Unified framework for the analysis and design of linear uplink power control in CDMA systems

In this work, it is proposed a unified framework to design and analyze uplink distributed power control schemes over flat-fading channels from a control theory perspective. The effects of linear detectors and round trip delays are explicitly characterized in this study. First, the optimal solution to the power minimization problem under signal to interference-noise ratio (SINR) restrictions is reviewed, where sufficient conditions for its existence are presented that depends on the detection strategy. Four different linear detection schemes are studied in this work: Matched Filter, Decorrelator, MMSE and Projector. Specifically, two special cases are analyzed with respect to the spreading codes properties: uniform cross-correlation and orthogonal codes, and under both conditions an explicit expression for the central solution is obtained. Nevertheless, one drawback of the central solution is its lack of robustness against channel estimation errors, transport delays and noise. Hence, it is proposed closed-loop control laws with linear power assignment which are capable of provide robustness to these channel effects. It is then presented that under certain conditions, stable feedback loops can be obtained considering SINR quantification, transmission and processing delays, and the resulting closed-loop power solutions tend to the central ones. Finally, it is illustrated that the selection of the linear detectors does not affect the resulting closed-loop dynamics, but the uplink transmission power in steady-state. An exhaustive simulation evaluation is included to validate the mathematical analysis presented for open and closed-loop solutions.