One-Bit DoA Estimation via Sparse Linear Arrays

Abstract

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 onebit 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.

On The Asymptotic Performance of One-Bit Co-Array-Based Music

“…We note that we have derived a closed-form expression for Σ by computing the fourth order moments of the orthant probability. Unfortunately, this closed-form expression is rather cumbersome and is derived for each element; we do not provide this expression of Σ due to the lack of space but we refer the interested readers to the journal extension of this work [29]. This closed form-expression shows that Σ is only a function of r.…”

“…Particularly, use of one-bit ADCs has received the most attention since they allow for sampling at an extremely high rate with a low cost and low power consumption. Recently, the problem of DoA estimation from one-bit data has gained considerable interest in the literature [22][23][24][25][26][27]. This problem has been investigated in [22][23][24][25] when a ULA is employed and it has been shown that one-bit quantization leads to a moderate performance loss compared to the case where infinite-bit quantized data is used.…”

“…This problem has been investigated in [22][23][24][25] when a ULA is employed and it has been shown that one-bit quantization leads to a moderate performance loss compared to the case where infinite-bit quantized data is used. Further, the problem of DoA estimation from one-bit SLA data has been addressed in [26,27]; it has been demonstrated that the performance degradation due to one-bit quantization can, to some extent, be compensated using SLAs.…”

Covariance Recovery for One-Bit Sampled Data With Time-Varying Sampling Thresholds— Part II: Non-Stationary Signals

“…Covariance matrix recovery plays an important role in statistical signal processing applications such as directions of arrival (DOA) estimation, radar waveform design, target parameter estimation, communication channel estimation, and adaptive radar detection [3]- [10]. When digital signal processing is concerned, using one-bit quantization and digitization, in which the input signals are compared with given threshold levels, allows for sampling at a very high rate and with lower energy consumption [11]- [14]. As a result of employing one-bit sampling, however, we can only use the sign data as partial available information to recover the signal covariance, and second order statistics in general, making it more challenging.…”

DoA Estimation Using Low-Resolution Multi-Bit Sparse Array Measurements

“…One-bit ADCs represent each sample of the analog array observations with only a single bit offering, an exceedingly high sampling rate at a low production cost and very low power consumption [16]. The analytical performance bounds for DoA estimation from one-bit data have been studied in [28][29][30]. Further, a number of one-bit DoA estimators have been provided in [23][24][25]27], which rest on retrieving the covariance matrix of unquantized array observations using the well-known Bussgang theorem [31].…”