# Amplitude Modeling of Specular Multipath Components for Robust Indoor Localization
## 1 Introduction  
The vision of an Internet-of-Things (IoT) has been discussed extensively, in recent years, covering end-user applications in a wide range of application domains, including industrial [1], health-care and assisted living [2], smart cities, and smart mobility [3]. Similarly, 5G and beyond-5G wireless networks are currently under development, aiming for instance at an end-to-end latency in the range of 1 ms, high user densities, and unprecedented data rates per volume for a heterogeneous set of end-user scenarios [4, 5, 6]. Location information is a critical component of many of these applications [7], creating context-awareness with different service quality requirements [8]. The relevant performance criteria extend far beyond the required level of accuracy. For assisted and autonomous driving, for example, location information is of mission-critical importance, making it a prime example of a high-end location-based application with a need for 100% availability [9, 10, 11, 12]. Robustness, security, and privacy issues in IoT applications have recently been discussed in [13]. High-accuracy location information is seen as a key enabler for location-based services in the IoT and in 5G networks [14, 12]. Much work has been done to address the various issues involved in accurate and robust position estimation, demonstrating the heterogeneity of scenarios and applications as discussed before. RSS-based techniques are very suitable for positioning basedon signals-of-opportunity, because it does not require dedicated time stamping and synchronization. RSS measurements can be used to compute the position from path-loss-based range estimates [15; 16], from ray-tracing based propagation predictions [17; 18], from fingerprinting/machine-learning-based methods [18; 19; 20], and from tomography-inspired, device-free measurements [21]. The main disadvantage of this approach is the low accuracy and low robustness compared with other measurement principles [22], in particular, when multipath fading and shadowing are taken into account. Time-of-flight (ToF) measurements and multilateration are usually the basis for robust, high-accuracy positioning systems, including global navigation satellite systems (GNSS) [23]. It is well known that the ToF _ranging_ error variance scales reciprocally with the squared bandwidth and the signal-to-noise ratio (SNR) [24], which motivates the advantage of having a high signal bandwidth available. The SNR depends only weakly on the range (ensured e.g., due to power control mechanisms in the network), however, multipath will have a severe influence [25; 26; 27; 28]. These basic insights have been used to study the _positioning_ performance of wireless networks [26; 29], showing the influence of the geometry (and number) of the nodes that are being involved in the position computation. The availability of sufficiently accurate location information is a facilitator for exploiting \"location awareness\" to enhance the performance of the radio access network [30]. Location-awareness leverages geometric information to optimize algorithms and protocols of a wireless communication system at different layers of the protocol stack, to satisfy the needs for higher throughput, lower latency, higher robustness, and other performance indicators [30]. At higher layers of the stack, location information has been employed directly for routing algorithms [31; 32]. At lower layers, a channel quality metric (CQM) is often introduced, which maps between a network performance indicator, e.g., the channel capacity or the signal-to-interference-plus-noise ratio (SINR) and the position, yielding a so-called \"radio environment map\" (REM) [33]. The REM is obtained from a database, which is acquired from measurements conducted beforehand. Crowd-sensing has been proposed for the data collection, where data covering a wide spatial area is being collected by a large number of agents navigating through an environment [34]. A regression tool is needed to handle the large database and perform predictions.