Scheduling schemes play a key role in the system performance of broadband wireless systems such as WLANs/WMANs. Maximal SNR and round robin are two conventional scheduling strategies that emphasize efficiency and fairness, respectively. The proportional fair scheme provides a trade-off between efficiency and fairness, and has been well studied in TDMA and CDMA systems. In this article we extended the PF scheduling scheme to OFDM-based BWSs (OPF). In addition, we propose three variations: adaptive OPF (AOPF), multimedia AOPF (MAOPF), and normalized MAOPF (NMAOPF) in order to meet the QoS requirements for multirate services in multimedia systems. The adaptive modulation and coding schemes in time varying and frequency selective fading are considered. The system performances of the algorithms are compared in terms of efficiency (throughput and mean packet delay) and fairness (user satisfaction rate and average user rate). Joint physical and media access control layer simulation results show that AOPF and MAOPF can improve throughput at the cost of fairness, and NMAOPF can provide the highest throughput without losing fairness.