Robust ergodic rate transmission for time division duplex beamforming systems

In time division duplex(TDD)beamforming systems,the base station estimates the channel state information(CSI)at transmitter based on uplink pilots and then uses it to generate the beamforming vector in the downlink transmission.Because of the constraints of the TDD frame structure and the uplink pilot overhead,there inevitably exists CSI delay and channel estimation error between CSI estimation and downlink transmission channel,which would degrade system ergodic rate.In this paper,we propose a robust ergodic rate transmission scheme,in which the uplink pilot time interval(UPTI)of an active user is adaptively adjusted according to the changing channel conditions such as Doppler frequency shift,uplink pilot signal to noise ratio(SNR),to minimize the impact of CSI delay and channel estimation error on the ergodic rate of TDD beamforming systems.In order to get the optimal UPTI,we first derive the average post-processing SNR for TDD beamforming systems with channel estimation error and CSI delay.We then obtain the optimal UPTI,which maximizes the average post-processing SNR,given the normalized pilot overhead(the number of pilot symbols per data symbol).The numerical simulation results validate that the the proposed robust ergodic rate transmission scheme not only maximizes the average post-processing SNR but also maximizes the system ergodic rate.Moreover,the scheme can adapt well to the changing channel environments compared with the current fixed UPTI scheme.Especially our research is valuable for the uplink sounding reference signal design in long term evolution advanced(LTEAdvanced)system.