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.