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

Fundamental limits in Gaussian channels with feedback: confluence of communication, estimation, and control

The emerging study of integrating information theory and control systems theory has attracted tremendous attention, mainly motivated by the problems of control under communication constraints, feedback information theory, and networked systems. An often overlooked element is the estimation aspect; however, estimation cannot be studied isolatedly in those problems. Therefore, it is natural to investigate systems from the perspective of unifying communication, estimation, and control;This thesis is the first work to advocate such a perspective. To make Matters concrete, we focus on communication systems over Gaussian channels with feedback. For some of these channels, their fundamental limits for communication have been studied using information theoretic methods and control-oriented methods but remain open. In this thesis, we address the problems of characterizing and achieving the fundamental limits for these Gaussian channels with feedback by applying the unifying perspective;We establish a general equivalence among feedback communication, estimation, and feedback stabilization over the same Gaussian channels. As a consequence, we see that the information transmission (communication), information processing (estimation), and information utilization (control), seemingly different and usually separately treated, are in fact three sides of the same entity. We then reveal that the fundamental limitations in feedback communication, estimation, and control coincide: The achievable communication rates in the feedback communication problems can be alternatively given by the decay rates of the Cramer-Rao bounds (CRB) in the associated estimation problems or by the Bode sensitivity integrals in the associated control problems. Utilizing the general equivalence, we design optimal feedback communication schemes based on the celebrated Kalman filtering algorithm; these are the first deterministic, optimal communication schemes for these channels with feedback (except for the degenerated AWGN case). These schemes also extend the Schalkwijk-Kailath (SK) coding scheme and inherit its useful features, such as reduced coding complexity and improved performance. Hence, this thesis demonstrates that the new perspective plays a significant role in gaining new insights and new results in studying Gaussian feedback communication systems. We anticipate that the perspective could be extended to more general problems and helpful in building a theoretically and practically sound paradigm that unifies information, estimation, and control

Situational Awareness Enhancement for Connected and Automated Vehicle Systems

Recent developments in the area of Connected and Automated Vehicles (CAVs) have boosted the interest in Intelligent Transportation Systems (ITSs). While ITS is intended to resolve and mitigate serious traffic issues such as passenger and pedestrian fatalities, accidents, and traffic congestion; these goals are only achievable by vehicles that are fully aware of their situation and surroundings in real-time. Therefore, connected and automated vehicle systems heavily rely on communication technologies to create a real-time map of their surrounding environment and extend their range of situational awareness. In this dissertation, we propose novel approaches to enhance situational awareness, its applications, and effective sharing of information among vehicles.;The communication technology for CAVs is known as vehicle-to-everything (V2x) communication, in which vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) have been targeted for the first round of deployment based on dedicated short-range communication (DSRC) devices for vehicles and road-side transportation infrastructures. Wireless communication among these entities creates self-organizing networks, known as Vehicular Ad-hoc Networks (VANETs). Due to the mobile, rapidly changing, and intrinsically error-prone nature of VANETs, traditional network architectures are generally unsatisfactory to address VANETs fundamental performance requirements. Therefore, we first investigate imperfections of the vehicular communication channel and propose a new modeling scheme for large-scale and small-scale components of the communication channel in dense vehicular networks. Subsequently, we introduce an innovative method for a joint modeling of the situational awareness and networking components of CAVs in a single framework. Based on these two models, we propose a novel network-aware broadcast protocol for fast broadcasting of information over multiple hops to extend the range of situational awareness. Afterward, motivated by the most common and injury-prone pedestrian crash scenarios, we extend our work by proposing an end-to-end Vehicle-to-Pedestrian (V2P) framework to provide situational awareness and hazard detection for vulnerable road users. Finally, as humans are the most spontaneous and influential entity for transportation systems, we design a learning-based driver behavior model and integrate it into our situational awareness component. Consequently, higher accuracy of situational awareness and overall system performance are achieved by exchange of more useful information

