# A Review of Wireless Positioning Techniques and Technologies: From Smart Sensors to 6G
## 2 Localization Techniques
### Round Trip Time (RTT)
#### 2.1.2 Angle-Based Measurements  
Angle-based measurements include phase measurements that compare the phase of the signal arriving at the target node (incident signal) with the phase of the signal transmitted and Angle of Arrival (AoA) measurements that utilize the angle between the nodes and the intersection of multiple directions of the wireless signal.  
Phase Difference of Arrival (PDoA)  
The PDoA utilizes the phase difference of the carrier signal for estimating the distance between the transmitting and receiving nodes. The incident signals arrive with a phase difference at different antennas, as shown in Figure 3a.  
Therefore, the phase difference of the signal received by more than two different antennas at the receiver side is used for estimating the distance between the transmitting and receiving nodes. The distance \(d\) is estimated by  
\[d=\lambda\left(\frac{\phi_{Rx}}{2\pi}+k\right), \tag{4}\]  
where \(k\) is a positive integer, \(\lambda\) is the wavelength, and \(\phi_{Rx}\) the phase of the received signal \(s(t)\), given by the following sine wave equation  
\[s(t)=A\sin(2\pi ft+\phi_{Rx}), \tag{5}\]  
where \(A\) is the amplitude and \(f\) the frequency. Note that the received phase \(\phi_{Rx}\) depends on the distance travelled by the signal, as follows,  
\[\phi_{Rx}+2\pi k=\frac{2\pi fd}{c} \tag{6}\]  
where \(c\) is the speed of light. By substituting the wavelength as \(\lambda=\frac{c}{f}\), then the distance can be directly computed using (4).  
PDoA resulting accuracy is generally low and so it is commonly used in combination with other measurements, such as ToA [35].  
Angle of Arrival (AoA)  
The AoA utilizes the angle between the transmitting and receiving nodes and the intersection of multiple directions of the wireless signal, as shown in Figure 3b. Compared to ToA and TDoA, AoA requires no time synchronization between nodes and its accuracy is proportional to the nodes' density. Its drawback is that additional hardware is required, such as an antenna array. Alternatively, electronically steered antennas can be used for the  
Figure 3: **(a) Phase of Arrival (PoA) reproduced with permission from [PERSON], A Survey of Indoor Localization Systems and Technologies; published by IEEE, 2019, (b) Angle of Arrival (AoA), reproduced with permission from Brena, Evolution of Indoor Positioning Technologies: A survey; published by Hindawi Limited, 2017.**direction finding. The steerable beam searches for the incoming signal and the received beam determines its direction; therefore, the AoA is estimated at the direction that the received signal power is the highest. Furthermore, directional antennas with a steerable beam can be used for estimating the AoA. Two or more directional antennas with different directions and beam overlapping can be used.  
Another way for estimating the AoA is by using subspace-based methods, which decompose the space into signal and noise subspaces and exploit their characteristics, such as the multiple signal identification and classification (MUSIC) algorithm [36]. It deals with the decomposition of the correlation matrix into two orthogonal matrices, the signal and noise subspaces. The direction estimation is carried out from one of these subspaces, with the assumption that the noise in each channel is highly uncorrelated, thus making the correlation matrix orthogonal. Similarly, the estimation of signal parameters via rotational invariant techniques (ESPRIT) [37] use the same model of the signal as MUSIC and significantly reduce the computing power and storage memory. The ESPRIT estimates the direction of arrival (DoA) and time delay of the incoming signals through their eigenvalues. In [37], the performance of both MUSIC and ESPRIT was evaluated using different parameters, and it was concluded that MUSIC is more accurate, while ESPRIT provides better resolution.