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 power are sufficiently high.