  Multiuser diversity (MUDiv) is one of the central concepts in multiuser (MU)
systems. In particular, MUDiv allows for scheduling among users in order to
eliminate the negative effects of unfavorable channel fading conditions of some
users on the system performance. Scheduling, however, consumes energy (e.g.,
for making users' channel state information available to the scheduler). This
extra usage of energy, which could potentially be used for data transmission,
can be very wasteful, especially if the number of users is large. In this
paper, we answer the question of how much MUDiv is required for energy limited
MU systems. Focusing on uplink MU wireless systems, we develop MU scheduling
algorithms which aim at maximizing the MUDiv gain. Toward this end, we
introduce a new realistic energy model which accounts for scheduling energy and
describes the distribution of the total energy between scheduling and data
transmission stages. Using the fact that such energy distribution can be
controlled by varying the number of active users, we optimize this number by
either (i) minimizing the overall system bit error rate (BER) for a fixed total
energy of all users in the system or (ii) minimizing the total energy of all
users for fixed BER requirements. We find that for a fixed number of available
users, the achievable MUDiv gain can be improved by activating only a subset of
users. Using asymptotic analysis and numerical simulations, we show that our
approach benefits from MUDiv gains higher than that achievable by generic
greedy access algorithm, which is the optimal scheduling method for energy
unlimited systems.
