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

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

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

Pilot based channel estimation improvement in orthogonal frequency-division multiplexing systems using linear predictive coding

Pilot based least square (LS) channel estimation is a commonly used channel estimation technique in orthogonal frequency-division multiplexing based systems due to its simplicity. However, LS estimation does not handle the noise effect and hence suffers from performance degradation. Since the channel coefficients are correlated in time and hence show a slower variation than the noise, it is possible to encode the channel using linear predictive coding (LPC) without the noise. In this work, the channel is estimated from the pilots using LS estimation and in a second step the channel’s LS estimated is encoded as LPC coefficients to produce an improved channel estimation. The estimation technique is simulated for space-time block coding (STBC) based orthogonal frequency-division multiplexing (OFDM) system and the bit error rate (BER) curves show improvement of the LPC estimation over the LS estimation of the channel

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 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

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