Distributed power allocation algorithm in wireless networks under SNR constraints

In this work, the distributed power allocation problem in wireless networks is studied under signal-to-noise ratio (SNR) constraints. The sources of uncertainty are assumed to come from the quantization process and measurement noise in the feedback system. The power allocation is formulated as a reference tracking problem of a pre-defined signal to noise-interference ratio. First, the synthesis problem with SNR constraints is studied as a 2-norm minimization process, which is equivalent to a linear-quadratic-regulator (LQR) problem. The solution of the associated Riccati equation in the LQR formulation is completely characterized, resulting in a feedback law with a recurrent structure. This control law is re-written in a transfer function format, where a simple control strategy is obtained which is dependant on the round-trip delay in the feedback system. In addition, the corresponding 2-norm closed-loop performance is also studied. Thus, the selection of the weight in the LQR problem establishes a compromise between robustness to quantization errors and measurement noise, and tracking performance. A comprehensive simulation evaluation validates the analytical derivations described in the paper.