  Randomized Stepped Frequency Radar (RSFR) is very attractive for tasks under
complex electromagnetic environment. Due to the synthetic high range resolution
in RSRFs, a target usually occupies a series of range cells and is called an
extended target. To reconstruct the range-Doppler information in a RSFR,
previous studies based on sparse recovery mainly exploit the sparsity of the
target scene but do not adequately address the extended-target characteristics,
which exist in many practical applications. Block sparsity, which combines the
sparsity and the target extension, better characterizes a priori knowledge of
the target scene in a wideband RSFR. This paper studies the RSFR range-Doppler
reconstruction problem using block sparse recovery. Particularly, we
theoretically analyze the block coherence and spectral norm of the observation
matrix in RSFR and build a bound on the parameters of the radar, under which
the exact recovery of the range-Doppler information is guaranteed. Both
simulation and field experiment results demonstrate the superiority of the
block sparse recovery over conventional sparse recovery in RSFRs.
