The proliferation of large multi-antenna configurations operating in high frequency bands has recently challenged the conventional far-field, rich-scattering paradigm of wireless channels. Extra large antenna arrays usually work in the near field where the probability of having multipath tends to be low, which are far from traditional assumptions in conventional wireless communication systems. The present study proposes to analyze the spatial multiplexing capabilities of large multi-antenna configurations under line-of-sight, near field conditions by considering the use of multiple orthogonal diversities at both transmitter and receiver. The analysis is carried out using aholographicapproximation to the problem, whereby the number of radiating elements is assumed to become large while their separation becomes asymptotically negligible. This emulates the operation of a continuous aperture of infinitesimal radiating elements, also recently known as holographic surfaces. The present study characterizes the asymptotic MIMO channel as seen by extra large uniform linear and planar arrays, as well as their associated achievable rates assuming access to perfect channel state information (CSI). It is shown, in particular, that for a given distance between the receiver and the center of the array and a given signal quality, there exists an optimum dimension of the multi-antenna surface that maximizes the spectral efficiency.

Graph Neural Networks (GNNs) are gaining popularity to solve wireless communication problems due to the inherent nature of viewing wireless networks as graphs. In this paper, we investigate the potential of using GNN for channel estimation in point-to-point multi-input and multi-output (MIMO) systems. The analysis includes an assessment of the channel estimation error performance, alongside the associated computational complexity. The performance is compared against benchmarks such as the conventional least squares, (linear) MMSE estimators, and shallow 1D convolutional neural network (1D-CNN) architectures from the literature. We evaluate the performance-complexity trade-off of GNN versus shallow 1DCNN which have been shown to outperform deep architectures for MIMO channel estimation.

We study cell-free massive multiple-input multiple-output precoders that minimize the power consumed by the power amplifiers subject to per-user per-subcarrier rate constraints. The power at each antenna is generally retrieved by solving a fixed-point equation that depends on the instantaneous channel coefficients. Using random matrix theory, we retrieve each antenna power as the solution to a fixed-point equation that depends only on the second-order statistics of the channel. Numerical simulations prove the accuracy of our asymptotic approximation and show how a subset of access points should be turned off to save power consumption, while all the antennas of the active access points are utilized with uniform power across them. This mechanism allows to save consumed power up to a factor of 9× in low-load scenarios.

One of the most relevant challenges in future 6G wireless networks is how to support a massive spatial multiplexing of a large number of user terminals. Recently, extremely large antenna arrays (ELAAs), also referred to as extra-large MIMO (XL-MIMO), have emerged as an potential enabler of this type of spatially multiplexed transmission. These massive configurations substantially increase the number of available spatial degrees of freedom (transmission modes) while also enabling to spatially focus the transmitted energy into a very small region, thanks to the properties of near-field propagation and the large number of transmitters. This work explores whether multiplexing of multiple orthogonal polarizations can enhance the system per-formance in the near-field. We concentrate on a simple scenario consisting of a Uniform Linear Array (ULA) and a single antenna element user equipment (UE). We demonstrate that the number of spatial degrees of freedom can be as large as 3 in the near-field of a Line of Sight (LoS) channel when both transmitter and receiver employ three orthogonal linear polarizations. In the far-field, however, the maximum number of spatial degrees of freedom tends to be only 2, due to the fact that the equivalent MIMO channel becomes rank deficient. We provide an analytical approximation to the achievable rate, which allows us to derive approximations to the optimal antenna spacing and array size that maximize the achievable rate.

This paper studies the mutual information for a general form of orthogonal M-ary frequency-shift keying modulations with non-coherent detection and Doppler frequency uncertainty at the receiver. The signal model includes as particular cases classical MFSK and special MFSK modulations, the later has been used in space communications for reporting spacecraft status and events during critical phases. The optimal code rates that minimize the energy-per-bit to noise power spectral density ratio required for reliable communications are studied. In addition, optimal and suboptimal metrics for soft-decoders are proposed for non-fading channels with or without average signal and noise power estimation and used to evaluate the performance of LDPC codes.

This work considers the problem of estimating the distance between two covariance matrices directly from the data. Particularly, we are interested in the family of distances that can be expressed as sums of traces of functions that are separately applied to each covariance matrix. This family of distances is particularly useful as it takes into consideration the fact that covariance matrices lie in the Riemannian manifold of positive definite matrices, thereby including a variety of commonly used metrics, such as the Euclidean distance, Jeffreys’ divergence, and the log-Euclidean distance. Moreover, a statistical analysis of the asymptotic behavior of this class of distance estimators has also been conducted. Specifically, we present a central limit theorem that establishes the asymptotic Gaussianity of these estimators and provides closed form expressions for the corresponding means and variances. Empirical evaluations demonstrate the superiority of our proposed consistent estimator over conventional plug-in estimators in multivariate analytical contexts. Additionally, the central limit theorem derived in this study provides a robust statistical framework to assess of accuracy of these estimators.

