Random matrix theory to predict the intensity fluctuations for a wave propagating through a range-dependent medium

There are currently no physics-based models to predict the Scintillation Index (SI) for a wave propagating in a random medium. The current predictions for SI use ray models, which are high frequency approximations, and work only at ranges that are either very close to the source or asymptotically far away. The far ranges lie in the "Rayleigh-regime" of propagation. Other physics-based models use modes of the waveguide in transport equations, and yet do not yield high-order statistics, such as the SI. This paper also uses modes but models the propagation across range as a product of random propagation matrices. The matrices are unitary, and independent of each other. These types of matrix-products are used to run Monte-Carlo simulations for mode, and wavefront statistics across different ranges. To confirm the predictions, this paper compares them against complementary parabolic equation simulations. This paper also shows that the product of random matrices is equivalent to a Dyson Brownian Motion (DBM) process across range. Expressions from DBM are used to analytically predict the statistics of the signal in the asymptotic limits for propagation and also suggest approximations prior to the Rayleigh-regime.