# Gaussian Process Modeling of Specular Multipath Components
## 1 Introduction  
Future 5G wireless communication technologies and the Internet of Things (IoT) paradigm will be characterized by supporting a variety of services with high quality requirements, addressing performance metrics such as reliability, latency, data throughput, and resource-efficient use of the infrastructure [1; 2; 3]. Spatial location information is expected to become an indispensable feature of these emerging wireless networks, considering that much more accurate position information will become available with those new generations of wireless networks [4; 5; 6]. These references elaborate, how such \"location-awareness\" can be exploited for improving the robustness and performance of wireless networks. Location-awareness is founded in the observation that many parameters of the propagation channel are directly linked with the geometry of the scenario and environment, starting from the distance-dependent path loss, spatial correlation of shadowing, to the arrival angle of individual multipath components. The availability of such geometric models thus allows for efficient and robust location-based routing and medium access schemes, or geometry-based beam steering, to name just a few popular examples. The prerequisites for implementing location awareness are accurate position estimation and the mapping of the propagation conditions, both of which must go hand in hand. The well-known simultaneous localization and mapping (SLAM) algorithms can be used to build a geometric model from past received signals, while locating the mobile user [7; 8; 9]. Note that these references are basedon the use of wireless signals, while SLAM was originally developed by the robotics community for efficiently fusing the data from optical and odometry sensors. By exploiting the position-related information acquired from the multipath channels, localization and mapping information is obtained. The obtained localization and mapping errors were continuously reduced from meters to centimeters, while moving from conventional wideband transceivers, through ultra-wideband (UWB), to mm-wave systems [7, 8, 9, 10, 11]. The robustness of the acquired location information strongly depends on the surrounding environment and hence on multipath propagation [12, 13, 14]. Strongly related to those works are papers on radio positioning systems that exploit map information. For instance, low-level descriptors of the channel, such as the RSS, the time-of-flight (ToF), the angle-of-arrival (AoA) are mapped to a location using fixed geometry models and triangulation/trilateration methods [15, 16]. In Reference [17], delay information of specular multipath components (SMCs) is used to enhance the robustness and reduce the infrastructure demand of a UWB localization system, see also Reference [12]. The concept extends straigthforwardly towards mm-wave systems, which will also make use of angle information [18]. These works indicate a strong link between map and position information. Specifically, the arrival time, arrival angles, and departure angles of so-called \"specular multipath components\" are all directly related to simple geometric models. It is thus common to separate these SMCs and use geometry-based models to describe their parameters. A popular approach is the use of clusters of scatter points for the modeling, characterized by a delay spread and angle spread [19, 20, 21], allowing to quantify the second-order statistic of geometry-related multipath components, that is, SMCs. Vice-versa, SMCs allow for a prediction of these channel parameters, given that the geometric models are available. In contrast to this delay and angle modeling by means of SMCs, the modeling of the amplitudes of the SMCs is much harder to achieve. This is because many factors need to be considered, beginning from free-space path loss, directional beampatterns of antennas, reflection characteristics of building materials, to the polarization state of the waves and the mutual coupling of the antennas with nearby objects.