Title :
Uplink power adjustment in wireless communication systems: a stochastic control analysis
Author :
Huang, Minyi ; Caines, Peter E. ; Malhamé, Roland P.
Author_Institution :
Dept. of Electr. & Comput. Eng., McGill Univ., Montreal, Que., Canada
Abstract :
This paper considers mobile to base station power control for lognormal fading channels in wireless communication systems within a centralized information stochastic optimal control framework. Under a bounded power rate of change constraint, the stochastic control problem and its associated Hamilton-Jacobi-Bellman (HJB) equation are analyzed by the viscosity solution method; then the degenerate HJB equation is perturbed to admit a classical solution and a suboptimal control law is designed based on the perturbed HJB equation. When a quadratic type cost is used without a bound constraint on the control, the value function is a classical solution to the degenerate HJB equation and the feedback control is affine in the system power. In addition, in this case we develop approximate, but highly scalable, solutions to the HJB equation in terms of a local polynomial expansion of the exact solution. When the channel parameters are not known a priori, one can obtain on-line estimates of the parameters and get adaptive versions of the control laws. In numerical experiments with both of the above cost functions, the following phenomenon is observed: whenever the users have different initial conditions, there is an initial convergence of the power levels to a common level and then subsequent approximately equal behavior which converges toward a stochastically varying optimum.
Keywords :
cellular radio; code division multiple access; fading channels; optimal control; power control; stochastic processes; telecommunication control; Hamilton Jacobi Bellman equation; lognormal fading channel; optimal control; power control; stochastic control analysis; uplink power adjustment; wireless communication system; Base stations; Communication system control; Control system analysis; Control systems; Cost function; Equations; Fading; Power control; Stochastic systems; Wireless communication; Dynamic programming; HJB; Hamilton–Jacobi–Bellman; equations; lognormal fading channels; power control; quality of service;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2004.835388