Research On Direction Of Arrival Estimation Algorithm In The Compressed Sensing Frame

Direction of arrival(DOA)estimation is a crucial segment of the passive direction finding system,which has been widely used in radar,sonar,coordinate detection and communication systems.The conventional DOA estimation algorithms need satisfy Nyquist sampling theorem and the prerequisite for the high direction finding performance is that the direction finding condition is ideal.However,signal bandwidth is wider and wider and the ideal direction finding condition is difficultly guaranteed in the now passive direction finding system,which can lead to huge waste of sources and serious performance degradation of conventional estimation algorithms.Since the source is sparse in the entire spatial domain,the emerging compressed sensing(CS)theory can be applied to DOA estimation,which can comeover the above questions and have some performance advantages.Therefore,in the CS frame,this paper studies DOA estimation algorithms deeply and proposes self-correction algorithms to improve direction finding performance for the DOA estimation problems of DOAs exactly located on the grid,DOAs located on the off-grid and two-dimension,especially in the direction finding environment with low signal to noise ratio(SNR),small number of snapshots and high correlation even coherent sources.The detailed works are described as follows:Firstly,for the DOA problems of DOAs located on the grid,two DOA estimation algorithms in the CS frame are proposed based on the grid.The first one solves the optimization problem by transforming the constrained linear programming into unconstrained convex optimization to overcome the drawback that l1-norm is non-differentiable when minimizing the l1-norm for the sparse reconstruction.Moreover,the proposed algorithm employs the alternate search step to improve the convergence rate and estimation performance and singular value decomposition(SVD)to reduce the computational complexity and sensitively to the noise.The second one proposes the modified covariance matching criterion by using regularization method to add penalties.In this criterion,the proposed algorithm realizes the DOA estimation by the augmented Lagrange method.We theoretically analyze the Cramer-Rao bound(CRB)and performance guarantee condition of the proposed algorithm and give the mathematical expressions.Simulation results verify the direction finding performance of the proposed two algorithms.Secondly,since DOA is random and any incident direction is equal probability,DOA is not on the grid with high probability.Therefore,for the DOA estimation problems of DOAs located on the off-grid and grid error caused by mismatching,two DOA estimation algorithms in the CS frame are proposed based on the off-grid.The first one is real-valued sparse Bayesian off-grid DOA estimation algorithm.The proposed algorithm transforms the complex-valued problem into a real-valued one by a unitary transformation.Then,a real-valued sparse Bayesian model is developed,and in this model,optimize and solve the posterior density function to estimate DOA based on prior information.The convergence rate and convergence stability is guaranteed in the iterative process.Meanwhile,we optimize this algorithm and analyze the unique convergence and complexity of this algorithm.The second one solves the mixed k-l norm minimization problem to reconstruct the sparse source and estimate the grid error.Since joint estimation will lead to a nonconvex optimization problem,the proposed algorithm uses an alternate iterative process,so that the intractable nonconvex optimization problem is transformed into the tractable convex optimization problem.To achieve better reconstruction properties,the block sparse source is exploited instead of conventional sparse source.The block is updated by the proposed block selection criterion,which can improve efficiency of the proposed algorithm.In addition,a detailed derivation process of proving the global convergence of the proposed algorithm is given.The direction finding performance of the proposed two algorithms is verified by simulation results.Finally,for the DOA estimation problems of two-dimension,one two-dimensional DOA estimation algorithm is proposed in the CS frame.The proposed algorithm separates the steering vector into two parts to construct two corresponding noise subspaces by introducing electric angles.Based on the constructed noise subspaces,electric angles are estimated by the proposed method.In terms of estimates of electric angles,arc-tangent functions are exploited to realize two-dimensional DOA estimation.Simulation results verify the direction finding performance of the proposed algorithm and prove that on estimation failure occurs for the entire spatial domain with the proposed algorithm.