On the Optimal Number of Active Receivers in Fading Broadcast Channels

For broadcast channels, a power allocation scheme is proposed to maximize the number of active receivers, for each of which, a minimum rate R_min > 0 can be achieved. Under the assumption of independent Rayleigh-fading channels for different receivers, as the total number of receivers n goes to infinity, the maximum number of active receivers is shown to be arbitrarily close to ln(Pln n)/R_min with probability approaching 1, where P is the total transmit power.