Heng Zhao, Ying Hu, Zijing Zhang, Fei Zhang
Direction-of-arrival (DOA) estimation with coprime arrays can synthesize an enlarged virtual aperture from a limited number of physical sensors. However, coherent incident sources lead to rank deficiency of the source covariance matrix, while unknown nonuniform sensor noise mainly contaminates the zero-lag component of the difference-coarray covariance. These two effects jointly degrade conventional Coarray Root-MUSIC, Coarray ESPRIT, and interpolation-based virtual-array methods. To address this problem, this paper proposes a Toeplitz-Hankel structured covariance reconstruction method for coherent-source DOA estimation with coprime arrays under unknown nonuniform noise. The method first performs redundancy-aware difference-coarray lag averaging. The zero-lag component is then suppressed during missing-lag interpolation to reduce the bias caused by sensor-dependent noise powers. A Toeplitz positive semidefinite projection is used to enforce covariance validity, and a relaxed Hankel truncated-singular-value-decomposition refinement is introduced to enhance the low-rank spectral structure of the reconstructed virtual covariance sequence. Finally, multi-scale forward-backward spatial smoothing MUSIC is applied for coherent-source DOA estimation. Simulation results with a coprime array of M=4 and N=5 show that the proposed method provides more accurate and stable DOA estimates than Coarray Root-MUSIC, Coarray ESPRIT, and RV-TSI. Compared with CVX-based THSCR, the proposed method avoids semidefinite programming and nuclear-norm optimization and reduces the average runtime from approximately 11.2 s per trial to approximately 0.11 s per trial under the tested setting.