Mixed-strategy based discrete power control approach for cognitive radios: A matrix game-theoretic framework

From the practical consideration, we capture the discrete power control problem in wireless cognitive communication system for a two user case. The power control problem is formulated as a matrix game model. Focus the possible deviation behavior of the selfish secondary user and the notable prisoner´s dilemma phenomenon under the Nash game modeling framework, the mixed-strategy solution for the matrix game is investigated. Meanwhile, in accordance with the max-min fairness principle an optimal power control approach is proposed. With introducing a powerfully amazing mathematical transformation, the complex non-cooperative Matrix Power Control Game (MPCG) is absolutely simplified, which is easily solved by the simplex method. The numerical results tell that the presented approach is efficient and the convergence is robust. Further, the algorithm makes a better tradeoff between the system performance and the fairness.