Multiple Instance Learning (MIL) offers a natural solution for settings where only coarse, bag-level labels are available, without having access to instance-level annotations. This is usually the case in digital pathology, which consists of gigapixel-sized images. While deterministic attention-based MIL approaches achieve strong bag-level performance, they often overlook the uncertainty inherent in instance relevance. In this paper, we address the lack of uncertainty quantification in instance-level attention scores by introducing SGPMIL, a new probabilistic attention-based MIL framework grounded in Sparse Gaussian Processes (SGP). By learning a posterior distribution over attention scores, SGPMIL enables principled uncertainty estimation, resulting in more reliable and calibrated instance relevance maps. Our approach not only preserves competitive bag-level performance but also significantly improves the quality and interpretability of instance-level predictions under uncertainty. SGPMIL extends prior work by introducing feature scaling in the SGP predictive mean function, leading to faster training, improved efficiency, and enhanced instance-level performance. Extensive experiments on multiple well-established digital pathology datasets highlight the effectiveness of our approach across both bag- and instance-level evaluations. Our code is available at https://github.com/mandlos/SGPMIL.

Cell-free (CF) massive multiple-input multiple-output (mMIMO) is a network architecture beyond fifth generation (B5G), which has the potential to deliver significantly higher spectral efficiency (SE) and energy conservation, when compared to the traditional cellular MIMO layout. Radio stripes form a particular realization of CF mMIMO topologies, which at a relatively modest deployment cost, promise to distribute part of the computational load of the centralized processing unit (CPU), while maintaining the same performance. However, the limited-capacity fronthaul (FH) network effect has not yet been adequately studied in this context. In this paper, we develop an uplink sequential processing algorithm that is optimal in the sense of locally minimizing the mean-squared error (MSE) at every antenna processing unit (APU). The performance is further enhanced by applying an effective Compare-and-Forward (CnF) strategy or by minimizing the compression error covariance trace, given the fronthaul capacity constraint. Additionally, we study the case where the radio stripe arrangement uses a distributed setup of access points (APs), aiming at minimizing path attenuation even more effectively. Based on analytical equations and simulation results, we conclude that throughput is maximized when the classic radio stripe setup is combined with the proposed algorithm and the CnF technique.

Smart wireless environments enabled by multiple distributed Reconfigurable Intelligent Surfaces (RISs) have recently attracted significant research interest as a wireless connectivity paradigm for sixth Generation (6G) networks. In this paper, using random matrix theory methods, we calculate the mean of the sum Mutual Information (MI) for the correlated Multiple-Input Multiple-Output (MIMO) Multiple Access Channel (MAC) in the presence of multiple RISs, in the large-antenna number limit. We thus obtain the capacity region boundaries, after optimizing over the tunable RISs’ phase configurations. Furthermore, we obtain a closed-form expression for the variance of the sum-MI metric, which together with the mean provides a tight Gaussian approximation for the outage probability. The derived results become relevant in the presence of fast-fading, when channel estimation is extremely challenging. Our numerical investigations showcased that, when the angle-spread in the neighborhood of each RIS is small, which is expected for higher carrier frequencies, the communication link strongly improves from optimizing the ergodic MI of the multiple RISs. We also found that, increasing the number of transmitting users in such MIMO-MAC-RIS systems results to rapidly diminishing sum-MI gains, hence, providing limits on the number of users that can be efficiently served by a given RIS.

Cell-Free Massive multiple-input multiple-output (MIMO) has proven to be an essential topology for 5G and beyond 5G (B5G) wireless communications, as it can offer unprecedented levels of spectral efficiency (SE) and energy efficiency (EE). The foremost issue of such systems is the highly centralized architecture that often leads to opposite results. Radio stripes (RS) form a versatile solution which can offer traffic load alleviation, infrastructure cost reduction and installation flexibility. This paper studies the uplink case of a limited-capacity RS system and proposes a novel MMSE algorithm that leads to optimal results, in the sense of local mean square error (MSE) minimization. Performance is further enhanced by the application of the heuristic Compare-and-Forward (CnF) strategy, which, by enabling dynamic clustering, it can optimally choose a subset of antenna processing units (APUs) to serve each user equipment (UE). That user-centric approach, combined with our optimal algorithm, can guarantee superior performance than any other radio stripe processing scheme.

Unmanned aerial vehicle (UAV)-aided communications is a promising emerging technology that will be adopted in the next generation communication networks. In this paper, a number of advanced cooperative UAV-aided communication solutions is proposed and evaluated, which considerably improve the performance of traditional terrestrial networks. Specifically, two generalized multi-UAV-selection schemes are introduced, depending on whether a direct link between the source and the destination is available or not. Once the UAVs have been selected, they may retransmit the source message to the destination using distributed space-time coding, or, in the presence of channel state information, distributed beamforming. A number of metrics to evaluate the performance on a realistic channel model was adopted, including the end-to-end outage probability (OP), the so-called goodput, and the average number of path estimations, as well as the total UAV communications power consumption. Exact expressions for the OP were obtained in terms of finite sums. Moreover, convenient closed-form expressions for the asymptotic OP were derived, valid for large numbers of UAVs, which are also very accurate for few UAVs. All results were compared with numerical simulations, which clearly depict the performance improvement induced by the proposed schemes as well as the impact of various system and channel parameters to the performance.

Reconfigurable Intelligent Surfaces (RISs) have been recently proposed as an enabling technology for programmable wireless environments. In this paper, we present asymptotic closed-form expressions for the mean and variance of the mutual information for a multi-antenna transmitter-receiver pair in the presence of RISs, using statistical physics methods. While nominally valid in the large-system limit, we show that the derived Gaussian approximation for the mutual information can be quite accurate, even for modest-sized antenna arrays and metasurfaces. The above results are particularly useful when fast-fading conditions are present, which renders channel estimation challenging. We find that, when the channel close to an RIS is correlated, for instance due to small angle spread, which is reasonable for wireless systems with increasing carrier frequencies, the communication link benefits significantly from statistical RIS optimization, resulting in gains that are surprisingly higher than the nearly uncorrelated case. Using our novel asymptotic properties of the correlation matrices of the impinging and outgoing signals at the RISs, we can optimize the metasurfaces without brute-force numerical optimization. When the desired reflection from any of the RISs departs significantly from geometrical optics, the metasurfaces can be optimized to provide robust communication links, without significant need for their optimal placement.

