Direction-of-arrival (DOA) estimation performance degrades when arrival angles of incident signals do not locate exactly on the discretized grid points. Existing off-grid DOA estimation algorithms either suffer from high computational complexity or are restricted to uniform linear arrays (ULAs). In order to overcome these disadvantages, we propose a simple but effective off-grid DOA estimation method, referred to as iterative phase offset correction (IPOC), for non-uniform linear arrays (NLAs) in this work. The proposed IPOC first transforms the received signal into the coarray domain and then iteratively corrects the phase offset between the coarray data and presumed model caused by angle biases according to a closed-form formula. In the case of multiple sources, we separate these sources using generalized inner product and then utilize IPOC to sequentially estimate the off-grid angle of one source in each iteration. The spectral leakage between multiple sources is reduced as well by subtracting cross-correlation terms, thus overcoming the shortage of requiring a large number of training snapshots. We calculate the mean squared error (MSE) of the proposed method theoretically. Simulation results demonstrate the effectiveness and efficacy of the proposed method for off-grid DOA estimation using NLAs with very few snapshots.

当入射信号的到达角不完全位于离散网格点上时，到达方向（DOA）估计性能会降低。现有的离网DOA估计算法要么运算量大，要么仅限于统一线性阵列（ULA）。为了克服这些缺点，我们为这项工作中的非均匀线性阵列（NLA）提出了一种简单但有效的离网DOA估计方法，称为迭代相位偏移校正（IPOC）。提出的IPOC首先将接收到的信号转换到coarray域中，然后根据闭式公式迭代地校正coarray数据和由角度偏差引起的假定模型之间的相位偏移。如果有多个来源，我们使用广义内积将这些源分开，然后利用IPOC在每次迭代中顺序估计一个源的离网角。通过减去互相关项，还可以减少多个源之间的频谱泄漏，从而克服了需要大量训练快照的不足。我们从理论上计算该方法的均方误差（MSE）。仿真结果表明，所提出的方法使用很少快照的NLA进行离网DOA估计的有效性和有效性。我们从理论上计算该方法的均方误差（MSE）。仿真结果表明，所提出的方法使用很少快照的NLA进行离网DOA估计的有效性和有效性。我们从理论上计算该方法的均方误差（MSE）。仿真结果表明，所提出的方法使用很少快照的NLA进行离网DOA估计的有效性和有效性。