Abstract: The short reference differential chaos shift keying (SR-DCSK) can effectively improve the transmission rate of the system, but the security performance is greatly reduced. To solve this problem, an SR-DCSK system based on scrambling matrix is proposed. Based on the forward shift matrix, a simple and orthogonal scrambling matrix is designed, which can disrupt the sequence of chaotic sequences and reduce the correlation between chaotic reference signals and information signals. Adopting the Gaussian approximation method, the bit error rate (BER) formula of system is derived in the additive Gaussian white noise channel, and the optimal performance parameters are solved accordingly. The simulation results show that the derived BER formula can accurately measure the BER performance of the system. Compared with the SR-DCSK system, the SMSR-DCSK system has a significant improvement in security and BER performance, and has the advantage of low implementation complexity.

Key words: differential chaos shift keying (DCSK), short-reference DCSK system based on scrambling matrix, scrambling matrix, bit error rate (BER)