An Optimal Scheme for TDD Beamforming Systems with Imperfect Channel State Information

An optimal scheme on uplink pilot time interval (UPTI) to maximize average post-processing SNR (signal to noise ratio) is proposed in order to overcome the impact of channel estimation error and delay on a time division duplex (TDD) multiple input single output (MISO) beamforming system. In TDD system, 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 delay and channel estimation error between CSI estimation and its use. In this paper, we first derive average post-processing SNR for TDD MISO beamforming system with channel estimation error and delay. We then obtain the optimal UPTI, which maximizes average post-processing SNR, given the normalized pilot overhead (the number of pilot symbols per data symbol). The simulation results validate that the optimal UPTI not only maximizes the average post-processing SNR but also minimizes the BER. Especially our research is valuable for the uplink sounding reference signal design in LTE- Advanced system.