Multi-Cell Beamforming With Decentralized Coordination in Cognitive and Cellular Networks

This paper considers a downlink beamforming problem in a cognitive radio network where multiple primary and secondary cells coexist. Each multiantenna primary and secondary transmitter serves its own set of single antenna users. The optimization objective is to minimize the sum transmission power over secondary transmitters while guaranteeing the minimum SINR for each secondary user and satisfying the maximum aggregate interference power constraint for each primary user. We propose a decentralized beamforming algorithm where the original centralized problem is decomposed via primal decomposition method into two levels, i.e., transmitter-level subproblems managed by a network-level master problem. The master problem is solved independently at each secondary transmitter using a projected subgradient method requiring limited backhaul signaling among secondary transmitters. To solve the independent transmitter-level subproblems, we propose three alternative approaches which are based on second order cone programming, semidefinite programming and uplink-downlink duality. Special emphasis is put on the last approach, which is also considered in a multi-cell MISO cellular network. Numerical results show that the proposed algorithm achieves close to optimal solution even after a few iterations in quasi-static channel conditions. Moreover, near centralized performance is demonstrated in time-correlated channels.