Multi-task Bayesian compressive sensing for direction-of-arrival estimation

The problem of the estimation of the direction-of-arrival (DoA) of signals has been a long standing problem in electromagnetics and it is still of great interest due to the need to enhance the effectiveness and the efficiency of the proposed methods and deal with more challenging scenarios as well as foster new applications. Standard approaches, such as the signal estimation parameter via rotational invariance technique (ESPRIT) [1], the multiple signal classification (MUSIC) [2,3], and the maximum likelihood (ML) DoAs estimator [4], have shown good results. However, they suffers some limitations like the requirement of a-priori knowing the number of impinging signals and the computation of the covariance matrix that is a computationally cumbersome task. More recently, efficient DoAs estimation approaches have been proposed that are based on l1-norm minimization techniques which exploit the sparsity of the problem [5,6] due to the fact that the number of signals arriving on an antenna is generally limited. Based on the same line of reasoning, also compressive sensing (CS) methods have been recently introduced due to their robustness and efficiency. As a matter of fact, they have been effectively used to deal with several problems in electromagnetics, like microwave imaging [7,8], antenna synthesis/design [9,10] and array diagnosis [11]. In [12], a Bayesian version of the CS (BCS) has been proposed for real-time DoAs estimation. In this case, the retrieval of the DoAs has been achieved directly exploiting the voltages/currents measured at the output of the array elements (without the need of computing the covariance matrix) and based on the information collected at a single time-instant (i.e., single snapshot). In this work, the method is extended to consider the measurements available at multiple snapshots in order to improve the accuracy of the estimation. Towards, this aim a multi-task version of the BCS (MT-BCS) [10] is proposed.