To move toward spaceborne weather radars that can be deployed routinely as part of an instrument set consisting of passive and active sensors requires the development of smaller, lighter-weight radars. At the same time, the addition of a second frequency and an upgrade to Doppler capability are essential to retrieve information on the drop size distribution (DSD), vertical air motion, and storm dynamics. One approach to the problem is to use a single broadband transmitter-receiver and antenna where two narrowband frequencies are spaced apart by 7--10%. Use of Ka-band frequencies (26.5--40 GHz) provides adequate spatial resolution with a relatively small antenna. Moreover, the differential reflectivity and mean Doppler signals in this band are directly related to the median mass diameter of the snow and raindrop size distributions. We present in the paper theoretical calculations of the differential reflectivity and Doppler for several frequency pairs including those proposed for the Global Precipitation Mission (GPM) at 13.6 and 35 GHz. Measurements from a zenith-directed radar operated at 9.1 and 10 GHz are used to investigate the qualitative characteristics of the differential signals. Disdrometer data taken at the surface, just below the radar, show that the differential signals are related to characteristics of the raindrop size distribution. The stability of the DSD estimation procedure is tested using a simulation. The results indicate that reasonably stable estimates of the particle size distribution are feasible with a <31.5 GHz, 35 GHz> combination as long as a large number of independent samples are obtained.