A Mathematical Theory of Network Interference and Its Applications

In this paper, we introduce a mathematical framework for the characterization of network interference in wireless systems. We consider a network in which the interferers are scattered according to a spatial Poisson process and are operating asynchronously in a wireless environment subject to path loss, shadowing, and multipath fading. We start by determining the statistical distribution of the aggregate network interference. We then investigate four applications of the proposed model: 1) interference in cognitive radio networks; 2) interference in wireless packet networks; 3) spectrum of the aggregate radio-frequency emission of wireless networks; and 4) coexistence between ultrawideband and narrowband systems. Our framework accounts for all the essential physical parameters that affect network interference, such as the wireless propagation effects, the transmission technology, the spatial density of interferers, and the transmitted power of the interferers.

[1]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[2]  J. Crank.  Tables of Integrals , 1962 .

[3]  P. Bello.  Characterization of Randomly Time-Variant Linear Channels , 1963 .

[4]  J. McFadden.  The Entropy of a Point Process , 1965 .

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

[6]  S. F. George,et al.  Detection of Targets in Non-Gaussian Sea Clutter , 1970, IEEE Transactions on Aerospace and Electronic Systems.

[7]  G. Trunk.  Further Results on the Detection of Targets in Non-Gaussian Sea Clutter , 1971, IEEE Transactions on Aerospace and Electronic Systems.

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

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

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

[11]  Norman Abramson,et al.  The Throughput of Packet Broadcasting Channels , 1977, IEEE Trans. Commun..

[12]  R. Morgan.  Mobile radio communications. , 1982, Hospital engineering.

[13]  John A. Silvester,et al.  On the Capacity of Multihop Slotted ALOHA Networks with Regular Structure , 1983, IEEE Trans. Commun..

[14]  Leonard Kleinrock,et al.  Optimal Transmission Ranges for Randomly Distributed Packet Radio Terminals , 1984, IEEE Trans. Commun..

[15]  J.E. Mazo,et al.  Digital communications , 1985, Proceedings of the IEEE.

[16]  John G. Proakis,et al.  Probability, random variables and stochastic processes , 1985, IEEE Trans. Acoust. Speech Signal Process..

[17]  Ting-Chao Hou,et al.  Transmission Range Control in Multihop Packet Radio Networks , 1986, IEEE Trans. Commun..

[18]  A. Izenman.  Introduction to Random Processes, With Applications to Signals and Systems , 1987 .

[19]  D. F. Hays,et al.  Table of Integrals, Series, and Products , 1966 .

[20]  K. Pahlavan,et al.  Slotted ALOHA radio networks with PSK modulation in Rayleigh fading channels , 1989 .

[21]  Mohsen Kavehrad,et al.  ALOHA with capture over slow and fast fading radio channels with coding and diversity , 1989, IEEE J. Sel. Areas Commun..

[22]  Kaveh Pahlavan,et al.  A new approach for the analysis of the slotted Aloha local packet radio networks , 1990, IEEE International Conference on Communications, Including Supercomm Technical Sessions.

[23]  Kaveh Pahlavan,et al.  Comment on slotted ALOHA radio networks with PSK modulation in Rayleigh fading channels (and reply) , 1990 .

[24]  John A. Silvester,et al.  Optimum Transmission Ranges in a Direct-Sequence Spread-Spectrum Multihop Packet Radio Network , 1990, IEEE J. Sel. Areas Commun..

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

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

[27]  Ward Whitt,et al.  The Fourier-series method for inverting transforms of probability distributions , 1992, Queueing Syst. Theory Appl..

[28]  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.

[29]  Chrysostomos L. Nikias,et al.  Performance of optimum and suboptimum receivers in the presence of impulsive noise modeled as an alpha-stable process , 1993, Proceedings of MILCOM '93 - IEEE Military Communications Conference.

[30]  C. L. Nikias,et al.  Signal processing with fractional lower order moments: stable processes and their applications , 1993, Proc. IEEE.

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

[32]  Marvin Kenneth Simon.  Digital Communication Techniques , 1994 .

[33]  J. Ilow,et al.  Detection for binary transmission in a mixture of Gaussian noise and impulsive noise modeled as an alpha-stable process , 1994, IEEE Signal Processing Letters.

[34]  Norman C. Beaulieu,et al.  Micro- and macrodiversity NCFSK (DPSK) on shadowed Nakagami-fading channels , 1994, IEEE Trans. Commun..

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

[36]  Rudolf Mathar,et al.  On the distribution of cumulated interference power in Rayleigh fading channels , 1995, Wirel. Networks.

[37]  Chrysostomos L. Nikias,et al.  Performance of optimum and suboptimum receivers in the presence of impulsive noise modeled as an alpha-stable process , 1995, IEEE Trans. Commun..

[38]  Gordon L. Stüber.  Principles of mobile communication , 1996 .

[39]  M. V. Clark,et al.  A new path-gain/delay-spread propagation model for digital cellular channels , 1997 .

[40]  Charles M. Grinstead,et al.  Introduction to probability , 1999, Statistics for the Behavioural Sciences.

