Low complexity energy efficient power allocation for green cognitive radio with rate constraints

This paper combines two emerging research areas: green communications and cognitive radio. A green cognitive radio network must be accountable for its energy expenditure. Energy expenditure of a cognitive base station is reduced by maximizing the bits/Joule energy efficiency (EE) of its transmissions. Any high complexity solution to this optimization problem will spend too much energy in computation. This paper presents a low complexity solution to the problem of finding the power allocation that maximizes the EE, while limiting the interference to the primary users and meeting the users´ minimum rate requirements. The objective function of the optimization problem is not concave. Charnes-Cooper Transformation is applied to the problem to convert it into a concave program. KKT conditions were analyzed instead of the Lagrangian dual in lieu of low complexity solutions. A power allocation procedure that branches into two main cases depending on the channel gains is proposed. In the first case, an exact solution is obtained by solving a single non-linear equation that produces a common water level. In the second case, a near optimal solution in closed form is given. Simulation results supporting the analytical green solutions are presented.