Gridless DOA Estimator for 1.5-Bit Sparse Massive MIMO Systems Based on Covariance Matrix Estimation

To reduce the hardware cost of massive multiple-input multiple-output (MIMO) systems, low-bit analog-to-digital converters (ADCs) and sparse arrays are widely used. Compared with traditional 1-bit and 2-bit quantization techniques, 1.5-bit quantization uses two symmetric non-zero thresholds to quantize signal power into three levels, thereby balancing quantization complexity against system performance. However, the quantization loss introduced by 1.5-bit quantization is still significant and leads to degradation in DOA estimation performance. To improve the DOA estimation accuracy of 1.5-bit sparse massive MIMO systems, a covariance matrix estimation method is proposed. This method exploits the Toeplitz property of the covariance matrix of sparse arrays and the relationship between 1.5-bit quantized signals and their unquantized counterparts to transform the covariance matrix estimation problem for 1.5-bit sparse arrays into a non-convex optimization problem with equality constraints. We then further exploit the properties of 1.5-bit quantized signals to relax this problem into a convex problem and solve it via semidefinite programming. Once the covariance is estimated, the DOAs can be recovered by subspace-based methods. Numerical results show that the proposed method achieves higher estimation accuracy than 1.5B-MUSIC and 1-bit covariance-fitting baselines on 1.5-bit sparse arrays, and is competitive with structured covariance-fitting baselines applied to unquantized data, especially on coprime arrays in low-snapshot scenarios.