Array communications in wireless sensor networks

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Optimal sensor arrangements in Angle of Arrival (AoA) and range based localization with linear sensor arrays

This paper investigates the linear separation requirements for Angle-of-Arrival (AoA) and range sensors, in order to achieve the optimal performance in estimating the position of a target from multiple and typically noisy sensor measurements. We analyse the sensor-target geometry in terms of the Cramer–Rao inequality and the corresponding Fisher information matrix, in order to characterize localization performance with respect to the linear spatial distribution of sensors. Here in this paper, we consider both fixed and adjustable linear sensor arrays

Sensor Array Processing with Manifold Uncertainty

<p>The spatial spectrum, also known as a field directionality map, is a description of the spatial distribution of energy in a wavefield. By sampling the wavefield at discrete locations in space, an estimate of the spatial spectrum can be derived using basic wave propagation models. The observable data space corresponding to physically realizable source locations for a given array configuration is referred to as the array manifold. In this thesis, array manifold ambiguities for linear arrays of omni-directional sensors in non-dispersive fields are considered. </p><p>First, the problem of underwater a hydrophone array towed behind a maneuvering platform is considered. The array consists of many hydrophones mounted to a flexible cable that is pulled behind a ship. The towed cable will bend or distort as the ship performs maneuvers. The motion of the cable through the turn can be used to resolve ambiguities that are inherent to nominally linear arrays. The first significant contribution is a method to estimate the spatial spectrum using a time-varying array shape in a dynamic field and broadband temporal data. Knowledge of the temporal spectral shape is shown to enhance detection performance. The field is approximated as a sum of uncorrelated planewaves located at uniform locations in angle, forming a gridded map on which a maximum likelihood estimate for broadband source power is derived. Uniform linear arrays also suffer from spatial aliasing when the inter-element spacing exceeds a half-wavelength. Broadband temporal knowledge is shown to significantly reduce aliasing and thus, in simulation, enhance target detection in interference dominated environments. </p><p>As an extension, the problem of towed array shape estimation is considered when the number and location of sources are unknown. A maximum likelihood estimate of the array shape using the field directionality map is derived. An acoustic-based array shape estimate that exploits the full 360$^\circ$ field via field directionality mapping is the second significant contribution. Towed hydrophone arrays have heading sensors in order to estimate array shape, but these sensors can malfunction during sharp turns. An array shape model is described that allows the heading sensor data to be statistically fused with heading sensor. The third significant contribution is method to exploit dynamical motion models for sharp turns for a robust array shape estimate that combines acoustic and heading data. The proposed array shape model works well for both acoustic and heading data and is valid for arbitrary continuous array shapes.</p><p>Finally, the problem of array manifold ambiguities for static under-sampled linear arrays is considered. Under-sampled arrays are non-uniformly sampled with average spacing greater than a half-wavelength. While spatial aliasing only occurs in uniformly sampled arrays with spacing greater than a half-wavelength, under-sampled arrays have increased spatial resolution at the cost of high sidelobes compared to half-wavelength sampled arrays with the same number of sensors. Additionally, non-uniformly sampled arrays suffer from rank deficient array manifolds that cause traditional subspace based techniques to fail. A class of fully agumentable arrays, minimally redundant linear arrays, is considered where the received data statistics of a uniformly spaced array of the same length can be reconstructed in wide sense stationary fields at the cost of increased variance. The forth significant contribution is a reduced rank processing method for fully augmentable arrays to reduce the variance from augmentation with limited snapshots. Array gain for reduced rank adaptive processing with diagonal loading for snapshot deficient scenarios is analytically derived using asymptotic results from random matrix theory for a set ratio of sensors to snapshots. Additionally, the problem of near-field sources is considered and a method to reduce the variance from augmentation is proposed. In simulation, these methods result in significant average and median array gains with limited snapshots.</p>Dissertatio

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

Ultra wideband antenna array processing under spatial aliasing

Given a certain transmission frequency, Shannon spatial sampling limit de¯nes an upper bound for the antenna element spacing. Beyond this bound, the exceeded ambiguity avoids correct estimation of the signal parameters (i.e., array manifold crossing). This spacing limit is inversely proportional to the frequency of transmis- sion. Therefore, to meet a wider spectral support, the element spacing should be decreased. However, practical implementations of closely spaced elements result in a detrimental increase in electromagnetic mutual couplings among the sensors. Further- more, decreasing the spacing reduces the array angle resolution. In this dissertation, the problem of Direction of Arrival (DOA) estimation of broadband sources is ad- dressed when the element spacing of a Uniform Array Antenna (ULA) is inordinate. It is illustrated that one can resolve the aliasing ambiguity by utilizing the frequency diversity of the broadband sources. An algorithm, based on Maximum Likelihood Estimator (MLE), is proposed to estimate the transmitted data signal and the DOA of each source. In the sequel, a subspace-based algorithm is developed and the prob- lem of order estimation is discussed. The adopted signaling framework assumes a subband hopping transmission in order to resolve the problem of source associations and system identi¯cation. The proposed algorithms relax the stringent maximum element-spacing constraint of the arrays pertinent to the upper-bound of frequency transmission and suggest that, under some mild constraints, the element spacing can be conveniently increased. An approximate expression for the estimation error has also been developed to gauge the behavior of the proposed algorithms. Through con- ¯rmatory simulation, it is shown that the performance gain of the proposed setup is potentially signi¯cant, speci¯cally when the transmitters are closely spaced and under low Signal to Noise Ratio (SNR), which makes it applicable to license-free communication

