Self-Adaptive Stochastic Rayleigh Flat Fading Channel Estimation

International audienceThis paper deals with channel estimation over flat fading Rayleigh channel with Jakes' Doppler Spectrum. Many estimation algorithms exploit the time-domain correlation of the channel by employing a Kalman filter based on a first-order (or sometimes second-order) approximation of the time-varying channel with a criterion based on correlation matching (CM), or on the Minimization of Asymptotic Variance (MAV). In this paper, we first consider a reduced complexity approach based on Least Mean Square (LMS) algorithm, for which we provide closed-form expressions of the optimal step-size coefficient versus the channel state statistic (additive noise power and Doppler frequency) and of corresponding asymptotic mean-squared-error (MSE). However, the optimal tuning of the step-size coefficient requires knowledge of the channel's statistic. This knowledge was also a requirement for the aforementioned Kalman-based methods. As a second contribution, we propose a self-adaptive estimation method based on a stochastic gradient which does not need a priori knowledge. We show that the asymptotic MSE of the self-adaptive algorithm is almost the same as the first order Kalman filter optimized with the MAV criterion and is better than the latter optimized with the conventional CM criterion. We finally improve the speed and reactivity of the algorithm by computing an adaptive speed process leading to a fast algorithm with very good asymptotic performance

Simplified Random-Walk-Model-Based Kalman Filter for Slow to Moderate Fading Channel Estimation in OFDM Systems

12 pagesInternational audienceThis study deals with multi-path channel estimation for orthogonal frequency division multiplexing systems under slow to moderate fading conditions. Advanced algorithms exploit the channel time-domain correlation by using Kalman Filters (KFs) based on an approximation of the time-varying channel. Recently, it was shown that under slow to moderate fading, near optimal channel multi-path complex amplitude estimation can be obtained by using the integrated Random Walk (RW) model as the channel approximation. To reduce the complexity of the high-dimensional RW-KF for joint estimation of the multi-path complex amplitudes, we propose using a lower dimensional RW-KF that estimates the complex amplitude of each path separately. We demonstrate that this amounts to a simplification of the joint multi-path Kalman gain formulation through the Woodbury's identities. Hence, this new algorithm consists of a superposition of independent single-path single-carrier KFs, which were optimized in our previous studies. This observation allows us to adapt the optimization to the actual multi-path multi-carrier scenario, to provide analytic formulae for the mean-square error performance and the optimal tuning of the proposed estimator directly as a function of the physical parameters of the channel (Doppler frequency, Signal-to-Noise-Ratio, Power Delay Profile). These analytic formulae are given for the first-, second-, and third-order RW models used in the KF. The proposed per-path KF is shown to be as efficient as the exact KF (i.e., the joint multipath KF), and outperforms the autoregressive-model-based KFs proposed in the literature

Third-Order Kalman Filter: Tuning and Steady-State Performance

4 pagesInternational audienceThis letter deals with the Kalman filter (KF) based on a third-order integrated random walk model (RW3). The resulting filter, noted as RW3-KF, is well suited to track slow time-varying parameters with strong trend behaviour. We first prove that the RW3-KF in steady-state admits an equivalent structure to the third-order digital phase-locked loops (DPLL). The approximate asymptotic mean-squared-error (MSE) is obtained by solving the Riccati equations, which is given in a closed-form expression as a function of the RW3 model parameter: the state noise variance. Then, the closed-form expression of the optimum state noise variance is derived to minimize the asymptotic MSE. Simulation results are given for the particular case where the parameter to be estimated is a Rayleigh channel coefficient with Jakes' Doppler spectrum

Complex Amplitudes Tracking Loop for multipath channel estimation in OFDM systems over slow to moderate fading

