Optimal Training in large TDD multi-user downlink systems under zero-forcing and regularized zero-forcing precoding

This paper considers a large multi-user time-division duplex (TDD) system, where the base station (BS) acquires channel state information via pilot signaling from the users. In the downlink the BS employs zero-forcing (ZF) and regularized zero-forcing (RZF) precoding. We derive the optimal sum rate maximizing amount of channel training using sum rate approximations from the large system analysis of MISO downlink channels under (R)ZF precoding. Moreover, in the regime of high signal-to-noise ratio (SNR), we derive approximate solutions of the optimal amount of training for both schemes that are of closed-form. By comparing the two schemes, we find that RZF requires less training than ZF, but the training interval of both schemes is equal for asymptotically high SNR. Furthermore, simulations are carried out which demonstrate the accuracy of our approximate solutions.