Sensor array calibration with joint-block-sparsity in the presence of multiple separable observations

In sparsity-based optimization problems, one of the major issue is computational complexity, especially when the unknown signal is represented in multi-dimensions such as in the problem of 2-D (azimuth and elevation) direction-of-arrival (DOA) estimation. In this paper, a low-complexity sparsity-based method is proposed for DOA estimation in the presence of array imperfections such as mutual coupling. In order to reduce the complexity of the optimization problem, this paper introduces a new sparsity structure that can be used to model the optimization problem in case of multiple data snapshots and multiple separable observations where the dictionary can be decomposed into two parts: azimuth and elevation dictionaries. The proposed sparsity structure is called joint-block-sparsity which exploits the sparsity in both multiple dimensions, namely azimuth and elevation, and data snapshots. In order to model the joint-block-sparsity in the optimization problem, triple mixed norms are used. In the simulations, the proposed method is compared with both sparsity-based techniques and subspace-based methods as well as the Cramer-Rao lower bound. It is shown that the proposed method effectively calibrates the sensor array with significantly low complexity and sufficient accuracy.