# Evaluation of 5G Positioning Performance Based on UTDoA, AoA and Base-Station Selective Exclusion
## 2 Signal Model
### Observable Calculation
#### 2.2.1 Observable Based on Time of Arrival  
The main source of ranging error in cellular networks is due to the effect of multipath, especially with the relative narrow bandwidth. Therefore, our characterization of the observable is based only on the multipath-induced error. The ranging errors are computed for specific propagation conditions, channel models, system bandwidth, signal-to-noise ratio (SNR) levels and time-delay estimator. The LoS conditions are computed according to the distance between receiver and Base Station (BS) and a random probability variable drawn from a uniform distribution between 0 and 1 following the physical-layer abstraction of 5G observables proposed in [16]. The channel models are based on the ones provided in [17]. Since this work is focused on cmWave scenarios, Urban Macro-cell (UMa) and Urban Micro-cell (UMi) scenarios of the 3 GPP standard models are considered. Its network operates at frequency bands between 900 MHz and 6 GHz, and the system bandwidth is limited up to 100 MHz. The time-delay estimator computes the maximum peak of the correlation between the received signal and the transmitted positioning pilots within a correlation range. The ranging errors are finally added with the Euclidean distance of user terminal to BS to model the ToA observables formulated as:  
\[\hat{\rho}_{\rm n}=c\cdot\hat{\tau}_{\rm n}=\parallel x_{\rm BS,n}-{\bf x} \parallel+c\cdot\delta t_{\rm 5G}+e_{\rm sync,n}+e_{\rm TDE,n}, \tag{1}\]  
where \(\hat{\tau}_{\rm n}\) is the time-delay of the 5G signal estimated from the \(n\)-th cmWave BS (for uplink signals), \(x_{\rm BS,n}=[x_{\rm BS,n},y_{\rm BS,n},z_{\rm BS,n}]\) is the \(n\)-th BS position, \({\bf x}=[x,y,z]\) is the receiver position, \(\delta t_{\rm 5G}\) is the clock offset of the receiver (referenced to 5G time), \(e_{\rm sync,n}\) is the BS synchronization error and \(e_{\rm TDE,n}\) is the Time-Delay Estimation (TDE) error. The BS synchronization error \(e_{\rm sync,n}\) is modeled as in [7], based on a truncated Gaussian distributed random variable with zero mean and standard deviation \(\sigma_{\rm sync}\) within the interval of values \([-2\sigma_{\rm sync},2\sigma_{\rm sync}]\). Calculating the differences in ToA observables eliminates \(\delta t_{\rm 5G}\) and yields the TDoA measurement in the time domain. Thus, the \(n\)-th TDoA observable is computed as the time difference of ranging observables from the serving and neighbor BSs as  
\[\hat{\rho}_{\rm TDoA,n}=\hat{\rho}_{1}-\hat{\rho}_{n+1}, \tag{2}\]  
for \(1\leq n<M_{BS-1}\), where \(\hat{\rho}_{1}\) is the ranging observable from the serving BS, i.e., the most powerful BS (with highest SNR) at the receiver position, \(\hat{\rho}_{n+1}\) is the ranging observable from the \((n+1)\)-th neighbor BS and \(M_{BS}\) is the total number of BSs used for positioning. The TDoA estimates are computed with downlink and uplink 5G signals, resulting in the Observed TDoA (OTDoA) and UTDoA location methods, respectively. Since the physical propagation channel is the same for both OTDoA and UTDoA methods, the main performance difference between both methods is due to inter-UE interference. For the downlink positioning, the UE is in charge of measuring the time delays on the reference or pilot signals it receives from serving and neighboring BSs, which actually provide the Euclidean distance between UE and BS. For the case of uplink positioning, the only task on the UE side is to generate and transmit the SRS, which needs less computational effort than calculating a time estimation. This means, in comparison with the downlink part, where the reference signal is generated by the network and the time estimation is done by the UE, the computational effort on the UE is reduced. Both received signals are simulated to estimate the respective ranging errors for different SNR levels. The calculation of SNR differs in the power, gain and noise figure of antennas. On the other hand, RTT is based on the time-delay estimates on the signals transmitted in the downlink and uplink.