Capacity of TDD MISO Beamforming Systems with Channel Estimation Error and Delay

This paper examines the capacity of a time division duplex (TDD) multiple input single output (MISO) beamforming system with channel estimation error and delay over the time varying fading channel. 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 the capacity upper bound for TDD MISO beamforming system with channel estimation error and delay. We then obtain the optimal uplink pilot time interval (UPTI), which maximizes the capacity upper bound, 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 capacity upper bound but also maximizes the system ergodic capacity. Especially our research is valuable for the uplink sounding reference signal design in LTE-Advanced system.