Wuhan ionospheric oblique backscattering sounding system (WIOBSS) is a low-power high-frequency monostatic radar used for ionospheric sensing and aircraft detection. In this study, a novel waveform combining the pseudo-random binary phase coding (PRBPC) and the chirp modulation is proposed for this radar. Furthermore, in terms of the radar waveform requirements, four subclasses of this waveform are theoretically compared to determine which one of them is most suitable for WIOBSS, including the inter-pulse PRBPC waveform where the width of the subpulse is equal to the chirp duration, the inter-pulse PRBPC waveform where the period of the coding sequence is equal to the chirp duration, the intra-pulse PRBPC waveform where the width of the subpulse is equal to the chirp duration, and the intra-pulse PRBPC waveform where the period of the coding sequence is equal to the chirp duration. The radar waveform requirements, the ambiguity function analysis, and the performance comparison of aforementioned waveforms are described. The analysis results show that the inter-pulse PRBPC waveform where the period of the coding sequence is equal to the chirp duration has the best performance, and can achieve higher range resolution, larger signal processing gain, and better Doppler tolerance than the conventional binary phase coded waveforms.