Research On Channel Estimation Algorithm Based On Fractional Fourier Transform

Fractional Fourier transform (FRFT) is a generalization of the ordinary Fourier transform, which can be considered as an angle rotation in the time-frequency plane. Signal in the FRFT domain contains both the signal's time domain and frequency domain information which makes FRFT have many properties that Fourier transform does not have and can be used to handle non-stationary signals. This paper has researched the time delay and frequency offset estimation problems based on FRFT.In the time delay estimation aspect, existing literature utilized the property that Chirp signal has the best energy aggregation character in FRFT domain and proposed a method by detecting the peak position of Chirp signal's amplitude spectrum in FRFT domain. To improve the estimation performance, this paper introduces correlation operator to the FRFT domain for obtaining the peak position of Chirp signal's amplitude spectrum. The simulation results under Gaussian white noise environment show that the improved method has better estimation performance in both mean and variance aspects. AMSFDF method is introduced for the signal form it uses is not limited only to Chirp signals and the transform order is also more flexible although it has worse performance than the previous two methods.In the aspect of joint estimation of time delay and frequency offset, the traditional method based on ambiguity function has the disadvantage of high complexity. This paper introduces three joint estimation methods based on fractional Fourier transform. The fractional domain correlation peak detection method is the improvement of fractional domain Chirp signal peak detection method, and both the two methods need two Chirp signals as the transmitting signal. The simulation results in single path and multipath channel case show that the improved method can accurately estimate the time delay and frequency offset at low SNR, and the estimated error is also less than fractional domain Chirp signal peak detection method. AMSFDF joint estimation method is the improvement of AMSFDF time delay estimation method and requires only one signal as the transmitting signal. In the computational complexity aspect, the three joint estimation methods based on fractional Fourier transform is far less than the traditional ambiguity function method, shows that FRFT based joint estimation methods have computational advantage.