Differentiated rate scheduling for gaussian broadcast channels

In this paper, we consider a fading broadcast channel where users have different rate demands. In particular, we assume users are divided into M groups, each group of which requires the same rate, and where the ratio of the rates of the groups are given. The transmitter would like to maximize the throughput (sum of the rates to all users) while maintaining the rational rate constraints. In general, this problem appears to be computationally intractable since the ergodic capacity region is described as the convex hull of (an infinite) set of rates. In this paper, we therefore, focus on the asymptotic regime of many users (large n) where explicit results can be found. In particular, we propose three scheduling schemes to provide the rational rate constraints namely, weighted opportunistic (WO), time division opportunistic (TO), and superposition coding (SC). The WO scheduling is a generalization of the opportunistic scheduling in which we transmit to only the user that has the maximum weighted signal to noise ratio (SNR). In TO, each group has its own time slot in which the transmitter chooses the user with the best SNR from the corresponding group. Superposition coding is the one that achieves the capacity region. For each scheduling we give explicit scheme to guarantee the rational rate constraints. We also analyze the throughput loss due to rate constraints for different schemes. In particular, we show that the throughput loss compared to the maximum throughput (i.e., the sum rate capacity without any rate constraints) tends to zero for large n, and finally, we analyze the convergence rate of all the schemes.