Theoretical and Experimental Comparison of Off-Grid Sparse Bayesian Direction-of-Arrival Estimation Algorithms

Off-grid sparse Bayesian learning algorithms for estimating the directions-of-arrival (DOAs) of multiple signals using an array of sensors are attractive in practice due to three primary reasons. First, these algorithms are fully automatic Bayesian algorithms and hence tuning of regularization parameters (hyper parameters) is not necessary. Second, since these algorithms are based on sparsity, they can produce high accuracy DOA estimates by exploiting the spatial sparsity of acoustic signals even when the signals are coherent. Third, they can also estimate the offset in the DOAs for signals, whose DOAs are not exactly aligned with the steering vectors. Two previously proposed off-grid sparse Bayesian DOA estimation algorithms are considered. The first off-grid model is based on the Taylor series expansion method (OGSBL-T algorithm) and the second is based on the linear interpolation method (OGSBL-I algorithm). The Cramer Rao lower bound (CRLB) of the off-grid bias parameters for both the algorithms is derived for multiple snapshots. It is shown that the CRLB of the off-grid bias parameters for the OGSBL-T algorithm is significantly less than that for the OGSBL-I algorithm. It is also shown that the CRLBs of the off-grid bias parameters for both the algorithms get worse when we move from the broadside to the endfire directions. A simulation study is also carried out to characterize the performances of both the algorithms in terms of the root-mean squared error in the DOA estimates. It is shown that the OGSBL-T algorithm performs comparably to the OGSBL-I algorithm when the signals are relatively broadside and better than the OGSBL-I algorithm when the signals are relatively endfire. Finally, the application of the OGSBL-T algorithm for high resolution DOA estimation in an underwater communication system is demonstrated by analyzing passive sonar data from the SWellEx-96 ocean acoustic experiment.