DOA Estimation Algorithm Based On Bayesian Compressive Sensing Theory

DOA estimation is one of the important branches of array signal processing.Since the Second World War,it has developed rapidly and has been widely used in military and civilian fields.The classic DOA estimation algorithm is divided into subspace division and subspace fitting two categories.These two types of algorithms are needed in multi snapshot condition,and each has its own flaws that are difficult to overcome.The theory of Compressive Sensing overcomes the limitation of Nyquist sampling theorem,and provides a new way for signal processing.Among them,the Bayesian Compressive Sensing theory is a new achievement of compressed sensing theory.From the statistical point of view,it uses the assumed prior knowledge to compute the posterior probability,and then obtains the estimated value.This paper studies how to estimate DOA more efficiently using Bayesian Compressive Sensing theory.First of all,the thesis introduces the research background,and introduces the Compressive Sensing theory research and DOA estimation,and then studies the narrowband and wideband signal under the DOA estimation model,and focuses on the three classical DOA estimation methods and the Cramer-Rao Bound of DOA estimation,laid the foundation of the study.Secondly,two kinds of important reconstruction algorithms,greedy algorithm and convex optimization algorithm,are studied.In the greedy algorithm,the single snapshot and multiple snapshots OMP is studied and is applied to DOA estimation respectively.The application of convex optimization algorithm in DOA estimation is studied.The L1-SVD algorithm is used to transform the L1-norm problem by penalty term,and the singular value decomposition is adopted to reduce the dimension of the data.Finally,the convex optimization is used to solve the problem.Then introduce the classical broadband signal DOA estimation,broadband in the frequency domain packet into a series of narrow,and the processing method of narrowband,gives the implementation scheme of L1-SVD under broadband,L1-SVD-WDOA algorithm.Simulation results show that L1-SVD-WDOA has better estimation performance,and the performance improvement is larger with the increase of antenna number.Finally,Bayesian Compressive Sensing based on RVM(RVM-BCS),Bayesian Compressive Sensing based on Laplace prior(LP-BCS),and multi snapshot Bayesian Compressed Sensing algorithm(MBCS)are studied.The biggest difference between RVM-BCS and LP-BCS is that a priori information is different.LP-BCS added a priori information than RVM-BCS,so the LP-BCS reconstruction performance is better than RVM-BCS.Formulas are derived to unify the updated parameter formulas of RVM-BCS and LP-BCS for comparison.LP-BCS and MBCS are then applied to the DOA estimation.Simulation shows that the application of BCS to DOAhas certain advantages in algorithm performance.