Achievable rates for additive isotropic α-stable noise channels

Impulsive noise arises in many communication systems - ranging from wireless to molecular - and is often modeled via the α-stable distribution. In this paper, we investigate properties of the capacity of complex isotropic α-stable noise channels, which can arise in the context of wireless cellular communications and are not well understood at present. In particular, we derive a tractable lower bound, as well as prove existence and uniqueness of the optimal input distribution. We then apply our lower bound to study the case of parallel α-stable noise channels and derive a bound that provides insight into the effect of the tail index α on the achievable rate.

[1]  G. Peters,et al.  Generalized Interference Models in Doubly Stochastic Poisson Random Fields for Wideband Communications: the PNSC(alpha) model , 2012, 1207.1531.

[2]  A. W. Marshall.  Markov's inequality for random variables taking values in a linear topological space , 1984 .

[3]  R. Bass,et al.  Review: P. Billingsley, Convergence of probability measures , 1971 .

[4]  Andrew W. Eckford,et al.  Stable Distributions as Noise Models for Molecular Communication , 2014, 2015 IEEE Global Communications Conference (GLOBECOM).

[5]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[6]  V. Zolotarev.  Integral Transformations of Distributions and Estimates of Parameters of Multidimensional Spherically Symmetric Stable Laws , 1981 .

[7]  Ibrahim C. Abou-Faycal,et al.  A cauchy input achieves the capacity of a Cauchy channel under a logarithmic constraint , 2014, 2014 IEEE International Symposium on Information Theory.

[8]  Ercan E. Kuruoglu,et al.  Alpha-Stable Channel Capacity , 2011, IEEE Communications Letters.

[9]  Ibrahim C. Abou-Faycal,et al.  On the capacity of additive white alpha-stable noise channels , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.

[10]  Hui Li,et al.  Capacity of the Memoryless Additive Inverse Gaussian Noise Channel , 2014, IEEE Journal on Selected Areas in Communications.

[11]  D. Applebaum.  Stable non-Gaussian random processes , 1995, The Mathematical Gazette.

[12]  J. Danskin.  The Theory of Max-Min and its Application to Weapons Allocation Problems , 1967 .

[13]  M. Win,et al.  Communication in a Poisson Field of Interferers , 2006, 2006 40th Annual Conference on Information Sciences and Systems.

[14]  Tetsunao Matsuta,et al.  国際会議開催報告:2013 IEEE International Symposium on Information Theory , 2013 .

[15]  Dimitrios Hatzinakos,et al.  Analytic alpha-stable noise modeling in a Poisson field of interferers or scatterers , 1998, IEEE Trans. Signal Process..

[16]  David Middleton,et al.  Statistical-Physical Models of Electromagnetic Interference , 1977, IEEE Transactions on Electromagnetic Compatibility.