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.

It is shown that the distribution of the estimated canonical correlation coefficients between the past and the future of a high-dimensional multivariate white noise sequence converges almost surely towards a limit distribution whose density is given in closed form. A sketch of proof, based on free probability technics, is provided. Finally, it is briefly explained how this result can be used to produce consistent uncorrelatedness tests in the high-dimensional context.

This paper addresses the behaviour of a classical multi-antenna GLR test that allows to detect the presence of a known signal corrupted by a multipath propagation channel when the number of sensors M, the sample size N, and the number of paths L are large and of the same order of magnitude. In the asymptotic regime where M, N and L converge towards ∞ at the same rate, the test statistics is shown to be asymptotically Gaussian under each hypothesis. The results of this paper extend previous contributions of the authors that addressed the case where the number of paths L is much smaller than M and N, and used these results in order to propose a pragmatic Gaussian approximation of the test statistics when L is large. Simulation results indicate that the proposed Gaussian approximation of the test statistics is more reliable than the above mentioned pragmatic approximation.

This paper addresses the statistical behaviour of spatial smoothing subspace DoA estimation schemes using a sensor array in the case where the number of observations N is significantly smaller than the number of sensors M, and that the number of virtual arrays L is such that M and NL are of the same order of magnitude. This context is modelled by an asymptotic regime in which NL and M both converge towards 1 at the same rate. As in recent works devoted to the study of (unsmoothed) subspace methods in the case where M and N are of the same order of magnitude, it is shown that it is still possible to derive improved DoA estimators termed as Generalized-MUSIC (G-MUSIC). The key ingredient of this work is a technical result showing that the largest singular values and corresponding singular vectors of low rank deterministic perturbation of certain Gaussian block-Hankel large random matrices behave as if the entries of the latter random matrices were independent identically distributed.

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 MUSIC method is widely used in the field of DoA estimation using an array of M sensors, and is known to perform well as long as the number of available samples N is much larger than M. Nevertheless, in the scenario where N is of the same order of magnitude than M, its performance degrades, essentially because the sample covariance matrix (SCM) is no more a good estimator. A classical improvement, known as "rectification", consists in forcing the SCM to have a Toeplitz structure. In this paper, we analyze this method, by considering the asymptotic regime where M, N both converge to infinity at the same rate, and by studying consistency and asymptotic normality of the related DoA estimates.

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.

This paper is devoted to the design of precoders maximizing the ergodic mutual information (EMI) of bi-correlated flat fading MIMO systems equipped with MMSE receivers. The channel state information and the second-order statistics of the channel are assumed available at the receiver side and at the transmitter side respectively. As the direct maximization of the EMI needs the use of nonattractive algorithms, it is proposed to optimize an approximation of the EMI, introduced recently, obtained when the number of transmit and receive antennastand τ converge to ∞ at the same rate. It is established that the relative error between the actual EMI and its approximation is aO( [ 1/(t2)]) term. It is shown that the left singular eigenvectors of the optimum precoder coincide with the eigenvectors of the transmit covariance matrix, and its singular values are solution of a certain maximization problem. Numerical experiments show that the mutual information provided by this precoder is close from what is obtained by maximizing the true EMI, but that the algorithm maximizing the approximation is much less computationally intensive.

In this contribution, an algorithm for evaluating the capacity-achieving input covariance matrices for frequency selective Rayleigh MIMO channels is proposed. In contrast with the flat fading Rayleigh case, 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 this paper, it is proposed to optimize (w.r.t. the input covariance matrix) a large system approximation of the average mutual information derived by Moustakas and Simon. The validity of this asymptotic approximation is clarified thanks to Gaussian large random matrices methods. It is shown that the approximation is a strictly concave function of the input covariance matrix and that the average mutual information evaluated at the argmax of the approximation is equal to the capacity of the channel up to aO(1/t) term, wheretis the number of transmit antennas. An algorithm based on an iterative waterfilling scheme is proposed to maximize the average mutual information approximation, and its convergence studied. 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 this paper, we consider user equipment which is not yet connected to a given UMTS-FDD network. We propose an algorithm which allows to the user equipment to estimate bit error rate (BER) of a potential downlink in term of the spreading factor and of the power that could be allocated by a base station to this virtual link. This problem is motivated by the context of cognitive radio. Our approach is based on the estimation of the instantaneous signal-to-noise-plus-interference ratio (SINR) of the virtual link. For this, we derive a closed-form approximation of the SINR which only depends on the powers and on the channels between each active base station and the user equipment ; these parameters can be estimated easily from the pilot channels transmitted by the active base stations.

