  Recent advances in the development of cryogenic particle detectors such as
magnetic microcalorimeters (MMCs) allow the fabrication of sensor arrays with
an increasing number of pixels. Since these detectors must be operated at the
lowest temperatures, the readout of large detector arrays is still quite
challenging. This is especially true for the ECHo experiment, which presently
aims to simultaneously run 6,000 two-pixel detectors to investigate the
electron neutrino mass. For this reason, we developed a readout system based on
a microwave SQUID multiplexer ($\mu$MUX) that is operated by a custom
software-defined radio (SDR) at room-temperature. The SDR readout electronics
consist of three distinct hardware units: a data processing board with a Xilinx
ZynqUS+ MPSoC; a converter board that features DACs, ADCs, and a coherent clock
distribution network; and a radio frequency front-end board to translate the
signals between the baseband and the microwave domains. Here, we describe the
characteristics of the full-scale SDR system. First, the generated frequency
comb for driving the $\mu$MUX was evaluated. Subsequently, by operating the SDR
in direct loopback, the crosstalk of the individual channels after frequency
demultiplexing was investigated. Finally, the system was used with a 16-channel
$\mu$MUX to evaluate the linearity of the SDR, and the noise contributed to the
overall readout setup.
