In this paper, we consider suboptimal cooperative downlink beamforming strategies to maximize the user sum rate in a clustered multicell system with limited feedback. We decouple the problem into multiple independent subproblems through the uplink-downlink duality theorem. Semidefinite relaxation is applied to transform the original nonconvex problem into a convex semidefinite programming problem, which can be efficiently solved in polynomial time. We propose a novel limited feedback scheme based on a compressive sensing technique that can yield high-quality channel state information (CSI) feedback. We also consider a limited feedback scenario where base stations within one cluster have different estimates of the same CSI knowledge. We investigate the channel quantization criterion by choosing the codeword vector that has the minimum norm of the difference between the codeword and the normalized channel. Numerical results demonstrate the effectiveness of the proposed beamforming algorithm and limited feedback schemes.