Chaotic Polarization-Assisted ${L}$ DPSK-MPPM Modulation for Free-Space Optical Communications

In this paper, we present a polarization-assisted <inline-formula> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula>-ary differential phase-shift keying multipulse pulse-position modulation (PA.<inline-formula> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula>DPSK-MPPM) technique that is secured in the physical layer by a discrete-chaos system. The all-optical PA.<inline-formula> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula>DPSK-MPPM scheme benefits from the polarization as an additional degree of freedom which greatly reduces the system complexity relative to prior implementations. The discrete-chaos scrambling is based on a message-seeded two-dimensional chaotic map tailored for independent perturbation of the occupied time-slot positions (MPPM information) and their relative phase shift (<inline-formula> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula>DPSK information). Synchronized and non-synchronized implementations of the chaotic PA.<inline-formula> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula>DPSK-MPPM technique are proposed with expressions for the corresponding spectral efficiencies being determined and compared with prior <inline-formula> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula>DPSK-MPPM setups. The performance of PA.<inline-formula> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula>DPSK-MPPM under gamma-gamma (GG) free-space optical (FSO) fading channels is analytically verified to outperform the prior designs for different FSO channel states which is supplemented by Monte Carlo (MC) simulations. The system security is numerically examined against various types of attacks, including brute-force, differential, and statistical attacks.