In the context of multivariate time series, a whiteness test against an MA(1) correlation model is proposed. This test is built on the eigenvalue distribution (spectral measure) of the non-Hermitian one-lag sample autocovariance matrix, instead of its singular value distribution. The large dimensional limit spectral measure of this matrix is derived. To obtain this result, a control over the smallest singular value of a related random matrix is provided. Numerical simulations show the excellent performance of this test.

A cloud radio access network (C-RAN) is considered where the first hop from the user equipments (UEs) to the basestations (BSs) is modeled by the fading Wyner soft-handoff model. The focus is on mixed-delay constraints where a set of messages (so called “slow” messages) are jointly decoded in the cloud unit (CU), whereas the remaining messages (called “fast” messages) have to be decoded immediately at the BSs. This paper presents inner and outer bounds on the capacity region for such a setup. Moreover, the multiplexing gain region is characterized exactly. The presented results show that for small fronthaul capacity it is beneficial to send both “fast” and “slow” messages. However, when the rate of “fast” messages is already large, then increasing it further, deteriorates the sum-rate of the system. In this regime, the stringent decoding delay on the “fast” messages penalizes the overall performance. Our results indicate that this penalty is larger at moderate SNR than at high SNR and it is also larger for random time-varying fading coefficients than for static ones.

Shannon's mutual information of a random multiple antenna and multipath time varying channel is studied in the general case where the process constructed from the channel coefficients is an ergodic and stationary process which is assumed to be available at the receiver. From this viewpoint, the channel can also be represented by an ergodic self-adjoint block-Jacobi operator, which is close in many aspects to a block version of a random Schrödinger operator. The mutual information is then related to the so-called density of states of this operator. In this paper, it is shown that under the weakest assumptions on the channel, the mutual information can be expressed in terms of a matrix-valued stochastic process coupled with the channel process. This allows numerical approximations of the mutual information in this general setting. Moreover, assuming further that the channel coefficient process is a Markov process, a representation for the mutual information offset in the large signal to noise ratio regime is obtained in terms of another related Markov process. This generalizes previous results from Levy et al.. It is also illustrated how the mutual information expressions that are closely related to those predicted by the random matrix theory can be recovered in the large dimensional regime.

The Douglas Rachford algorithm is an algorithm that converges to a minimizer of a sum of two convex functions. The algorithm consists in fixed point iterations involving computations of the proximity operators of the two functions separately. The paper investigates a stochastic version of the algorithm where both functions are random and the step size is constant. We establish that the iterates of the algorithm stay close to the set of solution with high probability when the step size is small enough. Application to structured regularization is considered.

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.

Correlation tests of multiple Gaussian signals are typically formulated as linear spectral statistics on the eigenvalues of the sample coherence matrix. This is the case of the Generalized Likelihood Ratio Test (GLRT), which is formulated as the determinant of the sample coherence matrix, or the locally most powerful invariant test (LMPIT), which is formulated as the Frobenius norm of this matrix. In this paper, the asymptotic behavior of general linear spectral statistics is analyzed assuming that both the sample size and the observation dimension increase without bound at the same rate. More specifically, almost sure convergence of a general class of linear spectral statistics is established, and an associated central limit theorem is formulated. These asymptotic results are shown to provide an accurate statistical description of the behavior of the GLRT and the LMPIT in situations where the sample size and the observation dimension are both large but comparable in magnitude.

Most statistical inference methods for array processing assume an array of size N fixed and a number of snapshots T large. In addition, many works are based on the assumption of a white noise model. These two assumptions are increasingly less realistic in modern systems where N and T are usually both large, and where the noise data can be correlated either across successive observations or across the sensor antennas. In this paper an approach to handle this kind of scenario is presented. New algorithms for source number estimation, power estimation, and localization by a sensor array under noise with unknown correlation model are proposed. The results fundamentally rely on recent advances in small rank perturbations of large dimensional random matrices.

