Demodulation of Weighted Fractional Fourier Transform Encrypted Chaotic Direct Spread Signals over Multipath Fading Channels

To demodulate the Weighted FRactional Fourier Transform encrypted Chaotic Direct Sequence Spread Spectrum (WFRFT-CD3S) signal over multipath fading channels, a generalized channel differential demodulation algorithm is proposed. The transmitter of the WFRFT-CD3S system modulates differentially the message bits. The receiver regards the product of the differential code and the channel as a generalized channel, and constructs a frequency-domain matched filter through the local spreading sequence to estimate the generalized channel impulse response. The receiver combines the path energies and recovers the message bits by de-differentiating the estimates of the generalized channel impulse response. The bit error rate of the proposed algorithm is analyzed theoretically, and the theoretical results are verified by numerical simulation. The numerical simulation results show that the proposed demodulation algorithm can demodulate the multipath WFRFT-CD3S signal under low signal-to-noise ratio, which ensures the anti-energy detection capability of the WFRFT-CD3S system.