The influence of random element displacement on DOA estimates obtained with (Khatri-Rao-)root-MUSIC

Although a wide range of direction of arrival (DOA) estimation algorithms has been described for a diverse range of array configurations, no specific stochastic analysis framework has been established to assess the probability density function of the error on DOA estimates due to random errors in the array geometry. Therefore, we propose a stochastic collocation method that relies on a generalized polynomial chaos expansion to connect the statistical distribution of random position errors to the resulting distribution of the DOA estimates. We apply this technique to the conventional root-MUSIC and the Khatri-Rao-root-MUSIC methods. According to Monte-Carlo simulations, this novel approach yields a speedup by a factor of more than 100 in terms of CPU-time for a one-dimensional case and by a factor of 56 for a two-dimensional case

Multi-source parameter estimation and tracking using antenna arrays

This thesis is concerned with multi-source parameter estimation and tracking using antenna arrays in wireless communications. Various multi-source parameter estimation and tracking algorithms are presented and evaluated. Firstly, a novel multiple-input multiple-output (MIMO) communication system is proposed for multi-parameter channel estimation. A manifold extender is presented for increasing the degrees of freedom (DoF). The proposed approach utilises the extended manifold vectors together with superresolution subspace type algorithms, to achieve the estimation of delay, direction of departure (DOD) and direction of arrival (DOA) of all the paths of the desired user in the presence of multiple access interference (MAI). Secondly, the MIMO system is extended to a virtual-spatiotemporal system by incorporating the temporal domain of the system towards the objective of further increasing the degrees of freedom. In this system, a multi-parameter es- timation of delay, Doppler frequency, DOD and DOA of the desired user, and a beamformer that suppresses the MAI are presented, by utilising the proposed virtual-spatiotemporal manifold extender and the superresolution subspace type algorithms. Finally, for multi-source tracking, two tracking approaches are proposed based on an arrayed Extended Kalman Filter (arrayed-EKF) and an arrayed Unscented Kalman Filter (arrayed-UKF) using two type of antenna arrays: rigid array and flexible array. If the array is rigid, the proposed approaches employ a spatiotemporal state-space model and a manifold extender to track the source parameters, while if it is flexible the array locations are also tracked simultaneously. Throughout the thesis, computer simulation studies are presented to investigate and evaluate the performance of all the proposed algorithms.Open Acces

Augmented Multi-Subarray Dilated Nested Array with Enhanced Degrees of Freedom and Reduced Mutual Coupling

Sparse linear arrays (SLAs) can be designed in a systematic way, with the ability for underdetermined DOA estimation where a greater number of sources can be detected than that of sensors. In this paper, as the first stage, a new systematic design named multi-subarray dilated nested array (MDNA), whose difference co-array (DCA) can be proved to be hole-free, is firstly proposed by introducing a sparse ULA and multiple identical dense ULAs with appropriate sub-ULA spacings. The MDNA will degenerate into the nested array under specific conditions, and the uniform degrees of freedom (uDOFs) of MDNA is larger than that of its parent nested array. On the basis of MDNA, to reduce the mutual coupling effect, an augmented multi-subarray dilated nested array (AMDNA) is constructed by migrating some elements of the dense segments of MDNA, without reducing the number of uDOFs. Several theoretical properties of the proposed array structures are proved, and simulation results are provided to demonstrate the effectiveness and superiority of the proposed AMDNA over some existing sparse arrays

Statistical Performance Analysis of Sparse Linear Arrays

Direction-of-arrival (DOA) estimation remains an important topic in array signal processing. With uniform linear arrays (ULAs), traditional subspace-based methods can resolve only up to M-1 sources using M sensors. On the other hand, by exploiting their so-called difference coarray model, sparse linear arrays, such as co-prime and nested arrays, can resolve up to O(M^2) sources using only O(M) sensors. Various new sparse linear array geometries were proposed and many direction-finding algorithms were developed based on sparse linear arrays. However, the statistical performance of such arrays has not been analytically conducted. In this dissertation, we (i) study the asymptotic performance of the MUtiple SIgnal Classification (MUSIC) algorithm utilizing sparse linear arrays, (ii) derive and analyze performance bounds for sparse linear arrays, and (iii) investigate the robustness of sparse linear arrays in the presence of array imperfections. Based on our analytical results, we also propose robust direction-finding algorithms for use when data are missing. We begin by analyzing the performance of two commonly used coarray-based MUSIC direction estimators. Because the coarray model is used, classical derivations no longer apply. By using an alternative eigenvector perturbation analysis approach, we derive a closed-form expression of the asymptotic mean-squared error (MSE) of both estimators. Our expression is computationally efficient compared with the alternative of Monte Carlo simulations. Using this expression, we show that when the source number exceeds the sensor number, the MSE remains strictly positive as the signal-to-noise ratio (SNR) approaches infinity. This finding theoretically explains the unusual saturation behavior of coarray-based MUSIC estimators that had been observed in previous studies. We next derive and analyze the Cramér-Rao bound (CRB) for general sparse linear arrays under the assumption that the sources are uncorrelated. We show that, unlike the classical stochastic CRB, our CRB is applicable even if there are more sources than the number of sensors. We also show that, in such a case, this CRB remains strictly positive definite as the SNR approaches infinity. This unusual behavior imposes a strict lower bound on the variance of unbiased DOA estimators in the underdetermined case. We establish the connection between our CRB and the classical stochastic CRB and show that they are asymptotically equal when the sources are uncorrelated and the SNR is sufficiently high. We investigate the behavior of our CRB for co-prime and nested arrays with a large number of sensors, characterizing the trade-off between the number of spatial samples and the number of temporal samples. Our analytical results on the CRB will benefit future research on optimal sparse array designs. We further analyze the performance of sparse linear arrays by considering sensor location errors. We first introduce the deterministic error model. Based on this model, we derive a closed-form expression of the asymptotic MSE of a commonly used coarray-based MUSIC estimator, the spatial-smoothing based MUSIC (SS-MUSIC). We show that deterministic sensor location errors introduce a constant estimation bias that cannot be mitigated by only increasing the SNR. Our analytical expression also provides a sensitivity measure against sensor location errors for sparse linear arrays. We next extend our derivations to the stochastic error model and analyze the Gaussian case. We also derive the CRB for joint estimation of DOA parameters and deterministic sensor location errors. We show that this CRB is applicable even if there are more sources than the number of sensors. Lastly, we develop robust DOA estimators for cases with missing data. By exploiting the difference coarray structure, we introduce three algorithms to construct an augmented covariance matrix with enhanced degrees of freedom. By applying MUSIC to this augmented covariance matrix, we are able to resolve more sources than sensors. Our method utilizes information from all snapshots and shows improved estimation performance over traditional DOA estimators