On the outage and diversity-multiplexing tradeoff of broadcast channels with 1-bit feedback

In this paper, a single antenna downlink channel with K users is analyzed in the presence of Rayleigh flat fading. A limited channel state information (CSI) feedback scheme is considered, where only 1-bit feedback per user is available at the base station for each fading block. We study the outage performance of such channels. The two cases of short-term and long-term average power constraints are analyzed. Closed-form expressions for the outage probability of the 1-bit feedback scheme are presented. At high SNR, the diversity-multiplexing tradeoff (DMT) is explicitly derived. We show that for the short-term average power constraint case, with only 1-bit feedback, the scheme achieves not only a DMT that increases linearly with the number of users in the system, but also the same tradeoff as if perfect CSI feedback were available at the base station. For long-term average power constraint, it is concluded that power allocation based on the feedback bit is crucial in further improving the DMT. An additional factor of two in the DMT is achieved compared with the short-term average power constraint case.