In this contribution, an algorithm for evaluating the capacity-achieving input covariance matrices for frequency selective Rayleigh MIMO channels is proposed. In contrast with the flat fading Rayleigh 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 this paper, it is proposed to optimize (w.r.t. the input covariance matrix) a large system approximation of the average mutual information derived by Moustakas and Simon. An algorithm based on an iterative water filling scheme is proposed, and its convergence is studied. 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 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.

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 is devoted to the study of the ergodic capacity of doubly correlated flat fading MIMO systems equipped with a MMSE receiver with full knowledge of the channel state information (CSI) at receiver side and when only the second order statistics of the channel at transmitter side are available. As the corresponding expression is complicated and difficult to exploit, the behavior of the capacity is studied when the number of transmit and receive antennas t and r converge to +infin at the same rate. In this asymptotic regime, a new approximation of the ergodic capacity is obtained, and it is established that the relative error between the actual capacity and its approximation is a O(1/(t3/2)) term. The new approximation appears to be more accurate that the proposal of which provides a O(1/t) relative error. The approximation is used in order to design an optimal precoder. It is shown that the left singular eigenvectors of the optimum precoder coincide with the eigenvectors of the transmit covariance matrix, and its singular values are solution of a certain maximization problem. Numerical experiments show that the capacity provided by this precoder is very close from the capacity obtained by maximizing the true ergodic capacity, but that the algorithm maximizing the approximation is much less computationally intensive.

In this paper, we deal with the estimation of the ergodic capacity of large MIMO systems, using training sequences whose lengths are of the same order of magnitude than the number of antennas. In this context, the traditional estimator becomes inconsistent. Following the ideas developed by Girko in the context of the so-called theory of G-estimation, we propose a new estimator. We analyze its asymptotic behaviour and show, using numerical simulations, that it tends to improve significantly the performance of the standard estimate for a realistic number of antennas.

This paper is devoted to the study of the ergodic capacity of frequency selective MIMO systems equipped with a MMSE receiver when the channel state information is available at the receiver side and when the second order statistics of the channel taps are known at the transmitter side. As the expression of this capacity is rather complicated and difficult to analyse, it is studied in the case where the number of transmit and receive antennas converge to +oo at the same rate. In this asymptotic regime, the main results of the paper are related to the design of an optimal precoder in the case where the transmit antennas are correlated. It is shown that the left singular eigenvectors of the optimum precoder coincide with the eigenvectors of the mean of the channel taps transmit covariance matrices, and its singular values are solution of a certain maximization problem.

This paper is devoted to the performance analysis of downlink MIMO-CDMA receivers based on a chip rate MIMO equalizer followed by despreading. The various transmit antennas send independent streams and the spreading codes are scrambled Walsh-Hadamard sequences, the various transmit antennas being allocated different scrambling codes. The behaviour of the SINR provided by the receiver is first studied when the spreading factor and the number of users per antenna converge to +infin at the same rate. It is shown that the SINR converges towards a simple expression depending on the particular realization of the frequency selective channel between the base station and the mobile of interest. In order to get more insights on the long term performance, the ergodic sum-capacity delivered by the system is evaluated in the large number of antennas regime in the case the impulse response taps of the channel are Gaussian random matrices. A simple expression is obtained. It appears to be quite reliable for a realistic number of antennas, and is discussed in order to get some insights on the overall performance.

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.

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.

We determine the capacity-achieving input covariance matrices for coherent block-fading correlated MIMO Rician channels. In contrast with the Rayleigh and uncorrelated Rician cases, no closed-form expressions for the eigenvectors of the optimum input covariance matrix are available. Both the eigenvectors and eigenvalues have to be evaluated by using numerical techniques. As the corresponding optimization algorithms are not very attractive, we evaluate the limit of the average mutual information when the number of transmit and receive antennas converge to +infin at the same rate. We propose an attractive optimization algorithm of the large system approximant, and establish some convergence results. Numerical simulation results show that, even for a quite moderate number of transmit and receive antennas, the new approach provides the same results than direct maximization approaches of the average mutual information, while being much more computationally attractive.

