Research On Robust DOA Estimation Algorithm Based On Sparse Recovery Under Non-ideal Conditions

As one of the important research contents of array signal processing,the direction of arrival（DOA）estimation has extensive and important application value in military and daily life.After a long period of development,scholars have applied compressed sensing（CS）theory to DOA estimation,which greatly reduces the difficulty of signal sampling,storage and processing in practical applications.Among them,the sparse signal recovery（SSR）algorithm based on compressed sensing theory has become a research hotspot due to its high signal recovery accuracy and good stability.However,in the practical application environment,the interaction of electromagnetic fields between the array elements will produce mutual coupling effect,the grid processing of sparse signal model will lead to off-grid error,the reflection and interference of target signal will make the antenna elements receive relevant signals.These factors will inevitably affect the traditional algorithm based on the ideal model,making the DOA estimation accuracy decline or even fail.Therefore,based on the sparse signal recovery theory,this paper studies the robust DOA estimation algorithm under non-ideal conditions such as mutual coupling,off-grid error and correlation source.Firstly,the mathematical models of traditional far-field narrowband signals and array received signals are introduced,and the basic knowledge of matrix analysis theory commonly used in DOA estimation algorithms is listed.Then the traditional subspace DOA estimation algorithms are introduced:MUSIC algorithm,ESPRIT algorithm and related derivative algorithms.Meanwhile,these algorithms are simulated and analyzed with using simulation tools.Secondly,aiming at the DOA estimation error caused by source-related conditions,based on the sparse recovery theory,an improved idea of preprocessing the sparse spectrum fitting algorithm with spatial smoothing algorithm is proposed,which reduces the computational complexity and improves the processing ability of the algorithm under related conditions.By establishing a grid sparse signal model,the representative algorithm of sparse recovery theory is introduced.Then,based on the derivation of the sparse spectral fitting algorithm,the sparse representation model of the spatial covariance matrix is simplified by assuming that the sources are uncorrelated,which reduces the computational complexity of the algorithm.The error analysis of the improved algorithm is carried out under the condition of source correlation,and the improvement idea of preprocessing is given.Finally,the algorithm is simulated under source related and uncorrelated conditions respectively,which verifies the superiority of the algorithm itself and the effectiveness of the improved algorithm.Secondly,on the basis of sparse signal recovery theory,a grid sparse signal model is established,and the representative algorithm of sparse signal recovery theory:l₁-SVD algorithm is introduced.Then,by establishing the sparse representation model of the covariance domain,the derivation of the sparse spectral fitting algorithm is introduced,and the sparse representation model of the spatial covariance matrix is simplified by assuming that the source is uncorrelated,thus the computational complexity of the algorithm is reduced.At the same time,the possible error of the improved sparse spectral fitting algorithm in source correlation is analyzed,and the improved idea of preprocessing with spatial smoothing algorithm is given.In the end,the sparse spectrum fitting algorithm and its improved algorithm are simulated and compared under the conditions of source correlation and uncorrelation respectively,the advantages of the algorithm and the effectiveness of the improved algorithm is verified.Finally,under non-ideal conditions,based on sparse spectral fitting a new DOA estimation algorithm is proposed,which can simultaneously deal with mutual coupling and off-grid errors,and achieves the improvement of sparse signal recovery accuracy under non-ideal conditions.Firstly,the sparse signal model under the condition of mutual coupling is established,and the selection matrix is constructed by using the banded complex symmetric Toeplitz structure of the mutual coupling matrix to eliminate the influence of mutual coupling.Then,the off-grid error caused by gridding sparsity is eliminated by parameterization method.The constraints of sparse signal recovery are optimized by using the statistical characteristics of the vectorized form of covariance estimation error.By comparing several algorithms through simulation experiments,the robustness and superiority of the proposed method under non-ideal conditions are verified.