Convergence of Iterative Water-Filling With Quantized Feedback: A Sufficient Condition

In this paper, the Iterative Water-Filling (IWF) algorithm is considered when the noise-plus-interference levels fed back from the receivers are quantized. A sufficient condition for this algorithm to have a unique Nash equilibrium is derived. This condition is shown to approach the corresponding condition for standard IWF when the quantization resolution or the transmission powers are sufficiently high. In open spectrum communication systems several user pairs share a common bandwidth of multiple orthogonal sub-channels. The users organize their transmissions autonomously without central coordination.