Conferences: A Rate-Splitting Approach to Fading Multiple-Access Channels with Imperfect Channel-State Information
Pastore, Koch and J. Rodríguez Fonollosa

Abstract

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.


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