The problem of estimating the distance between two covariance matrices is considered. A general estimator is provided for a class of metrics, the estimator of which has never been addressed before in the literature. This corresponds to distances that can be expressed as sums of traces of functions that are separately applied to each covariance, which is the case of multiple covariance distances recently derived by Riemannian geometry considerations. The proposed family of estimators is shown to be consistent when both the sample size and the observation dimension increase to infinity at the same rate. In particular, a closed form expression is derived for an estimator of the log-Euclidean metric between covariance matrices. Numerical evaluations demonstrate the effectiveness of this estimator even in relatively small dimensional settings.

Massive multiple input multiple output (MIMO) systems are typically designed under the assumption of linear power amplifiers (PAs). However, PAs are typically most energy-efficient when operating close to their saturation point, where they cause non-linear distortion. Moreover, when using conventional precoders, this distortion coherently combines at the user locations, limiting performance. As such, when designing an energy-efficient massive MIMO system, this distortion has to be managed. In this work, we propose the use of a neural network (NN) to learn the mapping between the channel matrix and the precoding matrix, which maximizes the sum rate in the presence of this non-linear distortion. This is done for a third-order polynomial PA model for both the single and multi-user case. By learning this mapping a significant increase in energy efficiency is achieved as compared to conventional precoders and even as compared to perfect digital pre-distortion (DPD), in the saturation regime.

This paper studies the capacity of orthogonal M-ary frequency-shift keying modulations with non-coherent detection and Doppler frequency uncertainty at the receiver. The optimal code rates that minimize the energy-per-bit to noise power spectral density ratio required for reliable communications are studied. In addition, optimal and suboptimal metrics for soft-decoders are proposed for non-fading channels with or without average signal and noise power estimation and used to evaluate the performance of LDPC codes.

Massive multiple-input multiple-output (MIMO) precoders are typically designed by minimizing the transmit power subject to a quality-of-service (QoS) constraint. However, current sustainability goals incentivize more energy-efficient solutions and thus it is of paramount importance to minimize the consumed power directly. Minimizing the consumed power of the power amplifier (PA), one of the most consuming components, gives rise to a convex, non-differentiable optimization problem, which has been solved in the past using conventional convex solvers. Additionally, this problem can be solved using a proximal gradient descent (PGD) algorithm, which suffers from slow convergence. In this work, in order to overcome the slow convergence, a deep unfolded version of the algorithm is proposed, which can achieve close-to-optimal solutions in only 20 iterations as compared to the 3500 plus iterations needed by the PGD algorithm. Results indicate that the deep unfolding algorithm is three orders of magnitude faster than a conventional convex solver and four orders of magnitude faster than the PGD.

A methodology to cluster multiple sets of Gaussian multivariate complex observations based on the alignment of their column spaces is presented. These subspaces are identified with points in the Grassmann manifold and compared according to a similarity measure drawn from a chosen manifold distance, which is proportional to the squared projection–Frobenius norm. In order to guarantee that distances between subspaces of different dimensions are comparable, we proposed to normalise the corresponding decision statistics with respect to their asymptotic mean and variance, assuming that (i) the dimensions of both the observation and the involved subspaces are large but comparable in magnitude and (ii) both subspaces are generated by the same statistical law. A procedure is derived to estimate these normalisation parameters, leading to a new statistic that can be built exclusively from the observations. The method is applied to a MIMO wireless channel clustering problem, where is shown to outperform conventional similarity measures in terms of classification performance.

In this paper, the outlier production mechanism of the G-MUSIC Direction-of-Arrival estimation technique is investigated using tools from Random Matrix Theory. The G-MUSIC Direction-of-Arrival estimation technique is an improved version of the conventional MUSIC method that provides superior performance in low sample size scenarios. The stochastic behavior of the G-MUSIC cost function is analyzed in the asymptotic regime where both the number of snapshots and the number of antennas increase without bound at the same rate. The finite dimensional distribution of the G-MUSIC cost function is shown to be asymptotically jointly Gaussian. Furthermore, the probability of resolution of the G-MUSIC Direction-of-Arrival estimator is characterized by means of the derived asymptotic probability density function of the G-MUSIC cost function.

The user clustering problem in an uplink MIMO Non-Orthogonal Multiple Access (NOMA) scheme is considered here. The receiver is assumed to operate in two sequential stages that employ Linear Minimum Mean Squared Error (LMMSE) receivers. At the first stage, the receiver is designed to recover the transmission from a cluster of selected users/nodes. The contribution of these users is then subtracted from the received signal and the remaining user transmissions are then linearly recovered. The determination of which users should be detected during the first stage is formulated as a deep learning based multiple classification problem. In order to guarantee that the selection is robust to fast fading, the input to the neural network is based on second order channel statistics. Furthermore, the training process is simplified by using a large system approximation of the resulting sum-rates. Simulation results indicate that the proposed deep learning-based solution is able to achieve a significant rate advantage with respect to other lazy approaches, such as fixed or random cluster assignments.

