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A Rate-Splitting Approach to Fading Channels with Imperfect Channel-State Information | Adriano Pastore
; Tobias Koch
; Javier Rodríguez Fonollosa
; | Date: |
25 Jan 2013 | Abstract: | As shown by M’edard ("The effect upon channel capacity in wireless
communications of perfect and imperfect knowledge of the channel," IEEE Trans.
Inf. Theory, May 2000), the capacity of fading channels with imperfect
channel-state information (CSI) can be lower-bounded by assuming a Gaussian
channel input X with power P and by upper-bounding the conditional entropy
h(X|Y,^H), conditioned on the channel output Y and the CSI ^H, by the entropy
of a Gaussian random variable with variance equal to the linear minimum
mean-square error in estimating X from (Y,^H). 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 M’edard’s lower bound first to bound the mutual information
between X1 and Y while treating X2 as noise, and by applying the lower bound
then to bound the mutual information between X2 and Y while assuming X1 to be
known, we obtain a lower bound on the capacity that is strictly larger than
M’edard’s lower bound. We then generalize this approach to an arbitrary number
K of layers, where X is expressed as the sum of K independent Gaussian random
variables of respective variances P_k, k = 1,...,K summing up to P. Among all
such rate-splitting bounds, we determine the supremum over power allocations
P_k and total number of layers K. This supremum is achieved for K tending to
infinity and gives rise to an analytically expressible lower bound on the
Gaussian-input mutual information. For Gaussian fading, this novel bound is
shown to be asymptotically tight at high signal-to-noise ratio (SNR), provided
that the variance of the channel estimation error H-^H tends to zero as the
SNR tends to infinity. | Source: | arXiv, 1301.6120 | Services: | Forum | Review | PDF | Favorites |
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