# Wireless Positioning in IoT: A Look at Current and Future Trends
## 3 Designing an IoT Positioning System
### Positioning Domains
#### 3.1.1 Power Domain  
Signal strength measurements are derived from the protocol operation, which most of the times results in a measurement of no additional cost to the device and battery consumption. However, positioning solutions in the power domain must tackle several challenges, in particular those related to the fast fluctuations of the Received Signal Strength (RSS) or of the backscattered power (BP), due to fading and shadowing caused by the surrounding environment. One key factor to model the RSS measurements relies on the possibility of understanding, with a given degree of accuracy, how the signal power changes in its surrounding environments. The signal power models as a function of the distance between the transmitter and the receiver are known as path-loss models, [10; 11]. A typical empirical Log distance model is the single-slope path loss model [11]:  
\[\mathrm{P_{r}}(d)=\mathrm{P_{r}}(\mathrm{d_{0}})-10\eta\log_{10}\ \left(\frac{d}{ \mathrm{d_{0}}}\right)+w, \tag{1}\]  
where \(\mathrm{P_{r}}(\cdot)<0\) is the received signal power in logarithmic scale dependent on distance \(d\), \(\mathrm{d_{0}}\) is a reference distance (usually 1 m), \(\eta>0\) is the path-loss exponent and \(w\sim log(\mathrm{N}(0,\sigma^{2}))\) is a log-normally distributed random variable that models the slow fading phenomenon and possible RSS measurements errors (e.g., due to quantization). Both \(\eta\) and \(w\) are dependent on the propagation environment and are typically dependent on the device type and environment type. In addition, \(w\) can depend on factors such as device orientation and the amount of people present in the measurement area at the time of acquisition. In terms of an IoT positioning system, the fact that one can extrapolate this information directly from the communication's signal, which means that there is no additional cost for the device. In terms of battery, the cost will depend on the amount of positioning location requests demanded per second. Ideally, if the requirement is to have an opportunistic location, based on the sporadic communication of the device, acquiring the RSS-based positioning will have no impact on the battery life. However, if the device or the infrastructure will have to listen periodically for a specific pilot signal, acquiring the RSS-based positioning will cause further demands in terms of battery consumption. One limitation of RSS-based approaches is that some current IoT standards support only a coarse RSS measurement (e.g., in steps of 6 dB), which can adversely impact the positioning accuracy, as the noise variance \(\sigma^{2}\) will increase. Another interesting aspect of the RSS measurements is that, based on simulations, RSS-based positioning errors are shown to be frequency independent (as shown later in Figure 1). However, one would expect different levels of location-based service at different frequency ranges. The frequency ranges can be coarsely divided into three categories: sub-GHz (i.e., carrier frequencies less than 1 GHz), GHz (1 to 30 GHz) and mmWave (above 30 GHz). The scattering becomes more prominent as frequency increases, thus one would expect different target positioning accuracy according to the frequency range. In addition, as the operating frequency increases, the antenna's effective area is smaller, and the signal coverage decreases. This is possible to see in Figure 2 where the ideal signal propagation in drawn over a 100 by 100 square area, based on the Friis equation and assuming zero system gains, \(G\),  
\[\mathrm{P_{r}}(d)=\mathrm{P_{t}}+G+20\log_{10}\left(\frac{c}{f4\pi}\right)-20 \log_{10}\left(d\right) \tag{2}\]  
where \(\mathrm{P_{t}}\) is the transmission power, \(f\) the operating frequency and c the speed of light. Based on the signal's behavior, it is easy to understand that a sparser infrastructure at higher frequencies will likely result in a degradation of the positioning performance (as shown later in Figure 1). Figure 1: Comparative analysis of RSS-based estimates at various carrier frequencies and various AN densities.