In this paper we investigate the performance of block-fading multiple input multiple output (MIMO) Rician correlated channels in the case where the number of transmit and receive antennas converge to infinity at the same rate. In this context we show that the expressions of classical performance indices such as the average mutual information or the output SINR of MMSE receivers converge to deterministic expressions. The analysis determines the parameter of interest and gives insight of the effect of the channel distribution on the performance metrics.

The issue of separating linear mixtures of independent linearly modulated signals stemming from unknown digital communication systems is addressed. The baud-rates of the various transmitted signals are in particular unknown and possibly different. Therefore, sampled versions of the received signal are cyclostationary sequences. Despite the non-stationary environment of the data, Godard's algorithm is shown to achieve separation in rather general contexts.

In this paper, we discuss the performance of space time transmit diversity (STTD) in the downlink of DS-CDMA over frequency-selective fading channels. We consider two kinds of receiver: the RAKE receiver and the chip-level MMSE equalizer-based receiver. These two receivers comparison turns out to be a very difficult task because their output signal to interference plus noise ratios (SINRs) depend in a complex way on the spreading and scrambling codes. To obtain tractable expressions, we study the SINRs in the asymptotic regime, i.e. we suppose that the spreading factor and the number of users both tend to infinity while their ratio remains constant. We further suppose that the code matrix is a random matrix obtained by multiplying a random scrambling code by a Walsh-Hadamard matrix. Under these conditions, the SINRs of the two receivers tend to deterministic values. We compare the asymptotic SINRs and draw some conclusions about the effect of the channel transfer function on the performance. Simulation results show that the asymptotic results allow us to predict the performance of real life systems like the UMTS-FDD.

In this paper, a blind estimator of the technical parameters of continuous phase modulated (CPM) signals is proposed. It consists in estimating jointly the modulation index, the symbol period and the frequency offset. It is based on the following observations. First, the inverse of the index is the smallest positive real number a CPM signal should be raised to in order to generate a deterministic harmonic signal; second, the frequencies of the harmonic signal are simply related to the symbol period and the carrier frequency. The practical implementation of this joint estimator is described and the asymptotic behavior of the estimation error is studied. If N is the number of signaling intervals, the estimate of the modulation index is shown to converge to a non-Gaussian distribution at rate 1/N, while the estimate of the frequency offset and the estimate of the symbol period converge at rate 1/N/sup 3/2/. We also investigate the case where the modulation index and the symbol period are available at the receiver side. An estimator of the frequency offset is proposed by adapting the above joint estimator to the latter case. The asymptotic behavior of this estimator is studied and compared with the case where all of the parameters are unknown, so as to evaluate the possible degradation of the performance due to the ignorance of certain technical parameters. Simulations results sustain our theoretical claims.

Recent results on the asymptotic empirical eigenvalue distribution of random matrices have enabled the study of the asymptotic limits of linear precoded orthogonal frequency-division multiplexing systems with minimum mean-square error (MMSE) equalization. In this letter, we extend these results to the MMSE successive interference cancellation detector and quantify the nonlinearity gain for certain type of precoding matrices.

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 this paper, a new nondata aided estimator of the technical parameters of continuous phase modulated (CPM) signals is proposed. It consists in estimating jointly the modulation index, the symbol period and the frequency offset. It is based on the following observations. Firstly, the inverse of the index is the smallest positive real number a CPM signal should be raised to in order to generate a deterministic harmonic signal; secondly, the frequencies of the harmonic signal are simply related to the symbol period and the carrier frequency. The asymptotic behavior of the estimation error is studied. If N is the number of signaling intervals, the estimate of the modulation index is shown to converge to a nonGaussian distribution at rate 1/N, while the estimate of the frequency offset and the estimate of the symbol period converge at rate 1/N/sup 3/2/. Simulations results sustain our theoretical claims.

