DOA Estimation via Tensor Truncated Convolution Nuclear Norm Minimization in MIMO Radar Under Array Sensor Failures

Exploring the inherent multidimensional structures has great potential to obtain more latent information for reconstructing the missing data resulting from array sensor failures in multiple-input–multiple-output (MIMO) radar. Most tensor completion (TC) methods based on the minimization of tensor nuclear norms are adopted to fill randomly distributed missing entries. However, the randomness of missing entries is violated in MIMO radar under sensor failures, where some slices are missing entirely. Thus, these existing methods become ineffective when faced with such type of structurally missing entries. To remedy this, we propose an improved TC method based on tensor truncated convolution nuclear norm minimization (CNNM) to reconstruct the failed sensor data in MIMO radar in order to handle sensor failure in direction-of-arrival (DOA) estimation. First, we formulate a new tensor by convoluting the third-order tensor of MIMO radar with a kernel tensor in a truncated manner and establish a low-rank TC model equipped with the truncated CNNM. Then, we introduce a tractable relaxation of our minimization function by deducing the equality relation between the truncated convolution nuclear norm of a tensor and the nuclear norm of the truncated convolution matrix of the same tensor. Finally, we derive an efficient algorithm implementation based on alternating direction method of multipliers (ADMM) to tackle our problem. Simulation results show that the proposed method is quite effective in completing tensors with structurally missing entries and facilitating more accurate data recovery by exploiting the inherent multidimensional nature. This provides superior DOA estimation performance in MIMO radar.