Pareto-Optimal Pilot Design for Cellular Massive MIMO Systems

We introduce a non-orthogonal pilot design scheme that simultaneously minimizes two contradicting targets of channel estimation errors of all base stations (BSs) and the total pilot power consumption of all users in a multi-cell massive MIMO system, subject to the transmit power constraints of the users in the network. We formulate a multi-objective optimization problem (MOP) with two objective functions capturing the contradicting targets and find the Pareto optimal solutions for the pilot signals. Using weighted-sum-scalarization technique, we first convert the MOP to an equivalent single-objective optimization problem (SOP), which is not convex. Assuming that each BS is provided with the most recent knowledge of the pilot signals of the other BSs, we then decompose the SOP into a set of distributed non-convex optimization problems to be solved at individual BSs. Finally, we introduce an alternating optimization approach to cast each one of the resulting distributed optimization problems into a convex linear matrix inequality (LMI) form. We provide a mathematical proof for the convergence of the proposed alternating approach and a complexity analysis for the LMI optimization problem. Simulation results confirm that the proposed approach significantly reduces pilot power, whilst maintaining the same level of channel estimation error as in [1].