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MASSIMO FRANCESCHETTI University of California at San Diego Information-theoretic and physical limits on the capacity of wireless networks TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A AAAA P. Minero (UCSD), M. D. Migliore (U. Cassino)

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Standing on the shoulder of giants

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The problem Computers equipped with power constrained radios Randomly located Random source-destination pairs Transmit over a common wireless channel Possible cooperation among the nodes Maximum per-node information rate (bit/sec) ?

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Scaling approach All pairs must achieve the same rate Consider the limit IEEE Trans-IT (2000)

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Information-theoretic limits Provide the ultimate limits of communication Independent of any scheme used for communication

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Assume physical propagation model Allow arbitrary cooperation among nodes Xie Kumar IEEE Trans-IT (2004) Xue Xie Kumar IEEE Trans-IT (2005) Leveque, Telatar IEEE Trans-IT (2005) Ahmad Jovicic Viswanath IEEE Trans-IT (2006) Gowaikar Hochwald Hassibi IEEE Trans-IT (2006) Xie Kumar IEEE Trans-IT (2006) Aeron Saligrama IEEE Trans-IT (2007) Franceschetti IEEE Trans-IT (2007) Ozgur Leveque Preissmann IEEE Trans-IT (2007) Ozgur Leveque Tse IEEE Trans-IT (2007) Classic Approach

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Information theoretic truths High attenuation regime Low attenuation regime without fading Low attenuation regime with fading No attenuation regime, fading only

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Good research should shrink the knowledge tree

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There is only one scaling law This is a degrees of freedom limitation dictated by Maxwells physics and by Shannons theory of information. It is independent of channel models and cannot be overcome by any cooperative communication scheme.

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Approach

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... Approach...

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Information flow decomposition A D V

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First flow component...

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Second flow component...

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Second flow component D O M

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Singular values have a phase transition at the critical value Hilbert-Schmidt decomposition of operator G

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Singular values of operator G

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Degrees of freedom theorem O

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The finishing touches O

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Understanding the space resource Space is a capacity bearing object Geometry plays a fundamental role in determining the number of degrees of freedom and hence the information capacity

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Geometrical configurations In 2D the network capacity scales with the perimeter boundary of the network In 3D the network capacity scales with the surface boundary of the network

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A different configuration Distribute nodes in a 3D volume of size Nodes are placed uniformly on a 2D surface inside the volume

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Different configurations

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The endless enigma (Salvador Dali) A hope beyond a shadow of a dream (John Keats) To be continued…

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