We propose a novel bit error rate (BER) analysis model of weighted-type fractional Fourier transform (WFRFT)-based systems with WFRFT order offset Δα. By using the traditional BPSK BER analysis method, we deduce the equivalent signal noise ratio (SNR), model the interference in the channel as a Gaussian noise with non-zero mean, and provide a theoretical BER expression of the proposed system. Simulation results show that its theoretical BER performance well matches the empirical performance, which demonstrates that the theoretical BER analysis proposed in this paper is reliable.

In this paper, a scramble phase assisting weighted-type fractional Fourier transform (SPA-WFRFT) based system is proposed to guarantee the communication's security. The original transmitting signal is divided into two parts. The first part is modulated by WFRFT and subsequently makes up the constellation beguiling. The other part is used to generate the scramble phase and also to assist in the encryption of the WFRFT modulated signal dynamically. The novel constellation optimal model is built and solved through the genetic algorithm (GA) for the constellation beguiling. And the double pseudo scheme is implemented for the scramble phase generation. Theoretical analyses show that excellent security performances and high spectral efficiency can be attained. Final simulations are carried out to evaluate the performances of the SPA-WFRFT based system, and demonstrate that the proposed system can effectively degrade the unauthorized receivers' bit error rate (BER) performance while maintaining its own communication quality.