The U.S. Army Research Laboratory (ARL) has developed the impulse-based, ground vehicle-based, forward-looking ultra-wideband (UWB), synthetic aperture radar (SAR) to detect concealed targets. Although the impulse-based architecture offers its own advantages, one of the important challenges is that when using this architecture it is very difficult to transmit a radar signal with an arbitrary bandwidth and shape. This feature is crucial for the radar to be compliant with the local frequency authority. In addition, being able to transmit signals with an arbitrary spectral shape is an important step in creating the next generation of smart (cognitive) radars. Therefore, we have designed a next-generation prototype radar to take advantage of the stepped frequency architecture. The design and building of the radar hardware is underway. In this paper, we study the radar transmit and acquisition scheme; the trade-offs between SAR image performance and various key radar parameters; and data reconstruction techniques for radar signals with an arbitrary spectrum. This study demonstrates performance, provides some guidelines for the radar design, and serves as a foundation for the signal and image processing stage.