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This thesis considers a downlink multicell cooperation model in which the base-stations (BSs) are connected to a central processor via rate-limited backhaul links and each scheduled user is cooperatively served by a potentially overlapped cluster of BSs. Two different problem formulations are considered respectively: optimal tradeoff between the total transmit power and backhaul capacity under fixed user rate constraints, and utility maximization for given per-BS power and backhaul constraints. Motivated by the compressive sensing literature, we propose to approximate the backhaul rate as a function of the weighted -norm square of the beamformers. This novel idea allows the optimal tradeoff to be converted into a weighted power minimization problem, which then can be solved efficiently using the well-known uplink-downlink duality approach; it also makes the utility maximization problem solvable through a generalized weighted minimum mean square error approach. The effectiveness of the proposed algorithms is justified through numerical simulation results.