  Communication systems with low-resolution analog-to-digital-converters (ADCs)
can exploit channel state information at the transmitter and receiver. This
paper presents codebook designs and performance analyses for limited feedback
MIMO systems with finite-bit ADCs. A point-to-point single-user channel is
firstly considered. When the received signal is sliced by 1-bit ADCs, the
absolute phase at the receiver is important to align the phase of the received
signals. A new codebook design for beamforming, which separately quantizes the
channel direction and the residual phase, is therefore proposed. For the
multi-bit case where the optimal transmission method is unknown, suboptimal
Gaussian signaling and eigenvector beamforming is assumed to obtain a lower
bound of the achievable rate. It is found that to limit the rate loss, more
feedback bits are needed in the medium SNR regime than the low and high SNR
regimes, which is quite different from the conventional infinite-bit ADC case.
Second, a multi-user system where a multiple-antenna transmitter sends signals
to multiple single-antenna receivers with finite-bit ADCs is considered. Based
on the derived performance loss due to finite-bit ADCs and finite-bit CSI
feedback, the number of bits per feedback should increase linearly with the ADC
resolution in order to restrict the rate loss.
