Abstract: Abstract: Focused on the issue that the lasso algorithm may introduce some false targets in the moving target detection in the presence of multipath reflections, the descending dimension method of the design matrix based on the lasso was proposed. Firstly, the multipath propagation increases the spatial diversity and provides different Doppler shifts over different paths. In addition, the application of broadband OFDM signal provides frequency diversity. The introduction of the spatial diversity and the frequency diversity to the system causes target space sparseness. The sparseness of multiple paths and the environment knowledge are applied to estimate paths along within receiving target responses. Simulation results show the target detection probability of the improved lasso algorithm based on the descending dimension method of the design matrix was 30% higher than the lasso in a certain false alarm rate. The proposed algorithm can effectively filter the false targets and improve the radar target detection probability.