International audienceThis paper deals with multipath channel estimation for Orthogonal Frequency-Division Multiplexing systems under slow to moderate fading conditions. Most of the conventionalmethods exploit only the frequency-domain correlation by estimating the channel at pilot frequencies, and then interpolating the channel frequency response. More advanced algorithms exploit in addition the time-domain correlation, by employing Kalman filters based on the approximation of the time-varying channel. Adopting a parametric approach and assuming a primary acquisition of the path delays, channel estimators have to track the complex amplitudes of the paths. In this perspective, we propose a less complex algorithm than the Kalman methods, inspired by second-order Phase-Locked Loops. An error signal is created from the pilot-aided Least-Squares estimates of the complex amplitudes, and is integrated by the loop to carry out the final estimates. We derive closed-form expressions of the mean squared error of the algorithm and of the optimal loop coefficients versus the channel state, assuming a Rayleigh channel with Jakes'Doppler spectrum. The efficiency of our reduced complexity algorithm is demonstrated, with an asymptotic mean squared error lower than the first-order auto-regressive Kalman filters reported in the literature, and almost the same as a second-order Kalman-based algorithm

Third-order Complex Amplitudes Tracking Loop for Slow Flat Fading Channel On-Line Estimation

12 pagesInternational audienceThis paper deals with channel estimation in tracking mode over a flat Rayleigh fading channel with Jakes' Doppler Spectrum. Many estimation algorithms exploit the time-domain correlation of the channel by employing a Kalman filter based on a first-order (or sometimes second-order) approximation model of the time-varying channel. However, the nature of the approximation model itself degrades the estimation performance for slow to moderate varying channel scenarios. Furthermore, the Kalman-based algorithms exhibit a certain complexity. Hence, a different model and approach has been investigated in this work to tackle all of these issues. A novel PLL-structured third-order tracking loop estimator with a low complexity is proposed. The connection between a steady-state Kalman filter based on a random walk approximation model and the proposed estimator is first established. Then, a sub-optimal mean-squared-error (MSE) is given in a closed-form expression as a function of the tracking loop parameters. The parameters that minimize this sub-optimal MSE are also given in a closed-form expression. The asymptotic MSE and Bit-Error-Ratio (BER) simulation results demonstrate that the proposed estimator outperforms the first and second order Kalman-based filters reported in literature. The robustness of the proposed estimator is also verified by a mismatch simulation

Traitement du signal pour les communications numériques au travers de canaux radio-mobiles

