On the Diversity-Multiplexing Region of Broadcast Channels with Partial Channel State Information

In this paper, we study the reliability (error probability) and rate tradeoffs among the receivers in single-antenna block Rayleigh-fading Gaussian broadcast channels. The rate and reliability tradeoffs are quantified through the notions of average multiplexing and diversity gains in the high signal to noise ratio (SNR) regime. Diversity and multiplexing gains that can be simultaneously achieved and the associated tradeoffs are well-understood in multi-antenna (MIMO) point-to-point systems. However, broadcast channels are different from pointto-point links in two important aspects (i) the availability of additional degrees of freedom in terms of flexible diversity tradeoffs among different users for the same set of multiplexing rates, and (ii) the opportunity to exploit the inherent multiuser diversity of the channel to improve the reliability. We study the diversity-multiplexing region defined as the set of 2K tuples of diversity and average multiplexing gains corresponding to all K receivers that are simultaneously achievable. We show that the diversity-multiplexing region can be significantly enlarged compared to the case where the transmitter has no channel state information (CSI) by exploiting only partial CSI in the form of the ordering of channel fading gains of users at the transmitter. This is done by proposing a time-division opportunistic scheduling scheme that can adjust to and support the average rate requirements of all receivers while exploiting the multiuser diversity of the channel. In particular, it is shown that when the average multiplexing gain of a receiver is small, its diversity gain is increased by a factor K (the number of receivers) compared to the case where no CSI is available.