Channel Prediction for Mobile MIMO Wireless Communication Systems

Temporal variation and frequency selectivity of wireless channels constitute a major drawback to the attainment of high gains in capacity and reliability offered by multiple antennas at the transmitter and receiver of a mobile communication system. Limited feedback and adaptive transmission schemes such as adaptive modulation and coding, antenna selection, power allocation and scheduling have the potential to provide the platform of attaining the high transmission rate, capacity and QoS requirements in current and future wireless communication systems. Theses schemes require both the transmitter and receiver to have accurate knowledge of Channel State Information (CSI). In Time Division Duplex (TDD) systems, CSI at the transmitter can be obtained using channel reciprocity. In Frequency Division Duplex (FDD) systems, however, CSI is typically estimated at the receiver and fed back to the transmitter via a low-rate feedback link. Due to the inherent time delays in estimation, processing and feedback, the CSI obtained from the receiver may become outdated before its actual usage at the transmitter. This results in significant performance loss, especially in high mobility environments. There is therefore a need to extrapolate the varying channel into the future, far enough to account for the delay and mitigate the performance degradation. The research in this thesis investigates parametric modeling and prediction of mobile MIMO channels for both narrowband and wideband systems. The focus is on schemes that utilize the additional spatial information offered by multiple sampling of the wave-field in multi-antenna systems to aid channel prediction. The research has led to the development of several algorithms which can be used for long range extrapolation of time-varyingchannels. Based on spatial channel modeling approaches, simple and efficient methods for the extrapolation of narrowband MIMO channels are proposed. Various extensions were also developed. These include methods for wideband channels, transmission using polarized antenna arrays, and mobile-to-mobile systems. Performance bounds on the estimation and prediction error are vital when evaluating channel estimation and prediction schemes. For this purpose, analytical expressions for bound on the estimation and prediction of polarized and non-polarized MIMO channels are derived. Using the vector formulation of the Cramer Rao bound for function of parameters, readily interpretable closed-form expressions for the prediction error bounds were found for cases with Uniform Linear Array (ULA) and Uniform Planar Array (UPA). The derived performance bounds are very simple and so provide insight into system design. The performance of the proposed algorithms was evaluated using standardized channel models. The effects of the temporal variation of multipath parameters on prediction is studied and methods for jointly tracking the channel parameters are developed. The algorithms presented can be utilized to enhance the performance of limited feedback and adaptive MIMO transmission schemes

Nonlinearity Mitigation in WDM Systems: Models, Strategies, and Achievable Rates

After reviewing models and mitigation strategies for interchannel nonlinear interference (NLI), we focus on the frequency-resolved logarithmic perturbation model to study the coherence properties of NLI. Based on this study, we devise an NLI mitigation strategy which exploits the synergic effect of phase and polarization noise compensation (PPN) and subcarrier multiplexing with symbol-rate optimization. This synergy persists even for high-order modulation alphabets and Gaussian symbols. A particle method for the computation of the resulting achievable information rate and spectral efficiency (SE) is presented and employed to lower-bound the channel capacity. The dependence of the SE on the link length, amplifier spacing, and presence or absence of inline dispersion compensation is studied. Single-polarization and dual-polarization scenarios with either independent or joint processing of the two polarizations are considered. Numerical results show that, in links with ideal distributed amplification, an SE gain of about 1 bit/s/Hz/polarization can be obtained (or, in alternative, the system reach can be doubled at a given SE) with respect to single-carrier systems without PPN mitigation. The gain is lower with lumped amplification, increases with the number of spans, decreases with the span length, and is further reduced by in-line dispersion compensation. For instance, considering a dispersion-unmanaged link with lumped amplification and an amplifier spacing of 60 km, the SE after 80 spans can be be increased from 4.5 to 4.8 bit/s/Hz/polarization, or the reach raised up to 100 spans (+25%) for a fixed SE.Comment: Submitted to Journal of Lightwave Technolog

