Contraction Approach to Power Control, with Non-Monotonic Applications

In wireless networks, monotonic, strictly subhomogeneous functions have been used to analyze power control algorithms. We provide an alternative analysis based on the observation that such functions are shrinking with respect to certain metrics. These metrics are then used to analyze problems involving two classes of non-monotonic functions. The first class consists of normalized interference functions that can be used to compute the maximum achievable signal-to-interference ratio under power constraints. The second class consists of absolutely subhomogeneous functions that are used to approximate power control dynamics with outages. The eigensolutions of monotonic, strictly subhomogeneous functions are characterized as part of this development.