## 2014 |

## Journal Articles |

Pastore A, ; Koch, Tobias ; Fonollosa, Javier Rodriguez A Rate-Splitting Approach to Fading Channels With Imperfect Channel-State Information Journal Article IEEE Transactions on Information Theory, 60 (7), pp. 4266–4285, 2014, ISSN: 0018-9448. Abstract | Links | BibTeX | Tags: channel capacity, COMONSENS, DEIPRO, Entropy, Fading, fading channels, flat fading, imperfect channel-state information, MobileNET, Mutual information, OTOSiS, Random variables, Receivers, Signal to noise ratio, Upper bound @article{Pastore2014a, title = {A Rate-Splitting Approach to Fading Channels With Imperfect Channel-State Information}, author = {Pastore, A, and Koch, Tobias and Fonollosa, Javier Rodriguez}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6832779 http://www.tsc.uc3m.es/~koch/files/IEEE_TIT_60(7).pdf http://arxiv.org/pdf/1301.6120.pdf}, issn = {0018-9448}, year = {2014}, date = {2014-01-01}, journal = {IEEE Transactions on Information Theory}, volume = {60}, number = {7}, pages = {4266--4285}, publisher = {IEEE}, abstract = {As shown by Médard, the capacity of fading channels with imperfect channel-state information can be lower-bounded by assuming a Gaussian channel input (X) with power (P) and by upper-bounding the conditional entropy (h(X|Y,hat Ħ)) by the entropy of a Gaussian random variable with variance equal to the linear minimum mean-square error in estimating (X) from ((Y,hat Ħ)) . 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 (X_1) and (X_2) and by applying Médard\'s lower bound first to bound the mutual information between (X_1) and (Y) while treating (X_2) as noise, and by applying it a second time to the mutual information between (X_2) and (Y) while assuming (X_1) to be known, we obtain a capacity lower bound that is strictly larger than Médard\'s lower bound. We then generalize this approach to an arbi- rary number (L) of layers, where (X) is expressed as the sum of (L) independent Gaussian random variables of respective variances (P_ell ) , (ell = 1,dotsc ,L) summing up to (P) . Among all such rate-splitting bounds, we determine the supremum over power allocations (P_ell ) and total number of layers (L) . This supremum is achieved for (L rightarrow infty ) and gives rise to an analytically expressible capacity lower bound. For Gaussian fading, this novel bound is shown to converge to the Gaussian-input mutual information as the signal-to-noise ratio (SNR) grows, provided that the variance of the channel estimation error (H-hat Ħ) tends to zero as the SNR tends to infinity.}, keywords = {channel capacity, COMONSENS, DEIPRO, Entropy, Fading, fading channels, flat fading, imperfect channel-state information, MobileNET, Mutual information, OTOSiS, Random variables, Receivers, Signal to noise ratio, Upper bound}, pubstate = {published}, tppubtype = {article} } As shown by Médard, the capacity of fading channels with imperfect channel-state information can be lower-bounded by assuming a Gaussian channel input (X) with power (P) and by upper-bounding the conditional entropy (h(X|Y,hat Ħ)) by the entropy of a Gaussian random variable with variance equal to the linear minimum mean-square error in estimating (X) from ((Y,hat Ħ)) . 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 (X_1) and (X_2) and by applying Médard's lower bound first to bound the mutual information between (X_1) and (Y) while treating (X_2) as noise, and by applying it a second time to the mutual information between (X_2) and (Y) while assuming (X_1) to be known, we obtain a capacity lower bound that is strictly larger than Médard's lower bound. We then generalize this approach to an arbi- rary number (L) of layers, where (X) is expressed as the sum of (L) independent Gaussian random variables of respective variances (P_ell ) , (ell = 1,dotsc ,L) summing up to (P) . Among all such rate-splitting bounds, we determine the supremum over power allocations (P_ell ) and total number of layers (L) . This supremum is achieved for (L rightarrow infty ) and gives rise to an analytically expressible capacity lower bound. For Gaussian fading, this novel bound is shown to converge to the Gaussian-input mutual information as the signal-to-noise ratio (SNR) grows, provided that the variance of the channel estimation error (H-hat Ħ) tends to zero as the SNR tends to infinity. |

