Outage-Optimized Multicast Beamforming With Distributed Limited Feedback

We consider a slowly fading multicast channel with one T-antenna transmitter and K single-antenna receivers with the goal of minimizing channel outage probability using quantized beamforming. Our focus is on a distributed limited feedback scenario where each receiver can only quantize and send feedback information regarding its own receiving channels. A classical result in point-to-point quantized beamforming is that a necessary and sufficient condition for full diversity is to have ⌈log
₂
T⌉ bits from the receiver with an appropriate quantizer. We first generalize this result to multicast beamforming systems and show that a necessary and sufficient condition to achieve full diversity for all receivers is to have ⌈log
₂
T⌉ bits from each receiver with an appropriate quantizer. Achievable diversity gains with a long-term power constraint are also discussed. Moreover, for a two-receiver system and with R feedback bits per receiver, we show that the outage performance with quantized R beamforming is within O(2
^-R/32T
2
)dBs to the performance with full channel state information at the transmitter (CSIT). This constitutes, in the context of multicast channels, the first example of a distributed limited feedback scheme whose performance can provably approach the performance with full CSIT. Numerical simulations confirm our analytical findings.