The Large-Aperture Experiment to Detect the Dark Age (LEDA) was designed to detect the predicted O(100)mK sky-averaged absorption of the Cosmic Microwave Background by Hydrogen in the neutral pre- and intergalactic medium just after the cosmological Dark Age. The spectral signature would be associated with emergence of a diffuse Ly$\alpha$ background from starlight during 'Cosmic Dawn'. Recently, Bowman et al. (2018) have reported detection of this predicted absorption feature, with an unexpectedly large amplitude of 530 mK, centered at 78 MHz. Verification of this result by an independent experiment, such as LEDA, is pressing. In this paper, we detail design and characterization of the LEDA radiometer systems, and a first-generation pipeline that instantiates a signal path model. Sited at the Owens Valley Radio Observatory Long Wavelength Array, LEDA systems include the station correlator, five well-separated redundant dual polarization radiometers and backend electronics. The radiometers deliver a 30-85MHz band (16<z<34) and operate as part of the larger interferometric array, for purposes ultimately of in situ calibration. Here, we report on the LEDA system design, calibration approach, and progress in characterization as of January 2016. The LEDA systems are currently being modified to improve performance near 78 MHz in order to verify the purported absorption feature.