## 5 Numerical Results
### Simulation Results
\"Energy\" (\"Energy is the data separation proposed in [6]) is a conventional data separation. In \"Energy\", the subcarriers are detected in terms of the top \(K\) spectrum power and the cost function of the data separation is composed of sensing results for tracking the time continuity of sensing results. Both of \"Cancel w/o Adaptation\" (\"Cancel w/o Adaptation\" is the data separation proposed in [27]) and \"Cancel w/ Adaptation\" use ICI cancellation for detecting the subcarriers. In both, the cost function of data separation is composed of sensing results, CSI and CFO and it is given by Equation (11). In \"Cancel w/ adaptation\", while detecting the duplication of the sensing results, the data tracking is switched into that composed of sensing results and reconstructed spectrum which is given by Equation (19). From this figure, \"Cancel w/ Adaptation\", which is proposed separation, achieves the minimum RMSE and thus results in highly accurate data separation. As the maximal CFO becomes larger, the RMSE of \"Cancel w/ Adaptation\" is degraded. The effect of ICI cancellation under the duplication of sensing results is limited. As CFO becomes larger, the power of ICI becomes larger and thus the residual ICI after ICI cancellation becomes larger. Therefore, the wrong recognition that the residual ICI is considered to be the subcarrier sent by the sensor occurs. As a result, RMSE is degraded. From these results, as the maximal CFO is smaller than 0.05, the average RMSE under 0.01 is achieved. Figure 8 shows the performance between the time correlation of CSI and CFO, \(\rho_{\gamma},\rho_{\varepsilon}\), and the average RMSE, where the time correlation of CSI is equal to that of CFO, \(\rho_{\gamma}=\rho_{\varepsilon}\). The number of sensor nodes, \(K\), is 5. The maximal CFO, \(\varepsilon_{M}\), is 0.05. In \"Cancel w/o Adaptation\", the improvement of RMSE is limited. This is because the duplication of sensing results causes the misunderstanding of sensor node and thus the error tracking causes the degradation of RMSE. \"Cancel w/ Adaptation\" is the best performance. As \(\rho_{\gamma},\rho_{\varepsilon}\) becomes larger, the RMSE of \"Cancel w/ Adaptation\" is improved. Owing to the high time continuity of CSI and CFO, the accuracy of data tracking is improved. In addition, the tracking with received spectrum aids in avoiding the error tracking. Figure 9 shows the performance between the number of sensor nodes, \(K\), and average RMSE. The maximal CFO, \(\varepsilon_{M}\), is 0.05 and the time correlations of CSI and CFO, \(\rho_{\varepsilon},\rho_{\gamma}\) are 0.999. From this figure, \"Cancellation w/ Adaptation\" achieves smallest RMSE. As the number of sensors becomes larger, the RMSE is degraded. This is because the occurrence probability of duplication of sensing results becomes larger and the power residual ICI by ICI cancellation also becomes larger. Figure 6: Snap shot of separation result under various RMSE. Figure 7: Performance between maximal frequency offset and RMSE. In this subsection, the sensing results obtained by the actual sensors are used for the sensing result in computer simulation. The purpose of performance evaluation is clarifying the accuracy of sensing result separation by proposed scheme in applying to the actual sensing results. We use two temperature sensing results. First one is as follows. Figures 10 and 11 show the images of experimental evaluation and the obtained sensing results, respectively. In this experimental evaluation, the temperature sensor is used and the number of sensors, \(K\), is 5. Every 1 minute, each sensor evaluates the temperature from 4 am to 1 pm in the last ten days of April. Since an automatic air conditioner is stopped, the cause of changing temperature is a climate shift, such as sunshine condition, wind condition, and so on. Figure 12 shows the obtained temperature results in the second situation and this test sensing results are given in [6]. Every 1 second, each sensor evaluates the temperature during 500 s in the end of November.