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

Innovation Rate Sampling of Pulse Streams with Application to Ultrasound Imaging

Signals comprised of a stream of short pulses appear in many applications including bio-imaging and radar. The recent finite rate of innovation framework, has paved the way to low rate sampling of such pulses by noticing that only a small number of parameters per unit time are needed to fully describe these signals. Unfortunately, for high rates of innovation, existing sampling schemes are numerically unstable. In this paper we propose a general sampling approach which leads to stable recovery even in the presence of many pulses. We begin by deriving a condition on the sampling kernel which allows perfect reconstruction of periodic streams from the minimal number of samples. We then design a compactly supported class of filters, satisfying this condition. The periodic solution is extended to finite and infinite streams, and is shown to be numerically stable even for a large number of pulses. High noise robustness is also demonstrated when the delays are sufficiently separated. Finally, we process ultrasound imaging data using our techniques, and show that substantial rate reduction with respect to traditional ultrasound sampling schemes can be achieved.Comment: 14 pages, 13 figure

Estimation of Sparse MIMO Channels with Common Support

We consider the problem of estimating sparse communication channels in the MIMO context. In small to medium bandwidth communications, as in the current standards for OFDM and CDMA communication systems (with bandwidth up to 20 MHz), such channels are individually sparse and at the same time share a common support set. Since the underlying physical channels are inherently continuous-time, we propose a parametric sparse estimation technique based on finite rate of innovation (FRI) principles. Parametric estimation is especially relevant to MIMO communications as it allows for a robust estimation and concise description of the channels. The core of the algorithm is a generalization of conventional spectral estimation methods to multiple input signals with common support. We show the application of our technique for channel estimation in OFDM (uniformly/contiguous DFT pilots) and CDMA downlink (Walsh-Hadamard coded schemes). In the presence of additive white Gaussian noise, theoretical lower bounds on the estimation of SCS channel parameters in Rayleigh fading conditions are derived. Finally, an analytical spatial channel model is derived, and simulations on this model in the OFDM setting show the symbol error rate (SER) is reduced by a factor 2 (0 dB of SNR) to 5 (high SNR) compared to standard non-parametric methods - e.g. lowpass interpolation.Comment: 12 pages / 7 figures. Submitted to IEEE Transactions on Communicatio

Pilot allocation based on simulated annealing for sparse channel estimation in UWB OFDM systems

In ultra wideband (UWB) orthogonal frequency-division multiplexing (OFDM) systems, compressive sensing (CS) is often employed to produce a pilot-assisted estimate of the sparse channel. The corresponding estimation performance depends to a large extent on the considered pilot allocation (PA) method, i.e., the way to select which OFDM subcarriers are best used to transmit the pilot symbols. The development of good practical PA methods has recently received a lot of attention in the scientific literature. The main challenge is to provide an attractive trade-off between the complexity of the PA method and the achieved channel estimation performance (and by extension the achieved bit error rate). In this paper, we propose a novel PA method based on simulated annealing (SA). Simulations are conducted to confirm the validity of our approach. Compared to the state-of-the-art method, the proposed PA method is shown to achieve better performance with a lower complexity

Sparse sampling of signal innovations

Sparse sampling of continuous-time sparse signals is addressed. In particular, it is shown that sampling at the rate of innovation is possible, in some sense applying Occam's razor to the sampling of sparse signals. The noisy case is analyzed and solved, proposing methods reaching the optimal performance given by the Cramer-Rao bounds. Finally, a number of applications have been discussed where sparsity can be taken advantage of. The comprehensive coverage given in this article should lead to further research in sparse sampling, as well as new applications. One main application to use the theory presented in this article is ultra-wide band (UWB) communications

Ultra-Wideband Relay Communication Systems

Impulse-radio ultra-wide-band (IR-UWB) signaling is a promising technique for high-speed, short-range relay communications networks. Depending on how the relay node retransmits the signal, there are two main relay schemes: conventional one-directional (one-way) relay model, and bi-directional (two-way) relay model. In bi-directional relay communications, wireless network coding (WNC), also called physical-layer network coding (PNC), could be applied to overcome the spectral efficiency limitation of the conventional one-way relay. In the first part of this work, we propose asynchronous, differential, and bidirectional decode and forward (ADBDF) and asynchronous, differential, and bidirectional denoise and forward (ADBDNF) UWB relay methods, where the relay node (RN) does not need to be synchronized with the end nodes (ENs). The proposed schemes are attractive for networks in which stringent/complicated synchronization between the RN and the ENs may not be feasible. The second part of this work focuses on UWB channel classification. We propose a 2-dimensional (2-D) LOS/NLOS classification scheme that uses skewness of the channel impulse/pulse response. The proposed channel classification decreases the complexity of existing channel classification methods and can be used in a variety of areas such as localization, relay communications, and cooperative communications. The final part of this work deals with compressive sensing (CS) algorithms that employ sub-Nyquist sampling for UWB communications. We develop coarse graining (CG) for the proposed CS sub-Nyquist sampling technique, which leads to: (1) reduced sampling rate at the receiver, and hence reduced use of analog-to-digital converters (ADCs) resources; and (2) low-complexity channel estimation

