Direction of Arrival Estimation and Tracking with Sparse Arrays

Direction of Arrival (DOA) estimation and tracking of a plane wave or multiple plane waves impinging on an array of sensors from noisy data are two of the most important tasks in array signal processing, which have attracted tremendous research interest over the past several decades. It is well-known that the estimation accuracy, angular resolution, tracking capacity, computational complexity, and hardware implementation cost of a DOA estimation and/or tracking technique depend largely on the array geometry. Large arrays with many sensors provide accurate DOA estimation and perfect target tracking, but they usually suffer from a high cost for hardware implementation. Sparse arrays can yield similar DOA estimates and tracking performance with fewer elements for the same-size array aperture as compared to the traditional uniform arrays. In addition, the signals of interest may have rich temporal information that can be exploited to effectively eliminate background noise and significantly improve the performance and capacity of DOA estimation and tracking, and/or even dramatically reduce the computational burden of estimation and tracking algorithms. Therefore, this thesis aims to provide some solutions to improving the DOA estimation and tracking performance by designing sparse arrays and exploiting prior knowledge of the incident signals such as AR modeled sources and known waveforms. First, we design two sparse linear arrays to efficiently extend the array aperture and improve the DOA estimation performance. One scheme is called minimum redundancy sparse subarrays (MRSSA), where the subarrays are used to obtain an extended correlation matrix according to the principle of minimum redundancy linear array (MRLA). The other linear array is constructed using two sparse ULAs, where the inter-sensor spacing within the same ULA is much larger than half wavelength. Moreover, we propose a 2-D DOA estimation method based on sparse L-shaped arrays, where the signal subspace is selected from the noise-free correlation matrix without requiring the eigen-decomposition to estimate the elevation angle, while the azimuth angles are estimated based on the modified total least squares (TLS) technique. Second, we develop two DOA estimation and tracking methods for autoregressive (AR) modeled signal source using sparse linear arrays together with Kalman filter and LS-based techniques. The proposed methods consist of two common stages: in the first stage, the sources modeled by AR processes are estimated by the celebrated Kalman filter and in the second stage, the efficient LS or TLS techniques are employed to estimate the DOAs and AR coefficients simultaneously. The AR-modeled sources can provide useful temporal information to handle cases such as the ones, where the number of sources is larger than the number of antennas. In the first method, we exploit the symmetric array to transfer a complex-valued nonlinear problem to a real-valued linear one, which can reduce the computational complexity, while in the second method, we use the ordinary sparse arrays to provide a more accurate DOA estimation. Finally, we study the problem of estimating and tracking the direction of arrivals (DOAs) of multiple moving targets with known signal source waveforms and unknown gains in the presence of Gaussian noise using a sparse sensor array. The core idea is to consider the output of each sensor as a linear regression model, each of whose coefficients contains a pair of DOAs and gain information corresponding to one target. These coefficients are determined by solving a linear least squares problem and then updating recursively, based on a block QR decomposition recursive least squares (QRD-RLS) technique or a block regularized LS technique. It is shown that the coefficients from different sensors have the same amplitude, but variable phase information for the same signal. Then, simple algebraic manipulations and the well-known generalized least squares (GLS) are used to obtain an asymptotically-optimal DOA estimate without requiring a search over a large region of the parameter space

