A rate-splitting approach to fading channels with imperfect channel-state information

Abstract — As shown by Médard, the capacity of fading chan-nels with imperfect channel-state information can be lower-bounded by assuming a Gaussian channel input X with power P and by upper-bounding the conditional entropy h(X|Y, Ĥ) by the entropy of a Gaussian random variable with variance equal to the linear minimum mean-square error in estimating X from (Y, Ĥ). We demonstrate that, using a rate-splitting approach, this lower bound can be sharpened: by expressing the Gaussian input X as the sum of two independent Gaussian variables X1 and X2 and by applying Médard’s lower bound first to bound the mutual information between X1 and Y while treating X2 as noise, and by applying it a second time to the mutual information between X2 and Y while assuming X1 to be known, we obtain a capacity lower bound that is strictly larger than Médard’s lower bound. We then generalize this approach to an arbitrar