Delay Analysis for Fair Power Allocation Strategy in Single Antenna Broadcast Channel

A single transmit antenna Broadcast Channel (BC) with large number of users in a Rayleigh fading environment is considered. It is assumed each user either receives a predetermined minimum rate constraint or remains silent. Recently, it is shown that by applying a proper power allocation strategy, one can maximize the maximum number of active users in such channel. The main contribution of this paper is to derive the expected delay of the optimum power allocation strategy in terms of fairness maximization, where the expected delay is defined as the minimum number of channel uses which guarantees all of the users are serviced at least once. Moreover, for sufficiently large number of channel uses, the average number of services received by a randomly selected user is derived.