Recent technology advances have profoundly changed the landscape of modern radiometry by enabling miniaturized, low-power, and low-noise radio-frequency receivers operating at frequencies near 200 GHz and beyond. These advances enable the practical use of receiver arrays to multiplex multiple broad frequency bands into many spectral channels. We use the term "hyperspectral microwave" to refer generically to microwave sounding systems with approximately 50 spectral channels or more. In this paper, we report on the design and analysis of the receiver subsystem (lensed antenna, RF frontend electronics, and IF processor module) for the Hyperspectral Microwave Atmospheric Sounder (HyMAS) comprising multiple receivers near the oxygen absorption line at 118.75 GHz and the water vapor absorption line at 183.31 GHz. The hyperspectral microwave receiver system will be integrated into a new scanhead compatible with the NASA GSFC Conical Scanning Microwave Imaging Radiometer/Compact Submillimeter-wave Imaging Radiometer (CoSMIR/CoSSIR) airborne instrument system to facilitate demonstration and performance characterization under funding from the NASA ESTO Advanced Component Technology program. Four identical radiometers will be used to cover 108-119 GHz, and two identical receivers will be used to cover 173-183 GHz. Subharmonic mixers will be driven by frequency-multiplied dielectric resonant oscillators, and single-sideband operation will be achieved by waveguide filtering of the lower sideband. A relatively high IF frequency is chosen to facilitate miniaturization of the IF processor module, which will be fabricated using Low Temperature Co-fired Ceramic (LTCC) technology. Corrugated feed antennas with lenses are used to achieve a FWHM beamwidth of approximately 3.5 degrees. Two polarizations are measured by each feed to increase overall channel count, and multiple options will be considered during the design phase for the polarization diplexing approach. Broadband operation over a relatively high intermediate frequency range (18-29 GHz) is a technical challenge of the front-end receiver systems, and a receiver temperature of approximately 2000-3000K is expected over the receiver bandwidth. This performance, together with approximately l00-msec integration times typical of airborne operation, yields channel NEDTs of approximately 0.35K, which is adequate to demonstrate the hyperspectral microwave concept by comparing profile retrievals with high-fidelity ground truth available either by coincident overpasses of hyperspectral infrared sounders and/or in situ radiosonde/dropsonde measurements.