A Mobile Wireless Channel State Recognition Algorihm: Introduction, Definition, and Verification - Sensing for Cognitive Environmental Awareness

This research includes mobile wireless systems limited by time and frequency dispersive channels. A blind mobile wireless channel (MWC) state recognition (CSR) algorithm that detects hidden coherent nonselective and noncoherent selective processes is verified. Because the algorithm is blind, it releases capacity based on current channel state that traditionally is fixed and reserved for channel gain estimation and distortion mitigation. The CSR algorithm enables cognitive communication system control including signal processing, resource allocation/deallocation, or distortion mitigation selections based on channel coherence states. MWC coherent and noncoherent states, ergodicity, stationarity, uncorrelated scattering, and Markov processes are assumed for each time block. Furthermore, a hidden Markov model (HMM) is utilized to represent the statistical relationships between hidden dispersive processes and observed receive waveform processes. First-order and second-order statistical extracted features support state hard decisions which are combined in order to increase the accuracy of channel state estimates. This research effort has architected, designed, and verified a blind statistical feature recognition algorithm capable of detecting coherent nonselective, single time selective, single frequency selective, or dual selective noncoherent states. A MWC coherence state model (CSM) was designed to represent these hidden dispersive processes. Extracted statistical features are input into a parallel set of trained HMMs that compute state sequence conditional likelihoods. Hard state decisions are combined to produce a single most likely channel state estimate for each time block. To verify the CSR algorithm performance, combinations of hidden state sequences are applied to the CSR algorithm and verified against input hidden state sequences. State sequence recognition accuracy sensitivity was found to be above 99% while specificity was determined to be above 98% averaged across all features, states, and sequences. While these results establish the feasibility of a MWC blind CSR algorithm, optimal configuration requires future research to further improve performance including: 1) characterizing the range of input signal configurations, 2) waveform feature block size reduction, 3) HMM parameter tracking, 4) HMM computational complexity and latency reduction, 5) feature soft decision combining, 6) recursive implementation, 7) interfacing with state based mobile wireless communication control processes, and 8) extension to wired or wireless waveform recognition

Timing and Frequency Synchronization and Channel Estimation in OFDM-based Systems

