Outage Behavior of Quasi-Static Fading Channels with Partial Power Control and Noisy Feedback

We investigate the outage behavior of multiple-antenna slowly fading channels with resolution constrained feedback and partial power control. A fixed-rate communication scheme is considered. It is known from the literature that with error-free feedback, the power control codebook that minimizes the outage probability with an average power constraint at the transmitter has a circular quantizer structure. Moreover, the diversity gain of the system increases polynomially with the cardinality of the power control codebook. Here, we study a similar system, but within a noisy feedback channel framework. We show that the optimal quantizer structure in this scenario is still circular. Furthermore, the optimal quantization codebook resembles a channel optimized scalar quantizer (COSQ). With noisy feedback, using the new power control codebook, the outage performance of the system is superior to that of a no-feedback system. However, we show through asymptotic analysis that the diversity gain is the same as a no-feedback scheme.