In this paper, we investigate the applicability of machine and deep learning (ML/DL) techniques to uplink beam selection problems with hybrid beamforming architectures. The goal is to select the element in the codebook of analog beamformers (ABF) yielding the highest sum-rate. The multi-antenna system operates in 5GNR's Frequency Range 2 (mmWave band). In this context, the presence of multi-path propagation along with the use of multi-carrier signals precludes the use of (single) angle-of-arrival information as an input to the learning system. Therefore, we investigate alternative statistics such as the singular vector/values of the (multi-carrier) channel matrix, the average covariance matrix, or the covariance matrix at a given subcarrier. Besides, we propose a novel ML/DL architecture enabling a continuous operation of the system which avoids the spectral efficiency losses associated to periodically switching to a dedicated ABF for the estimation of such statistics.

In this paper, a simple equalization strategy for OFDM waveforms is proposed that specifically targets the case where the cyclic prefix is insufficient to span the whole channel duration. The proposed architecture can be very efficiently implemented in the frequency domain without the need for complex matrix inversions or iterative estimation procedures. Furthermore, the equalizer is shown to outperform conventional methodologies as the system dimensions grow large. Numerical results confirm the excellent behavior of the proposed strategy even for conventional values of the system size.

In this paper, we address the problem of detection, in the frequency domain, of a M-dimensional time series modeled as the output of a M × K MIMO filter driven by a K-dimensional Gaussian white noise, and disturbed by an additive M-dimensional Gaussian colored noise. We consider the study of test statistics based of the Spectral Coherence Matrix (SCM) obtained as renormalization of the smoothed periodogram matrix of the observed time series over N samples, and with smoothing span B. To that purpose, we consider the asymptotic regime in which M, B, N all converge to infinity at certain specific rates, while K remains fixed. We prove that the SCM may be approximated in operator norm by a correlated Wishart matrix, for which Random Matrix Theory (RMT) provides a precise description of the asymptotic behaviour of the eigenvalues. These results are then exploited to study the consistency of a test based on the largest eigenvalue of the SCM, and provide some numerical illustrations to evaluate the statistical performance of such a test.

The Partial Relaxation approach has recently been proposed to solve the Direction-of-Arrival estimation problem [1], [2]. In this paper, we investigate the outlier production mechanism of the Partially Relaxed Deterministic Maximum Likelihood (PR-DML) Direction-of-Arrival estimator using tools from Random Matrix Theory. An accurate description of the probability of resolution for the PR-DML estimator is provided by analyzing the asymptotic stochastic behavior of the PR-DML cost function, assuming that both the number of antennas and the number of snapshots increase without bound at the same rate. The finite dimensional distribution of the PR-DML cost function is shown to be Gaussian in this asymptotic regime and this result is used to compute the probability of resolution.

The performance of short block length codes in the presence of multi-variate stationary Rayleigh fading coherent channels is studied. The channel model is inspired by multi-symbol OFDM transmissions for ultra-reliable low latency communication (URLLC) services, according to which information is sent in a small number of OFDM symbols to reduce latency. More specifically, the dispersion of the coherent fading channel is generalized from the scalar case, which is well known in the literature, to the multivariate one. The obtained expressions are then particularized to the Rayleigh fading statistics and expressed in closed form as a series expansion. Finally, a high SNR approximation of the ergodic capacity and channel dispersion is derived for this particular fading choice. Results show that the code performance depends on the time-frequency fading correlation through very simple functions of the channel correlation coefficients. In particular, it is shown that the channel dispersion converges to a constant plus the sum of the dilogarithms of the correlation coefficients of the channel process. These formulas provide a very useful tool to design physical layer system parameters from channel correlation information measured at the receiver.

An underdetermined multi-measurement vector linear regression problem is considered where the parameter matrix is row-sparse and where an additional constraint fixes the number of nonzero elements in the active rows. Even if this additional constraint offers side structure information that could be exploited to improve the estimation accuracy, it is highly nonconvex and must be dealt with with caution. A detection algorithm is proposed that capitalizes on compressed sensing results and on the generalized distributive law (message passing on factor graphs).

Offset-QAM-based filterbank multicarrier (FBMC-OQAM) modulations are known to progressively loose their orthogonality as the channel gets more selective in time and frequency. The effect of channel frequency selectivity on FBMC-OQAM systems has been extensively studied in the literature. Many compensations methods have been proposed to combat it. However, most of them have a significant implementation complexity and do not take into account the time selective nature of the channel. In this paper, we propose a MIMO equalizing structure for doubly selective channel based on a simple single-tap per-subcarrier decoding matrix. The decoding matrices are designed to minimize the mean squared error of the symbol estimate. This decoder exploits the degrees of freedom offered by the extra antennas at the receiver to compensate for the distortion induced by time and frequency selectivity. Simulation results demonstrate the performance gain of the proposed design with respect to classical designs.

