In this paper, we explore several widely available software-defined radio (SDR) platforms that could be used for locating with the signal Doppler frequency (SDF) method. In the SDF, location error is closely related to the accuracy of determining the Doppler frequency shift. Therefore, ensuring high frequency stability of the SDR, which is utilized in the location sensor, plays a crucial role. So, we define three device classes based on the measured frequency stability of selected SDRs without and with an external rubidium clock. We estimate the localization accuracy for these classes for two scenarios, i.e., short- and long-range. Using an external frequency standard reduces the location error from 20 km to 30 m or 15 km to 2 m for long- and short-range scenarios, respectively. The obtained simulation results allowed us to choose an SDR with appropriate stability. The studies showed that using an external frequency standard is necessary for minimizing SDR frequency instability in the Doppler effect-based location sensor. Additionally, we review small-size frequency oscillators. For further research, we propose two location sensor systems with small size and weight, low power consumption, and appropriate frequency stability. In our opinion, the SDF location sensor should be based on the bladeRF 2.0 micro xA4 or USRP B200mini-i SDR platform, both with the chip-scale atomic clock CSAC SA.45s, which will allow for minor positioning errors in the radio emitters.