Coordinated Nonorthogonal Pilot Design for Massive MIMO

Pilot contamination caused by the nonorthogonality of pilots is a main limiting factor in multi-cell massive multiple-input multiple-output (MIMO) systems because it can significantly impair channel estimation. Recent works have suggested coordinating pilot sequence design across multiple cells in order to reduce the channel estimation error due to pilot contamination. This paper further investigates this approach using a new optimization framework. Specifically, we reformulate the problem of choosing the pilots to minimize the weighted mean-squared error (MSE) in channel estimation as a matrix fractional program. This problem can be efficiently approximated as a sequence of convex optimizations via a matrix fractional programming approach. The proposed algorithm, named fractional programming pilot design (FP-Pilot), provides fast convergence to a stationary point of the weighted MSE objective. The paper further characterizes the achievable data rate under maximum ratio combining when optimized pilots are used for channel estimation. Finally, we derive a relation between rate maximization and MSE minimization, which provides insight into the appropriate setting of weights in weighted MSE minimization. Simulations demonstrate the advantage of the proposed pilot design over alternative approaches in enhancing channel estimation and data throughput.