Monotonic Optimization for Power Assignment in Two-Way Cognitive Radio Networks with Shared-Band Amplify-and-Forward Relays

In this work, we consider a cognitive radio network comprising a pair of sources and multiple relays exercising the amplify-and-forward cooperation in a shared frequency band. For such a network, we consider the problem of determining transmit powers of the sources and relays so that the lesser of the achievable error-free data rates from the two sources is maximized. The formulated problem is a non-convex optimization problem and does not have a structure to guarantee the quality of a solution. We present the transformation of this problem to an equivalent optimization problem for which the monotonic optimization methods can be applied. We establish that the polyblock outer approximation algorithm for this monotonic optimization terminates with an e-optimal solution after a finite number of iterations.