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

Communication Subsystems for Emerging Wireless Technologies

The paper describes a multi-disciplinary design of modern communication systems. The design starts with the analysis of a system in order to define requirements on its individual components. The design exploits proper models of communication channels to adapt the systems to expected transmission conditions. Input filtering of signals both in the frequency domain and in the spatial domain is ensured by a properly designed antenna. Further signal processing (amplification and further filtering) is done by electronics circuits. Finally, signal processing techniques are applied to yield information about current properties of frequency spectrum and to distribute the transmission over free subcarrier channels

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

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

Channel modeling and resource allocation in OFDM systems

The increasing demand for high data rate in wireless communication systems gives rise to broadband communication systems. The radio channel is plagued by multipath propagation, which causes frequency-selective fading in broadband signals. Orthogonal Frequency-Division Multiplexing (OFDM) is a modulation scheme specifically designed to facilitate high-speed data transmission over frequency-selective fading channels. The problem of channel modeling in the frequency domain is first investigated for the wideband and ultra wideband wireless channels. The channel is converted into an equivalent discrete channel by uniformly sampling the continuous channel frequency response (CFR), which results in a discrete CFR. A necessary and sufficient condition is established for the existence of parametric models for the discrete CFR. Based on this condition, we provide a justification for the effectiveness of previously reported autoregressive (AR) models in the frequency domain of wideband and ultra wideband channels. Resource allocation based on channel state information (CSI) is known to be a very powerful method for improving the spectral efficiency of OFDM systems. Bit and power allocation algorithms have been discussed for both static channels, where perfect knowledge of CSI is assumed, and time-varying channels, where the knowledge of CSI is imperfect. In case of static channels, the optimal resource allocation for multiuser OFDM systems has been investigated. Novel algorithms are proposed for subcarrier allocation and bit-power allocation with considerably lower complexity than other schemes in the literature. For time-varying channel, the error in CSI due to channel variation is recognized as the main obstacle for achieving the full potential of resource allocation. Channel prediction is proposed to suppress errors in the CSI and new bit and power allocation schemes incorporating imperfect CSI are presented and their performance is evaluated through simulations. Finally, a maximum likelihood (ML) receiver for Multiband Keying (MBK) signals is discussed, where MBK is a modulation scheme proposed for ultra wideband systems (UWB). The receiver structure and the associated ML decision rule is derived through analysis. A suboptimal algorithm based on a depth-first tree search is introduced to significantly reduce the computational complexity of the receiver