M-ary signal detection via a bistable system in the presence of Lévy noise

We study the problem of the M-ary signal detection via a bistable detector in the presence of Lévy noise. Based on the numerical solution of the space-fractional Fokker–Planck equation, the theoretical bit error rate is defined and used in the optimal detector design. The accuracy of the theoretical results are verified by the Monte Carlo simulations. It is shown that, with the same noise intensity, the optimal bistable detector performs better with the decreasing Lévy index α. Therefore, Lévy noise plays a more positive role in the nonlinear M-ary signal detection problem, compared to Gaussian noise.

► The M-ary signal in Lévy noise is processed via the nonlinear bistable detector. ► Solutions of the space-fractional Fokker–Planck equation are used to characterize the detector performance. ► Numerical simulations show that the detector performance can be predicted both accurately and efficiently. ► The detector performance increases with the decreasing Lévy index.