Objective To address the issues of structural complexity, large size, and high cost in traditional direction-finding platforms, and to achieve miniaturization and portability of direction-finding equipment, this paper proposes a multi-snapshot atomic norm minimization algorithm for direction-of-arrival (DOA) estimation based on channel switching.
Method The proposed approach utilizes a channel switching mechanism, where a switching matrix is designed to randomly vary across sampling instances. This strategy allows a reduced number of radio-frequency (RF) channels to sequentially sample a larger antenna array, thereby effectively emulating a virtual array aperture while significantly reducing hardware requirements. Based on these switched observations, a noisy multi-snapshot signal model is developed. The DOA estimation task is then formulated as a continuous-domain atomic norm minimization problem, overcoming the basis mismatch issue typically encountered in grid-based sparse reconstruction methods. By solving the resulting semidefinite programming (SDP) problem, a structured Toeplitz covariance matrix is recovered. The DOA parameters are then extracted through Vandermonde decomposition of this Toeplitz matrix, yielding high-resolution angle estimates. In addition, to provide a theoretical benchmark for performance evaluation, the Cramér–Rao bound (CRB) under the proposed channel switching observation model is rigorously derived.
Results Extensive numerical simulations were conducted to assess the effectiveness of the proposed method. The results indicate that, with 24 antenna elements, 12 RF channels, a signal-to-noise ratio (SNR) of 5 dB, and 100 snapshots, the proposed algorithm achieves a root mean square error (RMSE) of less than 0.1°. Furthermore, when the angular separation between two closely spaced sources is as small as 0.6°, the proposed method achieves a 100% success rate in resolution, demonstrating its strong super-resolution capability. Compared with conventional sparse reconstruction–based algorithms such as orthogonal matching pursuit (OMP) and traditional subspace-based methods such as MUSIC, the proposed approach exhibits significantly improved estimation accuracy and angular resolution. Moreover, as the SNR and the number of snapshots increase, the performance of the proposed algorithm progressively approaches the derived CRB, indicating near-optimal efficiency.
Conclusion The proposed method effectively reduces system complexity and hardware costs while maintaining high direction-finding accuracy and angular resolution, providing a practical solution for compact and high-precision DOA measurement systems.
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