Research On Rician Phase Distributions And Signal Detection In Phase Noise

The detection of communication signal is often affected by noise.When the useful signal travels in the phase of complex data,the phase of complex data is needed to detect the useful signal.When complex data is converted to phase data,the phase wrapping problem occurs and the complex noise is transformed into the phase noise which will continue to affect the signal detection in the phase domain.Considering that the phase noise of zero-mean complex Gaussian noise follows the Rician phase distribution,this thesis studies the functions and characteristics of the Rician phase distribution,and discusses the problem of signal detection in the Rician phase noise.The main works of this thesis can be summarized as follows:1.Research on the Rician phase distributionThe probability density functions and the cumulative distribution functions are introduced for the unwrapped phase noise and wrapped phase noise respectively.The formulas of the numeral characteristics,such as the mean and the variance,are derived.The approximation methods of numeral characteristics are proposed.Considering the non-integral expressions in distribution functions and numeral characteristics,an adaptive method is introduced for numerical integration.2.Research on signal detection in Rician phase noiseBased on the common matched filter,the thesis studies the theory of signal detection in the phase noise.Firstly,according to the phase signal model,the detectors are developed from the phase domain.Then,the distributions of test statistic and the formulas of test signal-to-noise ratio(TSNR)are derived for the two kinds of phase noise.Secondly,the maximum likelihood detector in the boundary effect is analyzed for the unwrapped phase noise.Finally,the experimental results based on binary phase shift keying(BPSK)modulation demonstrate that the simulation bit error rate is consistent with the theoretical bit error rate,so that the theoretical analysis is correct.3.Research on communication performance of weak signal detectionThe case of communication signal is weak,is analyzed.Firstly,considering the flat fading channel,the TSNR of communication signal is derived and the approximation calculation method is proposed.Then for the Rayleigh fading channel,the formula of the average TSNR is derived.Taking the BPSK as an example,the theoretical formula and approximate calculation method of bit error rate are analyzed.Finally,simulations of the signal-to-noise and the bit error rate demenstrate that the TSNR is non-linear to the complex signal-to-noise ratio,and the TSNR can be directly converted to the average bit error rate.