Understanding signal fading effect is essential for the application of Rayleigh-scattering-based distributed acoustic fibre sensors (DASs) due to the nature of coherent beam interference within the pulse length. Statistical properties for the intensity of the Rayleigh backscattered light (i.e. intensity fading) and its impact on the sensitivity of DAS systems have been intensely studied over the last decades. Here we for the first time establish an analytical model for the phase signal retrieved from the dual-pulse heterodyne demodulated DAS system, which can be exploited to investigate the phase fading effect in this system. The developed model reveals that the phase fading phenomenon mainly originates from the randomness in the phase retardant of the Rayleigh scatters. The quantitatively resolved statistical features of the phase fading is confirmed by experimental results. Based on the analytical model, a noise figure is defined to characterize the global fading-induced noise level via taking into account contributions from all channels along the sensing fiber. The model also reproduces the anti-correlation relation between the power spectrum density of retrieved phase at the heterodyne frequency and the phase fading noise level. Following the analysis and the definition of the noise figure, an optimized real-time weighted-channel stack algorithm is developed to efficiently suppress the fading noise. Experimental results show that the algorithm can achieve a maximum noise figure reduction of 15.8 dB without increasing the system complexity.