Source localization via time difference of arrival

Accurate localization of a signal source, based on the signals collected by a number of receiving sensors deployed in the source surrounding area is a problem of interest in various fields. This dissertation aims at exploring different techniques to improve the localization accuracy of non-cooperative sources, i.e., sources for which the specific transmitted symbols and the time of the transmitted signal are unknown to the receiving sensors. With the localization of non-cooperative sources, time difference of arrival (TDOA) of the signals received at pairs of sensors is typically employed. A two-stage localization method in multipath environments is proposed. During the first stage, TDOA of the signals received at pairs of sensors is estimated. In the second stage, the actual location is computed from the TDOA estimates. This later stage is referred to as hyperbolic localization and it generally involves a non-convex optimization. For the first stage, a TDOA estimation method that exploits the sparsity of multipath channels is proposed. This is formulated as an f1-regularization problem, where the f1-norm is used as channel sparsity constraint. For the second stage, three methods are proposed to offer high accuracy at different computational costs. The first method takes a semi-definite relaxation (SDR) approach to relax the hyperbolic localization to a convex optimization. The second method follows a linearized formulation of the problem and seeks a biased estimate of improved accuracy. A third method is proposed to exploit the source sparsity. With this, the hyperbolic localization is formulated as an an f1-regularization problem, where the f1-norm is used as source sparsity constraint. The proposed methods compare favorably to other existing methods, each of them having its own advantages. The SDR method has the advantage of simplicity and low computational cost. The second method may perform better than the SDR approach in some situations, but at the price of higher computational cost. The l1-regularization may outperform the first two methods, but is sensitive to the choice of a regularization parameter. The proposed two-stage localization approach is shown to deliver higher accuracy and robustness to noise, compared to existing TDOA localization methods. A single-stage source localization method is explored. The approach is coherent in the sense that, in addition to the TDOA information, it utilizes the relative carrier phases of the received signals among pairs of sensors. A location estimator is constructed based on a maximum likelihood metric. The potential of accuracy improvement by the coherent approach is shown through the Cramer Rao lower bound (CRB). However, the technique has to contend with high peak sidelobes in the localization metric, especially at low signal-to-noise ratio (SNR). Employing a small antenna array at each sensor is shown to lower the sidelobes level in the localization metric. Finally, the performance of time delay and amplitude estimation from samples of the received signal taken at rates lower than the conventional Nyquist rate is evaluated. To this end, a CRB is developed and its variation with system parameters is analyzed. It is shown that while with noiseless low rate sampling there is no estimation accuracy loss compared to Nyquist sampling, in the presence of additive noise the performance degrades significantly. However, increasing the low sampling rate by a small factor leads to significant performance improvement, especially for time delay estimation

Finite Rate of Innovation sampling techniques for embedded UWB devices.

This report studies the applicability of Finite Rate of Innovation (FRI) algorithms to UltraWide Band (UWB) communications, more precisely in the scope of Low Power Body Area Networks (LP-BAN ). Three main issues are studied and given proposed solutions. First, the classical FRI algorithm is modified to accomodate different symmetrical pulse shapes. Such a modification – necessary to get acceptable performances – is done by a simple equalization. Second, LP-BAN devices limitations such as drift, jitter and aggressive quantization are blended in the algorithm. It is done by adjusting the equalization template and development of a suited quantization algorithm. Third and last, the cost of FRI denoising procedure (Cadzow denoising) is greatly reduced to fit the requirements of a low power embedded device. It is centered on performing most of the computations in a low-dimension Krylov subspace of the matrix to be denoised. The particular structure of the projected matrix enables selective computation of the eigenpairs. The result is an algorithm able to resolve close paths within a reasonnable computational budget. Some issues remain on quantization

Receiver design and performance analysis for code-multiplexed transmitted-reference ultra-wideband systems

Ankara : The Department of Electrical and Electronics Engineering and the Institute of Engineering and Sciences of Bilkent University, 2010.Thesis (Master's) -- Bilkent University, 2010.Includes bibliographical references leaves 70-74.In transmitted-reference (TR) and frequency-shifted reference (FSR) ultrawideband (UWB) systems, data and reference signals are shifted relative to each other in time and frequency domains, respectively. The main advantage of these systems is that they remove strict requirements of channel estimation. In order to implement TR UWB systems, an analog delay line, which is difficult to build in an integrated fashion, is needed. Although FSR systems require frequency conversion at the receiver, which is much simpler in practice, they have data rate limitations. Instead, a code-multiplexed transmitted-reference (CM-TR) UWB system that transmits data and reference signals using two distinct orthogonal codes can be considered. This system requires a simpler receiver and has better performance than TR and FSR. In the first part of the thesis, CM-TR systems are investigated and probability of error expressions are obtained. For the single user case, a closed-form expression for the exact probability of error is derived. For the multiuser case, a closed-form expression is derived based on the Gaussian approximation, and the results are compared in different scenarios. In the second part of the thesis, some optimal and suboptimal receivers are studied. First, low complexity receivers, such as the blinking receiver (BR) and the chip discriminator, are presented. The requirements for these types of receivers are explained, and the conditions under which their performance can be improved are discussed. Then, an analytical analysis of the linear minimum mean-squared error (MMSE) receiver and the requirements to implement this MMSE receiver are provided. Lastly, the optimal maximum-likelihood (ML) detector is derived, which has higher computational complexity and more strict requirements than the other receivers. Finally, simulation results are presented in order to verify the theoretical results and to compare the performance of the receivers.Tutay, Mehmet EminM.S