Unified continuous- and discrete-time uplink power control problem formulation for SIR-based wireless networks

The nonlinear, multiplicative form of the signal-to-interference ratio (SIR) function can be put in the linear, additive form by representing the SIR function in the logarithmic scale. Most of the well-known discrete-time power control algorithms can be reformulated into simple continuous-time dynamic equations in the logarithmic scale. A ‘surrogate derivative’ model yields the continuous-time system dynamics for each local user. It reveals that many of the most popular and powerful existing power control update laws can actually be comprehended as the discrete-time versions of the standard continuous-time control strategies. The continuous-time dynamic system formulation provides a new avenue to the uplink power control designs for wireless networks such that many existing useful control methodologies can be directly employed for solving the SIR-based wireless communication power control problems. Yates' power convergence conditions for the distributed power control (DPC), originally given for the discrete-time power control updates, are also presented in the continuous-time framework in this paper. We have shown that CDMA 2000 (IS-95) standard for mobile power updates uses a sliding mode control technique, and that the DPC algorithm is based on a linear state feedback control law.