Testing the independence of the entries of multidimensional Gaussian observations is a very important problem in statistics, with a number of applications in signal processing, radar, cognitive radio, seismography, and multiple other fields. Typically, the problem is formulated as a binary hypothesis test, whereby the presence of correlation is declared when the value of a certain statistic is higher than a certain predetermined threshold. Most of the statistics for correlation tests are constructed from the sample correlation matrix (also known as sample coherence matrix in signal processing), which is defined as a power-normalized version of the sample covariance matrix. In this paper, correlation tests constructed from linear spectral statistics (LSS) of the sample correlation matrix are analyzed under the asymptotic framework where both sample size and observation dimension become large but comparable in magnitude. A central limit theorem (CLT) is established on this class of statistics, which is valid for generally correlated Gaussian observations. Results show that LSS asymptotically fluctuate as Gaussian random variables under both the hypotheses, with an asymptotic mean and variance that can be established for each particular test. In particular, this general CLT can be used to establish the asymptotic behavior of two of the most important correlation test statistics, namely the generalized likelihood ratio test and the Frobenius norm test, under both null and alternative hypotheses. As a by-product, it is established that LSS of sample covariance and sample correlation matrices have exactly the same first order behavior, but quite different asymptotic fluctuations in the second-order regime. In both the cases, the LSS asymptotically behave as Gaussian random variables, although with quite different asymptotic means and variances.

Scattered pilot-aided channel estimation in offset QAM-based filter bank multicarrier (FBMC/OQAM) systems has so far been only considered for channels of mild frequency selectivity. In more demanding scenarios, the classical auxiliary pilot (AP) idea has been shown to result in severe error floors. In this paper, a novel pilot-aided channel estimation method is developed which for the first time extends the applicability of the AP idea to highly frequency selective channels. The development relies on a Taylor series approximation of the signal model, which is able to accurately and concisely describe such scenarios. The obtained channel estimate can be viewed as a linear combination of the outputs of multiple parallel analysis filter banks each employing a derivative of the original prototype filter. The reported simulation results corroborate the analysis, demonstrating the effectiveness of the proposed method in estimating channels of strong frequency selectivity.

This paper investigates the optimal design of precoders or decoders under a channel inversion criterion for multi-user (MU) MIMO filterbank multicarrier (FBMC) modulations. The base station (BS) is assumed to use a single tap precoding/decoding matrix at each subcarrier in the downlink/uplink, resulting in a low complexity of implementation. The expression of the asymptotic mean squared error (MSE) for this precoding/decoding design in the case of strong channel selectivity is recalled and simplified. Optimizing the MSE under a channel inversion constraint, the expression of the optimal precoding/decoding matrix is found. It is shown that as long as the number of BS antennas is larger than the number of users, the optimized precoder and decoder can compensate for the channel frequency selectivity and even restore the system orthogonality for a large enough number of BS 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.

This paper addresses the statistical performance of subspace DoA estimation using a sensor array, in the asymptotic regime where the number of samples and sensors both converge to infinity at the same rate. Improved subspace DoA estimators were derived (termed as G-MUSIC) in previous works, and were shown to be consistent and asymptotically Gaussian distributed in the case where the number of sources and their DoA remain fixed. In this case, which models widely spaced DoA scenarios, it is established that the traditional MUSIC method also provides consistent DoA estimates having the same asymptotic MSE as the G-MUSIC estimates. In the case of closely spaced DoA (i.e. with a spacing of the order of a beamwidth), it is shown that G-MUSIC is still able to consistently separate the sources, while it is no longer the case for MUSIC.

The problem of eigenvector precoding for multi-stream MIMO transmission with filterbank multicarrier (FBMC) modulations is considered. The transmitter is assumed to use a different precoding matrix for each subcarrier, which is constructed by selecting some eigenvectors of the channel matrix. Surprisingly, the phase ambiguity that is inherent to the definition of the eigenvectors turns out to have a crucial effect on the system performance under strong channel frequency selectivity. This is due to the inherent lack of orthogonality of FBMC modulations in these situations. It is shown that by properly selecting the reference phase evolution of each eigenvector across the transmission bandwidth, the global performance of the system can be significantly improved. A phase reference construction strategy is presented that minimizes an upper bound on the total intersymbol/intercarrier interference (ISI/ICI) power.

The problem of MIMO transmission using filterbank multicarrier (FBMC) modulations in strong frequency selective channels is considered. A novel architecture for the implementation of MIMO precoders and linear receivers is derived, which consists of multiple parallel stages that are combined at the per-subcarrier level. Each of these stages is constructed like a classical FBMC modulator/demodulator, using the successive derivatives of the prototype pulse instead of the original one. The performance of the proposed architecture is theoretically characterized in terms of the residual distortion power at the output of the receiver, assuming an asymptotically large number of subcarriers. Results demonstrate the effectiveness of the proposed architecture in MIMO channels with severe frequency selectivity.