Reconfigurable Intelligent Surfaces (RISs), comprising large numbers of low-cost and passive metamaterials with tunable reflection properties, have been recently proposed as an enabler for programmable radio propagation environments. However, the role of the channel conditions near the RISs on their optimizability has not been analyzed adequately. In this paper, we present an asymptotic closed-form expression for the mutual information of a multi-antenna transmitter-receiver pair in the presence of multiple RISs, in the large-antenna limit, using the random matrix and replica theories. Under mild assumptions, asymptotic expressions for the eigenvalues and the eigenvectors of the channel covariance matrices are derived. We find that, when the channel close to an RIS is correlated, for instance due to small angle spread, the communication link benefits significantly from the RIS optimization, resulting in gains that are surprisingly higher than the nearly uncorrelated case. Furthermore, when the desired reflection from the RIS departs significantly from geometrical optics, the surface can be optimized to provide robust communication links. Building on the properties of the eigenvectors of the covariance matrices, we are able to find the optimal response of the RISs in closed form, bypassing the need for brute-force optimization.

Multiple Input Multiple Output (MIMO) technology offers the possibility of increased throughput in wireless communications, and as such, it is a potential candidate for High Frequency (HF) systems where only small bandwidths are available. However, the increased wavelength and size of antenna elements complicate the implementation of HF multi-antenna transceivers. In this paper, we consider multi-carrier (OFDM) MIMO HF communication systems where the multiple non co-located antennas at each communication end are interconnected through Radio Frequency (RF) links. We consider Minimum-Mean-Squared-Error- (MMSE) pilot-assisted channel estimation at the receiver side in OFDM transmission, and, leveraging results from random matrix theory, we present novel upper and lower bounds on the achievable throughput in the presence of imperfect channel estimation. Our representative numerical results for a 9 × 9 HF MIMO system quantify the achievable rate for realistic HF channel parameters, validating the interest in multi-antenna systems.

The use of multiple antenna arrays in transmission and reception has become an integral part of modern wireless communications. To quantify the performance of such systems, the evaluation of bounds on the error probability of realistic finite length codewords is important. In this paper, we analyze the standard Gallager error bound for both constraints of maximum average power and maximum instantaneous power. Applying techniques from random matrix theory, we obtain analytic expressions of the error exponent when the length of the codeword increases to infinity at a fixed ratio with the antenna array dimensions. Analyzing its behavior at rates close to the ergodic rate, we find that the Gallager error bound becomes asymptotically close to an upper error bound obtained recently by Hoydis et al. 2015. We also obtain an expression for the Gallager exponent in the case when the codelength spans several Rayleigh fading blocks, hence taking into account the situation when the channel varies during each transmission.

We propose a simple, novel and distributed power control algorithm, called dual averaging, that efficiently incorporates past information and regulates power to achieve better stability. The dual averaging power control algorithm converges to the optimal power vector in a feasible deterministic wireless network. More importantly, even if the network is stochastic and time- varying, as long as the channel is feasible on average, the proposed dual averaging power control algorithm converges almost surely to the deterministic optimal power vector, while existing power control algorithms (such as Foschini-Miljanic) may fail to converge (even to a distribution) altogether. We also provide an extensive set of simulations that demonstrate various interesting and desirable properties of the proposed algorithm.

Consider a dense wireless network of nodes, which can be used to transfer data between arbitrary sources and destinations. In this paper we develop a methodology based on variational calculus to optimize a number of path metrics, such as the success probability or the total power consumed by a packet delivery in the presence of external interference. We then extend the approach to the case of multiple origin-destination pairs, in which the relaying of each packet causes interference to the other. In both cases, we show that the optimal path may differ significantly from a straight line. We then discuss the consequences of these deviations in the context of network design.

This paper focuses on the effect that various co-transmission schemes have on a single receiver's SNR, under a stochastic-geometry setting for the emitters' location. The model includes all standard effects of ground propagation: power law to account for the distance, fast fading, shadowing, plus delay spread (resolvable multipath). The schemes addressed include: the dimension-expanding fully orthogonal case (namely channel-blind transmission on completely orthogonal dimensions); the two extreme co-transmission schemes of fully coherent (perfectly known channel) as well as fully incoherent (purely channel-blind) cases; randomly orthogonalized co-transmission; plus selected transmission schemes such as the strongest signal or the nearest node to the receiver. The emphasis is on outage statistics, but capacity and bit-error-rate are also computed in selective cases. The analysis highlights the role of the various parameters involved, in particular demonstrating the importance of resolvable multipath on the relative performance of the schemes addressed.

From the standpoint of Information theory, a time and frequency selective Ricean ergodic MIMO channel can be represented in the Hilbert space l2(ℤ) by a random ergodic self-adjoint operator whose Integrated Density of States (IDS) governs the behavior of the Shannon's mutual information. In this paper, it is shown that when the numbers of antennas at the transmitter and at the receiver tend to infinity at the same rate, the mutual information per receive antenna tends to a quantity that can be identified. This result can be obtained by analyzing the behavior of the Stieltjes transform of the IDS in the regime of the large numbers of antennas.

Technology is moving towards space division multiplexing in optical fiber to keep up the trend in rate increase over time and to avoid an imminent capacity crunch. Thus, it is of paramount interest to estimate the potential gains of this approach. As more spatial channels are being packed into a single fiber, the increased crosstalk necessitates the use of MIMO to guarantee reliable operation. In this paper, we exploit the analogy between an optical fiber and a model from mesoscopic physics - a chaotic cavity - to obtain a novel channel model for the optical fiber. The model captures both random distributed crosstalk and mode-dependent loss, which are described within the framework of scattering theory. Using tools from replica theory and random matrix theory, we derive the capacity of the fiber optical MIMO channel model.

Optical fiber communications can be modeled using the non-linear Schrödinger equation, which is integrable. In this paper we show how integrability can be exploited to communicate using multisoliton pulses. Starting with a white Gaussian input signal, we use the known distributions of eigenvalues and scattering data to derive an analytical expression for a lower bound to the spectral efficiency, taking into account the effects of noise due to amplification explicitly. We show that in the low noise regime, the soliton channel shows two different behaviors, interpolated by a single scalar parameter that controls the nonlinearity of the system. In the linear regime the soliton channel approaches an additive white Gaussian noise channel, while for strongly nonlinear systems the bound declines. The bound reaches a maximum between the two regions.

