Robust chance-constrained distributed beamforming for multicell interference networks

We propose a robust coordinated game theoretic approach that distributively minimizes the aggregate downlink transmit power in a multicell interference network in the presence of imperfect channel state information (CSI). The optimization is constrained to satisfying the signal-to-interference-plus-noise-ratio (SINR) requirements at individual user terminals within certain predefined SINR outage probabilities. This problem is numerically intractable due to the cross-link coupling effect among a cluster of base stations (BSs) as well as the robust constraints that involve the second order statistical CSI estimation error. By employing cumulative distribution function of standard normal distribution, Lemma 2 and semidefinite relaxation technique, we first convert the original problem to a linear matrix inequality form. Then, we introduce an iterative subgradient algorithm that decomposes the multicell-wise general problem into a set of parallel subproblems at individual BSs to find the global optimality. We show that the proposed design co-ordinates intercell interference among the BSs with a light inter-BS communication overhead. Simulation results demonstrate the advantages of the proposed chance-constrained distributed design in terms of power efficiency and achievable robustness trade-off.