A noncoherent demodulation method for chirp-rate modulation is proposed based on the fractional Fourier transform

and the peak output of the demodulator is derived. Thereafter

this method is compared with coherent demodulation with matched filter from two aspects of Doppler shift and bit synchronization. And the analytical expressions of influence caused by the two factors are obtained

from which we can see that chirp-rate modulation has strong robustness on Doppler shift but sensitivity of bit synchronization. Finally

the simulations are made to prove the above-mentioned theories

as well as to analyze Bit Error Rate (BER). The performance of this proposed method is worse than coherent demodulation with matched filter for the former’s noncoherent mode

but the difference in BER is 3 dB.