In this paper, a distributed stochastic approximation algorithm is studied. Applications of such algorithms include decentralized estimation, optimization, control or computing. The algorithm consists in two steps: a local step, where each node in a network updates a local estimate using a stochastic approximation algorithm with decreasing step size, and a gossip step, where a node computes a local weighted average between its estimates and those of its neighbors. Convergence of the estimates toward a consensus is established under weak assumptions. The approach relies on two main ingredients: the existence of a Lyapunov function for the mean field in the agreement subspace, and a contraction property of the random matrices of weights in the subspace orthogonal to the agreement subspace. A second-order analysis of the algorithm is also performed under the form of a central limit Theorem. The Polyak-averaged version of the algorithm is also considered.

In this paper, the joint fluctuations of the extreme eigenvalues and eigenvectors of a large dimensional sample covariance matrix are analyzed when the associated population covariance matrix is a finite-rank perturbation of the identity matrix, corresponding to the so-called spiked model in random matrix theory. The asymptotic fluctuations, as the matrix size grows large, are shown to be intimately linked with matrices from the Gaussian unitary ensemble. When the spiked population eigenvalues have unit multiplicity, the fluctuations follow a central limit theorem. This result is used to develop an original framework for the detection and diagnosis of local failures in large sensor networks, for known or unknown failure magnitude.

The distributed estimation of the average value of the sensors initial measures is one of the most popular issues in the Wireless Sensor Networks (WSN) area. In WSNs, broadcasting data seems natural to exchange information quickly because of the broadcast nature of the Wireless channel. Nevertheless, although broadcast-based algorithms converge faster than pairwise algorithms, the obtained consensus is not necessarily the true average. By the means of additional side-information exchange, we propose a broadcast-based algorithm converging rapidly to the true average. The convergence of this new algorithm is established and its convergence speed is exhibited. We remark that the proposed algorithm outperforms the existing ones.

In this work, a static relaying protocol, called Decode or Quantize and Forward (DoQF), is introduced for half duplex single-relay networks, and its performance is studied in the context of communications over slow fading wireless channels. The proposed protocol is inspired by the so-called Compress-and-Forward (CF) but only needs statistical Channel State Information at the Transmitter (CSIT). First, we analyze the behavior of the outage probability Poof the proposed protocol as the SNR p tends to infinity. In this case, we prove that ρ2Poconverges to a constant ξ. We refer to this constant as the outage probability gain and we derive its closed-form expression for a general class of wireless channels that includes Rayleigh and Rice. We furthermore prove that the DoQF protocol has the best achievable outage gain in the wide class of half-duplex static relaying protocols and we minimize ξ w.r.t the power allocation to the source and the relay and the durations of the slots. Next, we focus on Rayleigh channels to derive the Diversity-Multiplexing Tradeoff (DMT) of the DoQF. Our results show that the DoQF achieves the 2 by 1 MISO DMT upper-bound for multiplexing gains r <; 0.25.

The paper addresses the convergence of a decentralized Robbins-Monro algorithm for networks of agents. This algorithm combines local stochastic approximation steps for finding the root of an objective function, and a gossip step for consensus seeking between agents. We provide verifiable sufficient conditions on the stochastic approximation procedure and on the network so that the decentralized Robbins-Monro algorithm converges to a consensus. We also prove that the limit points of the algorithm correspond to the roots of the objective function. We apply our results to Maximum Likelihood estimation in sensor networks.

The Capon or minimum variance distorsionless response (MVDR) beamformer is a prominent example of spatial filtering structure in sensor array signal processing. Typical implementations of this beamformer are based on a regularized or diagonally-loaded version of the sample covariance matrix estimator. Conventionally, the performance evaluation of the beamformer relies on a measure of the signal-to-interference-plus-noise ratio (SINR) at the filter output. In this paper, we establish a central limit theorem characterizing the output SINR performance of MVDR beamforming implementations employing diagonal loading for both spatially and temporally correlated Gaussian observations.

