Sparsity-based estimation for target detection in multipath scenarios

We propose a sparsity-based estimation approach for detecting a moving target in multipath scenarios. We employ an orthogonal frequency division multiplexing (OFDM) radar to increase the frequency diversity of the system. Moreover, the multipath propagation increases the spatial diversity by providing extra looks at the target. First, we exploit the sparsity of multiple paths and the knowledge of the environment to develop a parametric OFDM radar model at a particular range cell. Then, to estimate the sparse vector, we apply a collection of multiple small Dantzig selectors (DS). We use the ℓ₁-constrained minimal singular value (ℓ₁-CMSV) of the measurement matrix to analytically evaluate the reconstruction performance and demonstrate that our decomposed DS performs better than the standard DS. We provide a few numerical examples to illustrate the performance characteristics of the sparse recovery.