Direction Of Arrival Estimation Algorithms Based On Sparse Signal Reconstruction

Direction of arrival (DOA) estimation is an important embranchment of array signal processing, and is widely used in radar, sonar and communication systems, etc. However, the conventional subspace based methods used in this field have had a series of drawbacks, for example, these methods can hardly acquire good performance under the condition of low SNR and a small number of snapshots. But compressed sensing (CS) theory offers people a new perspective to comprehend the DOA estimation problem. People try to transform the DOA estimation problem into a sparse signal reconstruction problem, and then solve it by using the methods used to solve the sparse signal reconstruction problem, looking forward to overcoming the drawbacks existing in the coventional subspace based methods. In recent years, with the continuous development of compressed sensing theory, many DOA estimation methods based on the sparse signal reconstruction are proposed by scholars. However, many of these methods also have drawbacks, and need to be improved.Our research also discusses the DOA estimation problem from the view of sparse signal reconstruction. For the narrowband signals, we develop our research from two perspectives of the data domain model and correlation domain model, and propose the corresponding sparse signal construction methods, respectively. For wideband signals, we make use of the joint sparsity of the different narrowband data after the frequency decomposition to derive the corresponding sparse signal construction method. The main content of our research can be presented as follows:1. For the problem that the sparse Bayesian method has low convergence speed, we construct the sparse construction problem whose overcomplete matrix is consisted of the off-grid steering vectors based on the array data model in the data domain. By using the subspace method, we firstly calculate the spectrum of the overcomplete array manifold matrix and obtain the prior vector reflecting the differences between potential signals arriving from different angles, then incorporate this prior vector into the construction of the prior assumption for the hyper parameters of the potential signals under the sparse Bayesian learning framework and finally propose the off-grid weighted sparse Bayesian learning method. Theoretical analysis and simulations both prove that the incorporation of the prior vector strengthens the sparse constraint of the sparse Bayesian learning method for signals, improve the estimation accuracy and reduce the computational load.2. For precisely approximating the steering vector containing the off-grid parameter, we propose a new approximate steering vector based on the first order Taylor expansion of the trigonometric function. Based on this approximate steering vector, we derive the sparse construction problem containing the off-grid parameters, and propose the trigonometric function off-grid sparse Bayesian learning method and off-grid maximum likelihood sparse Bayesian inference method. By comparing our methods with OGSBI-SVD method, we analyze the phenomenon that the performance of OGSBI-SVD method does not become better when the SNR is high and express the possible reasons.3. Aiming at estimating the DOA, we form the sparse construction problem, by transforming the sample covariance matrix into a single measured vector problem, whose equivalent signals are block sparse. Firstly, we utilize the known statistical distribution of the residual error matrix of the array autocorrelation matrix to normalize the noise issue in the single measured vector problem. Then the approximate steering vector containing the off-grid parameter is incorporated into the overcomplete matrix of the single measured vector problem. Finally, we estimate the parameters through the sparse Bayesian learning method using the two stage prior statistical assumption of the signals and propose the block sparse Bayesian learning method. The proposed method does not need to know the number of signals in advance, and improves the estimation performance significantly.4. For the estimation of DOAs of wideband signals, we firstly analyze the WSLIM method to prove that the cost functions used in WSLIM method are just the approximation expressions of the true cost functions, and analyze the reason why the approximation expression are used. Based on the above analysis, we make use of the feature of uncorrelaton between the data in different narrowband frequency bins to build the joint prior probability density function. Based on this joint prior probability density function, we construct the sparse signal construction problem and give the corresponding method to solve it. By assuming the same prior statistical distribution function for the signals in different narrowband frequency bins, the joint sparsity of the data in different frequency bins is fully utilized.