Research On Fractional Fourier Transform And Phase Spectrum Processing Techniques For Wireless Communications

As wireless communications theories and implementation capacity make a progress continuously, it is about to enter 4G communications era. When we look back to the former three generations of wireless communication systems, it can be found that the upgrade of wireless communication systems is based on the evolution of signal processing methods. The improvement of signal processing methods promotes the development of wireless communication systems, and the research on signal processing methods based on different transforms is a significant research direction.Traditional signal processing methods are in time domain and frequency domain, which use Fourier Transform to achieve signal conversion from time domain to frequency domain. With the rise of data transmission rate and moving speed, the time and frequency dual selective channel has became a major application channel, where time-frequency analysis tool should be used for better performance. And Fractional Fourier Transform (FrFT) is an excellent time-frequency analysis tool, which is the generalization of Fourier Transform in time-frequency two-dimensional plane. FrFT can achieve signal conversion in time-frequency two-dimensional plane with arbitrary transform angle. Because the base function of FrFT is linear frequency modulation signal (chirp), chirp signal has an energy concentration property in FrFT domain, and based on this property synchronization and channel parameter estimation in wireless communicatons can be achieved by peak detection. And in frequency domain traditional signal processing methods focus on amplitude spectrum and ignore phase spectrum, we foucus on chirp signal and illustrate the importance of phase spectrum. When signal processing method in phase domain is applied the wireless communication system has a better anti-narrowband interference performance. Based on FrFT and signal processing method of phase spectrum we focus on the applicatons of chirp signal in the following aspects:Firstly, a joint timing and frequency synchronization method based on chirp signal and FrFT for orthogonal frequency-division multiplexing (OFDM) system. Aimed at the limited timing synchronization accuracy and frequency offset estimation range, we propose to use chirp training signal and do FrFT at receiver side to achieve timing and frequency synchronization simultaneously. The combination of two chirp signals with opposite chirp rates are used as the training signal, the received training signal with timing and frequency offset is transformed by FrFT and the two peaks representing two chirps in FrFT domain are detected, then the position coordinates of the two peaks are precisely corrected and substituted into an equation group to calculate timing and frequency offset simultaneously. And we analyse the impact of chirp parameters on the estimation error and the frequency offset estimation range of the proposed method. This method has low computational complexity, large frequency estimation range and high estimation accuracy.Secondly, a channel parameters estimation method based on chirp signal and FrFT. The existing channel parameters estimation methods need prior information of channel model or statistics, we propose a channel parameters estimation method based on chirp training signal and FrFT without channel prior information. The combination of two chirp signals with opposite chirp rates are used as the training signal, the representation of received training signal under multipath channel is derivated to show the impact of multpath channel on the parameters of transmitted chirp signal. The parameters of chirp training signal are estimated by existed estimation method then the channel parameters can be derived. The proposed method is able to be applied in circumstance where different paths have different Doppler frequency shift and the calculation amount is half of the existing method. The simulation results show that the proposed method has less estimation error than the existed method in time delay and Doppler frequency shift estimations. Then a subchip multipath time delay estimation method based on chirp signal and FrFT is proposed. Single component chirp signal is used as training signal, the multipath chirps are processed by FrFT at receiver, then the relative delays between multipath chirps can be calculated after detecting peak positions according to the linear relationship between the relative delay in time domain and difference between peak positions of multipath chirps in FrFT domain. The delay estimation resolution in time domain is equal to the reciprocal of the bandwidth of chirp signal, so the chirp signal with bandwidth lager than that of direct sequence spread spectrum (DSSS) signal should be used to search for subchip multipath. And the calculation complexity is less than sliding correlation method by 3 orders of magnitude. To improve the energy efficiency of multipath signal, the combining method of subchip multipath is also introduced. Simulation results show that the proposed method can calculate the relative delays of subchip multipath effectively, and the BER performance of receiver can be improved after the equal-gain-combining process of the recognized subchip multipath.Finally, a BPSK modulation chirp signal receiving method based on signal processing method of phase spectrum. Aimed at the harmful impact of threshold value affected by interference power on amplitude spectrum restriction anti-narrowband interference performance stability, based on the phase spectrum which contains key information characterizing chirp signal, we propose a receiving method in phase domain for BPSK chirp signal. The phase characteristic disturbance model for chirp signal in additive white Gaussian noise (AWGN) environment is established, and the probability density function (PDF) of phase characteristic disturbance is obtained .Then a novel receiver model for BPSK chirp signal based on maximum likelihood (ML) criterion is proposed. The simulation results show that, comparing with correlation scheme, performance of the proposed receiving method for chirp signal is 1dB worse in AWGN environment but the BER performance suffer little from the narrowband interference. The proposed receiving method in phase domain can also be applied to DSSS signal because its phase spectrum contains key information as well as chirp signal, and the simulation results show that the proposed receiving method also work well for DSSS signal, and the suppression performance of narrowband interference of the proposed method is better than correlation method with amplitude spectrum restriction.