[41]  Marco Chiani.  Analytical distribution of linearly modulated cochannel interferers , 1997, IEEE Trans. Commun..

[42]  James S. Harris,et al.  Tables of integrals , 1998 .

[43]  Moe Z. Win,et al.  Impulse radio: how it works , 1998, IEEE Communications Letters.

[44]  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..

[45]  Moe Z. Win.  On the power spectral density of digital pulse streams generated by M-ary cyclostationary sequences in the presence of stationary timing jitter , 1998, IEEE Trans. Commun..

[46]  David Middleton,et al.  Non-Gaussian Noise Models in Signal Processing for Telecommunications: New Methods and Results for Class A and Class B Noise Models , 1999, IEEE Trans. Inf. Theory.

[47]  Xiaodai Dong,et al.  Error probabilities of two-dimensional M-ary signaling in fading , 1999, IEEE Trans. Commun..

[48]  Joseph Mitola,et al.  Cognitive radio: making software radios more personal , 1999, IEEE Wirel. Commun..

[49]  Moe Z. Win,et al.  MRC performance for M-ary modulation in arbitrarily correlated Nakagami fading channels , 2000, IEEE Communications Letters.

[50]  Moe Z. Win,et al.  Ultra-wide bandwidth time-hopping spread-spectrum impulse radio for wireless multiple-access communications , 2000, IEEE Trans. Commun..

[51]  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..

[52]  A. V. Vasilakos,et al.  Mobile Radio Communications, 2nd ed. , 2001 .

[53]  Moe Z. Win,et al.  The ultra-wide bandwidth indoor channel: from statistical model to simulations , 2002, IEEE J. Sel. Areas Commun..

[54]  Moe Z. Win,et al.  Characterization of ultra-wide bandwidth wireless indoor channels: a communication-theoretic view , 2002, IEEE J. Sel. Areas Commun..

[55]  Norman C. Beaulieu,et al.  Accurate DS-CDMA bit-error probability calculation in Rayleigh fading , 2002, IEEE Trans. Wirel. Commun..

[56]  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..

[57]  Moe Z. Win,et al.  On the inverse symbol-error probability for diversity reception , 2003, IEEE Trans. Commun..

[58]  Bo Hu,et al.  Precise bit error rate of TH-PPM UWB systems in the presence of multiple access interference , 2003, IEEE Conference on Ultra Wideband Systems and Technologies, 2003.

[59]  Bo Hu,et al.  Exact bit error rate analysis of TH-PPM UWB systems in the presence of multiple-access interference , 2003, IEEE Communications Letters.

[60]  Christian Bettstetter,et al.  Connectivity of Wireless Multihop Networks in a Shadow Fading Environment , 2003, MSWIM '03.

[61]  Paul Muhlethaler,et al.  A Spatial Reuse Aloha MAC Protocol for Multihop Wireless Mobile Networks , 2003 .

[62]  Moe Z. Win,et al.  Bit error outage for diversity reception in shadowing environment , 2003, IEEE Communications Letters.

[63]  John Orriss,et al.  Probability distributions for the number of radio transceivers which can communicate with one another , 2003, IEEE Trans. Commun..

[64]  R. Verdone,et al.  Collaborative signal processing for energy-efficient self-organizing wireless sensor network , 2004, International Workshop on Wireless Ad-Hoc Networks, 2004..

[65]  Bo Hu,et al.  Accurate evaluation of multiple-access performance in TH-PPM and TH-BPSK UWB systems , 2004, IEEE Transactions on Communications.

[66]  Gianluigi Ferrari,et al.  Minimum number of neighbors for fully connected uniform ad hoc wireless networks , 2004, 2004 IEEE International Conference on Communications (IEEE Cat. No.04CH37577).

[67]  Mohamed-Slim Alouini,et al.  Digital Communication over Fading Channels: Simon/Digital Communications 2e , 2004 .

[68]  Moe Z. Win,et al.  Invertible bounds for M-QAM in Rayleigh fading , 2005, IEEE Transactions on Wireless Communications.

[69]  Abbas Jamalipour,et al.  Wireless communications , 2005, GLOBECOM '05. IEEE Global Telecommunications Conference, 2005..

[70]  Eitan Altman,et al.  Coverage and connectivity of ad hoc networks presence of channel randomness , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[71]  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..

[72]  A. Giorgetti,et al.  The impact of OFDM interference on TH-PPM/BPAM transmission systems , 2005, IEEE Vehicular Technology Conference.

[73]  Martin Haenggi.  Outage and throughput bounds for stochastic wireless networks , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[74]  Simon Haykin,et al.  Cognitive radio: brain-empowered wireless communications , 2005, IEEE Journal on Selected Areas in Communications.

[75]  Moe Z. Win,et al.  Analysis of UWB transmitted-reference communication systems in dense multipath channels , 2005, IEEE Journal on Selected Areas in Communications.

[76]  Moe Z. Win,et al.  On the performance of wide-bandwidth signal acquisition in dense multipath channels , 2005, IEEE Transactions on Vehicular Technology.