This paper addresses the detection of a stochastic process in noise from a finite sample under various sampling schemes. We consider two hypotheses. The noise only hypothesis amounts to model the observations as a sample of a i.i.d. Gaussian random variables (noise only). The signal plus noise hypothesis models the observations as the samples of a continuous time stationary Gaussian process (the signal) taken at known but random time-instants and corrupted with an additive noise. Two binary tests are considered, depending on which assumptions is retained as the null hypothesis. Assuming that the signal is a linear combination of the solution of a multidimensional stochastic differential equation (SDE), it is shown that the minimum Type II error probability decreases exponentially in the number of samples when the False Alarm probability is fixed. This behavior is described by error exponents that are completely characterized. It turns out that they are related to the asymptotic behavior of the Kalman Filter in random stationary environment, which is studied in this paper. Finally, numerical illustrations of our claims are provided in the context of sensor networks.

In this paper, the capacity-achieving input covariance matrices for coherent block-fading correlated multiple input multiple output (MIMO) Rician channels are determined. In contrast with the Rayleigh and uncorrelated Rician cases, no closed-form expressions for the eigenvectors of the optimum input covariance matrix are available. Classically, both the eigenvectors and eigenvalues are computed numerically and the corresponding optimization algorithms remain computationally very demanding. In the asymptotic regime where the number of transmit and receive antennas converge to infinity at the same rate, new results related to the accuracy of the approximation of the average mutual information are provided. Based on the accuracy of this approximation, an attractive optimization algorithm is proposed and analyzed. This algorithm is shown to yield an effective way to compute the capacity achieving matrix for the average mutual information and numerical simulation results show that, even for a moderate number of transmit and receive antennas, the new approach provides the same results as direct maximization approaches of the average mutual information.

In wireless cooperative networks, the asynchronism between the relays can be a source of diversity which is similar in its essence to the multipath diversity of frequency selective channels. In this context, an asynchronous two-relay cooperative wireless network is studied for Decode-and-Forward (DF) and Amplify-and-Forward (AF) protocols. The outage probability in the high Signal to Noise Ratio (SNR) regime is derived and the impact of the relative delay between the two relays on this outage probability is evaluated. It is shown that for a sufficiently high relative delay, the outage probability performance becomes independent from the relative delay and approaches from the synchronous protocol performance. Besides, an optimization of the power distribution between the transmitting nodes of the network is carried out in the high SNR regime based on the outage probability minimization. Moreover, the Diversity Multiplexing Tradeoff (DMT) of the network is characterized for the two cooperative protocols DF and AF. The DMT curve does not depend on the relative delay as long as the latter is non-zero.

In wireless cooperative networks, the asynchronism between the relays can be a source of diversity which is similar in its essence to the multipath diversity of frequency selective channels. In this context, an asynchronous two-relay two-hop cooperative wireless network using the amplify-and-forward protocol is studied. The outage probability in the high signal to noise ratio (SNR) regime is derived for integer and real relative delay between the two relays. We also show that the diversity multiplexing tradeoff (DMT) of the network is d{r) = 2(1- 2r) for a non-zero relative delay.

This paper deals with the detection of a continuous random process described by an Ornstein-Uhlenbeck (O-U) stochastic differential equation. Randomly spaced sensors or equivalently a random time sampler which deliver noisy samples of the process are used for this detection. Two types of tests are considered: either H0 refers to the presence of the noisy O-U process or H0 refers to the sole presence of noise. For any fixed false alarm probability, it is shown that the type II error probability decreases to zero exponentially in the number of samples. The exponents, which do not depend on the false alarm probability, are characterized. This work completes former contributions that consider noiseless O-U process with a random sampling or noisy O-U processes with a regular sampling.

We address the optimization issue of the outage probability in Rician block fading channels with N transmit antennas and 1 receive antenna. It is already known that the eigenvectors of the covariance matrix of the transmit signal that minimizes the outage probability are the normalized mean vector of the Rician channel and N-1 orthonormal vectors belonging to the space orthogonal to the range of the mean vector. Our contribution is to optimize the eigenvalues. At high SNR, we show that the part of the power allocated to the orthogonal space of the range of the mean vector should be uniformly distributed amongst its N-1 eigenvectors. In addition, thanks to an original approximation of the outage probability, we characterize the part of power associated with the mean vector. We numerically observe improvement achieved by the proposed allocation scheme compared to uniform power allocation.