## 2012 |

## Inproceedings |

Pastore, Adriano ; Koch, Tobias ; Fonollosa, Javier Rodriguez Improved Capacity Lower Bounds for Fading Channels with Imperfect CSI Using Rate Splitting Inproceedings 2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel, pp. 1–5, IEEE, Eilat, 2012, ISBN: 978-1-4673-4681-8. Abstract | Links | BibTeX | Tags: channel capacity, channel capacity lower bounds, conditional entropy, Decoding, Entropy, Fading, fading channels, Gaussian channel, Gaussian channels, Gaussian random variable, imperfect channel-state information, imperfect CSI, independent Gaussian variables, linear minimum mean-square error, mean square error methods, Medard lower bound, Mutual information, Random variables, rate splitting approach, Resource management, Upper bound, wireless communications @inproceedings{Pastore2012, title = {Improved Capacity Lower Bounds for Fading Channels with Imperfect CSI Using Rate Splitting}, author = {Pastore, Adriano and Koch, Tobias and Fonollosa, Javier Rodriguez}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6377031}, isbn = {978-1-4673-4681-8}, year = {2012}, date = {2012-01-01}, booktitle = {2012 IEEE 27th Convention of Electrical and Electronics Engineers in Israel}, pages = {1--5}, publisher = {IEEE}, address = {Eilat}, abstract = {As shown by Medard (“The effect upon channel capacity in wireless communications of perfect and imperfect knowledge of the channel,” IEEE Trans. Inform. 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, and by upper-bounding the conditional entropy h(XY, Ĥ), conditioned on the channel output Y and the CSI Ĥ, by the entropy of a Gaussian random variable with variance equal to the linear minimum mean-square error in estimating X from (Y, Ĥ). We demonstrate that, by using a rate-splitting approach, this lower bound can be sharpened: we show that by expressing the Gaussian input X as as the sum of two independent Gaussian variables X(1) and X(2), and by applying Medard's lower bound first to analyze the mutual information between X(1) and Y conditioned on Ĥ while treating X(2) as noise, and by applying the lower bound then to analyze the mutual information between X(2) and Y conditioned on (X(1), Ĥ), we obtain a lower bound on the capacity that is larger than Medard's lower bound.}, keywords = {channel capacity, channel capacity lower bounds, conditional entropy, Decoding, Entropy, Fading, fading channels, Gaussian channel, Gaussian channels, Gaussian random variable, imperfect channel-state information, imperfect CSI, independent Gaussian variables, linear minimum mean-square error, mean square error methods, Medard lower bound, Mutual information, Random variables, rate splitting approach, Resource management, Upper bound, wireless communications}, pubstate = {published}, tppubtype = {inproceedings} } As shown by Medard (“The effect upon channel capacity in wireless communications of perfect and imperfect knowledge of the channel,” IEEE Trans. Inform. 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, and by upper-bounding the conditional entropy h(XY, Ĥ), conditioned on the channel output Y and the CSI Ĥ, by the entropy of a Gaussian random variable with variance equal to the linear minimum mean-square error in estimating X from (Y, Ĥ). We demonstrate that, by using a rate-splitting approach, this lower bound can be sharpened: we show that by expressing the Gaussian input X as as the sum of two independent Gaussian variables X(1) and X(2), and by applying Medard's lower bound first to analyze the mutual information between X(1) and Y conditioned on Ĥ while treating X(2) as noise, and by applying the lower bound then to analyze the mutual information between X(2) and Y conditioned on (X(1), Ĥ), we obtain a lower bound on the capacity that is larger than Medard's lower bound. |