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The emergence of video streaming over wireless home networks creates renewed interests in design and analysis of new MAC protocols toward QoS provisioning for video applications. IEEE 802.11e Hybrid coordination function Controlled Channel Access (HCCA) exhibits good QoS provisioning for constant bit rate (CBR) video streams in a single collision domain. However, its performance degrades significantly for variable bit rate (VBR) video streams particularly in multicollision domains. In addition, HCCA has the disadvantage of high complexity. In this paper, we introduce a deterministic backoff (DEB) method into the HCCA mechanism, which achieves virtual polling via carrier sense on the wireless channel. DEB intentionally sets each station's backoff counter to a different value, thus stations can access the shared wireless channel at different time slots, which avoids network collisions. By proper controlling of each station's backoff counter, DEB achieves polling like HCCA, but in a more flexible and efficient way. It considerably mitigates inter-AP interference as well due to its carrier sense nature. Results show that, compared to HCCA, DEB always exhibits improvement in performance, particularly in multicollision domains where improvement is remarkable.