On optimal training in massive MIMO systems with insufficient pilots

Abstract

This paper studies the optimization of pilot training signals in Massive MIMO systems with insufficient pilot length. We aim at finding the optimal pilot design and pilot length that maximize the Spectral Efficiency (SE) of the system. To achieve that, we firstly derive an approximation of average achievable capacity, which is related to channel estimation error and pilot signals. Then some analysis and discussions on finding the optimal non-orthogonal pilot design are presented in order to maximize average sum SE. Since previous research on Massive MIMO systems with pilot training mainly focus on orthogonal pilots, in this paper we give a design criterion of non-orthogonal pilots, and relate the system SE as a function of pilot length. Simulation results show the gap between simulation results and our analytical results. Meanwhile, the performance of uplink SE with orthogonal and non-orthogonal pilots is shown, where for insufficient block length, non-orthogonal pilots could lead to higher SE than the orthogonal pilots. Our analysis and results suggest that choosing non-orthogonal pilots can get a better performance than orthogonal pilots in Massive MIMO systems.