How Much Feedback Is Required for TDD Multi-Antenna Broadcast Channels with User Selection?

The enormous gains in a multi-antenna transmitter broadcast channel require the Channel State Information at the Transmitter (CSIT). Although the fundamental question "How much feedback is required for a broadcast channel?" has been treated in the literature to some extent, a more comprehensive treatment is certainly desirable. We study the time-division duplex broadcast channel with initial assumption of channel state information (CSI) neither at the base station (BS) nor at the users' side. We provide two transmission strategies through which the BS and the users get necessary CSI. We derive novel lower and upper bounds for the sum rate reflecting the rate loss compared to a perfect CSIT system. Corresponding approximate sum rate expressions are also developed for both schemes. These expressions fully capture the benefits of the CSIT feedback, allowing multi-user diversity gain and better inter-user interference cancellation, and the cost of exchange of information required. These expressions can be optimized for any set of system parameters to unveil the trade-off between the cost and the gains associated to feedback. Thus they allow to characterize the optimal amount of feedback which maximizes the sum rate of the broadcast channel, a well-accepted metric of system performance at the physical layer.