User-specified training symbol placement for channel prediction in TDD MIMO systems

In this paper, we design the training symbol placement for channel prediction in time-division-duplex multiple-antenna systems, where training symbols in a finite-length uplink frame are used for predicting downlink channels at the base station (BS). Aimed at minimizing the normalized sum mean square error of the Wiener predictor, we first prove that, for the first-order Gauss-Markov fading channel model, the optimal positions of training symbols lie at the end of the uplink frame, which is commonly recognized by intuition. For general channel models, we show that the ending placement is no longer optimal, and we propose a low-complexity method for designing training symbol placement based on alternating searching. In practice, the BS finds the optimal positions based on each user's temporal correlation, spatial correlation, and uplink signal-to-noise ratio (SNR) and then transmits the positions to the user, which needs low signaling overhead. Numerical results show significant prediction performance gain of the proposed training symbol placement over typical training placements under various SNR and Doppler frequency.