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28 March 2024
 
  » arxiv » 1301.6120

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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
AbstractAs 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
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