Lasso based performance evaluation for sparse one-dimensional radar problem under random sub-sampling and Gaussian noise

Sparse microwave imaging is the combination of microwave imaging and sparse signal processing, which aims to extract physical and geometry information of sparse or transformed sparse scene from least number of radar measurements. As a primary investigation on its performance, this paper focuses on the performance guarantee for a one-dimensional radar, which detects delays of several point targets located at a sparse scene via randomly sub-sampling of radar returns. Based on the Lasso framework, the quantity relationship among three important factors is discussed, including the sub-sampling ratio rho(M), sparse ratio rho(K) and signal-to-noise ratio (SNR), where rho(M) is the ratio of number of random sub-sampling to that of Nyquist's sampling, and rho(K) is the ratio of sparsity to the number of unknowns. In particular, to ensure correct delay detection and accurate back scattering coefficient reconstruction for each target, one needs rho(M) to be greater than C(rho(K))rho(K) logN and the input SNR be of order log N, where N is the number of range cells in scene.