In this work, we propose a unified approach to evaluating the CDF and PDF of indefinite quadratic forms in Gaussian random variables. Such a quantity appears in many applications in communications, signal processing, information theory, and adaptive filtering. For example, this quantity appears in the mean-square-error (MSE) analysis of the normalized least-mean-square (NLMS) adaptive algorithm, and SINR associated with each beam in beam forming applications. The trick of the proposed approach is to replace inequalities that appear in the CDF calculation with unit step functions and to use complex integral representation of the the unit step function. Complex integration allows us then to evaluate the CDF in closed form for the zero mean case and as a single dimensional integral for the non-zero mean case. Utilizing the saddle point technique allows us to closely approximate such integrals in non zero mean case. We demonstrate how our approach can be extended to other scenarios such as the joint distribution of quadratic forms and ratios of such forms, and to characterize quadratic forms in isotropic distributed random variables. We also evaluate the outage probability in multiuser beamforming using our approach to provide an application of indefinite forms in communications.

In this paper, we analyze the problem of power control in large, random wireless networks that are obtained by “erasing” a finite fraction of nodes from a regular d-dimensional lattice of N transmit-receive pairs. In this model, which has the important feature of a minimum distance between transmitter nodes, we find that when the network is infinite, power control is always feasible below a positive critical value of the users' signal-to-interference-plus-noise ratio (SINR) target. Drawing on tools and ideas from statistical physics, we show how this problem can be mapped to the Anderson impurity model for diffusion in random media. In this way, by employing the so-called coherent potential approximation method, we calculate the average power in the system (and its variance) for 1-D and 2-D networks. This approach is equivalent to traditional techniques from random matrix theory and is in excellent agreement with the numerical simulations; however, it fails to predict when power control becomes infeasible. In this regard, even though infinitely large systems are always unstable beyond a critical value of the users' SINR target, finite systems remain stable with high probability even beyond this critical SINR threshold. We calculate this probability by analyzing the density of low lying eigenvalues of an associated random Schrödinger operator, and we show that the network can exceed this critical SINR threshold by at least O((log N)-2/d) before undergoing a phase transition to the unstable regime. Finally, using the same techniques, we also calculate the tails of the distribution of transmit power in the system and the rate of convergence of the Foschini-Miljanic power control algorithm in the presence of random erasures.

International audience

Cognitive radio systems allow opportunistic secondary users (SUs) to access portions of the spectrum that are unused by the network's licensed primary users (PUs), provided that the induced interference does not compromise the PUs' performance guarantees. To account for interference constraints of this type, we consider flexible spectrum access pricing schemes that charge SUs based on the interference that they cause to the system's PUs, and we examine how SUs can react to maximize their achievable transmission rate in this setting. We show that the resulting noncooperative game admits a unique Nash equilibrium under very mild assumptions on the pricing mechanism employed by the network operator and under both static and ergodic (fast-fading) channel conditions. In addition, we derive a dynamic power allocation policy that converges to equilibrium within a few iterations (even for large numbers of users) and that relies only on local-and possibly imperfect-signal-to-interference-and-noise ratio measurements; importantly, the proposed algorithm retains its convergence properties even in the ergodic channel regime, despite its inherent stochasticity. Our theoretical analysis is complemented by extensive numerical simulations that illustrate the performance, robustness, and scalability properties of the proposed pricing scheme under realistic network conditions.

In this work, we consider the downlink of a single-cell multi-user MIMO system in which the base station (BS) makes use of N antennas to communicate with K single-antenna user equipments (UEs). The UEs move around in the cell according to a random walk mobility model. We aim at determining the energy consumption distribution when different linear precoding techniques are used at the BS to guarantee target rates within a finite time interval T. The analysis is conducted in the asymptotic regime where N and K grow large with fixed ratio under the assumption of perfect channel state information (CSI). Both recent and standard results from large system analysis are used to provide concise formulae for the asymptotic transmit powers and beamforming vectors for all considered schemes. These results are eventually used to provide a deterministic approximation of the energy consumption and to study its fluctuations around this value in the form of a central limit theorem. Closed-form expressions for the asymptotic means and variances are given. Numerical results are used to validate the accuracy of the theoretical analysis and to make comparisons. We show how the results can be used to approximate the probability that a battery-powered BS runs out of energy and also to design the cell radius for minimizing the energy consumption per unit area. The imperfect CSI case is also briefly considered.

We consider the downlink of a single-cell multi-user MIMO system in which the base station makes use of N antennas to communicate with K single-antenna user equipments (UEs) randomly positioned in the coverage area. In particular, we focus on the problem of designing the optimal linear precoding for minimizing the total power consumption while satisfying a set of target signal-to-interference-plus-noise ratios (SINRs). To gain insights into the structure of the optimal solution and reduce the computational complexity for its evaluation, we analyze the asymptotic regime where N and K grow large with a given ratio and make use of recent results from large system analysis to compute the asymptotic solution. Then, we concentrate on the asymptotically design of heuristic linear precoding techniques. Interestingly, it turns out that the regularized zero-forcing (RZF) precoder is equivalent to the optimal one when the ratio between the SINR requirement and the average channel attenuation is the same for all UEs. If this condition does not hold true but only the same SINR constraint is imposed for all UEs, then the RZF can be modified to still achieve optimality if statistical information of the UE positions is available at the BS. Numerical results are used to evaluate the performance gap in the finite system regime and to make comparisons among the precoding techniques.

In this work, we consider the downlink of a single-cell multi-user multiple-input multiple-output system in which zero-forcing precoding is used at the base station (BS) to serve a certain number of user equipments (UEs). A fixed data rate is guaranteed at each UE. The UEs move around in the cell according to a Brownian motion, thus the path losses change over time and the energy consumption fluctuates accordingly. We aim at determining the distribution of the energy consumption. To this end, we analyze the asymptotic regime where the number of antennas at the BS and the number of UEs grow large with a given ratio. It turns out that the energy consumption is asymptotically a Gaussian random variable whose mean and variance are derived analytically. These results can, for example, be used to approximate the probability that a battery-powered BS runs out of energy within a certain time period.

