Abstract
To track a desired signal-to-interference-plus-noise-ratio (SINR) that allows for higher system throughput and better link quality in an interference limited wireless communication system, a feedback power controller is designed to obtain the optimal SINR tracking control. In this paper, we propose the multi-objective (MO) H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> optimal power control for interference limited wireless systems that provides quality solutions for both objectives. The considered multi-objective H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> power tracking control is complicated in nature and an equivalent formulation that minimizes the upper bounds of both objectives is proposed. Furthermore, the resulting constraints for the MO H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> power control problem is transformed as three linear matrix inequalities (LMIs), leading to a LMIs-constrained MO problem (MOP). By combining the LMI toolbox in MATLAB with an evolutionary searching algorithm, a set of H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> solutions called Pareto optimal solutions can be obtained and a particular solution can be selected based on the tradeoff determined by the system designer. Finally, to illustrate our design procedure, we provide numerical simulations for a typical interference limited wireless system, i.e., a direct-sequence code division multiple access (DS-CDMA) cellular system. Simulation results demonstrate that the optimal tradeoff indeed can be achieved by the proposed MO H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> power control.
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