Achieving Sum-Capacity of the MIMO BC with Large Transmit Array using One-Shot Scalable Feedback Protocol

We consider a MIMO broadcast channel (BC) with large M and K, where M is the number of transmit antennas and K is the number of single-antenna users; and propose a scalable feedback protocol that achieves the sum-capacity with limited feedback of channel state information (CSI). In our earlier work, we showed that if feedback time slots correspond to channel gains and not to users, the sum-capacity M log log K can be achieved with feedback resources growing only as M log K, unlike linearly as M K for conventional schemes. In this work, we show that feedback requirement can further be reduced by half or more, while still achieving the sum-capacity. A scalable feedback (SF) protocol using random beamforming (RBF) is proposed, which a) requires finite number of feedback slots upper bounded by a constant, b) is fully distributed, c) needs finite transmission energy during feedback and d) achieves the sum-capacity. Numerical results show that feedback load is substantially reduced as compared to conventional schemes, as well as our own previously proposed SF scheme.