Stochastic discrete-time nash games forwireless networks

Stochastic linear-quadratic Gaussian nonzero-sum Nash games with constrained state information is proposed for joint control of power and rate in wireless networks. When each player(node) is constrained to use a linear Kalman-like state estimator to solve onepsilas optimal strategy, state estimators of two players are investigated according to information structure: the current output and a one-step delayed control input of the player. To model the loop delay in distributed wireless networks, an optimal power and rate control scheme that minimizes the energy of the difference between the actual and desired Signal-to-Interference-plus-Noise-Ratio (SNR) levels and the two playerspsila control sequence is obtained for the congestion levels and the information structure. Algorithms for computing Nash-optimal feedback gains are given. The optimal controllers of two players for the closed-loop Nash equilibrium solution are interrelated and cannot be determined separately. The fact exactly demonstrates a cooperative and influential relationship between players.