This article derives a novel unified signal processing scheme for WiFi-based passive radar in order to limit its complexity and enhance its suitability for short range civilian applications. To this purpose, the exploitation of a reciprocal filtering (RpF) strategy is investigated as an alternative to conventional matched filtering at the range compression stage. Along with the well-known advantage of a remarkable sidelobes control capability for the resulting range-Doppler response, the use of a RpF is shown to provide additional benefits for the specific sensor subject of this article. Specifically, it allows to streamline the disturbance cancellation stage and to implement a unified signal processing architecture which is capable to handle the different modulation schemes typically adopted in WiFi transmissions. Appropriate adjustments are also proposed to the theoretical RpF in order to cope with the inherent loss in terms of signal-to-noise power ratio. The effectiveness of the proposed signal processing scheme encompassing the RpF strategy is proved against both simulated and experimental datasets.