Fixed Broadband Wireless Access (BWA) for the last mile is a promising technology which can offer high speed voice, video and data service and fill the technology gap between Wireless LANs and wide area networks. This is seen as a challenging competitor to conventional wired last mile access systems like DSL and cable, even in areas where those technologies are already available. More importantly the technology can provide a cost-effective broadband access solution in rural areas beyond the reach of DSL or cable and in developing countries with little or no wired last mile infrastructure. Earlier BWA systems were based on proprietary technologies which made them costly and impossible to interoperate. The IEEE 802.16 set of standards was developed to level the playing field. An industry group the WiMAX Forum, was established to promote interoperability and compliance to this standard. This thesis gives an overview of the IEEE 802.16 WirelessMAN OFDM standard which is the basis for Fixed WiMAX. An in depth description of the medium access control (MAC) layer is provided and functionality of its components explained. We have concentrated our effort on enhancing the performance of Fixed WiMAX for VoIP services, and best effort traffic which includes e-mail, web browsing, peer-to-peer traffic etc. The MAC layer defines four native service classes for differentiated QoS levels from the onset. The unsolicited grant service (UGS) class is designed to support real-time data streams consisting of fixed-size data packets issued at periodic intervals, such as T1/E1 and Voice over IP without silence suppression, while the non-real-time polling service (nrtPS) and best effort (BE) are meant for lower priority traffic. QoS and efficiency are at opposite ends of the scale in most cases, which makes it important to identify the trade-off between these two performance measures of a system. We have analyzed the effect the packetization interval of a UGS based VoIP stream has on system performance. The UGS service class has been modified so that the optimal packetization interval for VoIP can be dynamically selected based on PHY OFDM characteristics. This involves cross layer communication between the PHY, MAC and the Application Layer and selection of packetization intervals which keep the flow within packet loss and latency bounds while increasing efficiency. A low latency retransmission scheme and a new ARQ feedback scheme for UGS have also been introduced. The goal being to guarantee QoS while increasing system efficiency. BE traffic when serviced by contention based access is variable in speed and latency, and low in efficiency. A detailed analysis of the contention based access scheme is done using Markov chains. This leads to optimization of system parameters to increase utilization and reduce overheads, while taking into account TCP as the most common transport layer protocol. nrtPS is considered as a replacement for contention based access. Several enhancements have been proposed to increase efficiency and facilitate better connection management. The effects of proposed changes are validated using analytical models in Matlab and verified using simulations. A simulation model was specifically created for IEEE 802.16 WirelessMAN OFDM in the QualNet simulation package. In essence the aim of this work was, to develop means to support a maximum number of users, with the required level of service, using the limited wireless resource.