Minimum variance beamformers are widely used for array signal processing. It is known that the diagonal loading method can improve the robustness against mismatches caused by the imprecise steering vector (or the channel vector) and the noise covariance matrix. Instead of concentrating on one aspect of the mismatches and assuming perfect knowledge of the other, we handle both estimation error in the steering vector and the noise covariance matrix caused by the finite sample size simultaneously. We employ high-dimensional asymptotics to reflect the finite sample size, and estimate the optimal loading factor based on random matrix theory. In an asymptotic setting where the number of samples is comparable to the array dimension, we obtain a beamformer that is as good as the beamformer with optimal diagonal loading. Monte Carlo simulations show the advantage of our beamformer in the finite sample size regime.

A point-to-point multiple-relay communication system with half-duplex constraints is considered. The relays operate under the amplify-and-forward paradigm and implement a linear dispersion distributed space-time code with randomized dispersion matrices of independent and identically distributed entries. The large-signal-to-noise-ratio behavior of the asymptotically large deterministic system is studied for both the optimum (maximum likelihood) receiver and the linear minimum mean squared error (LMMSE) receiver. The diversity order of the system is shown to have a strong dependence on the aspect ratio of the linear dispersion matrices. More specifically, when the linear dispersion matrices are sufficiently tall, both receivers achieve the maximum diversity order, i.e., the total number of relays plus one. Conversely, when the linear dispersion matrices are fat (in the sense that relays linearly compress the information received from the source), the optimum receiver is shown to achieve an asymptotic diversity order of two, whereas the LMMSE receiver is totally unable to exploit the available spatial diversity.

We consider the problem of subspace estimation in situations where the number of available snapshots and the observation dimension are comparable in magnitude. In this context, traditional subspace methods tend to fail because the eigenvectors of the sample correlation matrix are heavily biased with respect to the true ones. It has recently been suggested that this situation (where the sample size is small compared to the observation dimension) can be very accurately modeled by considering the asymptotic regime where the observation dimensionMand the number of snapshotsNconverge to +∞ at the same rate. Using large random matrix theory results, it can be shown that traditional subspace estimates are not consistent in this asymptotic regime. Furthermore, new consistent subspace estimate can be proposed, which outperform the standard subspace methods for realistic values ofMandN. The work carried out so far in this area has always been based on the assumption that the observations are random, independent and identically distributed in the time domain. The goal of this paper is to propose new consistent subspace estimators for the case where the source signals are modelled as unknown deterministic signals. In practice, this allows to use the proposed approach regardless of the statistical properties of the source signals. In order to construct the proposed estimators, new technical results concerning the almost sure location of the eigenvalues of sample covariance matrices of Information plus Noise complex Gaussian models are established. These results are believed to be of independent interest.

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.

A simple half-duplex decode-and-forward relay channel is presented and analyzed. Relays access the common channel by means of a randomized linear-dispersion space-time block code which is flexible with respect to the number of relays and the coding rate α. When the dimensions of the linear dispersion matrices grow large, but with constant ratio α, the spectral efficiency of the system converges fast to a deterministic quantity. Simulation results show that this asymptotic value is an extremely good approximation of the finite reality, even for not-so-large codes. Then, this asymptotic spectral efficiency is used to characterize the outage probability in the high-SNR regime. With maximum-likelihood reception, the proposed randomized coding scheme is shown to achieve full diversity order L+1, with L the total number of relays. On the contrary, with the sub-optimal LMMSE receiver, relays add diversity to the system only if the coding rate is small enough.

This paper is devoted to the subspace DoA (direction-of-arrival) estimation using a large antennas array when the number of available snapshots is of the same order of magnitude than the number of sensors. In this context, the traditional subspace methods fail because the empirical covariance matrix of the observations is a poor estimate of the true covariance matrix. Mestre et al. proposed recently to study the behaviour of the traditional estimators when the number of antennas M and the number of snapshots N converge to +infin at the same rate. Using large random matrix theory results, they showed that the traditional subspace estimate is not consistent in the above asymptotic regime and they proposed a new consistent subspace estimate which outperforms the standard subspace method for realistic values of M and N. However, the work of Mestre et al. assumes that the source signals are independent and identically distributed in the time domain. The goal of the present paper is to propose new consistent estimators of the DoAs in the case where the source signals are modelled as unknown deterministic signals. This, in practice, allows to use the proposed approach whatever the statistical properties of the source signals are.

This paper considers a cooperative communications system where a single relay aids a point-to-point transmission using an amplify and forward configuration. The relay linearly encodes the K received symbols into N new ones by means of a matrix multiplication, and the destination employs a LMMSE filter to estimate the information originally transmitted. A large- SNR approximation of the outage probability Poutis derived for this system. The analysis of Poutshows that the diversity order of the system depends on the ratio K/N: if such a ratio is too high (the relay excessively compresses the information), no diversity is added by introducing the relay. Conversely, if this ratio is smaller than a certain quantity, diversity order 2 is ensured. The derived expressions are finally used to establish the diversity-multiplexing tradeoff of the system.

