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A cross-layer design approach is considered for joint routing and resource allocation for the physical (PHY) and the medium access control (MAC) layers in multihop wireless backhaul networks. The access points (APs) are assumed to be equipped with multiple antennas capable of both transmit and receive beamforming. A nonlinear optimization problem is formulated, which maximizes the fair throughput of the APs in the network under the routing and the PHY/MAC constraints. Dual decomposition is employed to decouple the original problem into smaller subproblems in different layers, which are coordinated by the dual prices. The network layer subproblem can be solved in a distributed manner and the PHY layer subproblem in a semidistributed manner. To solve the PHY layer subproblem, an iterative minimum mean square error (IMMSE) algorithm is used with the target link signal-to-interference-and-noise-ratio (SINR) set dynamically based on the price generated from the upper layers. A scheduling heuristic is also developed, which improves the choice of the transmission sets over time. Simulation results illustrate the efficacy of the proposed cross-layer design.