## 2 The Ionosphere and Polarization Diversity  
The ionosphere is one of the layers of the atmosphere that, thanks to its physical characteristics, allows the refraction of radio signals between 3 and 30 MHz. Specifically, the ionization of the ionosphere is the responsible of this signal refraction. The ionization of the outer layers of the atmosphere depends on the degree of solar activity, which follows cycles of approximately 11 years and presents sunspots as an indicator [1]. The condition of the ionosphere not only changes annually, but also depends on the season and the time of day. These variations make ionospheric communications very challenging, requiring a system that adapts to the state of the ionosphere at all times. Communications through the ionosphere are classified according to the angle of incidence of the radio wave. NVIS communications are based on a 90\({}^{\circ}\) to 70\({}^{\circ}\) angle of incidence, and generate a coverage area of up to 250 km (depending on frequency and ionospheric conditions) from the point of transmission [11]. The focus of this article is to define the physical properties of the NVIS channel (Figure 1). Figure 1: Near vertical incidence skywave (NVIS) link scenario. The ionosphere presents multiple layers (D layer, E layer, and F layer, which splits into F\({}_{1}\) and F\({}_{2}\) layers during daytime), which depend on the sun's ionization [1]. NVIS communications can use both the E layer and the F\({}_{2}\) layer. Taking into account the distance between our nodes, and in order to maximize the received signal strength, we based our study on the F\({}_{2}\)-layer propagation. Furthermore, the ionosphere is a birefringent medium. Two modes or propagation (ordinary and extraordinary) are formed as soon as the radio wave enters the ionized plasma in the presence of a magnetic field. The plane-polarized wave is decomposed into two different waves, and the direction of energy is deviated from the direction of propagation [1]. This partition creates two totally different propagation paths, resulting in two independent communication channels. Specifically, when a radio wave reaches the ionosphere, the electrons in the layer start an elliptical movement [1]. As a result of this almost-circular spin, the radio wave has its polarization changed by the ionosphere. This leads to the return to the Earth of two different rays (the ordinary and extraordinary rays) with different properties, such as different critical frequencies, phase, amplitude, and arrival time [2]. Specifically, both of these waves have elliptical polarization and also have opposite rotation sense. For the Northern Hemisphere, the ordinary wave has the greater delay and left-hand circular polarization (LHCP), and the extraordinary wave presents the lesser delay and right-hand circular polarization (RHCP) [13]. These different properties can be used to improve telecommunication links, as polarization diversity techniques are an option in ionospheric channels. The different polarizations and the usage of the ionospheric characteristic waves as two different communication channels allow for the usage of polarization diversity techniques to improve the robustness and throughput of the link. The concept of polarization diversity was first introduced by the authors of [14] in the 1950s. The work presented in Reference [15] was one of the first to use polarization diversity at the receiver achieving 9600 bps for a 1800 km skywave link. The authors of [16] highlighted the importance of using both ordinary and extraordinary waves for multiple-input multiple-output (MIMO) in the case of NVIS propagation, and the cross-correlation of both channels was analyzed for narrowband transmissions. A channel model for dual polarized MIMO communications was proposed in [17] and some high throughput testbeds are presented in [18; 19], where the improved channel capacity was analyzed.