## 7 Simulation Results
### Performance Measures  
Throughput of each system is considered as one of the performance measures to be evaluated by the simulation [18].  
\(N_{WiFi}^{bit}\) and \(N_{WiMAX}^{bit}\) are the total number of successfully transmitted data bits of WiFi and WiMAX systems, respectively. \(N_{WiMAX,DL}^{bit}\) and \(N_{WiMAX,UL}^{bit}\) are the total number of successfully transmitted WiMAX data bits through DL (Downlink) and UL (Uplink), respectively:  
\[N_{WiFi}^{bit}=\sum_{i=1}^{N_{Sxi}}N_{WiFi}^{ofdm}\times 48\times M_{WiFi}^{i} \times C_{WiFi}^{i} \tag{1}\]  
where \(i\) is the index of a WiFi STA and \(N_{ST4}\) is the number of WiFi STAs. \(N_{WiFi}^{ofdm}\) is the number of transmitted OFDM symbols. Forty eight is the number of data subcarriers of 64 subcarriers for the  
Figure 10: Example of the revised PS-Request protocol.  
WiFi system based on IEEE802.11g. \(M_{WiFi}^{i}\) and \(C_{WiFi}^{i}\) denote the modulation order and the code rate of WiFi STA of index \(i\), respectively:  
\[N_{WiMAX,DL}^{bit}=\sum\
olimits_{j=1}^{N_{MS}}N_{WiMAX}^{slot,j}\times 48 \times M_{WiMAX}^{j}\times C_{WiMAX}^{j} \tag{2}\]  
\[N_{WiMAX,UL}^{bit}=\sum\
olimits_{j=1}^{N_{MS}}N_{WiMAX}^{tile,j}\times 12 \times M_{WiMAX}^{j}\times C_{WiMAX}^{j} \tag{3}\]  
where \(j\) is the index of WiMAX MS, and \(N_{MS}\) is the number of WiMAX MS's. \(M_{WiMAX}^{j}\) and \(C_{WiMAX}^{j}\) denote the modulation order and the code rate for each data burst of WiMAX MS of index \(j\), respectively. \(N_{WiMAX}^{slot,j}\) and \(N_{WiMAX}^{tile,j}\) denote the number of allocable resource units to the MS of index \(j\) for DL and UL, respectively. Forth eight and 12 denote the number of subcarriers in one slot and in one tile, respectively.  
\(N_{WiMAX}^{frame}\) is the number of WiMAX frames transmitted in a simulation. \(T_{WiMAX}^{frame}\) is the frame time of the WiMAX system, and is typically 5 ms:  
\[T_{WiMAX}^{frame}=\left(N_{DL}^{ofdm}+N_{CZ}^{ofdm}+N_{UL}^{ofdm}\right) \times T_{symbol}^{ofdm}+T_{TTG}+T_{RTG} \tag{4}\]  
\(N_{DL}^{ofdm}\), \(N_{CZ}^{ofdm}\) and \(N_{UL}^{ofdm}\) denote the number of WiMAX OFDM symbols allocated to the DL subframe, the coexistence zone and the UL subframe within a WiMAX frame structure, respectively. \(N_{DL}^{ofdm}\) includes one DL OFDM symbol for preamble, two DL OFDM symbols for FCH, DL-MAP and UL-MAP, and the other DL OFDM symbols for DL-Bursts of the WiMAX system. DL-Bursts of the WiMAX system are composed of DL OFDM symbols in multiples of two, and UL-Bursts of the WiMAX system are composed of UL OFDM symbols in multiples of three. \(T_{symbol}^{ofdm}\) is one OFDM symbol duration of the WiMAX system. \(T_{TTG}\) and \(T_{RTG}\) denote the transmit/receive transition gap (TTG) and the receive/transmit transition gap (RTG) within a WiMAX frame structure, respectively.  
For the performance evaluation of each system, the average throughputs of WiFi and WiMAX systems are defined, as follows:  
\[R_{WiFi}\triangleq\frac{N_{WiFi}^{bit}}{T_{WiFi}^{\Upsilon\chi 0N} \times N_{WiMAX}^{frame}}=\frac{N_{WiFi}^{bit}}{N_{CZ}^{ofdm}\times T_{symbol }^{ofdm}\times N_{WiMAX}^{frame}} \tag{5}\]  
\[R_{WiMAX}\triangleq\frac{N_{WiMAX}^{bit}}{T_{WiMAX}^{\Upsilon\chi 0N} \times N_{WiMAX}^{frame}}=\frac{N_{WiMAX,DL}^{bit}+N_{WiMAX,UL}^{bit}}{(N_{ DL}^{ofdm}+N_{UL}^{ofdm})\times T_{symbol}^{ofdm}\times N_{WiMAX}^{frame}} \tag{6}\]