This paper is devoted to the study of the performance of the linear minimum mean-square error (LMMSE) receiver for (receive) correlated multiple-input multiple-output (MIMO) systems. By the random matrix theory, it is well known that the signal-to-noise ratio (SNR) at the output of this receiver behaves asymptotically like a Gaussian random variable as the number of receive and transmit antennas converge to+infin at the same rate. However, this approximation being inaccurate for the estimation of some performance metrics such as the bit error rate (BER) and the outage probability, especially for small system dimensions, Li proposed convincingly to assume that the SNR follows a generalized gamma distribution which parameters are tuned by computing the first three asymptotic moments of the SNR. In this paper, this technique is generalized to (receive) correlated channels, and closed-form expressions for the first three asymptotic moments of the SNR are provided. To obtain these results, a random matrix theory technique adapted to matrices with Gaussian elements is used. This technique is believed to be simple, efficient, and of broad interest in wireless communications. Simulations are provided, and show that the proposed technique yields in general a good accuracy, even for small system dimensions.

This paper is devoted to the performance study of the linear minimum mean squared error (LMMSE) estimator for multidimensional signals in the large-dimension regime. Such an estimator is frequently encountered in wireless communications and in array processing, and the signal-to-interference-plus-noise ratio (SINR) at its output is a popular performance index. The SINR can be modeled as a random quadratic form which can be studied with the help of large random matrix theory, if one assumes that the dimension of the received and transmitted signals go to infinity at the same pace. This paper considers the asymptotic behavior of the SINR for a wide class of multidimensional signal models that includes general multiple-antenna as well as spread-spectrum transmission models. The expression of the deterministic approximation of the SINR in the large-dimension regime is recalled and the SINR fluctuations around this deterministic approximation are studied. These fluctuations are shown to converge in distribution to the Gaussian law in the large-dimension regime, and their variance is shown to decrease as the inverse of the signal dimension.

In the context of wireless relay networks operating on slow fading channels, the outage probability optimization is of central importance. It is often hard to give a closed form expression of the outage probability Pofor all possible values of the Signal to Noise Ratio (SNR). On the other hand, it is possible to analyze the behaviour of Poin the asymptotic regime where the SNR rho converges to infinity. In this regime, rhoN+1Pousually converges to a constant xi where N is the number of relays. This paper presents a general method for deriving and minimizing xi with respect to the power distribution between the source and the relays, and with respect to the durations of the slots specified by the relaying protocol. Convexity of xi with respect to the design parameters is shown. The method applies to a general class of radio channels that includes the Rayleigh and the Rice channels as particular cases. Decode-and-forward as well as amplify-and-forward protocols are considered in the half duplex mode. While the proposed approach is designed for the high SNR regime, simulations show that outage probability is reduced in a similar proportion at moderate SNR.

In this article, large random matrix theory is used to study Shannonpsilas mutual information of a general class of multiple input multiple output radio channels with random correlated gains. In the literature, there exists an approximation of this mutual information in the asymptotic regime where the number of transmitting antennas and the number of receiving antennas grow toward infinity at the same pace. This contribution is devoted to the study of the mutual informationpsilas fluctuations around this deterministic approximation under the form of a central limit theorem (CLT). In particular, this CLT provides an approximation of the outage probability, which represents a fundamental performance index for communications on slow fading channels. The proof of this CLT relies on martingale theory.

In wireless cooperative networks, the asynchronism between the relays can be a source of diversity which is similar in its essence to the multipath diversity of frequency selective channels. In this context, an asynchronous two-relay two-hop cooperative wireless network using the Decode-and-Forward protocol is studied. The outage probability in the high Signal to Noise Ratio (SNR) regime is derived and the impact of the relative delay between the two relays on this outage probability is evaluated. We show that for a sufficiently high relative delay, the outage performance becomes independent from the relative delay. Moreover, an outage probability minimization with respect to the power distribution between the transmitting nodes of the network is carried out in the high SNR regime.