Orthogonal frequency division multiplexing (OFDM) due to its appealing features, such as robustness against frequency selective fading and simple channel equalization, is adopted in communications systems such as WLAN, WiMAX and DVB. However, OFDM systems are sensitive to synchronization errors caused by timing and frequency offsets. Besides, the OFDM receiver has to perform channel estimation for coherent detection. The goal of this thesis is to investigate new methods for timing and frequency synchronization and channel estimation in OFDM-based systems. First, we investigate new methods for preamble-aided coarse timing estimation in OFDM systems. Two novel timing metrics using high order statistics-based correlation and differential normalization functions are proposed. The performance of the new timing metrics is evaluated using different criteria including class-separability, robustness to the carrier frequency offset, and computational complexity. It is shown that the new timing metrics can considerably increase the class-separability due to their more distinct values at correct and wrong timing instants, and thus give a significantly better detection performance than the existing timing metrics do. Furthermore, a new method for coarse estimation of the start of the frame is proposed, which remarkably reduces the probability of inter-symbol interference (ISI). The improved performances of the new schemes in multipath fading channels are shown by the probabilities of false alarm, missed-detection and ISI obtained through computer simulations. Second, a novel pilot-aided algorithm is proposed for the detection of integer frequency offset (IFO) in OFDM systems. By transforming the IFO into two new integer parameters, the proposed method can largely reduce the number of trial values for the true IFO. The two new integer parameters are detected using two different pilot sequences, a periodic pilot sequence and an aperiodic pilot sequence. It is shown that the new scheme can significantly reduce the computational complexity while achieving almost the same performance as the previous methods do. Third, we propose a method for joint timing and frequency synchronization and channel estimation for OFDM systems that operate in doubly selective channels. Basis expansion modeling (BEM) that captures the time variations of the channel is used to reduce the number of unknown channel parameters. The BEM coefficients along with the timing and frequency offsets are estimated by using a maximum likelihood (ML) approach. An efficient algorithm is then proposed for reducing the computational complexity of the joint estimation. The complexity of the new method is assessed in terms of the number of multiplications. The mean square estimation error of the proposed method is evaluated in comparison with previous methods, indicating a remarkable performance improvement by the new method. Fourth, we present a new scheme for joint estimation of CFO and doubly selective channel in orthogonal frequency division multiplexing systems. In the proposed preamble-aided method, the time-varying channel is represented using BEM. CFO and BEM coefficients are estimated using the principles of particle and Kalman filtering. The performance of the new method in multipath time-varying channels is investigated in comparison with previous schemes. The simulation results indicate a remarkable performance improvement in terms of the mean square errors of CFO and channel estimates. Fifth, a novel algorithm is proposed for timing and frequency synchronization and channel estimation in the uplink of orthogonal frequency division multiple access (OFDMA) systems by considering high-mobility situations and the generalized subcarrier assignment. By using BEM to represent a doubly selective channel, a maximum likelihood (ML) approach is proposed to jointly estimate the timing and frequency offsets of different users as well as the BEM coefficients of the time-varying channels. A space-alternating generalized expectation-maximization algorithm is then employed to transform the maximization problem for all users into several simpler maximization problems for each user. The computational complexity of the new timing and frequency offset estimator is analyzed and its performance in comparison with that of existing methods using the mean square error is evaluated . Finally, two novel approaches for joint CFO and doubly selective channel estimation in the uplink of multiple-input multiple-output orthogonal frequency division multiple access (MIMO-OFDMA) systems are presented. Considering high-mobility situations, where channels change within an OFDMA symbol interval, and the time varying nature of CFOs, BEM is employed to represent the time variations of the channel. Two new approaches are then proposed based on Schmidt Kalman filtering (SKF). The first approach utilizes Schmidt extended Kalman filtering for each user to estimate the CFO and BEM coefficients. The second approach uses Gaussian particle filter along with SKF to estimate the CFO and BEM coefficients of each user. The Bayesian Cramer Rao bound is derived, and performance of the new schemes are evaluated using mean square error. It is demonstrated that the new schemes can significantly improve the mean square error performance in comparison with that of the existing methods

Stochastic Modeling and Estimation of Wireless Channels with Application to Ultra Wide Band Systems

This thesis is concerned with modeling of both space and time variations of Ultra Wide Band (UWB) indoor channels. The most common empirically determined amplitude distribution in many UWB environments is Nakagami distribution. The latter is generalized to stochastic diffusion processes which capture the dynamics of UWB channels. In contrast with the traditional models, the statistics of the proposed models are shown to be time varying, but converge in steady state to their static counterparts. System identification algorithms are used to extract various channel parameters using received signal measurement data, which are usually available at the receiver. The expectation maximization (EM) algorithm and the Kalman filter (KF) are employed in estimating channel parameters as well as the inphase and quadrature components, respectively. The proposed algorithms are recursive and therefore can be implemented in real time. Further, sufficient conditions for the convergence of the EM algorithm are provided. Comparison with recursive Least-square (LS) algorithms is carried out using experimental measurements. Distributed stochastic power control algorithms based on the fixed point theorem and stochastic approximations are used to solve for the optimal transmit power problem and numerical results are also presented. A framework which can capture the statistics of the overall received signal and a methodology to estimate parameters of the counting process based on the received signal is developed. Furthermore, second moment statistics and characteristic functions are computed explicitly and considered as an extension of Rice’s shot noise analysis. Another two important components, input design and model selection are also considered. Gel’fand n-widths and Time n-widths are used to represent the inherent error introduced by input design. Kolmogorov n-width is used to characterize the representation error introduced by model selection. In particular, it is shown that the optimal model for reducing the representation error is a finite impulse response (FIR) model and the optimal input is an impulse at the start of the observation interval