# A Wideband Non-Stationary 3D GBSM for HAP-MIMO Communication Systems at Millimeter-Wave Bands
## 1 Introduction  
Recently, there has been a growing demand for flexible and agile connection solutions due to the increasing complexity of wireless communication and the proliferation of communication equipment [1; 2; 3]. To meet the demands, non-terrestrial networks (NTNs) have been introduced as part of sixth-generation (6G) technologies, enabling communication from urban centers to remote areas [4; 5]. The integrated air and terrestrial systems have been widely discussed by industries and academics [6]. Non-terrestrial network refers to networks, or segments of networks, that use an airborne or spaceborne vehicle for transmission, including satellites, high-altitude platform (HAP) stations, unmanned aircraft vehicles (UAVs), and so on [7]. Among them, HAP communication has gained considerable attention among researchers and practitioners. HAP is a crucial component of air-to-ground networks, providing access to many mobile and internet of things (IoT) users, particularly in rural areas with limited ground base station coverage [8; 9]. Compared to traditional communication methods, HAP communication systems offer several advantages, including wide coverage, high bandwidth transmission, quick deployment,and innovative approaches to expand and enhance communication networks [10; 11; 12; 13]. To realize high-performance HAP communication, it is crucial to accurately characterize its propagation channel and build accurate models [14]. The HAP communication model consists of two parts: stratospheric base station (SBS) and terrestrial mobile station (TMS), and they are constantly in motion. The SBS is located between 17 km and 22 km above the ground, and the high-altitude environment is very complex. Therefore, in the process of HAP modeling, it is necessary to consider the non-stationary characteristics in the time domain and the impact of large-scale parameters such as free space path loss and rainfall fading on the channel [15]. In [16], an efficient Markov-chain-based channel model was proposed for HAP communication channels. However, it did not take into account the dynamic propagation environment in practice. In order to more accurately simulate the transmission of signals in complex propagation environments, a 3D geometry-based stochastic model (GBSM) based on cylinders was proposed for HAP communication system in [17]. The birth-death process of the scatterers was considered in [18]. However, due to the high elevation angle, the Parsons pdf used was not appropriate. In [19], Markov processes were employed to describe scatterers' dynamic behavior. The non-stationary characteristics in the time domain of HAP channels were studied, and the influence of some parameters on the statistical characteristics of GBSM was simulated in [20; 21]. However, they did not consider the impact of large-scale parameters on the channel. Incorporating multiple-input multiple-output (MIMO) technology into HAP communication can improve spectral efficiency and reduce attenuation by utilizing spatial and multiplexing gains [22; 23]. In [24], the author constructed a \(2\times 2\) HAP-MIMO channel. The non-stationary characteristics in the HAP-MIMO channel were analyzed in [25]. However, in practical applications, we often need to use massive MIMO to provide high gain and directional beams. When using massive MIMO, there are non-stationary characteristics in the space domain, which have not been considered in previous work. With the development of 6G technology, it is expected that HAP communication will achieve higher channel capacity and meet the growing data demand, especially in emerging technologies such as autonomous driving and virtual reality [26; 27]. There is a clear need for HAP communication systems that can provide higher bandwidths and faster data transfer rates.