This paper adresses the behavior of the mutual information of correlated multiple-input multiple-output (MIMO) Rayleigh channels when the numbers of transmit and receive antennas converge to$+\infty $at the same rate. Using a new and simple approach based on PoincarÉ–Nash inequality and on an integration by parts formula, it is rigorously established that the mutual information when properly centered and rescaled converges to a standard Gaussian random variable. Simple expressions for the centering and scaling parameters are provided. These results confirm previous evaluations based on the powerful but nonrigorous replica method. It is believed that the tools that are used in this paper are simple, robust, and of interest for the communications engineering community.

This paper studies high SNR approximations of the ergodic mutual information of block fading MIMO correlated Rician channels. The exact expression of the mutual information of such channels is quite complicated, and difficult to use to obtain convenient high SNR approximations. In this paper, it is replaced by an accurate large system approximant obtained in the case where the number of transmit and receive antennas t and r converge to +infin at the same rate. The large system approximant is studied at high SNR, and it is shown that 3 different behaviours are possible depending on r/t, the rank of the line of sight component and the Rician factor. The accuracy of the high SNR approximant is shown to be connected to the support of the deterministic large system approximant of the eigenvalue distribution of the Gram matrix of the channel. This allows to infer that the approximant is accurate for realistic values of r and t if r and t or if r npar t, the line of sight component is invertible and the Rician factor is greater than a certain threshold.

The paper deals with design and performance analysis of orthogonal frequency-division multiple-access (OFDMA)-based downlink cellular wireless communications. Due to a high degree of user mobility, the base station is assumed to have only a statistical knowledge of the users' channels. Relying on the ergodic capacities connected to the user rates, a subcarrier and power allocation that minimizes the total transmitted power is proposed. The allocation strategy requires only the knowledge of the channel statistics and the rate requirements for all users. An extension and a performance analysis of this allocation algorithm in a multicell environment working with a frequency reuse factor equal to one is also conducted. A condition for the multicell network to be able to satisfy all rate requirements is derived

This paper investigates the parameters of time-hopping impulse radio ultra wide band (TH-IR-UWB). At a given spreading factor and a given system load, a trade-off has to be done in the choice of the frame length and the repetition factor. This trade-off lays on the condition of validity of the standard Gaussian approximation for multi user interferences (MUI). This study concerns both Pulse Amplitude Modulation and Pulse Position Modulation and may be applied to UWB networks with high density of users and low data rates like adhoc sensor networks, as well as networks with higher data rate and small number of users.

We derive the Cramer-Rao bound (CRB) on the joint estimates of the sampling clock offset and the channel impulse response when a training sequence is available. Simple closed form expressions are obtained for the CRB in the case where the observation window is large, and furthermore in the case where the channel degree is large. Our derivations are suited for single-carrier as well as for multi-carrier orthogonal frequency division multiplexing (OFDM) schemes. Data-aided maximum-likelihood (ML) estimates are also carried out.

In this paper, we investigate the performance of two linear receivers for code-division multiple-access (CDMA) downlink transmissions over frequency-selective channels, the users having possibly different powers. The optimum minimum mean-square error (MMSE) receiver is first considered. Because this receiver requires the knowledge of the code vectors attributed to all the users within the cell when these vectors are time varying, its use may be unrealistic in the forward link. A classical suboptimum receiver, consisting in a chip rate equalizer followed by a despreading with the code of the user of interest, is therefore studied and compared to the optimum MMSE receiver. Performance of both receivers is assessed through the signal-to-interference-plus-noise ratio (SINR) at their outputs. The analytical expressions of these SINRs depend in a rather nonexplicit way on the codes allocated to the users of the cell, and are therefore not informative. This difficulty is dealt with by modeling the users code matrix by a random matrix. Because the code matrices used in the forward link are usually isometric, the code matrix is assumed to be extracted from a Haar-distributed random unitary matrix. The behavior of the SINRs is studied when the spreading factor and the number of users converge to /spl infin/ at the same rate. Using certain results of the free probability theory, we establish the fact that the SINRs converge almost surely toward quantities that depend only on the complex amplitudes of propagation channel paths. We then use the expressions of these SINR limits to discuss the influence of the various parameters on the performance of the receivers.

