Sparse Bayesian learning (SBL) has become a popular approach for direction-of-arrival (DOA) estimation, but its computational complexity for Bayesian inference is quite high because calculating inverse of a large complex matrix per iteration is required. It is known that the computational load can be reduced by transforming the complex-valued problem into a real-valued one. However, the commonly used real-valued transformation works for uniform linear arrays (ULAs) only. In this paper, we propose a new real-valued transformation for DOA estimation with arbitrary linear arrays by exploiting the virtual steering of linear arrays. Then, we introduce an alternating optimization algorithm based on the variational Bayesian inference (VBI) methodology to iteratively obtain a stationary solution to the real-valued sparse representation problem. Because of utilizing the additional real-valued structure, the VBI scheme can achieve a better performance in terms of both estimation accuracy and computational complexity. Moreover, we embed the generalized approximate message passing (GAMP) into the VBI-based method for further complexity reduction. Although there may be a performance loss for the GAMP variant, simulation results reveal its substantial performance improvement over existing methods.

中文翻译：

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用于任意线性阵列 DOA 估计的实值稀疏贝叶斯学习


稀疏贝叶斯学习（SBL）已成为一种流行的到达方向（DOA）估计方法，但其贝叶斯推理的计算复杂度相当高，因为每次迭代都需要计算大型复杂矩阵的逆。众所周知，通过将复值问题转化为实值问题可以减少计算量。然而，常用的实值变换仅适用于均匀线性阵列 (ULA)。在本文中，我们通过利用线性阵列的虚拟转向，提出了一种新的实值变换，用于任意线性阵列的 DOA 估计。然后，我们引入基于变分贝叶斯推理（VBI）方法的交替优化算法，以迭代获得实值稀疏表示问题的平稳解。由于利用了附加的实值结构，VBI方案在估计精度和计算复杂度方面都可以获得更好的性能。此外，我们将广义近似消息传递（GAMP）嵌入到基于 VBI 的方法中，以进一步降低复杂性。尽管 GAMP 变体可能会出现性能损失，但模拟结果表明其性能比现有方法有显着提高。