  We consider a MIMO fading broadcast channel and compute achievable ergodic
rates when channel state information is acquired at the receivers via downlink
training and it is provided to the transmitter by channel state feedback.
Unquantized (analog) and quantized (digital) channel state feedback schemes are
analyzed and compared under various assumptions. Digital feedback is shown to
be potentially superior when the feedback channel uses per channel state
coefficient is larger than 1. Also, we show that by proper design of the
digital feedback link, errors in the feedback have a minor effect even if
simple uncoded modulation is used on the feedback channel. We discuss first the
case of an unfaded AWGN feedback channel with orthogonal access and then the
case of fading MIMO multi-access (MIMO-MAC). We show that by exploiting the
MIMO-MAC nature of the uplink channel, a much better scaling of the feedback
channel resource with the number of base station antennas can be achieved.
Finally, for the case of delayed feedback, we show that in the realistic case
where the fading process has (normalized) maximum Doppler frequency shift 0 < F
< 1/2, a fraction 1 - 2F of the optimal multiplexing gain is achievable. The
general conclusion of this work is that very significant downlink throughput is
achievable with simple and efficient channel state feedback, provided that the
feedback link is properly designed.
