Interference is a fundamental issue in wireless mesh networks (WMNs) and it seriously affects the network performance. In this paper we characterize the power interference in IEEE 802.11 CSMA/CA based wireless mesh networks using directional antennas. A model based centralized call admission control (CAC) scheme is proposed which uses physical collision constraints, and transmitter-side, receiver-side and when-idle protocol collision prevention constraints. The CAC assists to manage requests from users depending on the available bandwidth in the network: when a new virtual link establishment request from a user is accepted into the network, resources such as interface, bandwidth, transmission power and channel are allocated in the participating nodes and released once the session is completed. The proposed CAC is also able to contain the interference in the WMN by managing the transmission power of nodes.