How much training and feedback are needed in MIMO broadcast channels?

We consider a MIMO fading broadcast channel where channel state information is acquired at user terminals via downlink training and explicit analog feedback is used to provide transmitter channel state information (CSIT) to the base station. The feedback channel (the corresponding uplink) is modeled as a MIMO multiple access channel. Under the assumption that data transmission, downlink training, and feedback are performed within the same channel coherence interval of length T symbols, the optimization of a lower bound on the achievable ergodic rate sum yields a non-trivial resource allocation tradeoff.We solve this tradeoff and provide the optimal training and feedback resource allocation for the case of zero-forcing beamforming. When the same power level is used during all stages, it is found that the optimal length of the training + feedback phases increases as O(radicT) for large T. On the other hand, when different power levels can be used for different stages, for sufficiently large T it is optimal to use the minimum number of symbols for training + feedback but to use power of order O(radicT).