  In this paper, we introduce a novel approach for power allocation in cellular
networks. In our model, we use sigmoidal-like utility functions to represent
different users' modulation schemes. Each utility function is a representation
of the probability of successfully transmitted packets per unit of power
consumed by a user, when using a certain modulation scheme. We consider power
allocation with utility proportional fairness policy, where the fairness among
users is in utility percentage i.e. percentage of successfully transmitted
packets of the corresponding modulation scheme. We formulate our network
utility maximization problem as a product of utilities of all users and prove
that our power allocation optimization problem is convex and therefore the
optimal solution is tractable. We present a distributed algorithm to allocate
base station (BS) powers optimally with priority given to users running lower
modulation schemes while ensuring non-zero power allocation to users running
higher modulation schemes. Our algorithm prevents fluctuation in the power
allocation process and is capable of traffic and modulation dependent pricing
i.e. charges different price per unit power from different users depending in
part on their modulation scheme and total power available at the BS. This is
used to flatten traffic and decrease the service price for users.
