## 4 Performance Evaluation
### Basic Property Analysis  
In this analysis, the properties of the MRSS mechanism were evaluated by various smooth factors \((\alpha)\), moving average window sizes \((k)\), shadowing deviations and velocities in a WLAN and a \begin{table}
\begin{tabular}{|l|c|c|} \hline Wireless Environment & WLAN & Mobile WiMAX [35] \\ \hline Cell Radius (m) & 100 & 2000 \\ \hline Frequency (Hz) & 2.472e9 & 2.5e9 \\ \hline Path Loss Exponent & 4.0 & 3.5 \\ \hline Shadowing Deviation (dB) & 4.0 & 4.0 \\ \hline Transmitter Antenna Height (m) & 1 & 32 \\ \hline Receiver Antenna Height (m) & 1 & 1.5 \\ \hline Tx Power (dBm) & 22 & 40 \\ \hline Transmitter Antenna Gain (dB) & 1 & 15 \\ \hline Receiver Antenna Gain (dB) & 1 & 1 \\ \hline Rx Sensitivity (dBm) & -101 & -101 \\ \hline Sampling Interval (s) & 0.05 & 0.05 \\ \hline Sampling Size & 8 & 10 \\ \hline \end{tabular}
\end{table} 
Table 2: Default parameters for radio propagation. Figure 4: The mobility model and topology in simulations. Mobile WiMAX environment. The simulation uses a simple straight movement trajectory as shown in Figure 4(a). The MN moves from location A to location B at a velocity of 1 m/s in a WLAN environment. Figure 5(a) shows the effect of using various \(\alpha\) with a fixed \(k\) on the momentum of the MRSS-based motion detection algorithm, where \(k\) represents the size of the moving average window. Figure 5(a) reveals that \(\alpha\) barely affects the momentum value as a user approaches. Nevertheless, as a larger \(\alpha\) is applied, the momentum of MRSS will reduce rapidly when the MN moves away from the AP. Thus, the MN can rapidly detect the user's leaving state. Figure 5(b) presents the effect of using various \(k\) with a fixed \(\alpha\) on momentum. The value of \(k\) is related to the sample distance between two EWMA filters in MRSS. A larger \(k\) increases the motion detection delay in MRSS. When \(\alpha=0.16\), the minimum value of \(k\) is 32. In this analysis, various \(k\)\((k\geq 32)\) were configured in the simulation. The simulation results confirm that using a suitable \(k\) can detect user motion more quickly and accurately. Besides, because of the effects of radio propagation, a longer distance between the MN and the AP also corresponds to a smaller momentum change rate in MRSS. Figure 5: The performance evalution of \(\alpha\) and \(k\). The results in Figure 5(a) and Figure 5(b) indicate that using a suitable \(\alpha\) and \(k\) enables rapid and accurate identification of user motion state. Therefore, four \((\alpha,k)\) pairs, \((\alpha=0.08,k=64)\), \((\alpha=0.16,k=32)\), \((\alpha=0.29,k=16)\) and \((\alpha=0.5,k=8)\), are selected to evaluate the MRSS characteristics. In order to compare MRSS with MACD, an MACD method with \(\alpha=0.29\) and \(\beta=0.04\) is also simulated. Figure 5(c) presents the effect of \(\alpha\) and \(k\) on the momentum value. A larger \(\alpha\) causes momentum to drop quickly as the MN moves away from the AP but causes momentum to slowly rise as the MN approaches the AP. In addition, MRSS can detect user motion faster than MACD when the same value of \(\alpha\) is applied. Figure 5(d) shows the variation of the momentum value when a user is moving in a Mobile WiMAX environment at a speed of 13 m/s. The simulation results also confirm that the use of a suitable \(\alpha\) and \(k\) can improve the quality of user motion detection service. Figure 6 shows the effect of shadowing deviation on the momentum value as the MN moves from location A to location B at 1 m/s in a WLAN environment \((\alpha=0.16,k=32)\). The simulation result reveals that MRSS can eliminate all RSS fluctuations. Figures 7(a) and 7(b) show the impact of various velocity on the momentum value for the given movement trajectory when the user is in a WLAN environment. The results indicate that higher velocity corresponds to a greater rate of momentum change. **Figure 6.** The effect of shadow deviation when \(\alpha\) = 0.16, \(k\) = 32 in the WLAN environment. **Figure 7.** The effect of velocity in the WLAN environment.