Linear Quadratic Regulators for Wireless Data Transmission Scheduling

Continuous optimal linear quadratic control theory is adapted for the problem of optimal data transmission scheduling from base station to mobiles, in wireless CDMA based systems. Such discrete event scheduling problems have traditionally been treated within the computationally unwieldy, analytically difficult framework of multi class queues (e.g. cmu rules and their generalization (Van Meighem, 1995)). Instead here, a fluid modelling framework is adopted, and continuous control laws are sought for the data transmission rates. In the current setting, variability of the rates is penalized; this is unlike the usual queueing theoretic optimal control setting where rates (instantaneous or short term mean) can change arbitrarily fast. Resulting optimal fluid rates are converted into real schedules by means of a time varying generalized processor sharing scheme. The solution is entirely based on finite horizon linear quadratic regulator theory although the original problem does not fit into that framework. It results in feedback control laws which can be shown to be computable through a fixed size (sixth order) matrix differential Riccati equation, independent of the number of mobiles. This insures the scalability of the control algorithms. Numerical results suggest that the weights in the quadratic regulator can be modified to produce schedules that can go from opportunistic like (favoring best channels), to fair (indifferent to channel quality), to otherwise favoring special customers through a priority like scheme