Macroscopic mobility of users is important to determine the performance and energy efficiency of a wireless network, because of the temporal correlations it introduces in the consumed power and throughput. In this work, we introduce a methodology that allows to compute the long time statistics of such metrics in a network. After describing the general approach, we consider a specific example of the uplink channel of a mobile user in the vicinity of a base station equipped with a large number of antennas (the so called “massive MIMO” base station). To guarantee a fixed signal-to-noise ratio and rate, the user inverts the pathloss channel power, while moving around in the cell. To calculate the long time distribution of the corresponding consumed energy, we assume that its movement follows a Brownian motion, and then map the problem to the solution of the minimum eigenvalue of a partial differential equation, which can be solved either analytically, or numerically very fast. The single-user throughput is also treated. We then present some results and discuss how they can be generalized if the mobility model is assumed to be a Levy random walk. A roadmap to use this methodology is eventually given to extend results to a multiple user set-up with multiple base stations.

In this paper, we examine the problem of cost/energy-efficient power allocation in uplink multi-carrier orthogonal frequency-division multiple access (OFDMA) wireless networks. In particular, we consider a set of wireless users who seek to maximize their transmission rate subject to pricing limitations and we show that the resulting non-cooperative game admits a unique equilibrium for almost every realization of the system's channels. We also propose a distributed exponential learning scheme which allows users to converge to the game's equilibrium exponentially fast by using only local channel state information (CSI) and signal to interference-plus-noise ratio (SINR) measurements. Given that such measurements are often imperfect in practical scenarios, a major challenge occurs when the users' information is subject to random perturbations. In this case, by using tools and ideas from stochastic convex programming, we show that the proposed learning scheme retains its convergence properties irrespective of the magnitude of the observational errors.

In this paper, we apply statistical mechanics methods to the problem of detection of multiple primary wireless sources by a wireless sensor network. We assume that the location of the primary sources is known, but that the channel connecting them to the sensors is random. The sensor network tries to detect which sources are emitting by employing a belief propagation algorithm. We use the Replica approach to estimate the probability of error and we provide analytical expressions and numerical results for the case of random connectivity between sources and sensor nodes, for the fading channel model. This method can provide a simple way to calculate performance metrics for the detection problem.

Multiple-input and multiple-output processing techniques in fiber optical communications have been proposed as a promising approach to meet increasing demand for information throughput. In this context, the multiple channels correspond to the multiple modes or multiple cores or both in the fiber. In this paper, we characterize the distribution of the mutual information with Gaussian input in a simple channel model for this system. Assuming significant crosstalk between cores, negligible backscattering and near-lossless propagation in the fiber, we model the transmission channel as a random complex unitary matrix. The loss in the transmission may be parameterized by a number of unutilized channels in the fiber. We analyze the system in a dual fashion. First, we evaluate a closed-form expression for the outage probability, which is handy for small matrices. We also apply the asymptotic approach, in particular the Coulomb gas method from statistical mechanics, to obtain closed-form results for the ergodic mutual information, its variance as well as the outage probability for Gaussian input in the limit of large number of cores/modes. By comparing our analytic results to simulations, we see that, despite the fact that this method is nominally valid for large number of modes, our method is quite accurate even for small to modest number of channels.

MIMO processing techniques in fiber optical communications have been proposed as a promising approach to meet increasing demand for information throughput. In this context, the multiple channels correspond to the multiple modes and/or multiple cores in the fiber. The lack of back-scattering necessitates the modeling of the transmission coefficients between modes as elements of a unitary matrix. Also, due to the scattering between modes the channel is modeled as a random Haar unitary matrix between Nttransmitting and Nrreceiving modes. In this paper, we apply a large-deviations approach from random matrix theory to obtain the outage capacity for Haar matrices in the low outage limit, which is appropriate for fiber-optical communications. This methodology is based on the Coulomb gas method for the eigenvalues of a matrix developed in statistical physics. By comparing our analytic results to simulations, we see that, despite the fact that this method is nominally valid for large number of modes, our method is quite accurate even for small to modest number of channels.

Drawing ideas from Riemannian geometry, we develop a distributed optimization dynamical system for determining optimum input signal covariance matrices in MIMO multiple access channels. In this type of problems, standard (Euclidean) gradient ascent approaches fail because the problem's semidefiniteness constraints are generically violated along the gradient flow; however, by endowing the space of positive-definite matrices with a non-Euclidean geometry which becomes singular when the eigenvalues of the users' covariance matrices approach zero, we are able to derive a matrix-valued Riemannian gradient ascent scheme which converges to the system's optimum transmit spectrum. More to the point, we show that by tuning the geometry of the semidefinite cone, the algorithm's convergence speed changes significantly. As a result, for a specific choice of geometry (which extends the well-known replicator dynamics of evolutionary game theory to a matrix setting), our scheme converges within a few iterations and users are able to track the optimum signal profile even in the presence of rapidly changing channel conditions.

Consider a wireless network of transmitter-receiver pairs. The transmitters adjust their powers to maintain a particular SINR target at the corresponding receiver in the presence of interference from neighboring transmitters. In this paper we analyze the power vector that achieves this target (and hence is optimal) in the presence of randomness in the network. The randomness is realized by randomly turning off a fraction of transmitter-receiver pairs in a regular lattice. We show that the problem is identical to the so-called Anderson model, which describes the motion of electrons in a dirty metal. We show that traditional random matrix theory is only an approximation that, while accurate in some cases, fails to fully describe the system. We apply the coherent potential approximation (CPA), which is equivalent to random matrix theory, to evaluate the average power vector. We also find that although beyond a certain point the infinite system is infeasible with probability one, any arbitrarily large, but finite system has a typically small probability of becoming infeasible. The CPA framework allows us to calculate this outage probability with exponential accuracy by showing that it is proportional to the tails of the eigenvalue distribution of the system.

