Noncoherent compressive sensing with application to distributed radar

We consider a multi-static radar scenario with spatially dislocated receivers that can individually extract delay information only. Furthermore, we assume that the receivers are not phase-synchronized, so the measurements across receivers can only be combined noncoherently. We cast this scenario as a compressive sensing reconstruction problem, where the vector of unknowns consists of complex baseband coefficients of tentative targets at discrete positions within a region of interest. The difference to previous work is that each receiver has to have a separate set of variables to account for the noncoherent measurement model. This leads to multiple reconstruction problems that are individually ill-defined, but can be regularized by a shared sparsity pattern, as studied in jointly- or block-sparse reconstruction problems. We evaluate this approach in a simple scenario with three receivers and three closely spaced targets. Using the popular basis pursuit and orthogonal matching pursuit algorithms, we find that targets can be fully resolved and that the position estimation error is close to the Cramér-Rao lower bound based on an estimator that knows the number of targets.