Space-time processing for wireless mobile communications

Intersymbol interference (ISI) and co-channel interference (CCI) are two major obstacles to high speed data transmission in wireless cellular communications systems. Unlike thermal noise, their effects cannot be removed by increasing the signal power and are time-varying due to the relative motion between the transmitters and receivers. Space-time processing offers a signal processing framework to optimally integrate the spatial and temporal properties of the signal for maximal signal reception and at the same time, mitigate the ISI and CCI impairments. In this thesis, we focus on the development of this emerging technology to combat the undesirable effects of ISI and CCL We first develop a convenient mathematical model to parameterize the space-time multipath channel based on signal path power, directions and times of arrival. Starting from the continuous time-domain, we derive compact expressions of the vector space-time channel model that lead to the notion of block space-time manifold, Under certain identifiability conditions, the noiseless vector-channel outputs will lie on a subspace constructed from a set. of basis belonging to the block space-time manifold. This is an important observation as many high resolution array processing algorithms Can be applied directly to estimate the multi path channel parameters. Next we focus on the development of semi-blind channel identification and equalization algorithms for fast time-varying multi path channels. Specifically. we develop space-time processing algorithms for wireless TDMA networks that use short burst data formats with extremely short training data. sequences. Due to the latter, the estimated channel parameters are extremely unreliable for equalization with conventional adaptive methods. We approach the channel acquisition, tracking and equalization problems jointly, and exploit the richness of the inherent structural relationship between the channel parameters and the data sequence by repeated use of available data through a forward- backward optimization procedure. This enables the fuller exploitation of the available data. Our simulation studies show that significant performance gains are achieved over conventional methods. In the final part of this thesis, we address the problem identifying and equalizing multi path communication channels in the presence of strong CCl. By considering CCI as stochasic processes, we find that temporal diversity can be gained by observing the channel outputs from a tapped delay line. Together with the assertion that the finite alphabet property of the information sequences can offer additional information about the channel parameters and the noise-plus-covariance matrix, we develop a spatial temporal algorithm, iterative reweighting alternating minimization, to estimate the channel parameters and information sequence in a weighted least squares framework. The proposed algorithm is robust as it does not require knowledge of the number of CCI nor their structural information. Simulation studies demonstrate its efficacy over many reported methods

Fundamental Limits of Wideband Localization - Part II: Cooperative Networks

The availability of positional information is of great importance in many commercial, governmental, and military applications. Localization is commonly accomplished through the use of radio communication between mobile devices (agents) and fixed infrastructure (anchors). However, precise determination of agent positions is a challenging task, especially in harsh environments due to radio blockage or limited anchor deployment. In these situations, cooperation among agents can significantly improve localization accuracy and reduce localization outage probabilities. A general framework of analyzing the fundamental limits of wideband localization has been developed in Part I of the paper. Here, we build on this framework and establish the fundamental limits of wideband cooperative location-aware networks. Our analysis is based on the waveforms received at the nodes, in conjunction with Fisher information inequality. We provide a geometrical interpretation of equivalent Fisher information for cooperative networks. This approach allows us to succinctly derive fundamental performance limits and their scaling behaviors, and to treat anchors and agents in a unified way from the perspective of localization accuracy. Our results yield important insights into how and when cooperation is beneficial.Comment: To appear in IEEE Transactions on Information Theor

DOA estimation with known waveforms in the presence of unknown time delays and Doppler shifts

A novel DOA estimation method for known waveform sources with different unknown time delays and Doppler shifts is proposed. Based on the idea of maximum likelihood and the matrix projection theory, a decoupled cost function is first constructed and then the problem of estimating time delay and Doppler shift is transformed into a nonlinear least squares (NLS) problem. To solve the NLS problem efficiently without multidimensional search, a Toeplitz dominant rule is established to perform initial estimates with a reduced dimension. Finally, with the aid of time delay and Doppler shift estimates, DOAs and complex amplitudes of the incoming signals are obtained. Simulation results show that the proposed method can achieve a performance close to CRB at high SNR and with a large number of snapshots

Signal Subspace Processing in the Beam Space of a True Time Delay Beamformer Bank

A number of techniques for Radio Frequency (RF) source location for wide bandwidth signals have been described that utilize coherent signal subspace processing, but often suffer from limitations such as the requirement for preliminary source location estimation, the need to apply the technique iteratively, computational expense or others. This dissertation examines a method that performs subspace processing of the data from a bank of true time delay beamformers. The spatial diversity of the beamformer bank alleviates the need for a preliminary estimate while simultaneously reducing the dimensionality of subsequent signal subspace processing resulting in computational efficiency. The pointing direction of the true time delay beams is independent of frequency, which results in a mapping from element space to beam space that is wide bandwidth in nature. This dissertation reviews previous methods, introduces the present method, presents simulation results that demonstrate the assertions, discusses an analysis of performance in relation to the Cramer-Rao Lower Bound (CRLB) with various levels of noise in the system, and discusses computational efficiency. One limitation of the method is that in practice it may be appropriate for systems that can tolerate a limited field of view. The application of Electronic Intelligence is one such application. This application is discussed as one that is appropriate for a method exhibiting high resolution of very wide bandwidth closely spaced sources and often does not require a wide field of view. In relation to system applications, this dissertation also discusses practical employment of the novel method in terms of antenna elements, arrays, platforms, engagement geometries, and other parameters. The true time delay beam space method is shown through modeling and simulation to be capable of resolving closely spaced very wideband sources over a relevant field of view in a single algorithmic pass, requiring no course preliminary estimation, and exhibiting low computational expense superior to many previous wideband coherent integration techniques