Linear receivers offer a low complexity option for multiantenna communication systems. Therefore, understanding the outage behavior of the corresponding SINR is important in a fading mobile environment. In this paper, we introduce a large deviation method, valid nominally for a large number M of antennas, which provides the probability density of the SINR of Gaussian channel MIMO minimum mean square error (MMSE) and zero-forcing (ZF) receivers, with arbitrary transmission power profiles and in the presence of receiver antenna correlations. This approach extends the Gaussian approximation of the SINR, valid for large M asymptotically close to the center of the distribution, to obtain the non-Gaussian tails of the distribution. Our methodology allows us to calculate the SINR distribution to next-to-leading order ( O(1/M)) and showcase the deviations from approximations that have appeared in the literature (e.g., the Gaussian or the generalized Gamma distribution). We also analytically evaluate the outage probability, as well as the uncoded bit-error-rate. We find that our approximation is quite accurate even for the smallest antenna arrays (2 × 2).

We analyze the problem of finding the optimal signal covariance matrix for multiple-input multiple-output (MIMO) multiple access channels by using an approach based on ”ex-ponential learning”, a novel optimization method which applies more generally to (quasi-)convex problems defined over sets of positive-definite matrices (with or without trace constraints). If the channels are static, the system users converge to a power allocation profile which attains the sum capacity of the channel exponentially fast (in practice, within a few iterations); otherwise, if the channels fluctuate stochastically over time (following e.g. a stationary ergodic process), users converge to a power profile which attains their ergodic sum capacity instead. An important feature of the algorithm is that its speed can be controlled by tuning the users' learning rate; correspondingly, the algorithm converges within a few iterations even when the number of users and/or antennas per user in the system is large.

Consider a wireless network of transmitter-receiver pairs. The transmitters adjust their powers to maintain a particular SINR target at the corresponding receiver in the presence of interference from neighboring transmitters. In this paper we analyze the optimal power vector that achieves this target in the presence of randomness in the network. Specifically, starting from a regular lattice of transmitter-receiver pairs we randomly turn off a finite fraction of them. We apply random matrix theory to evaluate the asymptotic optimal power per link, as well as the variance of powers in the optimal power vector in the limit of a large number of links. Our analytical results show remarkable agreement with numerically generated networks, both in one- and two-dimensional network geometries. Interestingly, we observe that unlike regular lattices, the optimal power in random networks has a discontinuity at a finite value, while the variance of its powers diverges at that value. Beyond that critical point, no feasible power solution exists. We discuss the relevance of these results in realistic networks.

We analyze the power allocation problem for orthogonal multiple access channels by means of a non-cooperative potential game in which each user distributes his power over the channels available to him. When the channels are static, we show that this game possesses a unique equilibrium; moreover, if the network's users follow a distributed learning scheme based on the replicator dynamics of evolutionary game theory, then they converge to equilibrium exponentially fast. On the other hand, if the channels fluctuate stochastically over time, the associated game still admits a unique equilibrium, but the learning process is not deterministic; just the same, by employing the theory of stochastic approximation, we find that users still converge to equilibrium. Our theoretical analysis hinges on a novel result which is of independent interest: in finite-player games which admit a (possibly nonlinear) convex potential, the replicator dynamics converge to an ε-neighborhood of an equilibrium in time O(\log(1/ε)).

The “replica method” of statistical physics is employed for the large-system analysis of vector precoding for the Gaussian multiple-input multiple-output broadcast channel. The transmitter comprises a linear front-end combined with nonlinear precoding, minimizing transmit energy by means of input alphabet relaxation. For the common discrete lattice-based relaxation, the problem violates replica symmetry and a replica symmetry breaking (RSB) ansatz is taken. The limiting empirical distribution of the precoder's output and the limiting transmit energy are derived for one-step RSB. Particularizing to a “zero-forcing” (ZF) linear front-end, a decoupling result is derived. For discrete lattice-based relaxations, the impact of RSB is demonstrated for the transmit energy. The spectral efficiencies of the aforementioned precoding methods are compared to linear ZF and Tomlinson-Harashima precoding (THP). Focusing on quaternary phase shift-keying (QPSK), significant performance gains of both lattice and convex relaxations are revealed for medium to high signal-to-noise ratios (SNRs) when compared to linear ZF precoding. THP is shown to be outperformed as well. Comparing certain lattice-based relaxations for QPSK against a convex counterpart, the latter is found to be superior for low and high SNRs but slightly inferior for medium SNRs in terms of spectral efficiency.

There are a number of corrections for the above titled paper (ibid., vol. 58, no. 3, pp. 1413-1440, Mar. 2012). They are presented here.

Linear MMSE reception offers a low complexity option for multi-antenna communication systems. Understanding the outage behavior of the corresponding signal-to-interference-and-noise ratio (SINR) and per-antenna throughput r is important in a quasistatic mobile environment. In this paper we introduce a large deviations method, valid nominally for large antenna numbers N, which calculates the probability density of the SINR and r of Gaussian channel MIMO MMSE receivers, with arbitrary transmission power profiles and in the presence of transmitter antenna correlations. This approach extends the Gaussian approximation of the SINR, valid only very close to the center of the distribution, demonstrating the non-Gaussian tails of the distribution. Our methodology allows us to calculate the correct leading order (O(N)) of the SINR distribution and showcase the deviations from approximations that have appeared in the literature (e.g. the Gaussian or the generalized Gamma distribution). We are also able to calculate next-to-leading order corrections to the distribution, thereby making the approximation quite accurate even for the smallest antenna arrays (2 × 2).

A large deviations approach is introduced, which calculates the probability density and outage probability of the multiple-input multiple-output (MIMO) mutual information, and is valid for large antenna numbersN. In contrast to previous asymptotic methods that only focused on the distribution close to its most probable value, this methodology obtains the full distribution, including its non-Gaussian tails. The resulting distribution interpolates between the Gaussian approximation for ratesRclose its mean and the asymptotic distribution for large signal-to-noise ratios (SNRs) ρ. For large enoughN, this method provides the outage probability over the whole (R, ρ) parameter space. The presented analytic results agree very well with numerical simulations over a wide range of outage probabilities, even for smallN. In addition, the outage probability thus obtained is more robust over a wide range of ρ andRthan either the Gaussian or the large-ρ approximations, providing an attractive alternative in calculating the probability density of the MIMO mutual information. Interestingly, this method also yields the eigenvalue density constrained in the subset where the mutual information is fixed toRfor given ρ. Quite remarkably, this eigenvalue density has the form of the Marčenko-Pastur distribution with square-root singularities.

