Research On Performance Of Two-dimensional Random Frequency Hopping System Based On Fractional Fourier Transform

As a typical anti-jamming and anti-interception communication technology in frequency domain,Frequency Hopping technology is widely used in military and civil communication fields,because of its mature technology,stable performance and simple implementation.With the development of the times,signal detection and estimation methods become more diversified,and detection methods for frequency hopping signals are gradually mature.The relatively fixed parameter characteristics of traditional Frequency Hopping communication signals provide a breakthrough for signal detection and parameter interception by non-cooperative receivers.Therefore,in order to improve the anti-interception ability of the FH system under the new signal detection and estimation means,a new FH system is needed to be designed.On the basis of improving the concealment performance of the FH system,it can also effectively counteract interference.This paper refers to the realization of Frequency Hopping based on Orthogonal Frequency Division Multiplexing(OFDM-FH).A novel two-dimensional random Frequency Hopping system based on Fractional Fourier Transform(FrFT-TDR-FH)is proposed.The system uses Chirp signals of different frequency parameter as the base functions,which is different from the traditional Frequency Hopping system which uses sinusoidal base signals.The discrete Fractional Fourier Transform structure is used to modulate the FH base signal,and the modulation frequency and the center frequency of the base signal are respectively controlled by different pseudo-random codes,so that the two-dimensional random variation of system parameters can be realized.Specific research contents are described as follows:Firstly,the mathematical model of FrFT-TDR-FH system is established.The basic principle of each module is explained.The baseband signal modulation process and mathematical expression of the system are given,and the relationship between the subcarriers of the system is analyzed;Secondly,the paper analyzes the FrFT-TDR-FH signal power spectrum characteristic.Carrier frequency,frequency hopping period and timing synchronization error are estimated by simulating non-cooperative receivers and compared with traditional Frequency Hopping,analysised estimation error.The anti-scanning performance was analyzed by using constellation diagram.The simulation results show that the proposed FrFT-TDR-FH system signal power spectrum is wider and flatter,which is suitable for hidden in the noise.Due to the two-dimensional random variation of FrFT-TDR-FH signal parameters,the estimation errors of FrFT-TDR-FH signal carrier frequency,frequency hopping period,timing synchronization error and other parameters by parameter estimation methods are greater than that of traditional Frequency Hopping signals,verifying the FrFT-TDR-FH system has a better concealment.The anti-scan analysis results show that even if the non-cooperative party obtains the parameter information roughly through the signal estimation method,realized the non-cooperative reception,and it is known that the signal has been processed to the Fractional Fourier Transform,but due to the randomness of the transformation order,the non-cooperative party still needs to obtain the transformation order information through a large number of scans.Once the order deviation occurs,it is also difficult to demodulate the correct information;Finally,the FrFT-TDR-FH system communication performance were analyzed.The fractional domain characteristics of gaussian white noise and the system under white gaussian noise channel bit error rate performance was deduced.The theoretical results are verified by simulation.the simulation results show that the theoretical results are consistent with the results of simulation,and the Fractional Fourier Transform can't improve the system BER performance under white gaussian noise channel;The influence of Doppler frequency offset on signal reception in wireless channel is analyzed theoretically.The analysis results show that the anti-Doppler frequency offset performance of FRFT-TDR-FH system can be improved with appropriate conversion order range,and the performance of FRFT-TDR-FH system is better than that of traditional Frequency Hopping system under the same bandwidth.This paper establish the mathematical models of single tone interference and linear frequency modulation interference.The bit error rate performance of FrFT-TDR-FH system under monotone interference and linear frequency modulation interference is derived theoretically.The bit error rate formula is given and verified by simulation.The results show that the anti-jamming performance of FrFT-TDR-FH system is better than that of traditional frequency hopping system.On the basis of this conclusion,the anti-jamming performance results of FrFT-TDR-FH system with different modulation modes are compared.