[77]  Martin Haenggi,et al.  The impact of the topology on the throughput of interference-limited sensor networks with Rayleigh fading , 2005, 2005 Second Annual IEEE Communications Society Conference on Sensor and Ad Hoc Communications and Networks, 2005. IEEE SECON 2005..

[78]  Christian Bettstetter,et al.  Connectivity of Wireless Multihop Networks in a Shadow Fading Environment , 2005, Wirel. Networks.

[79]  Andrea Goldsmith,et al.  Wireless Communications , 2005, 2021 15th International Conference on Advanced Technologies, Systems and Services in Telecommunications (TELSIKS).

[80]  Moe Z. Win,et al.  The effect of narrowband interference on wideband wireless communication systems , 2005, IEEE Transactions on Communications.

[81]  M. Win,et al.  Diversity with practical channel estimation , 2005, IEEE Transactions on Wireless Communications.

[82]  Andrea Giorgetti,et al.  Ultra Wide Bandwidth communications towards Cognitive Radio , 2005 .

[83]  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.

[84]  Andrea Giorgetti,et al.  Coexistence Issues in Cognitive Radios Based on Ultra-Wide Bandwidth Systems , 2006, 2006 1st International Conference on Cognitive Radio Oriented Wireless Networks and Communications.

[85]  M. Haenggi,et al.  Shot Noise Models for Outage and Throughput Analyses in Wireless Ad Hoc Networks , 2006, MILCOM 2006 - 2006 IEEE Military Communications conference.

[86]  M. Win,et al.  Narrowband Communication in a Poisson Field of Ultrawideband Interferers , 2006, 2006 IEEE International Conference on Ultra-Wideband.

[87]  M.Z. Win,et al.  Design of Covert Military Networks: A Spectral Outage-based Approach , 2006, MILCOM 2006 - 2006 IEEE Military Communications conference.

[88]  L. Shepp,et al.  Error Performance of Ultrawideband Systems in a Poisson Field of Narrowband Interferers , 2006 .

[89]  Moe Z. Win,et al.  Energy Efficiency of Dense Wireless Sensor Networks: To Cooperate or Not to Cooperate , 2006, 2006 IEEE International Conference on Communications.

[90]  Vincent K. N. Lau,et al.  The Mobile Radio Propagation Channel , 2007 .

[91]  Alberto Zanella,et al.  A Connectivity Model for the Analysis of a Wireless Ad Hoc Network in a Circular Area , 2007, 2007 IEEE International Conference on Communications.

[92]  Moe Win,et al.  Spectral characterization of wireless networks , 2007, IEEE Wireless Communications.

[93]  Jingxian Wu,et al.  Approximating a Sum of Random Variables with a Lognormal , 2007, IEEE Transactions on Wireless Communications.

[94]  Moe Z. Win,et al.  Energy efficiency of dense wireless sensor networks: to cooperate or not to cooperate , 2007, IEEE Journal on Selected Areas in Communications.

[95]  A. Rabbachin,et al.  UWB Energy Detection in the Presence of Multiple Narrowband Interferers , 2007, 2007 IEEE International Conference on Ultra-Wideband.

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

[97]  M.Z. Win,et al.  Physical-layer security in stochastic wireless networks , 2008, 2008 11th IEEE Singapore International Conference on Communication Systems.

[98]  Moe Z. Win,et al.  Antenna subset diversity with non-ideal channel estimation , 2008, IEEE Transactions on Wireless Communications.

[99]  Alberto Zanella,et al.  Interference characterization in a finite poisson field of nodes with shadowing , 2008, 2008 IEEE 19th International Symposium on Personal, Indoor and Mobile Radio Communications.

[100]  M.Z. Win,et al.  A unified analysis of connectivity and throughput in packet radio networks , 2008, MILCOM 2008 - 2008 IEEE Military Communications Conference.

[101]  Scott R. Manalis,et al.  Presidential Early Career Award for Scientists and Engineers , 2008 .

[102]  A. Rabbachin,et al.  Effect of aggregate narrowband interference on the UWB autocorrelation receiver , 2008, 2008 IEEE International Conference on Ultra-Wideband.

[103]  Aarnout Brombacher,et al.  Probability... , 2009, Qual. Reliab. Eng. Int..

[104]  Moe Z. Win,et al.  A stochastic geometry approach to coexistence in heterogeneous wireless networks , 2009, IEEE Journal on Selected Areas in Communications.

[105]  Moe Z. Win,et al.  Communication in a Poisson Field of Interferers-Part II: Channel Capacity and Interference Spectrum , 2010, IEEE Transactions on Wireless Communications.

[106]  Moe Z. Win,et al.  Communication in a Poisson Field of Interferers--Part I: Interference Distribution and Error Probability , 2010, IEEE Transactions on Wireless Communications.

[107]  M. R. Leadbetter.  Poisson Processes , 2011, International Encyclopedia of Statistical Science.

[108]  Edward J. Wegman,et al.  Topics in Non-Gaussian Signal Processing , 2011 .