Uplink Pilot Allocation in Massive MIMO over Gauss-Markov Fading Channels

In a time-division duplex (TDD) massive multiple-input multiple-output (MIMO) system, the number of available orthogonal pilot sequences in each cell is limited. In this paper, by assuming Gauss-Markov fading channels, we consider a massive MIMO system where there are less available orthogonal pilots than the number of users. In order to optimize the long-term performance in estimating the uplink (UL) channels, the base station (BS) judiciously decides the allocation of the available pilots to different users in each training phase. The pilot allocation problem is a partially observable Markov decision process with an exploitation-exploration tradeoff that is difficult to analyze. We thus investigate the problem in the framework of restless multi-armed bandits (RMAB) problems and carry out an indexability analysis for the problem. Furthermore, we solve this problem by using the Whittle's index policy with a low complexity. Numerical results demonstrate the superiority of the Whittle's index policy.

I. Introduction

By deploying a large number of antennas at the base station (BS), massive multiple-input multiple-output (MIMO) is able to bring significant spectral efficiency gains when accurate knowledge of channel state information (CSI) is available at the BS [1]. To avoid the overwhelming CSI feedback overhead in frequency-division duplexing (FDD) systems, time-division duplexing (TDD) is widely studied. In a typical TDD system, the downlink (DL) CSI can be inferred by the estimated uplink (UL) CSI at the BS thanks to the channel reciprocity [2]. Due to limited channel coherence time and bandwidth, non-orthogonal pilot sequences are usually re-used for UL channel estimation in TDD systems, which results in pilot contamination and leads to significant performance degradation in massive MIMO [1].