Two-dimensional Frequency Hopping Communication System and Performance Analysis Based on Discrete Fractional Fourier Transform
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摘要: 传统跳频(FH)通信技术具有抗干扰能力强、截获概率低等优点，广泛应用在军民领域。针对检测传统跳频的手段越来越成熟，信息易被截获的问题，该文借鉴正交频分复用(OFDM)系统框架，提出一种基于离散分数阶傅里叶变换(DFrFT)的时宽与起始频率跳变的分数阶跳频(FrFT-FH-VTFB)系统，设计了一种新的系统框架，实现信息隐蔽传输的同时，通过DFrFT的工程实现规避传统跳频工程应用中跳速受频率合成器限制的问题。该系统通过两组不同伪随机序列选取时宽与起始频率跳变的Chirp基信号，实现系统参数的多维变换，打破系统的周期特性。此外，建立了系统发送与接收两端数学模型，并在此基础上推导了系统在白噪声信道下的理论误码率。仿真结果表明，该文所设计的系统有较好的抗衰落性能；且功率谱淹没在噪声之下，时频域特征无明显周期特性，有较好的隐蔽性。Abstract: Because of the advantages of strong anti-interference ability and low probability of interception, Frequency Hopping (FH) is widely used in military and civilian fields. In view of the increasingly mature means of detecting FH and the information is easy to be intercepted, by drawing on the Orthogonal Frequency Division Multiplexing (OFDM) system framework, a Fractional Fourier Transform Frequency Hopping with Variable Time Wide and Fixed Bandwidth (FrFT-FH-VTFB) system based on Discrete Fractional Fourier Transform (DFrFT) is proposed in this paper and a new system framework is designed. While realizing the covert transmission of information, the DFrFT is used to avoid the problem that the hopping speed is limited by the frequency synthesizer. The system uses two PN sequences to select Chirp signals with different time width and frequency to achieve multi-dimensional transformation of system parameters. In addition, this paper establishes the relevant mathematical model and derives the theoretical bit error rate of the system under white noise channel. The simulation results show that the system designed in this paper has better anti-fading performance, the power spectrum is submerged under noise and the time-frequency domain characteristics have no obvious periodic characteristics.
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表 1 各系统参数设置
系统 基信号 跳点 时宽个数 带宽个数 平均时宽带宽积 平均带宽(MHz) 平均时宽(μs) FrFT-FH-VTFB Chirp 16 8 1 250 20 12.5 FrFT-FH-FTFB Chirp 16 1 1 250 20 12.5 FrFT-FH-FTVB Chirp 16 1 8 250 20 12.5 FH 正弦信号 16 1 1 – 20 12.5 
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