Infostation communication is an innovative communication paradigm thought to provide connectivity in isolated areas. In infostation communications, wireless ports are deployed to act as gateways between the remote users and the communication infrastructure. However, users are allowed to exchange data with the infrastructure only when in the coverage area of one of them. In order to provide further connectivity to remote users far away from infostations, mobile nodes are assumed to be used to collect data at remote users not in the range of the infostations and, then, upload this data when they come into proximity of the infostation. In order for this process to be successful, the system stability conditions should be identified. More in depth, we denote collection process the process representing the data packets collected by the mobile node in the time between two consecutive visits of infostations and upload process the process representing the number of data packets delivered by the mobile node to the infostation. In this paper we derive conditions when the average of the upload process is higher than the average of the collection process. To this purpose a diffusion approach inherited from physics is presented and design guidelines for stable system design are identified.

Using a large deviations approach we calculate the probability distribution of the mutual information of MIMO channels in the limit of large antenna numbers. In contrast to previous methods that only focused to the distribution close to its most probable value, thus obtaining an asymptotically Gaussian distribution, we calculate the full distribution including its tails, which behave quite differently from the bulk of the distribution. Our resulting probability distribution seamlessly interpolates between the Gaussian approximation for rates R close to the ergodic value of the mutual information and the approach of Zheng and Tse [1], valid for large signal to noise ratios rho. This provides us with a tool to analytically calculate outage probabilities at any point in the (R, rho,N) parameter space, as long as the number of antennas N is not too small. In addition, this method also yields the probability distribution of eigenvalues constrained in the subspace where the mutual information per antenna is fixed to R for a given rho. Quite remarkably, this eigenvalue density is of the form of the Marcenko-Pastur distribution with square-root singularities.

Linear receivers are considered as an attractive low- complexity alternative to optimal processing for multi-antenna MIMO communications. In this paper we characterize the performance of MMSE MIMO receivers in the limit of large antenna numbers in the presence of channel correlations. Using a different approach, we generalize our results obtained in [1] to correlated channels showing that the mutual information converges in distribution to a Gaussian random variable whose mean and variance can be characterized analytically. Our results agree very well with simulations even with a moderate number of antennas. We conclude by observing that for a fixed target rate and operating SNR, using a larger number of antennas and with a simple linear MMSE receiver may be a convenient design choice compared to limiting the number of antennas and insisting on more complicated non-linear receivers.

Linear receivers are an attractive low-complexity alternative to optimal processing for multiple-antenna multiple-input multiple-output (MIMO) communications. In this paper, we characterize the information-theoretic performance of MIMO linear receivers in two different asymptotic regimes. For fixed number of antennas, we investigate the limit of error probability in the high-signal-to noise-ratio (SNR) regime in terms of the diversity-multiplexing tradeoff (DMT). Following this, we characterize the error probability for fixed SNR in the regime of large (but finite) number of antennas.As far as the DMT is concerned, we report a negative result: we show that both linear zero-forcing (ZF) and linear minimum mean- square error (MMSE) receivers achieve the same DMT, which is largely suboptimal even in the case where outer coding and deAcircnot coding is performed across the antennas. We also provide an apAcircnot proximate quantitative analysis of the markedly different behavior of the MMSE and ZF receivers at finite rate and nonasymptotic SNR, and show that while the ZF receiver achieves poor diversity at any finite rate, the MMSE receiver error curve slope flattens out progressively, as the coding rate increases. When SNR is fixed and the number of antennas becomes large, we show that the mutual information at the output of an MMSE or ZF linear receiver has fluctuations that converge in distribution to a Gaussian random variable, whose mean and variance can be characterized in closed form. This analysis extends to the linear reAcircnot ceiver case a well-known result previously obtained for the optimal receiver. Simulations reveal that the asymptotic analysis captures accurately the outage behavior of systems even with a moderate number of antennas.

The dynamics of handover between two coexisting wireless standards and the consequent exploitation of the offered diversity by the use of multi-standard terminals has been discussed. The potential capacity benefits of mobile-initiated vertical handovers are substantial. However, it is important to choose the correct VHO criteria in order to achieve optimum load balancing and equilibrium states (global and social). Two fast-handover schemes are presented, which exhibit fast convergence to the socially optimal states by allowing a subset of the necessary VHOs among the AIs. In all cases the scheme with replicator dynamics, had the best performance at the cost of an increased vertical handover rate.

We consider the use of entropy maximization methods as a tool to generate fading models for multiple-input multiple-output (MIMO) spatially correlated flat-fading channels. We focus in particular on various assumptions about the degree of knowledge on the full covariance matrix of the channel (namely in the power constraint, rank constraint, and average constraint case). We show that this method can provide closed-form probability density functions in all cases. In a second part, we analyze the statistical properties of the singular values of the resulting fading channel. In general, they are more spread out that in the classical Gaussian i.i.d. case, which incurs less optimistic ergodic capacity figures.

Abstract—We investigate the behavior of a large number of selfish users that are able to switch dynamically between multiple wireless access-points (possibly belonging to different standards) by introducing an iterated non-cooperative game. Users start out completely uneducated and naïve but, by using a fixed set of strategies to process a broadcasted training signal, they quickly evolve and converge to an evolutionarily stable equilibrium. Then, in order to measure efficiency in this steady state, we adapt the notion of the price of anarchy to our setting and we obtain an explicit analytic estimate for it by using methods from statistical physics (namely the theory of replicas). Surprisingly, we find that the price of anarchy does not depend on the specifics of the wireless nodes (e.g. spectral efficiency) but only on the number of strategies per user and a particular combination of the number of nodes, the number of users and the size of the training signal. Finally, we map this game to the well-studied minority game, generalizing its analysis to an arbitrary number of choices. Index Terms—Wireless networks, Nash equilibrium, correlated equilibrium, price of anarchy, evolutionary game, replicas

This paper studies a nonlinear vector precoding scheme which inverts the wireless multiple-input multiple-output (MIMO) channel at the transmitter so that simple symbol-by-symbol detection can be used in lieu of sophisticated multiuser detection at the receiver. In particular, the transmit energy is minimized by relaxing the transmitted symbols to a larger alphabet for precoding, which preserves the minimum signaling distance. The so-called replica method is used to analyze the average energy savings with random MIMO channels in the large-system limit. It is found that significant gains can be achieved with complex-valued alphabets. The analysis applies to a very general class of MIMO channels, where the statistics of the channel matrix enter the result via the R-transform of the asymptotic empirical distribution of its eigenvalues. Moreover, we introduce polynomial-complexity precoding schemes for binary and quadrature phase-shift keying in complex channels by using convex rather than discrete relaxed alphabets. In case the number of transmit antennas is more than twice the number of receive antennas, we show that a convex precoding scheme, despite its polynomial complexity, outperforms NP-hard precoding using the popular Tomlinson-Harashima signaling.