This manuscript of ''Habilitation à diriger les Recherches'' (Habilitation to conduct researches) gives me the opportunity to take stock of the last 14 years on my associate professor activities and on my research works in the field of signal processing for digital communications, particularly for radio-mobile communications. The purpose of this signal processing is generally to obtain a robust transmission, despite the passage of digital information through a communication channel disrupted by the mobility between the transmitter and the receiver (Doppler effect), the phenomenon of echoes (multi-path propagation), the addition of noise or interference, or by limitations in bandwidth, in transmitted power or in signal-to-noise ratio. In order to recover properly the digital information, the receiver needs in general to have an accurate knowledge of the channel state. Much of my work has focused on receiver synchronization or more generally on the dynamic estimation of the channel parameters (delays, phases, amplitudes, Doppler shifts, ...). We have developed estimators and studied their performance in asymptotic variance, and have compared them to minimum lower bound (Cramer-rao or Bayesian Cramer Rao bounds). Some other studies have focused only on the recovering of information (''detection'' or ''equalization'' task) by the receiver after channel estimation, or proposed and analyzed emission / reception schemes, reliable for certain scenarios (transmit diversity scheme for flat fading channel, scheme with high energy efficiency, ...).Ce mémoire de HDR est l'occasion de dresser un bilan des 14 dernières années concernant mes activités d'enseignant-chercheur et mes travaux de recherche dans le domaine du traitement du signal pour les communications numériques, et plus particulièrement les communications radio-mobiles. L'objet de ce traitement du signal est globalement l'obtention d'une transmission robuste, malgré le passage de l'information numérique au travers d'un canal de communication perturbé par la mobilité entre l'émetteur et le récepteur (effet Doppler), le phénomène d'échos, l'addition de bruit ou d'interférence, ou encore par des limitations en bande-passante, en puissance transmise ou en rapport-signal à bruit. Afin de restituer au mieux l'information numérique, le récepteur a en général besoin de disposer d'une connaissance précise du canal. Une grande partie de mes travaux s'est intéressé à l'estimation dynamique des paramètres de ce canal (retards, phases, amplitudes, décalages Doppler, ...), et en particulier à la synchronisation du récepteur. Quelques autres travaux se sont intéressés seulement à la restitution de l'information (tâches de ''détection'' ou d' ''égalisation'') par le récepteur une fois le canal estimé, ou à des schémas d'émission / réception spécifiques. La synthèse des travaux commence par une introduction générale décrivant les ''canaux de communications'' et leurs problèmes potentiels, et positionne chacun de mes travaux en ces termes. Une première partie s'intéresse aux techniques de réception pour les signaux à spectre étalé des systèmes d'accès multiple à répartition par codes (CDMA). Ces systèmes large-bande offrent un fort pouvoir de résolution temporelle et des degrés de liberté, que nous avons exploités pour étudier l'égalisation et la synchronisation (de retard et de phase) en présence de trajets multiples et d'utilisateurs multiples. La première partie regroupe aussi d'autres schémas d'émission/réception, proposés pour leur robustesse dans différents scénarios (schéma à diversité pour canaux à évanouissement plats, schéma à forte efficacité énergétique, ...). La seconde partie est consacrée à l'estimation dynamique Bayésienne des paramètres du canal. On suppose ici qu'une partie des paramètres à estimer exhibe des variations temporelles aléatoires selon une certaine loi à priori. Nous proposons d'abord des estimateurs et des bornes minimales d'estimation pour des modèles de transmission relativement complexes, en raison de la distorsion temporelle due à la forte mobilité en modulation multi-porteuse (OFDM), ou de la présence de plusieurs paramètres à estimer conjointement, ou encore de non linéarités dans les modèles. Nous nous focalisons ensuite sur le problème d'estimation des amplitudes complexes des trajets d'un canal à évolution lente (à 1 ou plusieurs bonds). Nous proposons des estimateurs récursifs (dénommés CATL, pour ''Complex Amplitude Tracking Loop'') à structure imposée inspirée par les boucles à verrouillage de phase numériques, de performance asymptotiques proches des bornes minimales. Les formules analytiques approchées de performances asymptotiques et de réglages de ces estimateurs sont établies sous forme de simples fonctions des paramètres physiques (spectre Doppler, retards, niveau de bruit). Puis étant donné les liens établis entre ces estimateurs CATL et certains filtres de Kalman (construits pour des modèles d'état de type marche aléatoire intégrée), les formules approchées de performances asymptotiques et de réglage de ces filtres de Kalman sont aussi dérivées

EM-Based Estimation and Compensation of Phase Noise in Massive-MIMO Uplink Communications

Phase noise (PN) is a major disturbance in MIMO systems, where the contribution of different oscillators at the transmitter and the receiver side may degrade the overall performance and offset the gains offered by MIMO techniques. This is even more crucial in the case of massive MIMO, since the number of PN sources may increase considerably. In this work, we propose an iterative receiver based on the application of the expectation-maximization algorithm. We consider a massive MIMO framework with a general association of oscillators to antennas, and include other channel disturbances like imperfect channel state information and Rician block fading. At each receiver iteration, given the information on the transmitted symbols, steepest descent is used to estimate the PN samples, with an optimized adaptive step size and a threshold-based stopping rule. The results obtained for several test cases show how the bit error rate and mean square error can benefit from the proposed phase-detection algorithm, even to the point of reaching the same performance as in the case where no PN is present{\color{black}, offering better results than a state-of-the-art alternative}. Further analysis of the results allow to draw some useful trade-offs respecting final performance and consumption of resources.Comment: Submitted to IEEE Transactions on Communication

