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The chaotic direct sequence spread spectrum (CD3S) is one of the distinguished techniques providing physical layer secrecy and low probability of intercept (LPI) in wireless communication. Due to the noise-like and aperiodic characteristics of chaotic signals, the synchronization of CD3S signals is a challenging issue. A synchronization approach for aperiodic CD3S signals based on bidirectional correlation search (BDCS) is proposed. Through a joint acquisition of forward frequency domain matched filtering (FDMF) and backward FDMF, the synchronization module aligns received CD3S signals with local chaotic sequences without aid of the pilot signal. The probability distribution of correlator output is derived with additive white Gaussian noise and narrowband jamming. The probability of detection, probability of false alarm, and bit error rate are analyzed mathematically. An approximate solution of the local optimal acquisition threshold coefficient is obtained. These theoretical analyses are verified by numerical simulations, the results of which demonstrate that the proposed synchronization approach enables the CD3S system to resist interception and adapt to the environment with low signal-to-noise and signal-tojammer ratios.

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Weighted fractional Fourier transform encrypted chaotic direct sequence spread spectrum (WFRFT-CD3S) signal is aperiodic and complex Gaussian distributed. The aperiodicity and complex Gaussian distribution are conducive to the covert transmission of information but also make it difficult to acquire the WFRFT-CD3S signal. An acquisition method implemented in two steps is proposed to acquire the Doppler-shifted WFRFT-CD3S signal. First, a bidirectional correlation search method is proposed to align the received signal with the local spreading sequence in the time domain. The correlation peak attenuation caused by the Doppler frequency shift is eliminated by differential. Second, the accumulated phase angle caused by the Doppler frequency shift is obtained by the differential correlation value between the aligned received signal and the local spreading sequence. Then, the Doppler frequency shift is estimated by the accumulated phase angle. The detection probability, the false alarm probability, and the root mean square error (RMSE) of the Doppler shift estimation are analyzed theoretically and simulated. The theoretical results are verified by simulation. Theoretical results and simulations show that the detection probability is higher than 0.999, the false alarm probability is less than 0.001, and the RMSE of Doppler shift estimation is lower than 63 Hz when the signal-to-noise ratio is higher than -7.3 dB.

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