Providing wireless service without spatial restriction has been realized due to rapid growth of IEEE 802.11 based wireless technologies. Recently, AB estimation of the wireless medium has received much attention with the widespread use of real-time multimedia applications which requires certain level of QoS guarantees. In this research, APBE is proposed considering a factor which has been ignored by the previous works: the RTS and CTS overheads in estimating the AB. APBE performs AB estimation with correct measurement of i) the proportion of DIFS and back-off, ii) acknowledgement delay iii) channel idle time in the measurement period and additionally considers the collision probability of RTS and CTS messages and the overhead caused by the RTS and CTS procedure. The performance of APBE has been compared with the previous works and from the simulation results, it is clear that APBE outperforms the existing research in terms of estimation accuracy. Based on correct estimation of AB in IEEE 802.11 based wireless networks, efficient network resource management, QoS guarantees of multimedia applications, and effective admission control can be realized.