## 1 Introduction  
Many wireless communication systems have been developed and deployed to support various kinds of wireless data services. Many of the developed frequency bands are becoming more congested, especially in the densely populated urban areas due to the scarcity of commercially usable frequency resources and the explosive increasing desire for wireless data service. Consequently, it is essential that several heterogeneous wireless communication systems share a frequency band if possible, such as the 2.4 GHz ISM (Industrial, Scientific, and Medical) band. The spectrum sharing of several heterogeneous systems is termed coexistence. Coexistence can improve the utilization of the frequency band, because all the participating systems are not fully using their frequency band. However, the coexistence of heterogeneous wireless communication systems sharing a spectrum simultaneously and in the same geographic region causes their mutual interference, the coexistence problem. This degrades the performance of each wireless communication system. Sharing in the unlicensed bands, including 2.4 GHz ISM band, has been studied for a long time. Well known wireless communication systems in the ISM band are WiFi for wireless local area network (WLAN) systems, Bluetooth or ZigBee for wireless personal area networks (WPANs), and the like.  
There has been growing demand for broadband connections, along with the proliferation of wireless data services. WiMAX (Worldwide Interoperability for Microwave Access) for wireless metropolitan area network (WMAN) systems is an attractive technology to address this need. WiMAX is being considered as a candidate system operated in the ISM band, because it can provide low price or free high speed wireless internet service. If the WiMAX system is newly deployed in the ISM band, like a kind of home base station, it inevitably generates interference with the other wireless communication systems that exist in the ISM band. WiFi is a popular wireless communication system operated in that band, and deployed in many indoor or outdoor places. Therefore, the coexistence of WiFi and WiMAX systems sharing a frequency band should be studied, when they operate in an adjacent or the same area, as shown in Figure 1.  
Figure 1: Coexistence of WiFi and WiMAX systems. (**a**) WiFi AP and WiMAX BS are not collocated; (**b**) WiFi AP and WiMAX BS are collocated.  
Table 1 defines the four types of coexistence of heterogeneous wireless communication systems. In this paper, we focus on the case in which WiFi system based on IEEE 802.11g and WiMAX system based on IEEE 802.16e are collaborative. We want to make them coexist, based on their minimum collaboration and the minimum change of their specifications.  
In Section 2, we explain related work on coexistence. In Section 3, we introduce the time division operation of WiFi and WiMAX systems to avoid their mutual interference. In Sections 4 and 5, we introduce the previously proposed PS-Request protocol of the WiFi system and coexistence zone within the WiMAX frame structure. In Section 6, we propose a revised PS-Request protocol to resolve drawbacks of the original PS-Request protocol. In Section 7, we evaluate by simulation the performance of the revised PS-Request protocol. Finally, we will conclude in Section 8.