  We propose a method for synthesizing high range resolution profiles (HRRP)
using stepped frequency waveform (SFW) processing. Conventional SFW radars
sweep over the available spectrum linearly to achieve high resolution from
their instantaneous bandwidth. However, they suffer from strong range-Doppler
coupling and coexisting spectral interference. Prior works are able to mitigate
only one of these drawbacks. We present a new \textit{ra}ndom \textit{s}parse
\textit{ste}p-frequency \textit{r}adar (RaSSteR) waveform that consumes less
spectral resources without loss of range resolution and estimates both
high-resolution range and Doppler by exploiting sparse recovery techniques. In
the presence of interference, the operation with the new waveform is made
cognitive by focusing available transmit power only in the few transmit bands.
Our theoretical analyses show that, even while using fewer carriers in the
available bandwidth, RaSSteR has identical recovery guarantees as the standard
random stepped frequency (RSF) waveform. Numerical experiments demonstrate
performance enhancements with RaSSteR over state-of-the-art such as SFW, RSF,
conventional pulse-compression-based pulse Doppler radar, and sub-Nyquist
radar. In addition, the target hit rate of RaSSteR in the presence of strong
interference is 30% more than conventional RSF.
