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MASSIMO FRANCESCHETTI University of California at San Diego

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

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MASSIMO FRANCESCHETTI University of California at San Diego

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

  2. Standing on the shoulder of giants

  3. 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) ?

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

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

  6. Classic Approach • Assume physical propagation model • Allow arbitrary cooperation among nodes Xie KumarIEEE Trans-IT (2004) Xue XieKumarIEEE Trans-IT (2005) Leveque, TelatarIEEE Trans-IT (2005) Ahmad Jovicic ViswanathIEEE Trans-IT (2006) Gowaikar Hochwald HassibiIEEE Trans-IT (2006) Xie KumarIEEE Trans-IT (2006) Aeron SaligramaIEEE Trans-IT (2007) FranceschettiIEEE Trans-IT (2007) Ozgur Leveque PreissmannIEEE Trans-IT (2007) Ozgur Leveque TseIEEE Trans-IT (2007)

  7. Information theoretic “truths” High attenuation regime Low attenuation regime without fading Low attenuation regime with fading No attenuation regime, fading only

  8. Good research should shrink the knowledge tree

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

  10. Approach

  11. Approach . . . . . . . . .

  12. Information flow decomposition A V D d

  13. First flow component . . . . . .

  14. Second flow component . . . . . . . . .

  15. O Second flow component M D

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

  17. Singular values of operator G

  18. O Degrees of freedom theorem

  19. O The finishing touches

  20. 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

  21. 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

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

  23. Different configurations

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

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