This paper analyzes a cooperative communications system where a set of decode and forward relays provides support to a point to point communication. Each relay linearly transforms the K received symbols, if correctly decoded, into N new ones to be sent to the destination. The coding matrices are randomly generated, making the system simple to design, scalable and robust to synchronism errors. It is shown that such a random code, together with the optimal maximum-likelihood receiver, achieves full diversity for any value of the ratio alpha = K/N. This is not true for the linear minimum mean square error receiver, which loses diversity when alpha increases beyond a given threshold. To avoid dealing with the randomness of the code, the analysis is carried out in the asymptotic domain, i.e. for K and N growing without bound but with ratio converging to a finite quantity alpha. Random matrix theory results are used to derive this asymptotic approximation.

This paper presents a communication system where point-to-point transmissions are aided by L half-duplex, amplify and forward relays which access a common channel by means of random spreading matrices. During the relaying phase, the source can either remain silent or send new symbols. The two cases are compared in terms of spectral efficiency, showing that the latter is always preferable. Next, a sufficient condition for the superiority of the presented relaying scheme over the simple direct-link channel is derived. Particularizing to the one relay case, this condition turns out to be also necessary and allows to identify which is the best time-sharing strategy between relay receiving and transmitting phases. We conclude the paper by discussing the suboptimal linear-minimum-mean-square-error receiver, which is known to be the linear filter that guarantees the maximum signal to noise and interference ratio at its output. To avoid dealing with the randomness introduced by the spreading matrices, the analysis is carried out in the asymptotic regime, i.e. when letting the number of transmitted symbols and the signature length grow without bound but with constant ratio. Under these hypotheses, indeed, random matrix theory results show that it is possible to derive deterministic almost sure equivalents which are excellent approximations of the finite reality.

We consider a two-hop wireless network where a transmitter communicates with a receiver via M relays with an amplify-and-forward (AF) protocol. Recent works have shown that the sophisticated linear processing such as beamforming and distributed space-time coding (DSTC) at relays enables to improve the AF performance. However, the relative utility of these strategies depends on the available channel state information at transmitter (CSIT), which in turn depends on the system parameters such as the speed of the underlying fading channel and that of training and feedback procedures. Moreover, it is of practical interest to have a single transmit scheme that handles different CSIT scenarios. This motivates us to consider a unified approach based on DSTC that potentially provides diversity gain with statistical CSIT and exploits some additional side information if available. Under individual power constraints at the relays, we optimize the amplifier power allocation such that pairwise error probability conditioned on the available CSIT is minimized. Under perfect CSIT, we propose an on-off gradient algorithm that efficiently finds a set of relays to switch on. Under partial and statistical CSIT, we propose a simple waterfilling algorithm that yields a non-trivial solution between maximum power allocation and a generalized STC that equalizes the averaged amplified noise for all relays. Moreover, we derive the closed-form solutions for M = 2 and in certain asymptotic regimes that enable an easy interpretation of the proposed algorithms. It is found that an appropriate amplifier power allocation is mandatory for DSTC to offer sufficient diversity and power gain in a general network topology.

Maximum likelihood estimation techniques demonstrate "performance breakdown" at low signal-to-noise ratios where observed estimation errors rapidly depart from the Cramer-Rao bound below a threshold SNR. Rather than rely on the classic asymptotic analysis for prediction of that threshold, random matrix theory (RMT) analysis is employed. Both analytic predictions and direct Monte-Carlo simulations demonstrate that the threshold value can be reliably predicted even for small sample support far removed from classic asymptotic assumptions.

Direction-of-arrival estimation performance of MUSIC in the so- called "threshold" area is often attributed to the "subspace swap" phenomena. We show that the subspace swap condition can be accurately predicted using recent results from Random Matrix Theory (RMT) analysis, but that subspace "leakage" rather than full sub- space swap is associated with the onset of performance degradation in closely spaced multiple source scenarios. Prediction of the "sub- space swap" phenomena is examined analytically and by the use of Monte-Carlo simulation.

The problem of estimating the eigenvalues and eigenvectors of the covariance matrix associated with a multivariate stochastic process is considered. The focus is on finite sample size situations, whereby the number of observations is limited and comparable in magnitude to the observation dimension. Using tools from random matrix theory, and assuming a certain eigenvalue splitting condition, new estimators of the eigenvalues and eigenvectors of the covariance matrix are derived, that are shown to be consistent in a more general asymptotic setting than the traditional one. Indeed, these estimators are proven to be consistent, not only when the sample size increases without bound for a fixed observation dimension, but also when the observation dimension increases to infinity at the same rate as the sample size. Numerical evaluations indicate that the estimators have an excellent performance in small sample size scenarios, where the observation dimension and the sample size are comparable in magnitude.

