Abstract
A wide range of communication systems are corrupted by non-Gaussian noise, ranging from wireless to power line. In some cases, including interference in uncoordinated OFDM-based wireless networks, the noise is both impulsive and multivariate. At present, little is known about the information capacity and corresponding optimal input distributions. In this paper, we derive upper and lower bounds of the information capacity by exploiting non-isotropic inputs. For the special case of sub-Gaussianα-stable noise models, a numerical study reveals that isotropic Gaussian inputs can remain a viable choice, although the performance depends heavily on the dependence structure of the noise.
Highlights
In many communication systems, additive Gaussian noise is the dominant form of signal corruption due to thermal fluctuations in the electronic devices comprising the receiver
A key property of impulsive noise is that higher-order moments are often infinite or undefined, arising in Student’s t (Hall, 1966), generalized Gaussian (Dytso et al, 2018), and α-stable models (Middleton, 1977; Sousa, 1992; Ilow and Hatzinakos, 1998; Gulati et al, 2010; Pinto and Win, 2010)
We show that there exists a unique optimal input achieving the information capacity and derive a general upper bound, which is applicable to all multivariate symmetric α-stable noise channels subject to fractional moment and power constraints
Summary
Additive Gaussian noise is the dominant form of signal corruption due to thermal fluctuations in the electronic devices comprising the receiver. Despite the utility of α-stable noise models in communications, the vast majority of work has focused on real-valued noise In this setting, information capacity bounds have been derived in (de Freitas et al, 2017) and the structure of optimal input distributions characterized in (Fahs and Abou-Faycal, 2017). We show that there exists a unique optimal input achieving the information capacity and derive a general upper bound, which is applicable to all multivariate symmetric α-stable noise channels subject to fractional moment and power constraints. To study the performance of non-isotropic inputs, we consider communication in sub-Gaussian α-stable noise subject to a power constraint, and numerically study the behavior of the bounds In this particular case, we observe that isotropic Gaussian inputs nearly achieve the capacity upper bound, suggesting that matching the input to the dependence structure of the noise is not always desirable
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