We apply the replica method to analyze vector pre-coding, a method to reduce transmit power in antenna array communications, in the limit of an infinite number of dimensions of the signal vector. The analysis applies to a very general class of channel matrices. The statistics of the channel matrix enter the transmitted energy per symbol via its R-transform. We specialize our result to inversion of an i.i.d. channel and two cases of signal point optimization (i) 2-point lattice pre-coding and (ii) compact relaxation. In the two cases the replica symmetric transmitted energy is found to be 4.3 dB and 9.6 dB above the orthogonal case for a square channel matrix, respectively.

We investigate the problem of establishing the joint probability distribution of the entries of a multiple-input multiple-output (MIMO) spatially correlated flat-fading channel, when little or no information about the channel properties are available. We show that the entropy of a random positive semidefinite matrix is maximized by the Wishart distribution. We subsequently obtain the maximum entropy distribution of the MIMO transfer matrix by establishing its distribution conditioned on the covariance, and by later marginalizing over the covariance matrix. The obtained distribution is isotropic, and is described analytically as a function of the Frobenius norm of the channel matrix.

The use of multiple-antenna arrays can dramatically increase the throughput of wireless communication systems. Thus, it is important to characterize the statistics of the mutual information for realistic correlated channels. Here, a mathematical approach is presented, using the method of replicas, that provides analytic expressions not only for the average, but also for the higher moments of the distribution of the mutual information for the most general zero-mean Gaussian multiple-input multiple-output (MIMO) channels when the channel is known at the receiver. These channels include multitap delay paths, and channels with covariance matrices that cannot be written as a Kronecker product, such as general dual-polarized correlated antenna arrays. This approach is formally valid for large antenna numbers, in which case all cumulant moments of the distribution, other than the first two, scale to zero. In addition, it is shown that the replica-symmetric result is valid if the variance of the mutual information is positive and finite. In this case, it is shown that the distribution of the mutual information tends to a Gaussian, which enables the calculation of the outage capacity. These results are quite accurate even for few antennas, which makes this approach applicable to realistic situations.

Many channel models for MIMO systems have appeared in the literature. However, with the exception of a few recent results, they are largely focussed on two dimensional (2D) propagation, i.e., propagation in the horizontal plane, and the impact of elevation angle is not considered. The assumption of 2D propagation breaks down when in some propagation environments the elevation angle distribution is significant. Consequently, the estimation of ergodic capacity assuming a 2D channel coefficient alone can lead to erroneous results. In this paper, for cross polarized channels, we define a composite channel model and channel coefficient that takes into account both 2D and 3D propagation. Using this composite channel coefficient we assess the ergodic channel capacity and discuss its sensitivity to a variety of different azimuth and elevation power distributions and other system parameters.

Fourth-generation (4G) systems are expected to support data rates of the order of 100 Mb/s in the outdoor environment and 1 Gb/s in the indoor/stationary environment. In order to support such large payloads, the radio physical layer must employ receiver algorithms that provide a significant increase in spectrum efficiency (and, hence, capacity) over current wireless systems. Recently, an explosion of multiple-input-multiple-output (MIMO) studies have appeared with many journals presenting special issues on this subject. This has occurred due to the potential of MIMO to provide a linear increase in capacity with antenna numbers. Environmental considerations and tower loads will often restrict the placing of large antenna spans on base stations (BSs). Similarly, customer device form factors also place a limit on the antenna numbers that can be placed with a mutual spacing of 0.5 wavelength. The use of cross-polarized antennas is widely used in modern cellular installations as it reduces spacing needs and tower loads on BSs. Hence, this approach is also receiving considerable attention in MIMO systems. In order to study and compare various receiver architectures that are based on MIMO techniques, one needs to have an accurate knowledge of the MIMO channel. However, very few studies have appeared that characterize the cross-polarized MIMO channel. Recently, the third-generation partnership standards bodies (3GPP/3GPP2) have defined a cross-polarized channel model for MIMO systems but this model neglects the elevation spectrum. In this paper, we provide a deeper understanding of the channel model for cross-polarized systems for different environments and propose a composite channel impulse model for the cross-polarized channel that takes into account both azimuth and elevation spectrum. We use the resulting channel impulse response to derive closed-form expressions for the spatial correlation. We also present models to describe the dependence of cross-polarization discrimination (XPD) on distance, azimuth and elevation and delay spread. In addition, we study the impact of array width, signal-to-noise ratio, and antenna slant angle on the mutual information (MI) of the system. In particular, we present an analytical model for large system mean mutual information values and consider the impact of elevation spectrum on MI. Finally, the impact of multipath delays on XPD and MI is also explored.

Differential unitary space–time modulation (DUSTM) and its earlier nondifferential counterpart, USTM, permit high-throughput multiple-input multiple-output (MIMO) communication entirely without the possession of channel state information by either the transmitter or the receiver. For an isotropically random unitary input we obtain the exact closed-form expression for the probability density of the DUSTM received signal, permitting the straightforward Monte Carlo evaluation of its mutual information. We compare the performance of DUSTM and USTM through both numerical computations of mutual information and through the analysis of low- and high-signal-to-noise ratio (SNR) asymptotic expressions. In our comparisons the symbol durations of the equivalent unitary space–time signals are equal to$T$. For DUSTM the number of transmit antennas is constrained by the scheme to be$M = T/2$, while USTM has no such constraint. If DUSTM and USTM utilize the same number of transmit antennas at high SNRs the normalized mutual information of the two schemes expressed in bits/s/Hz are asymptotically equal, with the differential scheme performing somewhat better. At low SNRs the normalized mutual information of DUSTM is asymptotically twice the normalized mutual information of USTM. If, instead, USTM utilizes the optimum number of transmit antennas then USTM can outperform DUSTM at sufficiently low SNRs.

