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Multicell cooperation has recently attracted tremendous attention because of its ability to eliminate intercell interference and increase spectral efficiency. However, the enormous amount of information being exchanged, including channel state information and user data, over backhaul links may deteriorate the network performance in a realistic system. This paper adopts a backhaul cost metric that considers the number of active directional cooperation links, which gives a first order measurement of the backhaul loading required in asymmetric Multiple-Input Multiple-Output (MIMO) cooperation. We focus on a downlink scenario for multi-antenna base stations and single-antenna mobile stations. The design problem is minimizing the number of active directional cooperation links and jointly optimizing the beamforming vectors among the cooperative BSs subject to signal-to-interference-and-noise-ratio (SINR) constraints at the mobile station. This problem is non-convex and solving it requires combinatorial search. A practical algorithm based on smooth approximation and semidefinite relaxation is proposed to solve the combinatorial problem efficiently. We show that semidefinite relaxation is tight with probability 1 in our algorithm and stationary convergence is guaranteed. Simulation results show the saving of backhaul cost and power consumption is notable compared with several baseline schemes and its effectiveness is demonstrated.