Performance of MUSIC and maximum likelihood direction-of-arrival estimation in the "threshold" region is compared with the performance of the recently introduced G-MUSIC, based on the general statistical analysis (GSA) methodology. While the superiority of G-MUSIC over MUSIC has been demonstrated, it remains to be established whether G-MUSIC also outperforms MLE in scenarios within the threshold region. Comparisons of likelihood functions for MUSIC and G-MUSIC generated solutions as well as clairvoyantly optimized solutions are conducted to address this question.

This paper proposes a new power estimation technique for array processing applications in the low sample size regime. The technique is especially suitable for applications where the direction of arrival (DoA) detection is performed using subspace identification techniques, because the eigenvalues and eigenvectors of the sample covariance matrix are already computed for DoA estimation and are therefore available for power estimation as well. The performance of the algorithm is similar to that of the traditional maximum likelihood (ML) power estimation technique, but it is more robust to the presence of outliers in the direction of arrival (DoA) detection process. This is because, contrary to the ML estimator, the proposed power estimator only depends on the signature of the source of interest.

This paper considers a relay communication system where cooperative diversity is achieved by spreading the relay transmissions using direct-sequence CDMA (DS/CDMA). We derive expressions for the signal to noise ratio (SNR) employing different receiver filters. The relay signatures are generated according to a random model and the SNR is evaluated in the asymptotic domain, assuming that the number of relays and the signature length grow without bound but with constant ratio. We will also see how the introduction of the signatures, together with the use of the linear minimum square error receiver, effectively transform the relay channel in a set of parallel connections, thus fully exploiting cooperative diversity.

A class of linear interference-suppression schemes is proposed that maximize the empirical SINR at the output of a DS-CDMA receiver under unknown multiuser interference conditions. We build upon well-known reduced-rank MVDR/MMSE solutions based on the Krylov-subspace spanned by the covari- ance matrix of the observations and the spreading sequence of the desired user. Only the effective signature of the intended user is assumed to be known at the receiver side. The optimum coefficients of the resulting polynomial expansion receiver are obtained by approximating the output SINR in the asymptotic regime defined when both the processing gain and the number of observations grow together without bound at the same rate.

A new method for subspace identification in array signal processing applications is proposed. The method is based on random matrix theory and provides consistent estimates even when the observation dimension increases without bound at the same rate as the number of observations. This guarantees a good behavior in finite sample size situations, where the number of sensors and the number of samples have the same order of magnitude. Consistency of the algorithm holds in situations where the signal and noise subspaces are asymptotically separable in the sense that, in the asymptotic sample eigenvalue distribution, signal and noise eigenvalues generate different spectral clusters

We derive the output SINR of a multi-stage CDMA receiver based on the Krylov-subspace spanned by the covariance matrix of the received signal, under the practical assumption of a finite number of samples available at the receiver. The evaluation of the SINR is addressed as an approximation problem in the asymptotic regime defined when both the sample-size and the observation dimension grow together without bound at the same rate. Limiting SINR values in this double-limit context are then more representative of the reality because, as it happens in realistic scenarios, both quantities are considered to be of the same order of magnitude. Our results are based on the asymptotic spectrum of the powers of certain random matrix models, which can be conveniently studied using the combinatorial approach to the theory of free probability

We address the problem of code-reference spatial filtering for multicode DS/CDMA. The large-system analysis of the asymptotic performance of three spatial filters, respectively based on the matched filter, the decorrelator and a projector onto the span of the codes of the desired user, is presented. We derive analytical expressions for the asymptotic covariance and output signal-to-interference-plus-noise ratio (SINR) of these filters, assuming that both the spreading factor and the number of parallel code sequences increase without bound at the same rate. A superior performance of the projecting filter against the other two solutions is revealed: the performance of the spatial filters based on the matched filter and the decorrelator saturates both for increasing values of the input signal-to-noise ratio (SNR), whereas the projecting solution is able to sustain an increasingly high SINR.

In this paper, we study the ergodic capacity of a multiple input multiple output (MIMO) uncorrelated flat fading channel with perfect channel state information at the receiver and partial channel state information at the transmitter. We focus our attention on the case where the transmitter is informed only with the modulus of the channel matrix coefficients. First, we prove that a simple power allocation strategy among transmitting antennas is the optimal scheme, in the sense that is a capacity achieving architecture. Next, for the particular case where only two antennas are used at each communication end, we derive closed form expressions for the ergodic capacity and the optimal power assigned to each antenna.

This work considers a high rate, multiple input multiple output (MIMO) systems using multiple codes, as well as channel coding and space time (ST) coding. The transmitter consists of a channel encoder followed by parallel linear dispersion codes (LDC) ST encoders using different spreading codes. The iterative receiver consists of a soft input and soft output (SISO) demodulator, followed by a SISO detector. Simulation results in realistic frequency selective third generation partnership project test cases reveal good performance even for high rate HSDPA services.

