Adaptive Sum Power Iterative Waterfilling for MIMO Cognitive Radio Channels

TL;DR

This paper formulates the sum capacity of MIMO Cognitive Radio Channels as a convex optimization problem and introduces an efficient iterative waterfilling algorithm that quickly converges to the optimal transmit policies.

Contribution

It presents a novel convex formulation of the sum capacity problem and develops a specialized iterative waterfilling algorithm exploiting problem structure.

Findings

Algorithm converges in few iterations

Achieves optimal sum capacity and transmit policies

Polynomial time solution for the convex problem

Abstract

In this paper, the sum capacity of the Gaussian Multiple Input Multiple Output (MIMO) Cognitive Radio Channel (MCC) is expressed as a convex problem with finite number of linear constraints, allowing for polynomial time interior point techniques to find the solution. In addition, a specialized class of sum power iterative waterfilling algorithms is determined that exploits the inherent structure of the sum capacity problem. These algorithms not only determine the maximizing sum capacity value, but also the transmit policies that achieve this optimum. The paper concludes by providing numerical results which demonstrate that the algorithm takes very few iterations to converge to the optimum.