Power Allocation Based on Proportional-Integral Controller in Femtocell Networks With Consideration of Maximum Power Constraint

In this paper, a two-tier uplink femtocell network operating in orthogonal frequency-division multiple access is investigated. Femtocell base stations endowed with cognitive capacity can sense the void spectrum of macrocell. We aim at an energy-saving scheme of power allocation for femtocell users. The new idea that performance of Femtocell networks can be analyzed using control theory is proposed in this paper. A simple and novel power control algorithm is designed based on the virtual Proportional-Integral (PI) controller. When considering the maximum power constraints, different from the proof of the convergence via standard interference functions, we establish a linear system with state saturation (maximum power constraint) for femtocell networks, and the power's convergence is verified in theory with iterative linear matrix inequality algorithm. Two introduced control parameters not only guarantee the stability of power control algorithm, but also can adjust the transient response and save energy. Numerical results illustrate the convergence performance and advantages of the PI algorithm.