In state-of-the-art frequency-modulated continuous-wave (FMCW) multiple-input multiple-output (MIMO) radar systems, antennas are usually designed based on microstrip technology. They are arranged in uniform arrays such that the synthesized virtual array maximizes the angular resolution. This paper presents the design of a 77-GHz FMCW MIMO radar frontend with antennas and feed structures based on substrate integrated waveguides (SIW) and non-uniform planar arrays optimized for sidelobe suppression. A design procedure for MIMO arrays with particular emphasis on sidelobe level suppression based on convex optimization is presented, and a novel transition from differential microstrip line to SIW is utilized to feed the transmit antennas. Measurements show the successful SIW and antenna design, as well as a sidelobe level of 40 dB within the field of view (FOV) of the radar system.