A correction and generalization to the sparse learning via iterative minimization method for target off the grid in MIMO radar imaging

The sparse learning via iterative minimization (SLIM) method has been shown to be effective in high resolution imaging for MIMO radar model in [1]. However, the echo model there is derived directly from the discrete form according to the prior gridding of the imaging space and the assumption that all scatterers are located exactly on the grid. Therefore, here we generalize the echo model to its continuous form for arbitrarily-located scatterers. By comparing the two models, we firstly point out one derivation mistake in the previous model. Then, we analyze the extent to which the previous model and the SLIM method would be influenced by the range and angle deviation of scatterers off the grid. Based on our analysis, since the sampling interval and the size of the discretized range bin in the previous model is designed according to the time duration of the transmitted subpulse, the range deviation has no significant influence on the imaging performance. However, the angle deviation is likely to lead to a mismatched basis matrix and thus severely affect the reconstruction result by SLIM. Therefore, the self-update basis SLIM (SUB-SLIM) method is proposed to deal with the off-angle-grid scatterers by alternatively sparse imaging and adaptively refining the angle bins. Numerical results illustrate the effectiveness of our method and the related analysis.