On the impact of signals time-frequency sparsity on the localization performance

In this paper, we investigate the localization performance of far field sources that have sparse time-frequency (T-F) representations. The Cramér-Rao Bound (CRB) under the sparsity assumption is developed and the impact of the T-F sparsity prior on the localization performance is analyzed. In particular, one studies how the different T-F sparsity properties i.e. local SNR level, source supports spreading and source overlapping and orthogonality affect the CRB of the Direction-of-Arrival (DoA) estimation. The obtained results show that the sources T-F orthogonality has the most significant impact on the localization performance. Simulation results are provided to illustrate the concluding remarks made out of this study.