Real-valued sparse representation methods have recently become popular for directions of arrival (DOAs) of unknown and possibly correlated signals using an array of sensors. Such a representation is useful when it is not straightforward to extend sparse representation algorithms, which are specifically designed in the real domain, to the complex domain or when the array output is represented in the sparse covariance domain. However, most existing real-valued sparse representation methods simply separate the real and imaginary parts of the signals, which are possibly complex, and treat them independently, rather than simultaneously, to impose the sparsity constraint. We use a unitary transformation-based real-valued sparse representation approach to convert the problem of estimating the DOAs from complex to the real domain for a uniform linear array. A fully automatic sparse Bayesian learning principle-based algorithm is then proposed to estimate the DOAs by simultaneously imposing the sparsity constraint on both the real and imaginary parts of the signals. This is in contrast to conventional deterministic sparse signal processing methods, which require tuning of regularization parameters, making them unsuitable to be used in practice where the ground truth is usually unknown. Since in practice, the DOAs of signals may not be exactly aligned with the predefined angular grids, we use an off-grid model to infer the off-grid DOAs. Using the singular value decomposition directly on the array output, the proposed real-valued DOA estimation can also be carried out in the same dimensional space as the original complex domain, which results in a reduction of computational complexity. Moreover, since in ocean acoustics, signals are usually wideband, we extend our proposed narrowband algorithm to the wideband case, where we estimate one spatial power spectrum by simultaneously exploiting sparsity from all frequency bins. Finally, we demonstrate the application of the proposed algorithms by analyzing both narrowband and wideband correlated multipath signals from a shallow water high-frequency (namely, HF97) ocean acoustic experiment.

中文翻译：

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用于海洋声学离网波达方向 (DOA) 估计的实值稀疏贝叶斯学习


实值稀疏表示方法最近在使用传感器阵列的未知且可能相关信号的到达方向 (DOA) 方面变得很流行。当无法直接将稀疏表示算法（在实数域中专门设计）扩展到复数域时，或者当数组输出在稀疏协方差域中表示时，这种表示非常有用。然而，大多数现有的实值稀疏表示方法只是将信号的实部和虚部（可能很复杂）分开，并独立而不是同时处理它们，以施加稀疏性约束。我们使用基于酉变换的实值稀疏表示方法将均匀线性阵列的 DOA 估计问题从复杂域转换为实域。然后提出了一种基于稀疏贝叶斯学习原理的全自动算法，通过同时对信号的实部和虚部施加稀疏性约束来估计 DOA。这与传统的确定性稀疏信号处理方法形成对比，传统的确定性稀疏信号处理方法需要调整正则化参数，这使得它们不适合在实际情况通常未知的情况下使用。由于在实践中，信号的 DOA 可能与预定义的角度网格不完全对齐，因此我们使用离网模型来推断离网 DOA。直接对阵列输出使用奇异值分解，所提出的实值DOA估计也可以在与原始复域相同的维空间中进行，从而降低了计算复杂度。 此外，由于在海洋声学中，信号通常是宽带的，因此我们将提出的窄带算法扩展到宽带情况，其中我们通过同时利用所有频率仓的稀疏性来估计一个空间功率谱。最后，我们通过分析浅水高频（即 HF97）海洋声学实验中的窄带和宽带相关多径信号来演示所提出算法的应用。