Direction Of Arrival Estimation Algorithms For Array Signals Based On Sparse Signal Reconstruction

Direction of Arrival (DOA) estimation is one of the most important issues in the array signal processing, not only giving the spatial positioning of the target, and also providing the technical support for the signal enhancement in receiving; hence it has a wide range of applications in radar, sonar, communication, and meeting systems. Continuous development of compressed sensing (CS) theory in recent years prompts the researchers to re-examine the DOA estimation problem and solve it via the perspective of sparse signal reconstruction, expecting to circumvent those existing problems in the conventional subspace-based methods. Correspondingly, a series of DOA estimation methods based on sparse signal reconstruction are emerging nowadays.In order to go through the common ideas of DOA estimation based on sparse signal reconstruction, addressing two different objects of narrowband signals and wideband signals, respectively, our research is developed from the two perspectives of sparse representation of array data and second-order statistics. The main purpose of this dissertation is to provide the common solving ideas of DOA estimation via sparse signal reconstruction for various scenarios, in the meanwhile of proposing a series of sparse signal reconstruction based DOA estimation algorithms (mainly based on Basis Pursuit (BP) method). The main contributions and innovative points of this dissertation are listed as follows:1. Most of the DOA estimation methods for narrowband signals can be attributed to solving a subspace matching problem with the corresponding weighting matrices. We study the weighted subspace matching (WSF) problem with the optimal weighting matrix, and transform it into a sparse signal reconstruction problem with multiple measurement vectors (MMV). By building the upper bound of the residual error constraint of reconstruction according to its statistical property, the DOAs are estimated via solving the constructed BP optimization problem. Theory and simulation experiments prove that the proposed algorithm can not only directly deal with the scenario of coherent signals, but also improve the estimation performance in low signal-to-noise ratio (SNR).2. We transform the vectorized covariance matrix of narrowband array signals into the sparse representation of a single measurement vector (SMV), and according to the statistical property of the sample covariance matrix, we address the upper bounds of sparsity constraint and residual error constraint, respectively, to build two BP problems which are solved to derive the DOA estimation. The proposed algorithms have a great complexity reduction compared with other DOA estimation algorithms based on sparse signal reconstruction of MMV, and do not require knowing the source number as the precondition of estimating the spatial spectrum. In particular, for the particular application scenario of sparse arrays, the proposed algorithms directly illustrate the aperture extension capacity of the sparse array, and do not require the construction of augmented covariance matrix for DOA estimation.3. Based on interpolating the wideband signals using the prolate spheroidal wave functions (PSWFs), we consider the way of directly processing the array sampling data of wideband signals, and reveal that the DOA estimation problem in this scenario in fact corresponds to a block sparse signal reconstruction problem, which is solvable by many prevalent methods addressing this block-style problem. Compared with the conventional way of dividing the wideband data into several narrow subbands through narrow-band filters and applying joint sparse signal reconstruction methods, the proposed algorithms improves the DOA estimation performance when the number of samples are highly limited.4. Considering the model of wideband DOA estimation by frequency decomposition, based on the homotopy transform idea in solving BP problem, we simultaneously take advantage of the joint sparsity feature in and among different subbands, to iteratively update the sparse support set in solving the wideband WSF problem for DOA estimation. The proposed algorithm can be directly applied to the scenario of coherent signals, and do not need the procedure of focusing and preliminary angle estimation.5. Referring to the Spatial-only model, we extract the elements of the spatial covariance matrix of wideband array output samples to form a vector, which can be expressed by the sparse representation. According to the particular feature that the diagonal elements of the spatial covariance matrix of wideband samples are equivalent to the sum of variances of the noise and all the signals, we construct a BP problem which is solved for DOA estimation. The proposed algorithm, compared with the conventional wideband DOA estimation algorithms, gives better performances especially when the number of samples is small. This algorithm also avoids the problems existing in those algorithms based on the Spatial-only model, such as high computational complexity, low degree of freedom and weak resolution capacity.