A Rate-Splitting Approach to Fading Multiple-Access Channels with Imperfect Channel-State Information

As shown by Médard, the capacity of fading channels with imperfect channel-state information (CSI) can be lowerbounded by assuming a Gaussian channel input and by treating the unknown portion of the channel multiplied by the channel input as independent worst-case (Gaussian) noise. Recently, we have demonstrated that this lower bound can be sharpened by a rate-splitting approach: by expressing the channel input as the sum of two independent Gaussian random variables (referred to as layers), say X = X1+X2, and by applying Médard’s bounding technique to first lower-bound the capacity of the virtual channel from X1 to the channel output Y (while treating X2 as noise), and then lower-bound the capacity of the virtual channel from X2 to Y (while assuming X1 to be known), one obtains a lower bound that is strictly larger than Médard’s bound. This ratesplitting approach is reminiscent of an approach used by Rimoldi and Urbanke to achieve points on the capacity region of the Gaussian multiple-access channel (MAC). Here we blend these two rate-splitting approaches to derive a novel inner bound on the capacity region of the memoryless fading MAC with imperfect CSI. Generalizing the above rate-splitting approach to more than two layers, we show that, irrespective of how we assign powers to each layer, the supremum of all rate-splitting bounds is approached as the number of layers tends to infinity, and we derive an integral expression for this supremum. We further derive an expression for the vertices of the best inner bound, maximized over the number of layers and over all power assignments.