Owing to the capacity of processing linearly frequency-modulated signals with GHz-bandwidths in the optical domain, microwave photonic receivers with de-chirp processing are key to realizing radars with high resolution. In this paper, general theoretical models for microwave photonic receivers with de-chirp processing are proposed, based on which the gains for eletrical signal in the de-chirp processing are derived. Moreover, the noise and dynamic range of the receiver are analyzed using the proposed models. The results reveal that the gain for noise in the microwave photonics-based de-chirping receiver with one output channel is twice that for the signal. Additionally, the impact of key parameters on the performances of a typical receiver is investigated via numerical simulations. We employs an electrical pre-amplifier with a gain of 20 dB in a photonics-based de-chirping receiver. This helps us obtain an improvement of 10.8 dB on the sensitivity with a dynamic range degradation of less than 2 dB when the half wave voltage of the electro-optical modulator decreases from 6 V to 1.5 V. However, if the half wave voltage is less than 3 V, an electrical pre-amplifier with a gain lower than 30 dB is recommended to avoid major deterioration of the dynamic range.