Optimal training for Time-Division Duplexed systems with transmit beamforming

In this paper, we perform a large system analysis of regularized channel inversion (RCI) beamforming with channel uncertainty in Time-Division Duplexed (TDD) training based broadcast channels. In the analysis, we consider the problem of finding the optimal training period and power allocation for the uplink training and data transmission. Each user sends training symbols orthogonally via uplink transmission. Neglecting uplink data transmission and so there is no power adaptation in the training process, the optimal training period is equal to or larger than the number of users. Next we consider the uplink communication and allocate the available power between uplink training and data transmission. We found that the optimal training period is equal to the number of users. The optimal period for downlink or uplink data transmission and the optimal power allocation can be obtained using standard numerical optimization algorithm.