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

As shown by Medard, 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 M´edard’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 M´edard’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.