In this paper, we define the power region as the set of power allocations for
K users such that everybody meets a minimum signal-to-interference ratio (SIR).
The SIR is modeled in a multiuser CDMA system with fixed linear receiver and
signature sequences. We show that the power region is convex in linear and
logarithmic scale. It furthermore has a componentwise minimal element. Power
constraints are included by the intersection with the set of all viable power
adjustments.
In this framework, we aim at minimizing the total expended power by
minimizing a componentwise monotone functional. If the feasible power region is
nonempty, the minimum is attained. Otherwise, as a solution to balance
conflicting interests, we suggest the projection of the minimum point in the
power region onto the set of viable power settings. Finally, with an
appropriate utility function, the problem of minimizing the total expended
power can be seen as finding the Nash bargaining solution, which sheds light on
power assignment from a game theoretic point of view. Convexity and
componentwise monotonicity are essential prerequisites for this result.Comment: To appear in the proceedings of the 2005 IEEE International Symposium
on Information Theory, Adelaide, Australia, September 4-9, 200
