Robust cognitive beamforming for cell-edge coverage in multicell networks with probabilistic constraints

In this paper, we introduce a downlink beamforming strategy in a cognitive cell located at the boarder of two adjacent cells of a multicell network to support the local cell-edge users of both cells. The proposed strategy is formulated as an optimization problem to minimize a linear combination of total transmit power of the cognitive base station (BS) and the resulting total interference on the other users located outside of the cognitive cell, so that the signal-to-interference-plus-noise ratio (SINR) targets of the cell-edge users are maintained. In a realistic scenario where CSI may be imperfect, the beamforming design for the cognitive BS based on perfect channel state information (CSI) can easily end up violating the tolerable interference levels of the users falling outside of the cognitive cell. We reformulate the proposed strategy as a robust optimization problem with outage-probability based constraints to account for the imperfection in CSI. Using the S-Procedure, we transform the intractable probabilistic constraints to a computationally tractable set of conservative deterministic constraints. Finally, applying the rank relaxation, we rewrite the resulting problem in semidefinite programming (SDP) form that can be solved using the standard convex optimization packages. The simulation results confirm the effectiveness of the proposed robust scheme in power-efficiently expanding the range of achievable SINR targets for the cell-edge users.