# Positioning Energy-Neutral Devices: Technological Status and Hybrid RF-Acoustic Experiments
## 3 Hybrid Acoustic-RF Approaches for Positioning Energy-Neutral Devices
### RF Backscattering
#### 3.3.1 Antenna Scattering  
In this paper, we adopt customized backscattering for the energy-neutral localization of a mobile device, by which it will communicate the information embedded in the received acoustic signals back to a central system. Backscattering is based on radar principles. The far-field parameter used to characterize the scattering properties of a radar target is the RCS (\(\sigma\)). According to [47], it is defined as _a fictive area intercepting that amount of power, which, when scattered isotropically, produces at the receiver a density which is equal to that scattered by the actual target_. This depends on the relative position between the target and transmitter/receiver, target geometry and material, frequency, angular orientation and transmitter/receiver polarization [48].  
A more intuitive approach for the RCS in a bistatic setup, in which the transmitter and receiver at the infrastructure side are separated, is depicted in Figure 5. In this bistatic setup, \(R_{1}\) represents the distance between the transmitting antenna and the backscatter device and \(R_{2}\) is the distance between the backscatter device and receiving antenna. The transmitted power (\(P_{t}\)) is observed by a target, at a distance \(R_{1}\) from the source. The incident power (\(P_{i}\)) that is intercepted by the target is determined by the incident power density (\(W_{i}\)) and the cross-section \(\sigma\), so that the captured power is \(\sigma W_{i}\). This intercepted power is either reradiated as scattered power or absorbed as heat. Isotropical reradiation delivers a scattered power density at distance \(R_{2}\) from the target given by:  
\[W_{i}=\frac{P_{t}}{4\pi R_{1}^{2}} \tag{1}\]  
\[W_{s}=\frac{\sigma W_{i}}{4\pi R_{2}^{2}} \tag{2}\]  
Combining the above equations with the radar range equation gives the relation between the radar cross-section, the power transmitted by the transmitting antenna, and the power received by the receiving antenna as a function of the different distances and the RCS in the case of polarization matched and aligned antennas:  
\[P_{r}=\sigma\frac{G_{t}G_{r}}{4\pi}\left(\frac{\lambda}{4\pi R_{1}R_{2}} \right)^{2} \tag{3}\]  
A digital or analog signal can be backscattered by altering this RCS value. The above equation provides a description of the RCS but does not clearly state how it can be altered at the hardware level. Green [49] introduced a load-dependent radar cross-section defined as:  
\[\sigma_{i}=\frac{\lambda^{2}}{4\pi}G_{0}^{2}|\Gamma_{i}-A_{s}|^{2}. \tag{4}\]With the load-dependent term:  
\[\Gamma_{i}\triangleq\frac{Z_{i}-Z_{a}^{a}}{Z_{i}+Z_{a}}, \tag{5}\]  
where \(Z_{a}\) is the antenna and \(Z_{i}\) is the load impedance. This term refers to the _antenna mode_ and depends on the power absorbed in the load of a lossless antenna and the power which is reradiated by the antenna due to load mismatch. The second mode that can be derived from Equation (4) is the _structural mode_ (\(A_{S}\)) scattering term which depends on the antenna geometry and materials [50; 51].  
By varying the antenna load, only the structural mode of the RCS value is altered, resulting in a changing electromagnetic field at the receiving antenna. For analog signals, a linear load, such as the transimpedance of a JFET, can be changed depending on the incoming signal. For digital signals, the difference in RCS between a '1' and a '0' should be optimized for a maximal reading distance. Ideally, this should incorporate both the antenna and structural modes. However, complex measurements are necessary to determine the _structural_ mode of the RCS. As a solution, the antenna commonly switches between the short and open state, trading the potential improved reading distance in for ease of use.