Recent results on the asymptotic empirical eigenvalue distribution of the sum or product of matrices, based on the free probability theory, have enabled the study of the asymptotic limits of linear precoded OFDM systems with MMSE equalization for ergodic and non-ergodic channels. We extend these results to the MMSE successive interference cancellation detector with realistic channels and give an explicit answer on the impact of the choice of certain types of spreading codes.

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.

In this paper, a new non data aided estimator of the modulation index of a CPM signal is proposed. It is based on the observation that the inverse of the index is the smallest positive real number to which the CPM signal should be expanded in order to generate a sinusoid of frequency 1 over 2Ts. The asymptotic behavior of the estimate is studied. If N is the sample size, the estimate is shown to converge to a non Gaussian distribution at rate 1 over N. Simulations results sustain our theoretical claims.

This paper considers the problem of blind symbol rate estimation of signals linearly modulated by a sequence of unknown symbols. Oversampling the received signal generates cyclostationary statistics that are exploited to devise symbol-rate estimators by maximizing in the cyclic domain a (possibly weighted) sum of modulus squares of cyclic correlation estimates. Although quite natural, the asymptotic (large sample) performance of this estimator has not been studied rigorously. The consistency and asymptotic normality of this symbol-rate estimator is established when the number of samples N converges to infinity. It is shown that this estimator exhibits a fast convergence rate (proportional to N/sup -3/2/), and it admits a simple closed-form expression for its asymptotic variance. This asymptotic expression enables performance analysis of the rate estimator as a function of the number of estimated cyclic correlation coefficients and the weighting matrix. A justification for the high performance of the unweighted estimator in high signal-to-noise scenarios is also provided.

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.

This paper proposes to analyze the performance of a family of non-data aided open-loop carrier frequency offset (FO) estimators for a linearly modulated signal transmitted through an unknown flat-fading (possibly frequency-selective) channel. The exact asymptotic (large sample) performance of these estimators is established and analyzed as a function of the received signal sampling frequency, signal-to-noise ratio (SNR), timing delay, and number of samples (N). It is shown that in the presence of timing errors, the performance of the estimators can be improved by oversampling (fractionally sampling) the received signal and by taking into account the entire cyclostationary information that is present in the received sequence.

We address the problem of second order statistics estimation of a selective Rayleigh channel in the context of the wideband CDMA mode of the UMTS. The data to be transmitted are sent over slots over which the channel is assumed to remain constant. Each slot contains a pilot symbol sequence from which the channel can be estimated. The covariance matrix of the channel is usually estimated by a denoised version of the empirical covariance matrix of the trained channel estimate. However, this estimate is not consistent in the UMTS context. We propose a new consistent estimate of the channel covariance matrix, and evaluate the performances of two Wiener-like channel estimation schemes based on the proposed estimate.

Upper-bounds on the bit error probability of an OFDM/CDMA system in a single user context are derived for a linear minimum mean-square-error (MMSE) receiver structure. All the calculus are performed in presence of a frequency-selective Rayleigh fading channel both in a coded (convolutive forward error correcting scheme) and uncoded scenario. Surprisingly, we show that coded SOFDM outperforms COFDM if the signal to noise ratio is greater than a given threshold which only depends on the code rate and not on the code structure. These theoretical results provide tools to optimally combine coding and spreading for increasing the spectral efficiency of OFDM/CDMA schemes.

The blind estimation of the symbol period of an unknown linearly modulated signal is addressed. We propose an original methodology relying on the concept of blind deconvolution, which does not suffer from the drawbacks of the classical approaches relying upon the cyclostationarity of the received signal. Under suitable technical conditions, we show that the optimization of certain cost functions leads to the identification of the symbol rate. Simulation results illustrate the excellent performance of the method.

By exploiting the received signal's second-order cyclostationary statistics, blind algorithms have been previously proposed for joint estimation of the frequency offset and the symbol timing delay of a linearly modulated waveform transmitted through a flat-fading channel. The goal of this paper is to establish and analyze the asymptotic (large sample) performance of the Gini-Giannakis (1998) and Ghogho-Swami-Durrani (1999) estimators as a function of the pulse shape bandwidth and the oversampling factor. It is shown that the performance of these estimators improves as the pulse shape bandwidth increases, and the best performance is obtained by selecting small values for the oversampling factor.

