LASSO BASED PERFORMANCE EVALUATION FOR SPARSE ONE-DIMENSIONAL RADAR PROBLEM UNDER RANDOM SUB-SAMPLING AND GAUSSIAN NOISE

Sparse microwave imaging is the combination of mi- crowave 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 in- vestigation 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 ‰M, sparse ratio ‰K and signal-to-noise ratio (SNR), where ‰M is the ratio of number of random sub-sampling to that of Nyquist's sam- pling, and ‰K is the ratio of sparsity to the number of unknowns. In particular, to ensure correct delay detection and accurate back scat- tering coe-cient reconstruction for each target, one needs ‰M to be greater than C(‰K)‰K logN and the input SNR be of order logN, where N is the number of range cells in scene.