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.

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Keywords Convergence, Nash equilibrium, noncooperative games, nonnegative matrix, power allocation
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Journal IEEE Transactions on Signal Processing
Gohary, R, & Yanikomeroglu, H. (2012). Convergence of iterative water-filling with quantized feedback: A sufficient condition. IEEE Transactions on Signal Processing, 60(5), 2688–2693. doi:10.1109/TSP.2012.2188715