# A Joint Positioning Algorithm in Industrial IoT Environments with mm-Wave Communications
## 5 Simulation Results
### Performance of SRS-Pos under Different Configuration  
Positioning accuracy depends on the measurement results, such as timing delay and angle, which is impacted by the transmission environment denoted as SNR. Therefore, we should evaluate the detection accuracy vs. SNR. The detection accuracy is computed by (16)  
\[\left\{ \begin{array}{l}\text{Angle estimation error rate}=\frac{1}{N}\sum \limits_{n=1}^{N}\text{Y}(|estimated angle_{n}-true\text{ angle value}|\ >\text{ angle threshold}),\\ \\ \text{Time estimation error rate}=\frac{1}{N}\sum\limits_{n=1}^{N}\text{Y}(|estimated time_{n}-true\text{ time value}|\ >\text{ time threshold})\\ \\ \text{where }N\text{ is the total simulation time, }\text{Y}(x)\text{ is a function as}\\ \\ \text{Y}(x)=\left\{\begin{array}{ll}1&\text{if }x\text{ is }ture\\ 0&\text{if }x\text{ is }false\\ \end{array}\right.\end{array} \right. \tag{16}\]  
and represents whether the estimate is wrong. The angle threshold is set to the range of plus or minus two degrees of the true angle value, and the time threshold is set to the range of plus or minus 4 ns of the true time value. Once the estimated result exceeds that  
Figure 6: Simulation scenario of indoor square factory. \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Simulation environment & Indoor, 500 m \(\times\) 500 m \\ \hline Total TRP number & 12 \\ \hline TRP number for localization & 3 \\ \hline Network duplex mode & TDD \\ \hline Frequency range & 27–28 GHz \\ \hline System bandwidth & 400 MHz \\ \hline Subcarrier spacing & 120 KHz \\ \hline SNR & 22 dB \\ \hline \(N_{\text{R}}\) & 64 \\ \hline \(K_{\text{IC}}^{\text{SRS}}\) & 2 \\ \hline \(N_{\text{SYD}}^{\text{SRS}}\) & 1 \\ \hline \(N_{\text{PREB}}^{\text{SRS}}\) & 272 \\ \hline \(N_{\text{FFT}}\) & 4096 \\ \hline \end{tabular}
\end{table} 
Table 3: Simulation setting. range, it is considered that the estimation is wrong and \(x\) is true. So the value of \(\mathrm{Y}(x)\) is one. After completing \(N\) times of estimation, the proportion of the times of wrong estimation to the total estimation times is calculated, as in (16), and the value of _Angle estimation error rate_ or _Time estimation error rate_ is obtained. Considering the detection error due to the randomization of the transmission environment, the average operation is performed. Figure 7 shows angle estimation error of SRS-Pos with a combination configuration \(\left\{K_{\mathrm{TC}}^{\mathrm{SRS}},N_{\mathrm{symb}}^{\mathrm{SRS}},N_{ \mathrm{PRB}}^{\mathrm{SRS}}\right\}\). In Figure 7, the ordinate represents the angle estimation error, and it is calculated by i (16). The full line and the dotted line compares the results under a maximum SRS-Pos bandwidth, i.e., \(N_{\mathrm{PRB}}^{\mathrm{SRS}}=272\) and \(N_{\mathrm{PRB}}^{\mathrm{SRS}}=128\), respectively. Obviously, it can be observed that the performance is enhanced with the increase in bandwidth. The square marker and the circle marker denotes the result under \(N_{\mathrm{symb}}^{\mathrm{SRS}}=4\) and \(N_{\mathrm{symb}}^{\mathrm{SRS}}=1\) OFDM symbol in time domain. With the same configuration of bandwidth and comb size, the accuracy is improved with the increase in \(N_{\mathrm{symb}}^{\mathrm{SRS}}\), since the cumulated power increases with \(N_{\mathrm{symb}}^{\mathrm{SRS}}\). Further, it can be observed from Figure 7 that the accuracy is always better under a smaller \(K_{\mathrm{TC}}^{\mathrm{SRS}}\), since the valid sequence length is inversely proportional with \(K_{\mathrm{TC}}^{\mathrm{SRS}}\). Fortunately, the performance degradation of larger comb size can be compensated by the time domain duration. As illustrated, \(\left\{4,1,272\right\}\) and \(\left\{2,1,128\right\}\) have a similar performance. Though there is 3 dB degradation under \(K_{\mathrm{TC}}^{\mathrm{SRS}}=4\), the bandwidth size is around two times that of the \(\left\{2,1,128\right\}\) case. The SRS-Pos sequence lengths under \(\left\{4,1,272\right\}\) and \(\left\{2,1,128\right\}\) are 816 and 768, respectively.