On the Throughput of Broadcast Channels with Imperfect CSI

In a broadcast channel in which one transmitter provides independent streams of data for n receivers, the amount of channel state information (CSI) at the transmitter can affect the capacity region dramatically. Having the accurate SNR of all users at the transmitter, the opportunistic strategy can be used to maximize the throughput (sum-rate) of the system. However, evaluating the SNR is basically an estimation problem at the receiver which in practice is not error free. In this paper, we analyze the effect of the noisy estimation of SNR on the throughput of a broadcast channel. We propose a modified opportunistic scheme in which the transmitter serves the user with the highest estimated SNR, but backs off on the transmit rate based on the variance of the estimation error. This scheme can achieve the maximum achievable rate while the CSI is limited to a noisy estimation of channel coefficients. We obtain the optimum rate back off and find the asymptotic behavior of the throughput under the scheduling scheme we have proposed. We show that the effect of a nonzero estimation error variance can be modeled as an SNR hit proportional to this variance