Direction of Arrival (DoA) estimation using Sparse Linear Arrays (SLAs) has recently gained considerable attention in array processing thanks to their capability to provide enhanced degrees of freedom in resolving uncorrelated source signals. Additionally, deployment of one-bit Analog-to-Digital Converters (ADCs) has emerged as an important topic in array processing, as it offers both a low-cost and a low-complexity implementation. In this paper, we study the problem of DoA estimation from one-bit measurements received by an SLA. Specifically, we first investigate the identifiability conditions for the DoA estimation problem from one-bit SLA data and establish an equivalency with the case when DoAs are estimated from infinite-bit unquantized measurements. Towards determining the performance limits of DoA estimation from one-bit quantized data, we derive a pessimistic approximation of the corresponding Cramér-Rao Bound (CRB). This pessimistic CRB is then used as a benchmark for assessing the performance of one-bit DoA estimators. We also propose a new algorithm for estimating DoAs from one-bit quantized data. We investigate the analytical performance of the proposed method through deriving a closed-form expression for the covariance matrix of the asymptotic distribution of the DoA estimation errors and show that it outperforms the existing algorithms in the literature. Numerical simulations are provided to validate the analytical derivations and corroborate the resulting performance improvement.

中文翻译：

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稀疏线性阵列一位 DoA 估计的性能


使用稀疏线性阵列 (SLA) 的到达方向 (DoA) 估计最近在阵列处理中获得了相当多的关注，因为它们能够在解析不相关的源信号时提供增强的自由度。此外，一位模数转换器 (ADC) 的部署已成为阵列处理中的一个重要主题，因为它提供了低成本和低复杂性的实施方案。在本文中，我们研究了根据 SLA 接收到的一位测量值进行 DoA 估计的问题。具体来说，我们首先研究来自一位 SLA 数据的 DoA 估计问题的可识别性条件，并建立与根据无限位非量化测量估计 DoA 的情况的等价性。为了根据一位量化数据确定 DoA 估计的性能限制，我们推导了相应的 Cramér-Rao Bound (CRB) 的悲观近似。然后将该悲观 CRB 用作评估一位 DoA 估计器性能的基准。我们还提出了一种从一位量化数据估计 DoA 的新算法。我们通过推导 DoA 估计误差渐近分布的协方差矩阵的封闭式表达式来研究该方法的分析性能，并表明该方法优于文献中的现有算法。提供数值模拟来验证分析推导并证实由此产生的性能改进。