Robust Single-Bit Direction-of-Arrival Estimation With Magnitude Recovery

Single-bit direction-of-arrival (DoA) estimation utilizes the sign information of received signals to estimate the DoAs of interesting targets. This approach enables the use of single-bit analog-to-digital converters (ADCs) for quantization, reducing cost and hardware complexity significantly. However, the single-bit ADCs conceal the signal magnitude, leading to a limited dynamic range in radar systems. Moreover, the existing methods for single-bit DoA estimation typically require the prior knowledge of the target number or necessitate a computationally expensive grid search to determine an auxiliary parameter. In this work, we propose a new single-bit quantization model by incorporating a non-zero threshold for the received signal. Then, we employ the capped Frobenius norm and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{2,0}$</tex-math></inline-formula>-norm to formulate the single-bit DoA estimation problem, where the former measures the fitting error and the latter is used for estimating the target number. Subsequently, the resultant task is solved by combining proximal alternating minimization and forward-backward splitting. In our algorithm, an adaptive strategy is introduced to determine the regularization parameter associated with the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{2,0}$</tex-math></inline-formula>-norm, thus allowing for automatic estimation of the target number. Additionally, we analyze the algorithm convergence behavior, proving that both the objective function value and the variable sequence are convergent. Simulation results demonstrate that the devised method can estimate both the target number and signal magnitude with high probability. Furthermore, it outperforms state-of-the-art single-bit approaches in terms of DoA estimation accuracy.