Joint Block Sparse Signal Recovery Problem and Applications in LTE Cell Search

We consider the problem of jointly recovering block sparse signals that share the same support set, using multiple measurement vectors (MMVs). We consider the generalized MMV (GMMV) model wherein the different measurement vectors could have been obtained by using different sensing matrices. We study greedy- and convex-programming-based recovery algorithms and theoretically establish their support recovery guarantees. Our results present insights into how the correlation among block sparse signals plays a role in the recovery performance. Next, we consider the problem of cell search in heterogeneous cellular networks (HetNets). With the cell search process, the mobile terminal (MT) acquires synchronization parameters, such as frame timing, residual frequency offset, and the physical-layer identity of a base station (BS), suitable for its connection. In HetNets, due to the increased density of the BS, the MT may receive strong interference from several BSs in its neighborhood. We establish that the problem of cell search in HetNets can be solved by using the GMMV joint block sparse signal recovery framework. We numerically study the performance of the cell search algorithms proposed by using our framework and show that they perform significantly better than the successive interference cancelation algorithm that exists in the literature.