Space-Time Parameter Estimation in Radar Array Processing

This thesis is about estimating parameters using an array of spatially distributed sensors. The material is presented in the context of radar array processing, but the analysis could be of interest in a wide range of applications such as communications, sonar, radio astronomy, seismology, and medical diagnosis. The main theme of the thesis is to analyze the fundamental limitations on estimation performance in sensor array signal processing. To this end, lower bounds on the estimation accuracy as well as the performance of the maximum likelihood (ML) and weighted least-squares (WLS) estimators are studied. The focus in the first part of the thesis is on asymptotic analyses. It deals with the problem of estimating the directions of arrival (DOAs) and Doppler frequencies with a sensor array. This problem can also be viewed as a two-dimensional (2-D) frequency estimation problem. The ML and WLS estimators for this problem amount to multidimensional, highly non-linear optimization problems which would be expensive to solve in real-time in a radar system. Therefore, simplifications of this problem are of great interest. It is shown in this thesis that, under some circumstances, the 2-D problem decouples into 1-D problems. This means a dramatic reduction in computational complexity with insignificant loss of accuracy. The second part contains a performance analysis of the ML DOA estimator under conditions of low signal-to-noise ratio (SNR) and a small number of data samples. It is well known that the ML estimator exhibits a threshold effect, i.e. a rapid deterioration of estimation accuracy below a certain SNR. This effect is caused by outliers and is not captured by standard analysis tools. In this thesis, approximations to the mean square estimation error and probability of outlier are derived that can be used to predict the threshold region performance of the ML estimator with high accuracy. Moreover, these approximations alleviate the need for time-consuming computer simulations when evaluating the ML performance

Space-Time Parameter Estimation in Radar Array Processing

This thesis is about estimating parameters using an array of spatially distributed sensors. The material is presented in the context of radar array processing, but the analysis could be of interest in a wide range of applications such as communications, sonar, radio astronomy, seismology, and medical diagnosis. The main theme of the thesis is to analyze the fundamental limitations on estimation performance in sensor array signal processing. To this end, lower bounds on the estimation accuracy as well as the performance of the maximum likelihood (ML) and weighted least-squares (WLS) estimators are studied. The focus in the first part of the thesis is on asymptotic analyses. It deals with the problem of estimating the directions of arrival (DOAs) and Doppler frequencies with a sensor array. This problem can also be viewed as a two-dimensional (2-D) frequency estimation problem. The ML and WLS estimators for this problem amount to multidimensional, highly non-linear optimization problems which would be expensive to solve in real-time in a radar system. Therefore, simplifications of this problem are of great interest. It is shown in this thesis that, under some circumstances, the 2-D problem decouples into 1-D problems. This means a dramatic reduction in computational complexity with insignificant loss of accuracy. The second part contains a performance analysis of the ML DOA estimator under conditions of low signal-to-noise ratio (SNR) and a small number of data samples. It is well known that the ML estimator exhibits a threshold effect, i.e. a rapid deterioration of estimation accuracy below a certain SNR. This effect is caused by outliers and is not captured by standard analysis tools. In this thesis, approximations to the mean square estimation error and probability of outlier are derived that can be used to predict the threshold region performance of the ML estimator with high accuracy. Moreover, these approximations alleviate the need for time-consuming computer simulations when evaluating the ML performance

Applications of Continuous Spatial Models in Multiple Antenna Signal Processing

This thesis covers the investigation and application of continuous spatial models for multiple antenna signal processing. The use of antenna arrays for advanced sensing and communications systems has been facilitated by the rapid increase in the capabilities of digital signal processing systems. The wireless communications channel will vary across space as different signal paths from the same source combine and interfere. This creates a level of spatial diversity that can be exploited to improve the robustness and overall capacity of the wireless channel. Conventional approaches to using spatial diversity have centered on smart, adaptive antennas and spatial beam forming. Recently, the more general theory of multiple input, multiple output (MIMO) systems has been developed to utilise the independent spatial communication modes offered in a scattering environment. ¶ ..