Detection and localization of stationary targets behind walls is primarily challenged by the presence of the overwhelming electromagnetic signature of the front wall in the radar returns. In this paper, we use the discrete prolate spheroidal sequences to represent spatially extended stationary targets, including exterior walls. This permits the formation of a linear block sparse model relating the range profile and observation vectors. Effective wall clutter suppression can then be performed prior to sparse signal image reconstruction. We consider steppedfrequency radar with two cases of frequency measurement distributions over antenna positions. In the first case, the same subset of frequencies is used for each antenna in physical or synthetic aperture arrays, whereas the other case allows different sets of few frequency observations to be available at different antennas. Using experimental data, we demonstrate that the proposed scheme enables sparsity-based image reconstruction techniques to effectively detect and localize behind-the-wall stationary targets from reduced measurements.Index Terms-Compressive sensing (CS), discrete prolate spheroidal sequence (DPSS), sparse reconstruction, through-thewall radar imaging, wall clutter mitigation.

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