Coordinated Multicell Beamforming for Massive MIMO: A Random Matrix Approach

Abstract

We consider the problem of coordinated multicell downlink beamforming in massive multiple input multiple output (MIMO) systems consisting of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> cells, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N_{t}$ </tex-math></inline-formula> antennas per base station (BS) and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> user terminals (UTs) per cell. In particular, we formulate a multicell beamforming algorithm for massive MIMO systems that requires limited amount of information exchange between the BSs. The design objective is to minimize the aggregate transmit power across all the BSs subject to satisfying the user signal-to-interference-noise ratio (SINR) constraints. The algorithm requires the BSs to exchange parameters which can be computed solely based on the channel statistics rather than the instantaneous channel state information (CSI). We make use of tools from random matrix theory to formulate the decentralized algorithm. We also characterize a lower bound on the set of target SINR values for which the decentralized multicell beamforming algorithm is feasible. We further show that the performance of our algorithm asymptotically matches the performance of the centralized algorithm with full CSI sharing. While the original result focuses on minimizing the aggregate transmit power across all the BSs, we formulate a heuristic extension of this algorithm to incorporate a practical constraint in multicell systems, namely the individual BS transmit power constraints. Finally, we investigate the impact of imperfect CSI and pilot contamination effect on the performance of the decentralized algorithm, and propose a heuristic extension of the algorithm to accommodate these issues. Simulation results illustrate that our algorithm closely satisfies the target SINR constraints and achieves minimum power in the regime of massive MIMO systems. In addition, it also provides substantial power savings as compared with zero-forcing beamforming when the number of antennas per BS is of the same orders of magnitude as the number of UTs per cell.