The significant progress of quantum sensing technologies offer numerous radical solutions for measuring a multitude of physical quantities at an unprecedented precision. Among them, Rydberg atomic quantum receivers (RAQRs) emerge as an eminent solution for detecting the electric field of radio frequency (RF) signals, exhibiting great potential in assisting classical wireless communications and sensing. So far, most experimental studies have aimed for the proof of physical concepts to reveal its promise, while the practical signal model of RAQR-aided wireless communications and sensing remained under-explored. Furthermore, the performance of RAQR-based wireless receivers and their advantages over classical RF receivers have not been fully characterized. To fill these gaps, we introduce the RAQR to the wireless community by presenting an end-to-end reception scheme. We then develop a corresponding equivalent baseband signal model relying on a realistic reception flow. Our scheme and model provide explicit design guidance to RAQR-aided wireless systems. We next study the performance of RAQR-aided wireless systems based on our model, and compare them to classical RF receivers. The results show that Doppler broadening-free RAQRs are capable of achieving a substantial received signal-to-noise ratio (SNR) gain of over 27 decibel (dB) and 40 dB in the photon shot limit and standard quantum limit regimes, respectively.