  The topic of this study is the outage behavior of multiple-antenna slow
fading channels with quantized feedback and partial power control. A fixed-rate
communication system is considered. It is known from the literature that with
error-free feedback, the outage-optimal quantizer for power control has a
circular structure. Moreover, the diversity gain of the system increases
polynomially with the cardinality of the power control codebook. Here, a
similar system is studied, but when the feedback link is error-prone. We prove
that in the high-SNR regime, the optimal quantizer structure with noisy
feedback is still circular and the optimal Voronoi regions are contiguous
non-zero probability intervals. Furthermore, the optimal power control codebook
resembles a channel optimized scalar quantizer (COSQ), i.e., the Voronoi
regions merge with erroneous feedback information. Using a COSQ, the outage
performance of the system is superior to that of a no-feedback scheme. However,
asymptotic analysis shows that the diversity gain of the system is the same as
a no-CSIT scheme if there is a non-zero and non-vanishing feedback error
probability.