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.

We provide a theoretical framework of de-noising for UMTS TDD-like mobile radio communication systems. Based on the Bayesian approach, we show how to de-noise channel estimates provided by the training-based estimation procedure. The proposed schemes allow not only for eliminating major drawbacks of hard thresholding but also for a low complexity implementation.

We consider blind estimation of the carrier frequency offset of a linearly modulated non-circular transmission through an unknown frequency selective channel. A frequency estimator is developed based on the unique conjugate cyclic frequency of the received signal that equals twice the frequency offset. We establish consistency and asymptotic normality of the frequency estimator, and calculate its asymptotic variance in closed form. This expression enables performance analysis of the proposed frequency offset estimator as a function of the number of estimated cyclic correlation coefficients used. Numerical simulations show that estimation and compensation of the carrier frequency offset in the presence of an unknown frequency selective channel can be performed with no loss in performance relative to methods where the channel is pre-equalized first and the frequency offset is compensated afterwards.

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.

Blind channel estimation for periodic sequence DS-CDMA systems can be cast into the framework of "structured" blind estimation of multi-input/multi-output (MIMO) FIR systems, where the structure is imposed by the user's signatures. The well known subspace method can in particular be adapted to this context, but it suffers from a lack of robustness to an over-determination of the order of the channel. In a previous work, we showed that the use a structured linear prediction approach can overcome this drawback. However, the statistical performance of the corresponding estimate are disappointing. In this paper, we concentrate on the forward link channel estimation, and propose to use a weighted linear prediction approach. The optimal weighting matrix is in practice quite difficult to use. We therefore propose a sub-optimum matrix, leading to a quite simple estimation algorithm, and which is shown to have optimum performance when the signal to noise ratio converges to +/spl infin/. Some simulation results confirm the potential of the new approach.

We study the performance of a semi-blind subspace channel estimate in the particular context of the uplink of the UMTS time division duplexing (TDD) mode. The TDD mode of the third generation system UMTS is a multiuser DS-CDMA scheme of maximal spreading factor N=16. In the uplink, each slot corresponds to 2560 chips and the channel estimation is classically achieved by using a 512 training chips midamble. In this well defined context, we study the improvements (in terms of bit error rate) provided by a semi-blind channel estimation technique introduced in the context of the single user system of Gorokhov and Loubaton (see Proc. ICASSP, p.3905-3908, 1997) and studied in detail by Buchoux, Moulines, Cappe and Gorokhov (see SPAWC, 1999).

A discrete time implementation of the RAKE receiver (DTR) is proposed. The suggested approach works without knowledge of the path delays and their number. It is based on a global estimation of the multipath channel convolutioned with the shaping filter. Since the DTR performance is very sensitive to the channel estimation quality, we suggest a disregarding method for the least significant estimated channel coefficients while taking into account the known impulse response of the shaping filter. The performance of the DTR and the conventional RAKE are then compared.

Blind channel estimation for periodic sequence DS-CDMA systems can be cast into the framework of "structured" blind estimation of multi-input/multi-output (MIMO) FIR systems, where the structure is imposed by the user's signatures. A possible approach to tackle this problem consists in looking for a structured solution to one of the so-called "blind" MIMO-FIR system identification techniques proposed previously. This is the approach undertaken, among others, by Wang and Poor (see IEEE Trans. on Communications, vol.46, no.1, p.92-103, 1998), who proposed an adaptation of the subspace method originally developed by Moulines et al. (see IEEE Trans. on Signal Processing, vol.43, no.2, p.516-25, 1995) for single-input multiple outputs (SIMO) FIR systems, and later extended by Abed-Meraim et al. (see IEEE Trans. on Information Theory, vol.43, no.2, p.499-511, 1997) to MIMO-FIR systems. In this article, we follow this approach to consider the particular blind forward channel estimation problem, and improve quite significantly the results presented by Wang and Poor.