In code-division multiple-access (CDMA) transmissions, computing the multiuser minimum mean-squared error (MMSE) detector coefficients requires the inversion of the covariance matrix associated to the received vector signal, an operation usually difficult to implement when the spreading factor and the number of users are large. It is therefore interesting to approximate the inverse by a matrix polynomial. In this correspondence, means for computing the polynomial coefficients are proposed in the context of CDMA downlink transmissions on frequency-selective channels, the users having possibly different powers. Derivations are made in the asymptotic regime where the spreading factor and the number of users grow toward infinity at the same rate. Results pertaining to the mathematics of large random matrices, and in particular to free probability theory, are used. Spreading matrices are modeled as isometric random matrices (spreading vectors orthonormality is a natural assumption in downlink) and also as random matrices with independent and identically distributed (i.i.d.) elements.

We revisit recent papers of M.L. Honig and W. Xiao (see IEEE Trans. on Inf. Theory, vol.47, no.5, p.1928-46, 2001) and L.G.F. Trichard et al. (see Proc. IEEE Int. Conf. on Commun., p.1461-5, 2002; Proc. ISIT 2002) devoted to the asymptotic analysis of reduced rank Wiener filters. Appropriate connections between the asymptotic behavior of the signal-to-noise ratios (SNRs) at the outputs of these filters and the theory of orthogonal polynomials for the power moment problem are established. Using some classical results of this theory, it can be established, in particular, that the reduced rank filter output SNR converges exponentially in the filter rank toward the full rank Wiener filter output SNR. The convergence rate is given. Interestingly, it depends only on the support of the limiting eigenvalue distribution of the observation covariance matrix, but not on its particular form.

Linear precoding consists in multiplying by an N/spl times/K matrix a K-dimensional vector obtained by serial-to-parallel conversion of a symbol sequence to be transmitted. In this paper, new tools, borrowed from the so-called free probability theory, are introduced for the purpose of analyzing the performance of minimum mean-square error (MMSE) receivers for certain large random isometric precoded systems on fading channels. The isometric condition represents the case of precoding matrices with orthonormal columns. It is shown in this contribution that the signal-to-interference-plus-noise ratio (SINR) at the equalizer output converges almost surely to a deterministic value depending on the probability distribution of the channel coefficients when N/spl rarr/+/spl infin/ and K/N/spl rarr//spl alpha//spl les/1. These asymptotic results are used to analyze the impact of orthogonal spreading as well as to optimally balance the redundancy introduced between linear precoding versus classical convolutional coding, while preserving a simple MMSE equalization scheme at the receiver.

This paper deals with CDMA based multiple access communication over an in-house power line channel. Three receivers are described: a RAKE receiver; a MMSE equalizer which estimates the symbols sent at the chip rate, assuming these symbols are i.d.d. (independent and identically distributed); a MMSE equalizer which acts directly on the information symbols. Performance of these receivers is assessed with a special emphasis on the tradeoff between performance and complexity.

Linear precoding consists in multiplying by a N/spl times/K matrix a K-dimensional vector obtained by serial to parallel conversion of a symbol sequence to be transmitted. We analyse the performance of MMSE receivers for certain large random isometric precoded systems on fading channels. Using new tools, borrowed from the so-called free probability theory, it can be shown that the signal to interference plus noise ratio at the equalizer output converges almost surely to a deterministic value depending on the probability distribution of the channel coefficients when N/spl rarr/+/spl infin/ and K/N/spl rarr//spl alpha//spl les/1. These asymptotic results are used to optimally balance the redundancy introduced between linear precoding and classical convolutional coding, while preserving a simple MMSE equalization scheme at the receiver.

The previously introduced transmitter induced cyclostationarity (TIC) techniques are applied to the CDMA uplink blind identification problem. In the proposed transmission model, the spreading code vectors are periodic, each user having a period of his own. As a consequence, a cyclic covariance function is associated to each user. This function generates a structured signal subspace which depends only on the transfer function of this user. The approach leads to clear and mild identifiability conditions. An identification algorithm is described and its theoretical asymptotic performance is presented. Simulations and comparisons with the existing stationary subspace techniques are provided. The algorithm is particularly adapted to systems where the number of users is close to the spreading factor.