Sparse Bayesian Learning Based Algorithm for DOA Estimation of Closely Spaced Signals
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摘要: 离格(off-grid)波达方向(DOA)估计解决的是实际DOA和假设网格点的失配问题。对于空间紧邻信号的DOA，稀疏的网格点会导致精度和分辨率的下降，密集的网格点虽然可以提高估计精度却显著增加计算负担。针对此问题，该文提出基于稀疏贝叶斯学习(SBL)的空间紧邻信号DOA估计算法，主要包括3个步骤。首先，通过最大化阵列输出的边缘似然函数，推导了信号在拉普拉斯先验下的新不动点迭代方法，进行超参数的预估计，相比其他经典SBL算法提高了收敛速度；其次，利用新网格插值方法优化网格点集，并二次估计噪声方差和信号功率以分辨空间紧邻信号的DOA；最后，推导了似然函数关于角度的最大化公式以改进离格DOA搜索。仿真表明该算法比其他经典SBL类算法对空间紧邻信号的DOA具有更高的精度和分辨率，同时有计算效率的提升。Abstract: Off-grid Direction Of Arrival (DOA) estimation aims to handle the mismatch between the actual DOA and the presumed grid points. For DOAs of closely spaced signals, sparse grid points leads to degradation of accuracy and resolution, although dense grid points can improve the estimation accuracy, it significantly increases the computational burden. To solve this problem, this paper proposes a Sparse Bayesian Learning (SBL) based algorithm for DOA estimation of closely spaced signals, which consists of three steps. Firstly, a novel fixed point iterative method for signal of Laplace priori is derived to pre-estimate the hyper-parameters by maximizing the array’s marginal likelihood function, which results in faster convergence speed compared to other classical SBL algorithms. Secondly, a new grid interpolation method is implemented to optimize a set of grid points, and signal power and noise variance are estimated again to resolve closely spaced DOAs. Finally, an expression of maximum likelihood function with respect to angle is derived to improve the search of the off-grid DOA. Simulation results show that the proposed algorithm has higher accuracy and resolution for closely spaced DOAs with higher computational efficiency compared with other classical algorithms based on SBL.
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表 1 算法的计算复杂度
算法 计算复杂度 本文GI-MSBL $\begin{gathered} {l_1}\left( {2MNL + (M + 1)MN} \right) \\ + {l_2}\left( {M\bar NL + (M + 1)M\bar N} \right) + (2{M^2} + 2M)K{N_0} \\ \end{gathered} $ iRVM-DOA[7] $\begin{gathered} {l_{{\rm{iRVM - DOA}}}}\left( {MNL + M{N^2} + {M^2}N} \right) \\ + (2{M^2}{\rm{ + }}6M)K{N_1} \\ \end{gathered} $ OGSBI[8] ${l_{{\rm{OGSBI}}}}\left( {2MNL + M{N^2} + {M^2}N + MN(L + K)} \right)$ rootSBL[12] ${l_{{\rm{rootSBL}}}}\left( {2MNL + M{N^2} + {M^2}N{\rm{ + }}M(N - 1)L} \right)$ PSBL[9,10] $ \begin{array}{l}{l}_{\rm{PSBL}}\left(2MNL+M(N-1{)}^{2}+{M}^{2}(N-1)\right)\\ +{l}_{\rm{PSBL}}\left(L(N-1)(M+K)\right)\end{array}$ L1-SVD[3] $O({(KN)^3})$ MUSIC[2] $(M - K)ML{N_{{\rm{MUSIC}}}}$ 
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