The paper analyzes the asymptotic capacity per receive antenna in a multiple input multiple output (MIMO) system with fading correlation at either the transmitter or the receiver. The objective is the derivation of a closed form solution for the asymptotic capacity under fading correlation when the number of transmit and receive antennas increases without bound at the same rate. To do that, we consider a particular correlation model that yields a closed form expression for the asymptotic density of the channel eigenvalues. We proposed the correlation model (Mestre, X. et al., IEEE JSAC, 2003) to analyze the asymptotic capacity of a correlated MIMO system under a uniform power allocation strategy. We extend those results to the closed-loop configuration under waterfilling power allocation. The asymptotic expressions provide some new interesting insights into the different influence of fading correlation on the channel capacity.

This paper investigates the asymptotic uniform power allocation capacity of frequency nonselective multiple-input multiple-output channels with fading correlation at either the transmitter or the receiver. We consider the asymptotic situation, where the number of inputs and outputs increase without bound at the same rate. A simple uniparametric model for the fading correlation function is proposed and the asymptotic capacity per antenna is derived in closed form. Although the proposed correlation model is introduced only for mathematical convenience, it is shown that its shape is very close to an exponentially decaying correlation function. The asymptotic expression obtained provides a simple and yet useful way of relating the actual fading correlation to the asymptotic capacity per antenna from a purely analytical point of view. For example, the asymptotic expressions indicate that fading correlation is more harmful when arising at the side with less antennas. Moreover, fading correlation does not influence the rate of growth of the asymptotic capacity per receive antenna with high Eb/N/sub 0/.

This paper proposes a spatial filtering technique for the reception of pilot-aided multi-rate multi-code DS/CDMA systems such as WCDMA. These systems introduce a code-multiplexed pilot sequence that can be used for the estimation of the filter weights, but the presence of the traffic signal (transmitted at the same time as the pilot sequence) corrupts that estimation up to the point that it might render the filter completely useless. The traffic and pilot signals are designed to be orthogonal, but the frequency selectivity of the channel degrades this orthogonality in the received signal. Here we propose a semi-blind technique that eliminates the self-noise caused by the code-multiplexing. We derive analytically the asymptotic performance of both the training-only and the semi-blind techniques and compare it with the actual simulated performance. It is shown, both analytically and via simulation, that high gains can be achieved with respect to training-only based techniques.

This paper proposes and analyzes two different spatial filter architectures for the reception of OFDM signals: the classical sample matrix inversion (SMI) algorithm and the' recently proposed Matched Desired Impulse Response (MDIR) beamformer. We derive the asymptotic output signal to interference plus interference ratio (SINR) provided by the two spatial filters and compare their performance in different scenarios. The results are useful in the sense that they provide the asymptotically optimum number of adjacent carriers to be processed by a single beamformer in a finite sample size situation.

This paper analyzes the influence of channel estimation errors on the performance of linear multiuser receivers. Assuming randomized codes and asymptotically high spreading factors and noise power, we show that the performance of the decorrelating and the minimum mean squared error (MMSE) receivers tend to the same limit in terms of signal-to-noise ratio and bit error rate (but not in terms of mean squared error). Using these results and assuming Gaussian-distributed channel estimators, we derive two simple approximations to the bit error rate and compare them with the actual values via simulation.

This paper analyzes the asymptotic performance of maximum likelihood (ML) channel estimation algorithms in wideband code division multiple access (WCDMA) scenarios. We concentrate on systems with periodic spreading sequences (period larger than or equal to the symbol span) with high spreading factors, where the transmitted signal contains a code division multiplexed pilot for channel estimation purposes. Assuming randomized training and code sequences, we derive and compare the asymptotic covariances of the training-only (TO), semi-blind conditional ML (CML) and semi-blind Gaussian ML (GML) channel estimators.

The problem of joint beamforming and channel estimation for multi-rate multi-code systems is addressed. Usual schemes perform this filtering/estimation operation making use of a training sequence time-multiplexed with the transmitted data. However if pilot and traffic signals are transmitted simultaneously using distinct code allocation-as it is the case in recent standards such as cdma2000 or WCDMA-these schemes tend to fail. This paper proposes semi-blind techniques to overcome the uplink auto-interfering effects of such systems. It is shown that the semi-blind approach yields substantially better performance results thanks to the implicit modeling of the unknown traffic data.

This paper addresses a new architecture for blind adaptive beamforming when dealing with frequency hopping (FH) modulation in cellular mobile communications systems. The proposed code reference beamformer (CRB) takes advantage of the inherent frequency diversity to estimate beforehand the noise plus interference correlation matrix, which is employed as the first part of the framework. Then, a second stage is adaptively obtained without any a priori knowledge of either the direction of arrival or the array manifold. Using this information, the first stage is in turn readjusted and, as a result, the scheme is able to track non-stationary scenarios following the channel variations with no previous references.