Asymptotically optimal sum-rate of random unitary beamforming with double thresholds

The capacity of Multiple-Input Multiple-Output Broadcast Channel (MIMO-BC) is known to be achieved by Dirty Paper Coding (DPC). In multi-user environment, the sum-rate of DPC scales like M log log K for a large number of K users and fixed M antennas at the base station. Unfortunately, due to the limited feedback channel, the random unitary beamforming (RUB) has been presented as a simple and practical technique capable of supporting spatial division multiple access (SDMA) instead of DPC. Moreover, the multi-beam transmission with selective binary feedback (MBTSB) has been proposed to schedule the users simply as well as to reduce the amount of feedback per user by exploiting threshold. In this paper, we propose the RUB scheme with two different predetermined thresholds to extend the MBTSB. We first show that our proposed scheme can outperform the MBTSB without changing the amount of feedback per user. From our analysis, we show that the scaling law of our proposed scheme approaches to M log log K asymptotically for a large number of K users and the fixed M antennas.