# A Novel 3D Analytical Scattering Model
## 1 Introduction  
The wireless communication link of a node at high altitude with a node at the ground is often encountered in various different scenarios. The applications of such air-to-ground (A2G) and ground-to-air (G2A) communication links include the provision of navigation services for aeroplanes, airborne Internet access for passengers in aeroplanes and communication links to unmanned air vehicles (UAVs) for military applications, cargo delivery, industrial inspection, weather monitoring, emergency humanitarian missions, law enforcement, border control and remote sensing. Moreover, high altitude platforms (HAP) to assist the land mobile radio cellular networks are expected to play a vital role [1,2] in emerging fifth generation (5G) communication systems for delivering high speed, large volume, power efficiency, low latency and global coverage of the data networks. In delivering the dynamic demands of A2G/G2A communication links, it is essential to have a reliable understanding of the propagation channel. Therefore, various studies to characterize the behaviourof A2G/G2A channels are available in the literature [3; 4; 5; 6; 7; 8; 9; 10]. In various scenarios of A2G/G2A radio propagation environments, the scatterers in the vicinity of the ground station (GS) often lead to a rich multipath propagation, causing small-scale fading [4; 11; 12]. The high speed mobility of a high altitude node in such a rich multipath environment imposes spread in the spectrum, which further leads to fast time variations in the channel characteristics. It thus becomes essential to thoroughly investigate the small-scale fading characteristics of such A2G/G2A communication links. Several studies on the characterization of the power delay profile, channel correlations and the Doppler spectrum of A2G/G2A communication links are available in the literature [3; 4; 5; 6; 7; 8; 9; 10; 11; 13; 14; 15; 16]. A comprehensive review of various A2G/G2A communication channels in terms of the channel's bandwidth and suitable frequency range is provided in [5]. A large number of experimental works relating to the characterization and modelling of the A2G/G2A channel over land areas (desert, mountain, etc.) is given in [11; 14; 16; 17]. In [16], a measurement-based multipath channel model for wideband aeronautical telemetry communication links is proposed. In [11], a study on wideband channel characteristics is presented based on measurement campaigns using low altitude antenna arrays at 2 GHz. For A2G/G2A communications over the sea surface, only a few experimental studies for channel characteristics are available in the literature (e.g., [4; 13; 18]); thus, there is a substantial scope to conduct a comprehensive study on challenging scenarios of A2G/G2A communications over the sea surface. The measurement-based studies in [4; 13] are limited only for the C band and are applicable for low altitude airborne communications. Channel characterization for UAV systems is conducted for hilly suburban propagation environments in [6]. The measurements are conducted for power delay profiles, which are further used in computing the propagation path loss and root-mean square (rms) delay spread of the channel. An early notable contribution on modelling of A2G/G2A channels is presented in [19] for the selective and non-selective behaviour of multipath A2G/G2A environments. An analysis on the capacity of multiple-input multiple-output (MIMO) systems for UAV communication links with GS is presented in [20]. [PERSON] et al. in [9] proposed a two-dimensional (2D) geometric model for the spatial characteristics of the A2G/G2A channel. Recently, a detailed analysis on the plain angle of arrival (AoA) statistics of three-dimensional (3D) A2G/G2A propagation channels is presented in [21]. In [7], an empirical study on the Doppler spectrum conducted at an airport is presented. In [22], a measurement-based study on the Doppler spectrum at 5.2 GHz is conducted. An analysis on the Doppler spectrum of satellite-to-earth MIMO channels is presented in [23].