Signal Subspace Processing in the Beam Space of a True Time Delay Beamformer Bank

A number of techniques for Radio Frequency (RF) source location for wide bandwidth signals have been described that utilize coherent signal subspace processing, but often suffer from limitations such as the requirement for preliminary source location estimation, the need to apply the technique iteratively, computational expense or others. This dissertation examines a method that performs subspace processing of the data from a bank of true time delay beamformers. The spatial diversity of the beamformer bank alleviates the need for a preliminary estimate while simultaneously reducing the dimensionality of subsequent signal subspace processing resulting in computational efficiency. The pointing direction of the true time delay beams is independent of frequency, which results in a mapping from element space to beam space that is wide bandwidth in nature. This dissertation reviews previous methods, introduces the present method, presents simulation results that demonstrate the assertions, discusses an analysis of performance in relation to the Cramer-Rao Lower Bound (CRLB) with various levels of noise in the system, and discusses computational efficiency. One limitation of the method is that in practice it may be appropriate for systems that can tolerate a limited field of view. The application of Electronic Intelligence is one such application. This application is discussed as one that is appropriate for a method exhibiting high resolution of very wide bandwidth closely spaced sources and often does not require a wide field of view. In relation to system applications, this dissertation also discusses practical employment of the novel method in terms of antenna elements, arrays, platforms, engagement geometries, and other parameters. The true time delay beam space method is shown through modeling and simulation to be capable of resolving closely spaced very wideband sources over a relevant field of view in a single algorithmic pass, requiring no course preliminary estimation, and exhibiting low computational expense superior to many previous wideband coherent integration techniques

Indoor Positioning Using Acoustic Pseudo-Noise Based Time Difference of Arrival

The Global Positioning System (GPS) provides good precision on a global scale, but is not suitable for indoor applications. Indoor positioning systems (IPS) aim to provide high precision position information in an indoor environment. IPS has huge market opportunity with a growing number of commercial and consumer applications especially as Internet of Things (IoT) develops. This paper studies an IPS approach using audible sound and pseudo-noise (PN) based time difference of arrival (TDoA). The system’s infrastructure consists of synchronized speakers. The object to be located, or receiver, extracts TDoA information and uses multilateration to calculate its position. The proposed IPS utilizes sound waves since they travel much slower compared to electromagnetic waves, allowing for easier measurements. Additionally, the audible spectrum has a large availability of low directivity speakers and microphones allowing for a large coverage area compared to highly directive ultrasonic transceivers. This paper experimentally evaluates the feasibility of the proposed IPS

Experimental results of underwater cooperative source localization using a single acoustic vector sensor

This paper aims at estimating the azimuth, range and depth of a cooperative broadband acoustic source with a single vector sensor in a multipath underwater environment, where the received signal is assumed to be a linear combination of echoes of the source emitted waveform. A vector sensor is a device that measures the scalar acoustic pressure field and the vectorial acoustic particle velocity field at a single location in space. The amplitudes of the echoes in the vector sensor components allow one to determine their azimuth and elevation. Assuming that the environmental conditions of the channel are known, source range and depth are obtained from the estimates of elevation and relative time delays of the different echoes using a ray-based backpropagation algorithm. The proposed method is tested using simulated data and is further applied to experimental data from the Makai’05 experiment, where 8–14 kHz chirp signals were acquired by a vector sensor array. It is shown that for short ranges, the position of the source is estimated in agreement with the geometry of the experiment. The method is low computational demanding, thus well-suited to be used in mobile and light platforms, where space and power requirements are limited