Uniform Power Allocation with Thresholding over Rayleigh Slow Fading Channels with QAM Inputs

In this paper, we consider the power allocation problem that minimizes the outage probability for Rayleigh slow fading channels with equiprobable QAM inputs. We focus on the uniform power allocation with thresholding (UPAT) policy that assigns nonzero constant power only to a subset of the subchannels. This simple suboptimal policy can significantly alleviate the feedback overhead and the complexity compared to the optimal mercury/water-filling (MWF) solution. Through asymptotic analysis and numerical simulations, we first show that the optimal UPAT, namely, the UPAT with the optimal threshold, performs close to MWF if the constellation size M is large enough that log₂ M ≫ R, where R is the fixed target transmission rate. This condition log₂ M ≫ R turns out to define a natural system operating point. As we show through numerical results, if log₂M ≈ R, both MWF and the optimal UPAT perform poorly due to having too small M and their performance can be significantly improved by using a larger M. From these results, we conclude that for a given target transmission rate, the optimal UPAT performs close to MWF as long as the constellation size is chosen appropriately not to limit the performance.