Communication in a Poisson Field of Interferers

This paper presents a mathematical model for communication subject to both interference and noise. The spatial distribution of the interfering nodes is accounted for by resorting to a Poisson point process in the two-dimensional plane. We consider a realistic scenario of slowly-moving, asynchronous nodes in a wireless environment subject to both log-normal shadowing and fast Rayleigh fading. Under this scenario, we determine the statistical distribution of the cumulative interference at the output of a linear receiver, located anywhere to the two-dimensional plane. Furthermore, we provide the corresponding error performance analysis, which is valid for any linear modulation scheme. The proposed model captures all the essential physical parameters that impact network interference, but is simple enough to allow a tractable analysis and provide fundamental insights. Furthermore, the work generalizes the conventional analysis of linear detection in the presence of additive white Gaussian noise (AWGN) and fast fading, allowing the traditional results to be extended in a simple way to include the effect of interference.

[1]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[2]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[3]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[4]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[5]  Andrew J. Viterbi,et al.  Advances in coding and modulation for noncoherent channels affected by fading, partial band, and multiple-access interference , 1975 .

[6]  C. Mallows,et al.  A Method for Simulating Stable Random Variables , 1976 .

[7]  John G. Proakis,et al.  Digital Communications , 1983 .

[8]  V. Zolotarev.  One-dimensional stable distributions , 1986 .

[9]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[10]  J. Craig.  A new, simple and exact result for calculating the probability of error for two-dimensional signal constellations , 1991, MILCOM 91 - Conference record.

[11]  E.S. Sousa,et al.  Performance of a spread spectrum packet radio network link in a Poisson field of interferers , 1992, IEEE Trans. Inf. Theory.

[12]  Jean-Paul M. G. Linnartz,et al.  Narrowband land-mobile radio networks , 1993 .

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

[14]  C. L. Nikias,et al.  Signal processing with alpha-stable distributions and applications , 1995 .

[15]  Norman C. Beaulieu,et al.  Bandwidth efficient QPSK in cochannel interference and fading , 1995, IEEE Trans. Commun..

[16]  Theodore S. Rappaport,et al.  Propagation measurements and models for wireless communications channels , 1995, IEEE Commun. Mag..

[17]  Gordon L. Stuber,et al.  Principles of Mobile Communication , 1996 .

[18]  K. Knight.  Stable Non-Gaussian Random Processes Gennady Samorodnitsky and Murad S. Taqqu Chapman and Hall, 1994 , 1997, Econometric Theory.

[19]  Dimitrios Hatzinakos,et al.  Performance of FH SS radio networks with interference modeled as a mixture of Gaussian and alpha-stable noise , 1998, IEEE Trans. Commun..

[20]  Mohamed-Slim Alouini,et al.  Digital Communication Over Fading Channels: A Unified Approach to Performance Analysis , 2000 .

[21]  Moe Z. Win,et al.  Virtual branch analysis of symbol error probability for hybrid selection/maximal-ratio combining in Rayleigh fading , 2001, IEEE Trans. Commun..

[22]  Moe Z. Win,et al.  A unified spectral analysis of generalized time-hopping spread-spectrum signals in the presence of timing jitter , 2002, IEEE J. Sel. Areas Commun..

[23]  Athina P. Petropulu,et al.  Ieee Transactions on Signal Processing Co-channel Interference Modeling and Analysis in a Poisson Field of Interferers in Wireless Communications , 2022 .

[24]  David Tse,et al.  Fundamentals of Wireless Communication , 2005 .

[25]  D. Staelin,et al.  The performance of linear multiple-antenna receivers with interferers distributed on a plane , 2005, IEEE 6th Workshop on Signal Processing Advances in Wireless Communications, 2005..

[26]  Walter Hirt,et al.  Uncoordinated rate-division multiple-access scheme for pulsed UWB signals , 2005, IEEE Transactions on Vehicular Technology.

[27]  Andrea Giorgetti,et al.  Influence of fading on the Gaussian approximation for BPSK and QPSK with asynchronous cochannel interference , 2005, IEEE Transactions on Wireless Communications.

[28]  Marvin K. Simon,et al.  Digital Communication Techniques: Signal Design and Detection , 2008 .