Previous results have shown that blind channel estimators, which are robust to the location of channel zeros and channel order overestimation errors, can be derived for communication channels equipped with transmitted induced cyclostationarity (TIC) precoders. This paper addresses the problem of joint estimation of the unknown intersymbol interference (ISI) and carrier frequency offset using TIC-based set-ups. First, it is shown that the second-order cyclic statistics of the output allow recovery of the channel taps under a scaling factor ambiguity dependent on the unknown carrier offset frequency. Next, a carrier frequency estimator is proposed, and its asymptotic (large sample) performance is analyzed. It is shown that the asymptotic performance of the frequency estimator improves in the presence of a channel equalizer for high SNRs. Finally, numerical simulations are presented to collaborate the performance of proposed algorithms.

In this paper, we address the problem of the separation of convolutive mixtures in the case where the non-Gaussian source signals are not necessarily filtered versions of i.i.d. sequences. In this context, we show that the contrast functions, used in the linear process source case, still allow to separate the sources by a deflation approach. Some particular properties of higher order cumulants based contrast functions are also given.

Periodic modulation precoders allow blind identification of SISO channels from output second-order cyclic statistics, irrespective of the location of channel zeros, color of additive stationary noise, or the channel order overestimation errors. The performance of blind channel estimators relying on periodic precoders is investigated. Criteria for optimal designs of periodic modulation precoders are also presented.

Most of the second order based fractionally sampled blind equalizers are known to perform poorly in the context of band-limited signals. In this paper, we analyse the behaviour of the subspace method in the particular context of band-limited signals. As it is well known, the subspace channel estimate is obtained as the eigenvector associated to the eigenvalue 0 of a certain positive quadratic form Q. We show that apart from 0, Q has quite small eigenvalues, and that this induces poor statistical performance. More importantly, we characterize the numerical kernel of Q, and show that it contains vectors constructed from certain spheroidal wave sequences. From this, we deduce that the subspace method does not allow to estimate accurately the transfer function of the channel on a certain frequency interval.

We consider the problem of blind separation of causal minimum phase convolutive mixtures of two sources. We study in detail the so-called decorrelation approach. It consists in finding a causal minimum phase filter which, driven by the observations, produces decorrelated outputs. It is well established that this approach allows one to separate the sources if the mixing filter is a non-static FIR filter. We show that this result is no longer true in the IIR case. We establish that there exists infinitely many causal minimum phase filters producing decorrelated outputs and provide a parameterisation of these filters. This clearly shows that the decorrelation approach is, in practice, non-robust. In order to overcome this drawback, we propose an alternative approach based on a linear prediction scheme, which, as the decorrelation approach, uses essentially the second order statistics of the observations.

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We present a new subspace-based method for blind identification of multichannel finite impulse response (FIR) systems. Instead of assuming spatially white additive noise as commonly used, we consider the case where the noise spatial covariance matrix is unknown. We show how a standard subspace method can be simply modified so that the channel estimate does not depend on the zero-lag correlation coefficient of the observation vector and, thus, is independent of the spatial covariance matrix of the additive noise.

We address the problem of blind second-order equalization of scalar-valued polynomial channels. When an almost periodic deterministic function modulates the initial symbol sequence, the observation exhibits second-order cyclostationarity. This property is shown to give rise to a structured spectral factorization problem. The identification of the unknown channel is then always possible via a structured version of the subspace method. No assumption on the channel is required, except the knowledge of a lower bound of the order. The estimate is consistent, and this property remains unchanged in the presence of stationary noise and when the symbols are colored.

The problem of blind identification of p-inputs/q-outputs FIR transfer functions is addressed. Existing subspace identification methods derived for p=1 are first reformulated. In particular, the links between the noise subspace of a certain covariance matrix of the output signals (on which subspace methods build on) and certain rational subspaces associated with the transfer function to be identified are elucidated. Based on these relations, we study the behavior of the subspace method in the case where the order of the transfer function is overestimated. Next, an asymptotic performance analysis of this estimation method is carried out. Consistency and asymptotical normality of the estimates is established. A closed-form expression for the asymptotic covariance of the estimates is given. Numerical simulations and investigations are presented to demonstrate the potential of the subspace method. Finally, we take advantage of our new reformulation to discuss the extension of the subspace method to the case p>1. We show where the difficulties lie, and we briefly indicate how to solve the corresponding problems. The possible connections with classical approaches for MA model estimations are also outlined.

