## 5 Numerical Results  
### Simulation Results  
The number of DFT points, \(N\), is 256. A trial is composed of 30 times transmission of sensing results. In computer simulation, 1000 trials are performed for evaluating the accuracy of data collection. The CFO of the \(k\)th sensor in \((t+1)\)th time slot is defined as the following equation using that in \(t\)th time slot. \[\varepsilon_{k}(t+1)=\rho_{\varepsilon}\varepsilon_{k}(t)-\sqrt{1- \rho_{\varepsilon}{}^{2}}\varepsilon_{0} \tag{21}\] \[\varepsilon_{k}(1)=\frac{2\varepsilon_{M}(k-1)}{K-1}-\varepsilon _{M},\ \ \ t\geq 1, \tag{22}\]  
where \(\varepsilon_{0}\) is a uniform random variable with \([-\varepsilon_{M},\varepsilon_{M}]\) and \(\varepsilon_{M}\) being the maximal value of CFO. \(\rho_{\varepsilon}\) is the time correlation of CFO. \(\varepsilon_{k}(1)\) is the initial value of CFO of \(k\)th user. For deciding the initial CFO, the range from \(-\varepsilon_{M}\) to \(\varepsilon_{M}\) is uniformly divided into \(K\) values and each value of CFO is assigned to each user. The CSI of \(k\)th sensor in \((t+1)\)th time slot is decided as the following equation by that in \(t\)th time slot. \[\gamma(t+1)=\rho_{\gamma}\gamma(t)+\sqrt{1-\rho_{\gamma}{}^{2}}\gamma_{0}, \tag{23}\]  
where \(\rho_{\gamma}\) is the time correlation of CSI and \(\gamma_{0}\) is the random variable with independency for each user and each time slot. We assume the two paths with equivalent delay profile whose path duration is 1 sample. First path and second path are modeled by a rice fading with 10 dB rice factor and a Rayleigh fading, respectively. The primary objective of the computer simulation is explaining the effect of ICI cancellation and the accuracy of sensing result separation. In this paper, the evaluation of robustness with respect to the noise component is future work and thus the simulation assumes the signal power to be sufficiently large to avoid the false alarm, which means FC wrongly recognizes the noise component as the subcarrier sent by sensor. In the proposed technique, the threshold for confirming the existence of subcarrier is \(1/10\) smaller than the average signal power. The sensing result is modeled by random walk and it is defined as  
\[n_{k}(t=0) = \left\lfloor\frac{N}{(10(K+1))}\right\rfloor k+\left\lfloor \frac{N}{4}\right\rfloor \tag{24}\] \[n_{k}(t+1)=n_{k}(t)+\left[\beta\right], \tag{25}\]  
where \(\left\lfloor\cdot\right\rfloor\) is floor function and \(\left[\cdot\right]\) is the rounding off function. \(\beta\) is a uniform random variable with \([-3,3]\). In the initial time slot, the different sensing result is assigned to each user. For data tracking, in the cost functions given by Equation (11) and Equation (19), the normalization factors of sensing result, CSI, CFO, and received spectrum are the median of total subcarrier numbers, the average power of CSI, the maximal CFO, \(\varepsilon_{M}\), and the average power of received spectrum, respectively. For evaluating the accuracy of sensing results separation, we define a root mean square error (RMSE) as follows. \[\text{RMSE}=\sqrt{E\left[\frac{(\bar{n}-\bar{n})^{2}}{\bar{n}^{2}}\right]}, \tag{26}\]where \(\bar{n}\) is the sensing result detected by FC and \(\hat{n}\) is the true sensing result. Root mean square error (RMSE) is averaged for all the trials and all the sensors and thus the average RMSE is derived. Figure 6 shows the snap shot of the separation results. The ground truth and the tracked result are the original sensing result and the result separated by tracking, respectively. We can observe in RMSE = 0.0123, the separation error is limited but if RMSE exceeds 0.0123, the burst separation errors occur, and these are error tracking. Therefore, our required RMSE is approximately 0.01. Figure 7 shows the performance between maximal CFO \(\varepsilon_{M}\) and a RMSE, where the number of sensors, \(K\), is 5, the time correlations of CSI \(\rho_{\gamma}\) and CFO \(\rho_{\varepsilon}\) are 0.999.