A promising new method from the field of representations of Lie groups is applied to calculate integrals over unitary groups, which are important for multiantenna communications. To demonstrate the power and simplicity of this technique, a number of recent results are rederived, using only a few simple steps. In particular, we derive the joint probability distribution of eigenvalues of the matrix GGdagger, with G a nonzero mean or a semicorrelated Gaussian random matrix. These joint probability distribution functions can then be used to calculate the moment generating function of the mutual information for Gaussian multiple-input multiple-output (MIMO) channels with these probability distribution of their channel matrices G. We then turn to the previously unsolved problem of calculating the moment generating function of the mutual information of MIMO channels, which are correlated at both the receiver and the transmitter. From this moment generating function we obtain the ergodic average of the mutual information and study the outage probability. These methods can be applied to a number of other problems. As a particular example, we examine unitary encoded space-time transmission of MIMO systems and we derive the received signal distribution when the channel matrix is correlated at the transmitter end

We propose a promising multi-antenna scheme specifically suitable for hybrid code and time division multiplexed (CTDM) high speed shared channels commonly employed in 3GPP and 3GPP2 standards, such as HS-DPA, 1xEVDO (HDR), and 1xEVDV. The scheme is called phase sweep transmit diversity (PSTD) and was originally proposed for power controlled dedicated voice channels. PSTD is shown to provide the benefits of beamforming without the requirement for channel or weight information feedback from the receiver to the transmitter. We evaluate the benefits of PSTD for two antenna configurations: (a) the so-called BF-2V configuration that encompasses two closely-spaced (/spl lambda//2) vertically polarized antenna columns: (b) the so-called DIV-2V antenna configurations, in which the two antenna columns are widely-spaced (10-20 /spl lambda/). When compared to selection transmit diversity (STD) and the baseline case of a single antenna transmission, PSTD offers significant gains for low-tier mobility users. In addition, the closely spaced antenna configuration produces consistently higher sector throughput as compared to the widely spaced configuration.

Channel information at the transmitter is known to significantly increase information throughput. However, practical constraints in the opposite link limit the possible amount of feedback. In this paper we describe a way to calculate the capacity of a simple, yet relevant feedback scheme. In particular, we consider the case of a two-antenna transmitter and a single antenna receiver, and limit the amount of feedback to 2 bits. This case is of practical interest because it is included in the UMTS standards. We determine the transmission weights maximizing the outage mutual information, and find that they interpolate between beamforming and orthogonal coding. Further, the case of the feedback bits having finite and generally unequal probabilities of error is also considered. In the latter case, the optimal relative phase between the two transmitting antennas deviates from their symmetric /spl plusmn//spl pi//spl plusmn//spl pi//4 value. This effect is important, if the bits are fed back at different times and thus their reliability is not the same (one feedback bit being more stale than the other).

The use of multi-antenna arrays has been predicted to provide substantial throughput gains for wireless communication systems. However, these predictions have to be assessed in realistic situations, such as correlated channels and in the presence of interference. We present a model which provides expressions for the average and the variance of the distribution of the mutual information of multi-antenna systems with arbitrary correlations and interferers. This model, even though it is based on analytic calculations in the limit of large antenna numbers, produces extremely accurate results, even for small arrays. We use this model to optimize over the input signal covariance with channel covariance feedback and thus to calculate closed-loop capacities We analyze in detail two specific examples and also compare simulations to establish its validity. This method provides a simple tool to analyze the statistics of throughput for arrays of any size.

We consider a narrowband point-to-point communication system with n/sub T/ transmitters and n/sub R/ receivers. We assume the receiver has perfect knowledge of the channel, while the transmitter has no channel knowledge. We consider the case where the receiving antenna array has uncorrelated elements, while the elements of the transmitting array are arbitrarily correlated. Focusing on the case where n/sub T/=2, we derive simple analytic expressions for the ergodic average and the cumulative distribution function of the mutual information for arbitrary input (transmission) signal covariance. We then determine the ergodic and outage capacities and the associated optimal input signal covariances. We thus show how a transmitter with covariance knowledge should correlate its transmissions to maximize throughput. These results allow us to derive an exact condition (both necessary and sufficient) that determines when beamforming is optimal for systems with arbitrary number of transmitters and receivers.

We consider a narrow-band point-to-point communication system with many (input) transmitters and a single (output) receiver (i.e., a multiple-input single output (MISO) system). We assume the receiver has perfect knowledge of the channel but the transmitter only knows the channel distribution. We focus on two canonical classes of Gaussian channel models: (a) the channel has zero mean with a fixed covariance matrix and (b) the channel has nonzero mean with covariance matrix proportional to the identity. In both cases, we are able to derive simple analytic expressions for the ergodic average and the cumulative distribution function (c.d.f.) of the mutual information for arbitrary input (transmission) signal covariance. With minimal numerical effort, we then determine the ergodic and outage capacities and the corresponding capacity-achieving input signal covariances. Interestingly, we find that the optimal signal covariances for the ergodic and outage cases have very different behavior. In particular, under certain conditions, the outage capacity optimal covariance is a discontinuous function of the parameters describing the channel (such as strength of the correlations or the nonzero mean of the channel).

The use of multiple-antenna arrays in both transmission and reception promises huge increases in the throughput of wireless communication systems. It is therefore important to analyze the capacities of such systems in realistic situations, which may include spatially correlated channels and correlated noise, as well as correlated interferers with known channel at the receiver. Here, we present an approach that provides analytic expressions for the statistics, i.e., the moments of the distribution, of the mutual information of multiple-antenna systems with arbitrary correlations, interferers, and noise. We assume that the channels of the signal and the interference are Gaussian with arbitrary covariance. Although this method is valid formally for large antenna numbers, it produces extremely accurate results even for arrays with as few as two or three antennas. We also develop a method to analytically optimize over the input signal covariance, which enables us to calculate analytic capacities when the transmitter has knowledge of the statistics of the channel (i.e., the channel covariance). In many cases of interest, this capacity is very close to the full closed-loop capacity, in which the transmitter has instantaneous channel knowledge. We apply this analytic approach to a number of examples and we compare our results with simulations to establish the validity of this approach. This method provides a simple tool to analyze the statistics of throughput for arrays of any size. The emphasis of this paper is on elucidating the novel mathematical methods used.