A Multi-Carrier $M$ -Ary Differential Chaos Shift Keying System With Low PAPR

An improved multi-carrier <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -ary differential chaos shift keying (MM-DCSK) system is presented, where differential modulation and demodulation are carried out across multiple carriers in the frequency domain, so channel estimation is not needed. For one data frame transmission, only one non-information-bearing reference sub-carrier signal is required, and the reference of each information-bearing sub-carrier is its previous sub-carrier signal, thus high energy efficiency is attained. If channel response changes during a frame period, the time diversity is achieved. In addition, the peak-to-average power ratio (PAPR) is considered, and it is found that adjacent symbols with a large Euclidean distance achieve a low PAPR. Accordingly, a low-complexity PAPR reduction algorithm is proposed based on symbol-interleaving with only one inverse fast Fourier transform processor. The simulation results demonstrate that the system with the proposed algorithm dramatically reduces the PAPR. Analytical bit-error-rate expressions are derived and verified by simulations over additive white Gaussian noise and multi-path fading channels.