Time Delay Estimation from Low Rate Samples: A Union of Subspaces Approach

Time delay estimation arises in many applications in which a multipath medium has to be identified from pulses transmitted through the channel. Various approaches have been proposed in the literature to identify time delays introduced by multipath environments. However, these methods either operate on the analog received signal, or require high sampling rates in order to achieve reasonable time resolution. In this paper, our goal is to develop a unified approach to time delay estimation from low rate samples of the output of a multipath channel. Our methods result in perfect recovery of the multipath delays from samples of the channel output at the lowest possible rate, even in the presence of overlapping transmitted pulses. This rate depends only on the number of multipath components and the transmission rate, but not on the bandwidth of the probing signal. In addition, our development allows for a variety of different sampling methods. By properly manipulating the low-rate samples, we show that the time delays can be recovered using the well-known ESPRIT algorithm. Combining results from sampling theory with those obtained in the context of direction of arrival estimation methods, we develop necessary and sufficient conditions on the transmitted pulse and the sampling functions in order to ensure perfect recovery of the channel parameters at the minimal possible rate. Our results can be viewed in a broader context, as a sampling theorem for analog signals defined over an infinite union of subspaces

Super-resolution time delay estimation in multipath environments

The problem of super-resolution time delay estimation in multipath environments is addressed in this paper. Two cases, active and passive systems, are considered. The time delay estimation is first converted into a sinusoidal parameter estimation problem. Then the sinusoidal parameters are estimated by generalizing the Multiple Signal Classification (MUSIC) algorithm for single-experiment data. The proposed method, referred to as the MUSIC-type algorithm, approximates the Cramer-Rao bound (CRB) in terms of the mean square errors (MSEs) for different signal-to-noise ratios (SNRs) and separations of muitipath components. Simulation results show that the MUSIC-type algorithm performs better than the classical correlation approach and the conventional MUSIC method for the closely spaced components in muitipath environments.published_or_final_versio

Multipath time-delay estimation via the EM algorithm

We consider the application of the EM algorithm to the multipath time delay estimation problem. The algorithm is developed for the case of deterministic (known) signals, as well as for the case of wide-sense stationary Gaussian signals.Funding was provided by the Naval Underwater Systems Center under contract No. N00014-80-C-0381

Multipath Parameter Estimation from OFDM Signals in Mobile Channels

We study multipath parameter estimation from orthogonal frequency division multiplex signals transmitted over doubly dispersive mobile radio channels. We are interested in cases where the transmission is long enough to suffer time selectivity, but short enough such that the time variation can be accurately modeled as depending only on per-tap linear phase variations due to Doppler effects. We therefore concentrate on the estimation of the complex gain, delay and Doppler offset of each tap of the multipath channel impulse response. We show that the frequency domain channel coefficients for an entire packet can be expressed as the superimposition of two-dimensional complex sinusoids. The maximum likelihood estimate requires solution of a multidimensional non-linear least squares problem, which is computationally infeasible in practice. We therefore propose a low complexity suboptimal solution based on iterative successive and parallel cancellation. First, initial delay/Doppler estimates are obtained via successive cancellation. These estimates are then refined using an iterative parallel cancellation procedure. We demonstrate via Monte Carlo simulations that the root mean squared error statistics of our estimator are very close to the Cramer-Rao lower bound of a single two-dimensional sinusoid in Gaussian noise.Comment: Submitted to IEEE Transactions on Wireless Communications (26 pages, 9 figures and 3 tables

Global Positioning System (GPS) Receiver Design for Multipaths Mitigation

Multipath effects are a source of error degrading the accuracy of DGPS signal processing. The statistical models of multipath are determined by user location and, in addition are time varying. There is no unified statistical model for the multipath signal. Therefore the solution of the multipath problem using statistical models is difficult. This research introduces a new estimator that can detect the presence of multipath, can determine the unknown number of multipath components and can estimate multipath parameters in the GPS receiver (time delay and attenuation coefficients). Furthermore the multipath signal parameters are estimated at any instant of observation. The new estimator is based on maximum likelihood estimation applied to multiple observations of a linear model (regression form) of the received signal. In addition, the estimator is based on a recursive deployment of the multipath time delay. An improvement is achieved to the accuracy of multipath estimates at a low signal-to-noise level by applying Kalman filtering as a cascaded estimator. Kalman filtering application can be considered as an important tool for separating the direct path signal from multipath in noise. This dissertation also includes the design of new modified tracking loops endowed with the mentioned estimator: a modified Phase Lock Loop (PLL) for carrier tracking and a modified Delay Locked-Loop (DLL) in the code tracking. The modified loops can properly track the received direct signal in the presence of multipaths where the standard tracking loops are disabled. Simulations of the standard and the modified loops are presented. Tracking and performance in noise are investigated and a future work is suggested

Receiver-channel based adaptive blind equalization approach for GPS dynamic multipath mitigation

AbstractAiming at mitigating multipath effect in dynamic global positioning system (GPS) satellite navigation applications, an approach based on channel blind equalization and real-time recursive least square (RLS) algorithm is proposed, which is an application of the wireless communication channel equalization theory to GPS receiver tracking loops. The blind equalization mechanism builds upon the detection of the correlation distortion due to multipath channels; therefore an increase in the number of correlator channels is required compared with conventional GPS receivers. An adaptive estimator based on the real-time RLS algorithm is designed for dynamic estimation of multipath channel response. Then, the code and carrier phase receiver tracking errors are compensated by removing the estimated multipath components from the correlators’ outputs. To demonstrate the capabilities of the proposed approach, this technique is integrated into a GPS software receiver connected to a navigation satellite signal simulator, thus simulations under controlled dynamic multipath scenarios can be carried out. Simulation results show that in a dynamic and fairly severe multipath environment, the proposed approach achieves simultaneously instantaneous accurate multipath channel estimation and significant multipath tracking errors reduction in both code delay and carrier phase

Multipath Time-delay Estimation with Impulsive Noise via Bayesian Compressive Sensing

Multipath time-delay estimation is commonly encountered in radar and sonar signal processing. In some real-life environments, impulse noise is ubiquitous and significantly degrades estimation performance. Here, we propose a Bayesian approach to tailor the Bayesian Compressive Sensing (BCS) to mitigate impulsive noises. In particular, a heavy-tail Laplacian distribution is used as a statistical model for impulse noise, while Laplacian prior is used for sparse multipath modeling. The Bayesian learning problem contains hyperparameters learning and parameter estimation, solved under the BCS inference framework. The performance of our proposed method is compared with benchmark methods, including compressive sensing (CS), BCS, and Laplacian-prior BCS (L-BCS). The simulation results show that our proposed method can estimate the multipath parameters more accurately and have a lower root mean squared estimation error (RMSE) in intensely impulsive noise