DOA Estimation in Distributed Nested Arrays Using Multifrequency Information Extrapolation

Distributed arrays can achieve an extended effective aperture through sparse spatial deployment, significantly enhancing the resolution of parameter estimation. However, the incomplete array aperture induced by long baselines between subarrays inevitably introduces angle ambiguity. To address this issue, this paper proposes a distributed nested array interpolation method that leverages multi-frequency information and low-rank matrix reconstruction for unambiguous direction-of-arrival (DOA) estimation. For distributed arrays with nested subarrays, the physical array is first mapped into the virtual array domain by vectorizing the covariance matrix. Subsequently, multi-frequency measurements are incorporated to extrapolate the virtual array, effectively expanding the aperture of sparse distributed subarrays. To recover residual missing elements, a low-rank covariance matrix completion model is established, employing the Schatten-p norm to enforce low-rank constraints and incorporating sparsity priors within an optimization framework. The resulting problem is efficiently solved via an iteratively reweighted least squares (IRLS) algorithm. Finally, the completed covariance matrix enables high-resolution DOA estimation through subspace-based techniques. Extensive simulation and field experimental results demonstrate the proposed method’s effectiveness and robustness in achieving unambiguous, high-resolution DOA estimation in distributed array scenarios.