Mainly motivated by the challenging problem of the increase of mobile radio network capacity, some authors have addressed the so-called multi-user blind equalization problem. In this context, p independent users are assumed to share the same carrier frequency as well as the same linear modulation in order to transmit several messages on the same frequency channel. It is then necessary to retrieve the symbols emitted by each user from the received signal in the case where no training sequence is available, and when multipath effects occur. We propose a blind second order method allowing the retrieval of several signals in the context of multipath channels/multi-users. This is achieved by using cycle-stationary and subspace techniques. The simulation results are very encouraging.

In this paper, the blind separation of convolutive mixtures is addressed. Provided that there are more sensors than sources, it can be solved using almost only the second order statistics of the observed signal, through a three-step method (analysis, instantaneous separation and synthesis). A decomposed and normalized lattice synthesis filter is introduced. It solves the problem of singularity, and it is stable for any choice of its parameters. It can be adaptively computed via a least squares lattice (LSL) algorithm, as shown by the simulation results.

Multipath propagation appears to be a typical limitation in mobile digital communications where it leads to severe intersymbol interference. The classical techniques to overcome this problem use either periodically sent training sequences or blind approaches. This paper addresses the blind identification of FIR multiple input multiple output (MIMO) transfer functions in the case where the number of inputs is strictly less than the number of outputs. We consider a second order identification providing signals extraction up to a regular instantaneous mixture matrix. A novel method of second order channel estimation is presented. Basically exploiting the simultaneous MA and AR nature of the observations, it displays however a considerable improvement as compared to the original linear prediction approach. Performance study and comparison with the existing approach is provided by computer simulations.

Blind identification of single-input multiple-output (SIMO) FIR systems based on second order statistics has attracted a lot of research efforts. We focus on subspace estimation procedures, which exploit the structure of the range space of certain matrix-valued statistics constructed by arranging in a prescribed order the covariance coefficients of the observations. General subspace identifiability results are obtained, based on the properties of minimal polynomial bases of rational subspaces. Several subspace estimation procedures are then derived. These estimators are all based on the (possibly weighted) least-square solution of an overdetermined system of linear equations and are thus well-suited for practical implementations.

Blind channel identification methods based on the oversampled channel output is a problem of theoretical and practical interest. It is first demonstrated that the subspace methods developed in Moulines are not robust to errors in the determination of the model order. An alternative solution is then proposed, based on a linear prediction approach. The effect of overestimating the channel order is investigated by simulations: it is demonstrated that the prediction error method is "robust" to over-determination.

In this paper, we address the adaptive blind source separation of independent sources using higher order statistics. Although this problem was considered in numerous works, none of the existing algorithms is guaranteed to converge to a relevant solution. Here, we propose a new separation scheme whose convergence is proved analytically. It is based on the observation that it is possible to extract one of the source signals by a simple algorithm obtained by extending to the source separation context some of the ideas developed by Shalvi-Weinstein in the framework of blind deconvolution. A low cost deflation procedure allows the extraction of the other source signals by means of the same algorithm. Simulation results illustrate the behaviour of this separation method.>

The set M( Omega ) of all (discrete-time) power spectra supported on a known interval (- Omega , Omega ), (with Omega>

The estimation problem for rational-type spectral signal subspaces in the time domain is discussed. Two methods are presented. The first is the transcription of the methods proposed by K.M. Buckley and L.J. Griffiths (1988) to the rational modeling context. It is based on the fact that a one-to-one correspondence exists between the polynomial vector-valued functions of the noise spectral subspace and the eigenspace corresponding to the smallest eigenvalue of the covariance matrix of the data. In the second method, the authors exploit the fact that the noise spectral subspace admits rational-type orthonormal bases related to the causal rational transfer functions with coisometric values on the unit circle, the action of which on the data produces a minimum energy output. This optimization problem is solved by using an efficient parametrization of these transfer functions in conjunction with a gradient algorithm, the initial conditions of which are calculated by using the first method. By contrast with the first approach, it is shown that the corresponding estimator is related to a quadratic reconstruction criterion which can be interpreted as a maximum-likelihood criterion in a particular case.>

For a 2-D wide sense stationary process, the Prediction Theory is revisited and a spectral factorization procedure is obtained via 1-D factorizations.