Reweighted Atomic Norm Minimization for Line Spectral Estimation With One-Bit Samples

Quantization is one of the key processes in the operation of an analog-to-digital converter. Among various quantization schemes, one-bit quantization has received widespread attention due to its low hardware complexity and energy consumption. In this paper, we investigate the line spectral estimation problem with one-bit samples. We propose a gridless sparse optimization algorithm by finding the sparsest candidate signal consistent with the one-bit samples. In particular, a new log-det sparsity metric is proposed inspired by the recent Hankel-Toeplitz model characterizing the atomic ℓ₀ norm. A nonconvex optimization algorithm is presented, which effectively performs reweighted atomic norm minimization (RAM) and iteratively promotes signal sparsity, termed one-bit RAM. An alternating direction method of multipliers algorithm is further proposed to accelerate the computation of one-bit RAM. The behavior of the Cramér-Rao bound is also theoretically analyzed. Numerical results are provided to demonstrate the superior performance of the proposed method compared to the state of the art.