Grid-lessDOA Estimation of Compressed Covariance for Millimeter-Wave Hybrid Arrays

To address compressed observations and colored noise caused by the limited number of radio-frequency (RF) chains and low-bit phase shifters in millimeter-wave (mmWave) subarray-connected hybrid arrays, this paper studies direction-of-arrival (DOA) estimation in the continuous angular domain. A multi-configuration compressed covariance observation model is first established, where the configuration-dependent noise covariance induced by hybrid combining is explicitly retained. Then, by exploiting the Toeplitz and positive semidefinite (PSD) priors of the uniform linear array (ULA) signal covariance, a Toeplitz-parameterized gridless atomic norm minimization method is developed to reconstruct the structured signal covariance and jointly estimate the noise power. Finally, diagonally loaded Root-MUSIC is used to extract DOAs from the reconstructed covariance matrix. Monte Carlo simulations show that the proposed method achieves lower angular root-mean-square error and stronger resolution of closely spaced sources than grid-based sparse reconstruction and compressed-domain MVDR scanning baselines under moderate-to-high SNR, finite snapshots, low-bit quantization, and colored-noise conditions.