends on the overall number of degrees of freedom available on the channel. Design guidelines for multiantenna LMS channels are gained studying the low signal-to-noise ratio (SNR) behavior of the capacity, still under the assumption of absence of knowledge of the channel matrix (or its statistics) at the transmitter. The results are illustrated through several examples, aimed at assessing the impact on the performance of the diversity order and/or the line-of-sight (LOS) fluctuations.

We consider static ad hoc wireless networks comprising significant inhomogeneities in the node spatial distribution over the area and analyze the scaling laws of their transport capacity as the number of nodes increases. In particular, we consider nodes placed according to a shot-noise Cox process (SNCP), which allows to model the clustering behavior usually recognized in large-scale systems. For this class of networks, we propose novel scheduling and routing schemes that approach previously computed upper bounds to the per-flow throughput as the number of nodes tends to infinity.

We study the performance of signal estimation and reconstruction systems, that exploit the linear minimum mean square error (LMMSE) technique. This model often occurs in signal processing and wireless communications; some examples are radar applications, MIMO communications, or sensor networks sampling a physical field. Our performance analysis implies the characterization of a random matrix product, involving a multifold Vandermonde matrix with complex exponential entries. We therefore derive the LMMSE by computing the eta-transform of this matrix product, which can be evaluated either by implicit as well as by explicit expression, using the matrix asymptotic moments. Finally, we show how our results can be applied in some cases of practical interest.

We consider static ad hoc wireless networks comprising significant inhomogeneities in the node spatial distribution over the area, and analyze the scaling laws of their transport capacity as the number of nodes increases. In particular, we consider nodes placed according to a shot-noise Cox process, which allows to model the clustering behavior usually recognized in large-scale systems. For this class of networks, we propose novel scheduling and routing schemes which approach previously computed upper bounds to the per-flow throughput as the number of nodes tends to infinity.

We analyze the capacity scaling laws of wireless ad hoc networks comprising significant inhomogeneities in the node spatial distribution over the network area. In particular, we consider nodes placed according to a shot-noise Cox process, which allows to model the clustering behavior usually recognized in large-scale systems. For this class of networks, we introduce novel techniques to compute upper bounds to the available per-flow throughput as the number of nodes tends to infinity, which are tight in the case of interference limited systems.

Coordinating the reception and transmission of signals across spatially distributed base stations has been shown to improve sum-rate performance by mitigating the effects of intercell interference in Multiple-Input-Multiple-Output (MIMO) cellular networks. Relying on recent results on the freeness of certain non-Gaussian random matrices, we provide an information theoretic analysis of cooperative MIMO networks. This analysis applies to the case where full channel state information is known at a subset of the bases and where statistical information is known at all others. Tools for evaluating random matrix transforms traditionally exploited in Mean Square Error (MSE) and mutual information analysis are provided, and the general model formulation paves the way for future work, where specific scheduling and/or power assignment schemes could be embodied in the newly presented framework.

The distribution of the sum of non-negative random variables plays an essential role in the performance analysis of diversity schemes for wireless communications over fading channels. While for common fading models such as the Rayleigh, Rice, and Nakagami, the performance of diversity systems is well understood, a minor attention has been devoted to the shadowed-Rice (SR) case, namely a Rice fading channel with fluctuating (e.g. random) Line of Sight (LOS) component. Indeed, the analytical performance evaluation of diversity systems on SR fading channels requires the availability of handy expressions for the distribution of the combined received power. To this end, the rationale of this paper is twofold: first, to evaluate the distribution of the sum of SR random variables, both for the case of independent as well as correlated LOS components, and then to carry out an extensive performance analysis of maximal ratio combining (MRC) detection scheme on SR fading channels.

This paper characterizes the marginal probability density function of an unordered eigenvalue of finite-dimensional random matrices of particular interest in MIMO (multiple-input multiple-output) wireless communications. Specifically, a technique is presented for deriving the eigenvalue statistics in one-side correlated Rayleigh-faded channels and in Ricean-faded channels, with or without cochannel interferers. The exact expressions found turn out to be extremely useful in calculating information-theoretic quantities. As an application, we calculate the ergodic mutual information for all the abovementioned channel fading conditions, obtaining a closed form formula for the Rayleigh case and, in turn, a series expression for the Ricean faded one.