Radars performing observations of resident space objects (RSO) measure Doppler variations in wave events of several minutes duration, with frequencies in the 0.2–1 Hz range peaking near 0.5–0.7 Hz, consistent with variations in electron density induced by waves in the intervening ionosphere. The two mid-latitude radars used were a Very High Frequency (VHF) radar operating at 55 MHz, and a High Frequency (HF) radar operating at 30 MHz, both in southern Australia.The VHF radar wave observations exibited a peak in wave occurrence in the post-dawn sector (0600–1200 local solar time). The seasonal occurrence of the waves had a strong minimum during winter compared with the other seasons. Comparison between observations in 2018/19 (near solar minimum) and 2021/22 (mid-rise to cycle 25 peak) suggests wave occurrence is anti-correlated with sunspot number and hence with EUV and ionospheric strength. Generally the waves had higher frequencies during night than day, and low sunspot number than mid solar cycle, when there was a weaker ionosphere.Given the oscillation frequency of the wave events, the most likely geophysical phenomena that is consistent with the observations are electro-magnetic ion cyclotron (EMIC) plasma waves in the Pc1 (0.2–5 Hz) frequency range. No other candidate geophysical disturbance appears to fit the wave characteristics. The majority of geomagnetic field-guided transverse Pc1 EMICWs project from the outer magnetosphere down onto the polar ionosphere, where they can convert to compressional fast-mode waves propagating parallel to the Earths surface in the ionospheric F2 layer waveguide, both equatorwards to mid-latitudes and polewards. It is likely the majority of the Doppler oscillations in the Pc1 frequency range observed by the radars at mid-latitudes are these ducted compressional waves. However, sources of transverse EMICWs from the magnetosphere onto the mid-latitude ionosphere do exist, and these may cause some of the observed oscillations. The micro-physics of these compressional waves causing Doppler oscillations in radio observations is not inconsistent with the history of ionospheric Doppler measurements and theory, although the radar trans-ionospheric radio propagation and the observed waves being higher frequency than previous studies is different.If the observed Doppler oscillations are compressional EMICW in the ionospheric waveguide then several of the statistical results can be explained. The anti-correlation of the wave occurrence with sunspot number (and resultant ionospheric strength) can be attributed to lower ionospheric attenuation at the higher latitudes, between where geomagnetically field-guided transverse EMIC waves initially enter the high-latitude ionospheric waveguide from the magnetosphere above, and their observation at mid-latitudes. The observation of higher frequency waves during low sunspot number may also be explained by a source effect in the magnetosphere that preferentially selects the higher frequency field-guided transverse EMIC waves to propagate down to the ionosphere.Comparisons will be shown with results from ground and space based magnetometers of compressional waves in the waveguide, highlighting consistent results and areas where the measurement techniques differ. Theory suggests the radar Doppler measurements are far more sensitive to variations in in-situ ionospheric electron density than magnetic field variations. This agrees with existing literature which highlights the very strong contribution from the compressional component. Theory also suggests that the Doppler sensitivity of a radar to ionospheric electron density variations is frequency dependent, with lower frequencies being more sensitive. This is borne out by the measurements, with the HF radar being more sensitive than the VHF radar.