Performance Simulation And Optimization Of Time-varying Filter Based On Time-frequency Transform

In recent years,the wireless communication industry has developed rapidly,and the quality of communication has also improved.It evolved from the initial 1G analog communications to 4G which has achieved large-scale commercialisation,and now 5G is almost ready to come out.Various types of communication services emerge in endlessly,which greatly facilitates production and daily life.However,with the rapid growth of the total number of mobile communications users,the problem of spectrum resource shortage is getting worse.If a filter can separate the signals which is very closed to each other on the spectrum,the spectral efficiency will be improved greatly.The Fourier transform can only analyze stationary signals.For non-stationary signals,it can only give the frequency components,but can not tell when the component appears.To resolve this problem,a series of time-frequency distributions have been developed in recent years,which enables us to analyze non-stationary signals from two dimensions simultaneously.In this paper,the method of timefrequency transform is used to design time-varying filters.The filters are based on short-time Fourier transform(STFT),Wegener Wiley distribution(WVD)and S transform.For comparison,two traditional filters are used,such as time-invariant filter and Calman filter.This paper uses the Matlab software to simulate the performance of the filters above.The signals analyzed are linear frequency modulated signal(Chirp),modulated Gauss signal and modulated root raised cosine signal.There is a phase mutation at the time window junction.In this paper,the method of time window overlap is used to restrain the mutation.Then optimize the step of time window and the number of zero-padding in time domain to improve the filtering performance.And the method of joint filtering is proposed because the performance of time-invariant filter is better than time-varying filter.Thus,the time-frequency characteristics of non-stationary signals can be more fully used.For the root raised cosine signal,the relation between the length of time window and the time-frequency distribution of the signal is obtained.Finally,the length of time window is chosen as half of the symbol's length,so a more stable time-frequency distribution is obtained.On the basis of that,two effective time-frequency filtering pass regions are designed.For Chirp signal and modulated Gauss signal,the mean square error(MSE)is used as a measure of filtering effect.For modulated root raised cosine signal,the bit error rate is used.Simulation results show that: For Chirp signal,time-varying filter based on STFT has better performance than the time-invariant filter;For modulated Gauss signal,it performes better to use the time-invariant filter first and then the time-varying filter based on STFT;For modulated root raised cosine signal,it also performes better to use the time-invariant filter first and then the time-varying filter based on STFT,but it needs to use different filtering pass regions under different interference conditions.