  To achieve high range resolution profile (HRRP), the geometric theory of
diffraction (GTD) parametric model is widely used in stepped-frequency radar
system. In the paper, a fast synthetic range profile algorithm, called
orthogonal matching pursuit with sensing dictionary (OMP-SD), is proposed. It
formulates the traditional HRRP synthetic to be a sparse approximation problem
over redundant dictionary. As it employs a priori information that targets are
sparsely distributed in the range space, the synthetic range profile (SRP) can
be accomplished even in presence of data lost. Besides, the computational
complexity is reduced by introducing sensing dictionary (SD) and it mitigates
the model mismatch at the same time. The computation complexity decreases from
O(MNDK) flops for OMP to O(M(N +D)K) flops for OMP-SD. Simulation experiments
illustrate its advantages both in additive white Gaussian noise (AWGN) and
noiseless situation, respectively.
