DOA Estimation Through Bayesian Compressive Sensing Algorithm

As one of the important research directions in array signal processing field,DOA (Direction of Arrival) estimation is widely applicated in military-and nationalcivil-area. However, conventional DOA estimation methods require a-prioriknowledge on the number of incident signals and sampling data with a great deal ofsnapshots, which is difficult to carry out in the practical application environment.The estimation precision of conventional methods decreases quickly and evenbecomes invalid completely where highly correlated or coherent sources arepresented. Bayesian Compressive Sensing (BCS) offers a new solution to estimateDOA of array signals, which breaks through the bottleneck on Nyquist rate, andimplements inference of signal reconstruction from a Bayesian statisticalperspective. To overcome the drawbacks of conventional strategies, DOAestimation formulated within the BCS framework is presented and discussed mainlyin this paper.Combined with DOA estimation model of narrow-band far-field signals, twodifferent DOA estimation models are established. The former is concerned withsingle snapshot to ennable the real-time estimation, while the latter, is focussed onprocessing over multiple snapshots to give high-resolution estimations. To aim atreducing computational complexity, a fast algorithm is presented hereafter.Furthermore, the noise parameter is a nuisance parameter with an identifiabilityissue, whose value may contaminate algorithm. To overcome the drawback andimprove robustness to the parameter setting over the original BCS, a modified BCSalgorithm is demonstrated in the paper. Based on this, the conventional DOAestimation algorithm, i.e., MUSIC, the common compressive sensing algorithm, i.e.,Orthogonal Matching Pursuit (OMP) and BCS theory are compared togetherthrough the following respects: signal to noise rate (SNR), incident signal spacing,elements number, snapshots， coherent sources estimation and computationalcomplexity.Last of all, in view of the sparsity of source signals and the priori on thehyperparameter, two different improved algorithms are proposed respectively:(1)Modified Algorithm by Using Uniform Sine Grid Division (BCS-sin), the conclusion that BCS-sin has better mutual incoherence property (MIP) than thetraditional process that the array manifold matrix obtained by using uniform anglegrid division is proved through theoretical analysis.(2) DOA estimation based onBCS using Laplace priori (Lap-BCS), single snapshot and multiple snapshotsestimation models based on Lap-BCS algorithm are formulated respectively. On thebasis, the effectiveness of the two proposed approaches is assessed throughsimulation ananlysis addressing different scenarios as well, which proves thevalidity of the two improved methods.