SHOT NOISE MODELS FOR THE DUAL PROBLEMS OF COOPERATIVE COVERAGE AND OUTAGE IN RANDOM NETWORKS

The performance analysis of ad hoc networks requires the characterization of the network’s self-interference. However, thus far, the exact distribution of the interference has been analytically tractable only for a path loss exponent of 4. Further, conventional power law decay models for signal propagation have a singularity at the origin that causes all the moments of the network self-interference to diverge, resulting in no useful insight into the statistics of the interference. In this paper, we employ a 2D shot noise process with a stochastic power law impulse response function together with a bounded path loss to model the interference in large wireless networks, where the nodes are distributed according to a Poisson point process. We further show that this interference problem and the problem of coverage in cooperative sensor networks are duals of each other — they can be solved using the same shot noise-based approach.

[1]  S. Rice.  Mathematical analysis of random noise , 1944 .

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

[3]  T. Apostol.  Mathematical Analysis , 1957 .

[4]  W. Root,et al.  An introduction to the theory of random signals and noise , 1958 .

[5]  H. Pollak,et al.  Amplitude distribution of shot noise , 1960 .

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

[7]  Malvin Carl Teich,et al.  Power-law shot noise , 1990, IEEE Trans. Inf. Theory.

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

[9]  J. Mendel.  Lessons in Estimation Theory for Signal Processing, Communications, and Control , 1995 .

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

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

[12]  Panganamala Ramana Kumar,et al.  RHEINISCH-WESTFÄLISCHE TECHNISCHE HOCHSCHULE AACHEN , 2001 .

[13]  Bartomiej Baszczyszyn,et al.  On a Coverage Process Ranging from the Boolean Model to the Poisson Voronoi Tessellation , 2000 .

[14]  Branimir R. Vojcic,et al.  Ad hoc, multihop CDMA networks with route diversity in a Rayleigh fading channel , 2001, 2001 MILCOM Proceedings Communications for Network-Centric Operations: Creating the Information Force (Cat. No.01CH37277).

[15]  F. Baccelli,et al.  On a coverage process ranging from the Boolean model to the Poisson–Voronoi tessellation with applications to wireless communications , 2001, Advances in Applied Probability.

[16]  Srikanth V. Krishnamurthy,et al.  Distributed power control in ad-hoc wireless networks , 2001, 12th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications. PIMRC 2001. Proceedings (Cat. No.01TH8598).

[17]  Miodrag Potkonjak,et al.  Coverage problems in wireless ad-hoc sensor networks , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

[18]  Ian F. Akyildiz,et al.  Wireless sensor networks: a survey , 2002, Comput. Networks.

[19]  Martin Haenggi.  On routing in random Rayleigh fading networks , 2005, IEEE Transactions on Wireless Communications.

[20]  Zhiming Ma,et al.  Coverage Problem of Wireless Sensor Networks , 2005, CJCDGCGT.

[21]  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..

[22]  Wei Wang,et al.  Information coverage for wireless sensor networks , 2005, IEEE Communications Letters.

[23]  Jeffrey G. Andrews,et al.  Transmission capacity of wireless ad hoc networks with outage constraints , 2005, IEEE Transactions on Information Theory.

[24]  Daniele Puccinelli,et al.  Routing in ad hoc networks: a case for long hops , 2005, IEEE Communications Magazine.

[25]  K. J. Ray Liu,et al.  Clustered cooperative communications in wireless networks , 2005, GLOBECOM '05. IEEE Global Telecommunications Conference, 2005..

[26]  François Baccelli,et al.  Impact of interferences on connectivity in ad hoc networks , 2005, IEEE/ACM Transactions on Networking.

[27]  François Baccelli,et al.  An Aloha protocol for multihop mobile wireless networks , 2006, IEEE Transactions on Information Theory.

[28]  Umberto Spagnolini,et al.  Energy Aware Power Allocation strategies for Multihop-Cooperative transmission schemes , 2006, 2006 40th Annual Conference on Information Sciences and Systems.

[29]  Wei Wang,et al.  Sensor Density for Complete Information Coverage in Wireless Sensor Networks , 2006, EWSN.

[30]  U. Spagnolini,et al.  Energy aware power allocation strategies for multihop-cooperative transmission schemes , 2007, IEEE Journal on Selected Areas in Communications.