Advanced methods in automatic modulation classification for emerging technologies

Modulation classification (MC) is of large importance in both military and commercial communication applications. It is a challenging problem, especially in non-cooperative wireless environments, where channel fading and no prior knowledge on the incoming signal are major factors that deteriorate the reception performance. Although the average likelihood ratio test method can provide an optimal solution to the MC problem with unknown parameters, it suffers from high computational complexity and in some cases mathematical intractability. Instead, in this research, an array-based quasi-hybrid likelihood ratio test (qHLRT) algorithm is proposed, which depicts two major advantages. First, it is simple yet accurate enough parameter estimation with reduced complexity. Second the incorporation of antenna arrays offers an effective ability to combat fading. Furthermore, a practical array-based qHLRT classifier scheme is implemented, which applies maximal ratio combining (MRC) to increase the accuracy of both carrier frequency offset (CFO) estimation and likelihood function calculation in channel fading. In fact, double CFO estimations are executed in this classifier. With the first the unknown CFO, phase offsets and amplitudes are estimated as prerequisite for MRC operation. Then, MRC is performed using these estimates, followed by a second CFO estimator. Since the input of the second CFO estimator is the output of the MRC, fading effects on the incoming signals are removed significantly and signal-to-noise ratio (SNR) is augmented. As a result, a more accurate CFO estimate is obtained. Consequently, the overall classification performance is improved, especially in low SNR environment. Recently, many state-of-the-arts communication technologies, such as orthogonal frequency division multiplexing (OFDM) modulations, have been emerging. The need for distinguishing OFDM signal from single carrier has become obvious. Besides, some vital parameters of OFDM signals should be extracted for further processing. In comparison to the research on MC for single carrier single antenna transmission, much less attention has been paid to the MC for emerging modulation methods. A comprehensive classification system is proposed for recognizing the OFDM signal and extracting its parameters. An automatic OFDM modulation classifier is proposed, which is based on the goodness-of-fittest. Since OFDM signal is Gaussian, Cramer-von Mises technique, working on the empirical distribution function, has been applied to test the presence of the normality. Numerical results show that such approach can successfully identify OFDM signals from single carrier modulations over a wide SNR range. Moreover, the proposed scheme can provide the acceptable performance when frequency-selective fading is present. Correlation test is then applied to estimate OFDM cyclic prefix duration. A two-phase searching scheme, which is based on Fast Fourier Transform (FFT) as well as Gaussianity test, is devised to detect the number of subcarriers. In the first phase, a coarse search is carried out iteratively. The exact number of subcarriers is determined by the fine tune in the second phase. Both analytical work and numerical results are presented to verify the efficiency of the proposed scheme

On the use of tracking loops for low-complexity multi-path channel estimation in OFDM systems

International audience—This paper treats pilot aided multi-path channel estimation with tracking loops for OFDM systems under slow to moderate fading conditions. Recent works have presented theoretical results for the tuning of second-order and third-order tracking loops in the particular context of Jakes's Doppler spectrum channel. The method for getting the loop coefficients resorted either to the use of a given constraint, which made the obtained coefficients sub-optimal, or was obtained in part by simulations. Here, we perform a global optimization of the coefficients without constraints to get the optimal coefficients, and analytical formulas are provided. One remarkable result of this optimization is that only the natural frequency depends on the transmission parameters, i.e., the channel Doppler spectrum, the power delay profile, and the noise variance. Consequently, only one parameter has to be tuned. Moreover, asymptotic performance is formulated in a more general way as a function of the 2rth moments of the Doppler spectrum (r is the loop order). Hence, all our derivations are usable for any Doppler spectrum and are not specific to Jakes's Doppler spectrum. A complete table sums up for the three orders the theoretical results of the optimal coefficients together with the asymptotic performance. The performance is also compared with that of the asymptotic Kalman filter