稀疏恢复辅助DOA估计：一种新方法

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"利用稀疏贝叶斯学习的稀疏恢复辅助Doa估计" 本文主要探讨了一种创新的稀疏恢复辅助到达方向（SR-DOA）估计方法，该方法特别适用于处理多源信号的接收与定位问题。在无线通信、雷达探测以及音频处理等领域，到达方向（DOA）估计是一项关键任务，它旨在确定信号源相对于接收阵列的方向。传统DOA估计方法通常面临噪声干扰和计算复杂性的挑战，而本文提出的新方法则通过利用信号空间频谱的稀疏特性来优化这些问题。首先，文章介绍了如何将DOA估计转化为一个稀疏的非负最小二乘问题。这一转换是基于假设信号源数量相对接收器阵列的元素数量较少，即信号空间频谱具有稀疏性。通过最大化这种稀疏性，可以更准确地识别出信号源的位置，同时减少噪声对估计结果的影响。其次，为了进一步提升估计精度，该方法允许在一定程度上牺牲自由度以抑制加性高斯噪声。通过对噪声的渐近分布进行分析，可以有效地减小采样误差。这一步骤对于在实际环境中，如存在强烈噪声干扰的情况下，提高DOA估计的稳健性至关重要。接下来，文章引入了非负拉普拉斯先验的稀疏贝叶斯学习框架。在贝叶斯统计中，拉普拉斯先验常用于鼓励解决方案的稀疏性，因为它倾向于产生大部分为零的系数。应用这一先验，可以引导DOA估计过程产生更稀疏的解，从而更精确地估计信号源的位置。通过数值模拟和与其他两种现有方法的比较，该文证明了所提出的SR-DOA算法在估计精度上的优越性。实验结果不仅验证了新方法的有效性，也揭示了其在应对不同场景和噪声水平时的鲁棒性。 "利用稀疏贝叶斯学习的稀疏恢复辅助Doa估计"为DOA估计提供了一种新的策略，结合了稀疏表示理论和贝叶斯学习，旨在克服传统方法的局限性，提高在复杂环境下的估计精度。这一研究成果对于进一步推动无线通信和信号处理领域的技术发展具有重要意义。

SPARSE RECOVERY ASSISTED DOA ESTIMATION UTILIZING SPARSE BAYESIAN

LEARNING

Min Huang, Lei Huang

College of Information Engineering, Shenzhen University, China

ABSTRACT

This paper proposes a novel approach to sparse recovery as-

sisted direction-of-arrival (SR-DOA) estimation. By exploit-

ing the sparsity inherent in the spatial spectrum, the DOA es-

timation is formulated as a sparse nonnegative least squares

problem. Meanwhile, in order to enhance the estimation accu-

racy, the devised method is able to suppress the additive Gaus-

sian noise but at the expense of a few degrees-of-freedom,

and mitigate the sampling errors by exploiting its asymptotic

distribution. Subsequently, the sparse Bayesian learning with

nonnegative Laplace prior is utilized to yield the DOA esti-

mation. The performances of the proposed SR-DOA estima-

tor along with other two existing approaches are investigated

and compared. Numerical results show that the proposed SR-

DOA algorithm is superior to the state-of-the-art methods in

terms of the estimation accuracy.

Index Terms— DOA, sparse recovery, sparse nonnega-

tive least squares problem, sparse Bayesian learning, nonneg-

ative Laplace prior

1. INTRODUCTION

Since direction-of-arrival (DOA) estimation can be widely

used in many areas, such as radar, sonar and wireless com-

munications, it has received considerable attention in litera-

ture. However, the estimation performances of the existing

algorithms usually degrade seriously in the situations of low

signal-to-noise ratio (SNR) or small number of snapshots.

Because the number of source signals is usually limited,

the spatial spectrum observed is sparse. Thus, by properly u-

tilizing the compressive sensing techniques, the sparse prop-

erty inherent in the array signal model can be exploited to im-

prove the DOA estimation performance. In particular, DOA

is estimated by minimizing the data ﬁtting error as well as the

This work was supported in part by the Natural Science Founda-

tion of China under Grants U1501253, 61601300, 6160010632, 61501300,

61601304 and 61501485; in part by the China Postdoctoral Science Foun-

dation under Grant 2016M592535; in part by the Natural Science Fund-

ing of Guangdong Province under Grant 2017A030313336; in part by the

Foundation of Shenzhen under Grants JCYJ20170302142545828 and J-

CYJ20160520165659418; in part by the Foundation of Shenzhen University

under Grants 2016057 and 201557; and in part by the China Scholarship

Council.

sparsity of solution. In [1], the sparsity of solution is gen-

erated by forming an ℓ

-norm penalty function. In order to

enforce the sparsity of solution, a weighted ℓ

-norm penal-

ty function which utilizes the property of noise subspace is

proposed by [2]. In addition, the regularization parameter,

which is used to control the trade-off between the data ﬁtting

error and the sparsity of solution, is obtained with the aid of

the Lagrangian duality in [3, 4]. Although, the regularization

parameter derived in [4] does not rely on any a pr iori knowl-

edge, it is suboptimal because it only satisﬁes the sufﬁcient

conditions of optimal solution. Furthermore, when the grid

is dense, the computational complexities of the above algo-

rithms are unaffordable.

Alternatively, the sparse Bayesian learning (SBL) [5],

which avoids the regularization parameter selection, can be

used to solve the sparse recovery problem. Speciﬁcally, the

DOA is determined by maximizing its posterior probability,

namely, the product of the likelihood probability and the prior

probability. In order to obtain more degrees-of-freedom (D-

OFs) to estimate DOA, the DOA estimation problem is ﬁrstly

converted to a sparse nonnegative least squares (S-NNLS)

problem [6]. Then, the nonnegative Gaussian probability

density function (PDF) is considered as the prior probability

to solve the S-NNLS problem [7]. To enforce the sparsity

of solution, the nonnegative Gaussian PDF is replaced by

the Laplace PDF [8]. Although it is is not conjugate to the

Gaussian likelihood function, it can be implemented by a

hierarchical way. In other words, the Laplace PDF can be

constructed by Gaussian PDF and Exponential PDF. Nev-

ertheless, according to [9, 10], the power of Gaussian noise

estimated by SBL may not be accurate, leading performance

degradation.

In this paper, a sparse recovery assisted DOA (SR-DOA)

estimator is proposed. First, we show that the high-resolution

DOA estimation can be formulated as a sparse optimization

problem. Second, a selection matrix is designed for mitigat-

ing the effect of additive Gaussian noise but at the expense of

a small amount of DOFs. Third, a whitening ﬁlter is intro-

duced for coping with the sampling errors. Last, SBL with

nonnegative Laplace is used to determined the DOAs. Our

simulation results show that the proposed SR-DOA estimator

outperforms all the benchmark DOA estimators when SNR is

in low region.

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