I. Introduction
As a result of propagation through ionosphere electron density irregularities, transionospheric radio signals may experience amplitude and phase fluctuations. The signal fluctuations, referred to as scintillations, are created by random fluctuations of the medium's refractive index, which are caused by inhomogeneities inside the ionosphere[1]. As far as the ionospheric scintillation is concerned, the accurate quantification of the statistical characteristics of the instantaneous variation of signal amplitude plays an important role in the design of satellite services and systems. Generally, there are three methods to reproduce the fading characteristics of amplitude scintillations. The first method is based on scintillation time histories recorded by an ionospheric scintillation monitor. Although a system testing strategy based on historical data is attractive for its realism, nonetheless it's difficult for system designers or test engineers to adjust the scintillation behavior and extend testing scenes under different scintillation statistics [2]. The second method is to synthesize scintillation data based on first-principles physics-based ionospheric models and phase screen models [3]–[4], which is heavy computing burden and difficult for engineering applications. The third method is to adopt some statistical models, which may be the simplest scintillation model in terms of number of parameters and computing burden. At the same time, the statistical models could retain the scintillation properties [5]. There are two kinds of available statistical models. One kind is just like the Cornell Scintillation Model (CSM). The CSM specifies scintillation statistics by two parameters, S4 and To. To is the autocorrelation time of the scintillation [5]. For most of the system designers, they have little knowledge of the parameter τ0. The other kind is the statistical distribution models. The most frequently used distributions are the Nakagami-m distribution and the Rayleigh distribution [6]. For weak and moderate scintillation regimes, the statistics of the instantaneous variation of amplitude is assumed to follow the Nakagami-m distribution, where the Nakagami “m-coefficient” is related to the scintillation index by m = In the strong scintillation regime, as the index approaches 1.0, the statistics of the instantaneous variation of amplitude is assume to follow a Rayleigh distribution, where . Although the α-µ distribution model has one more degree of freedom than the Nakagami-m distribution, but it is also difficult to describe the variation of the parameter α and µ [7]–[8]. The Nakagami-m distribution and the Rayleigh distribution are validated based on the amplitude scintillation data recoreded at Haikou station (geographic 20.0°N, 110.3°E; geomagnetic10.1°N, 177.4°W, dip 28.2°). A new relationship function between the S4 index and the Nakagami “m-coefficient” with enough accuracy is put forward in this paper, which could much better describe the statistics of the instantaneous variation of signal amplitude in the whole range of S4 and is also easy enough for engineering application.