One-Bit Cramér–Rao Bound of Direction of Arrival Estimation for Deterministic Signals
Mingyang Chen, Qiang Li, Lei Huang, Lifang Feng, Mohamed Rihan
Abstract
One-bit direction of arrival (DOA) estimation has received considerable attention in recent years due to its ability to reduce complexity, cost, and storage in radar and wireless communication systems. This brief focuses on the impact of one-bit quantization on deterministic DOA estimation accuracy using the Cramér-Rao Bound (CRB). Especially, we consider a practical scenario where the noise standard deviation is unknown, and thus the resultant one-bit Fisher information matrix (FIM) is singular. To this end, unknown nuisance parameters involving the signal waveform and the noise standard deviation are formulated as a ratio between them, then we derive a one-bit CRB expression of DOAs. To analyze the performance loss of DOA estimation caused by one-bit quantization using the proposed CRB in one source and one snapshot, we first approximate FIM and then attain an explicit expression of CRB for one-bit DOA estimation. Numerical results are presented to verify the analytical expressions and some insightful explanations are given.