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1Ergodic and Outage Performance of Fading Broadcast Channels with 1Bit Feedback
"... Abstract—In this paper, the ergodic sumrate and outage probability of a downlink singleantenna channel with K users are analyzed in the presence of Rayleigh flat fading, where limited channel state information (CSI) feedback is assumed. Specifically, only 1bit feedback per fading block per user i ..."
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Abstract—In this paper, the ergodic sumrate and outage probability of a downlink singleantenna channel with K users are analyzed in the presence of Rayleigh flat fading, where limited channel state information (CSI) feedback is assumed. Specifically, only 1bit feedback per fading block per user is available at the base station. We first study the ergodic sumrate of the 1bit feedback scheme, and consider the impact of feedback delay on the system. A closedform expression for the achievable ergodic sumrate is presented as a function of the fading temporal correlation coefficient. It is proved that the sumrate scales as log logK, which is the same scaling law achieved by the optimal nondelayed full CSI feedback scheme. The sumrate degradation due to outdated CSI is also evaluated in the asymptotic regimes of either large K or low SNR. The outage performance of the 1bit feedback scheme for both instantaneous and outdated feedback is then investigated. Expressions for the outage probabilities are derived, along with the corresponding diversitymultiplexing tradeoffs (DMT). It is shown that with instantaneous feedback, a power allocation based on the feedback bits enables to double the DMT compared to the case with shortterm power constraint in which a dynamic power allocation is not allowed. But, with outdated feedback, the advantage of power allocation is lost, and the DMT reverts to that achievable with no CSI feedback. Nevertheless, for finite SNR, improvement in terms of outage probability can still be obtained. Index Terms—Ergodic sumrate, outage probability, limited feedback, feedback delay, outdated channel state information, multiuser diversity, scaling law, power allocation, diversitymultiplexing tradeoff, Rayleigh fading. I.