Research On Sparse Reconstruction Based DOA Estimation Algorithms For Massive Arrays

Massive array systems,with the merits of high spectrum and energy efficiency,wide detection field of view,have become one of the research hotspots in the field of array signal processing,and have been widely adopted in many practical applications such as radars,smart city,5G communications,medical science,autonomous driving,et al.For massive array systems,direction-of-arrival（DOA）estimation is one of the charming research topics,which has attracted extensive attention from the researchers and practitioners alike.While for more complex signal environments,including the development of stealth technology,the application of low-frequency interception and various types of complex electromagnetic interference,the array receiving signals cannot guarantee the sampling conditions with large snapshots and high SNR,therefore the traditional algorithms cannot achieve effective DOA estimation.The sparse signal reconstruction（SSR）based DOA estimation algorithms rely on the spatial sparsity of signals to build the optimization model,other than the environmental factors.Hence,the SSR based algorithms are robust to the conditions with low SNR and small snapshots.However,due to some practical factors,such as discrete grid mismatch,array imperfection errors and one-bit quantization,the DOA estimation performance of SSR based algorithms with massive arrays will be reduced sharply or even invalid.Discrete grid mismatch problem leads to the fact that the real DOAs are not located in the pre-divided dictionary grids,resulting in off-grid errors and affecting the estimation accuracy.Array imperfection errors lead to misalignment of system array manifold matrix and the lack of aperture,which makes the sparse dictionary under the sparse framework unable to effectively characterize the angular distribution.With one-bit quantization,the measurements are susceptible to interference from noise,resulting in the sign flips problems,which affect the consistency of sparse reconstruction.In this paper,we mainly focus on the research of the SSR based DOA estimation algorithms for massive array systems under the following three practical problems of discrete grid mismatch,array imperfections and one-bit quantization.The main research contents are as follows,Firstly,the ideal model of traditional arrays is established,and some related concepts and statistical properties of received signals are analyzed while traditional DOA estimation algorithms based on statistical properties are introduced.In addition,the sparse representation models based on ideal array conditions are given,and the theoretical basis for accurate sparse reconstruction is studied.Then,the relationship between the conventional algorithms and SSR based DOA estimation algorithms are compared and analyzed.To solve the grid mismatch problems existing in SSR based algorithms,an off-grid DOA estimation algorithm based on grid learning is proposed.The grid mismatch model is first established by utilizing the first-order Taylor expansion.By using the properties of orthogonal between subspaces,the off-grid error can be estimated and compensated effectively.Based on the estimated off-grid errors,the discretized grid can be iteratively learned and approaches the true DOAs.With the newly learned grid,accurate DOA estimation can be achieved through the SSR scheme.Secondly,the improved SSR based DOA estimation algorithms for massive arrays are investigated.Unlike conventional arrays,with the increasing of antenna elements,the dimensions and amounts of data will expand rapidly,the computational complexity of SSR based algorithms increase either which reduced the real-time performance.To solve this problem,a low-complexity off-grid DOA estimation algorithm based on frequency sparsity is proposed.By introducing the Fourier transformation matrix as the sparse dictionary,the method can establish an effective sparse representation model without increasing the dimension of data.In order to solve the grid mismatch problem,a low-complexity frequency iterative interpolation method is proposed to achieve accuracy DOA estimation.On the other hand,the interpolation compensation algorithm can achieve efficient estimation performance with single snapshot,though,it is not suitable for the multiple measurement vector（MMV）structures.Therefore,for the MMV models of massive arrays,a sparse reconstruction model with a compact structure is established,and a reduction off-grid method is proposed to solve it,which suppresses the grid mismatch problem effectively and improves the performance of DOA estimation.Thirdly,the improved SSR based DOA estimation algorithms for massive arrays are investigated with array imperfections.To solve the gain-phase uncertainties,an off-grid DOA estimation algorithm based on error compensation scheme is proposed.Based on the orthogonal properties between signal and noise subspaces,a joint parameter estimation model is constructed by extracting the off-grid errors with the approximation of Taylor expansion.Then an alternating iterative optimization algorithm based on closed-form solution is utilized to estimate the off-grid errors and compensate the gain-phase errors,which realized the effective DOA estimation.To solve the mutual coupling problems,an off-grid DOA estimation algorithm with block sparsity reconstruction is proposed.With the parametric transformation of the steering vectors,a block sparsity representing model that does not change the aperture of array systems is derived,where the mutual coupling factors are embedded.Meanwhile,an equivalent reduction optimization structure of mixed nuclear-₁l minimization is given based on the block sparsity reconstruction model.The proposed method can improve the DOA estimation accuracy without compensating for the mutual coupling influence.Finally,the SSR based DOA estimation algorithms for massive arrays with one-bit quantization measurements are investigated.Aiming at the sign flips problems caused by noise interference,an atomic norm denoising model based DOA estimation algorithm is proposed for massive arrays.The off-grid sparse reconstruction model is established with atomic norm minimization while the linear loss function is utilized to constrain the outliers caused by sign flips to ensure the consistency of signal reconstruction.In order to further reduce the computational burden while solving the sparse reconstruction model with atomic norm denoising,an atomic norm discretization based SSR model is derived.With the derivation of the closed-form solution of the optimal solution,the computational complexity is reduced significantly.Nevertheless,the discretization relaxation process will cause the performance loss for DOA estimation.In order to compensate for the performance loss,a compensation algorithm based on the compressed matrix optimization is proposed.The proposed algorithm can improve the DOA estimation effectively while ensuring computational efficiency.