Practical robust uplink pilot time interval optimisation scheme for time-division duplex multiple-input-single-output beamforming system

Focusing on a time-division duplex (TDD) multiple-input-single-output (MISO) beamforming system, this study investigates the robust uplink pilot time interval (UPTI) design to overcome the impact of delay and channel estimation error. In TDD beamforming systems, the base station estimates the downlink (DL) channel state information (CSI) by exploiting the received uplink (UL) pilots and the channel reciprocity. Then, utilising the estimated DL CSI, the beamforming vector in the DL transmission is generated. Owing to the constraints of the TDD frame structure and the UL pilot overhead, there inevitably exist delay and estimation error between the estimated and the actual DLCSI, which would degrade system performance. In this study, the upper bound is first derived on ergodic rate for TDD MISO beamforming systems with channel estimation error and delay. Then, with any one given setting of the normalised UL pilot overhead, the optimal robust UPTI is designed, which maximises the upper bound on ergodic rate in the worst case of the CSI delay (i.e. in the case of maximum delay). Simulation results validate that the designed optimal robust UPTI can not on I y maximise the upper bound on ergodic rate but also be adaptive to the variation of channel conditions very well.