Information-theoretic and physical limits on the capacity of wireless networks
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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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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



The problem
The problem wireless networks

  • 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) ?


Scaling approach
Scaling approach wireless networks

  • All pairs must achieve the same rate

  • Consider the limit

IEEE Trans-IT (2000)


Information theoretic limits
Information-theoretic limits wireless networks

  • Provide the ultimate limits of communication

  • Independent of any scheme used for communication


Classic approach
Classic Approach wireless networks

  • 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)


Information theoretic truths
Information theoretic “truths” wireless networks

High attenuation regime

Low attenuation regime without fading

Low attenuation regime with fading

No attenuation regime, fading only


Good research should shrink the knowledge tree
Good research should wireless networksshrink the knowledge tree


There is only one scaling law
There is only one scaling law wireless networks

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.


Approach
Approach wireless networks


Approach1
Approach wireless networks

. . .

. . .

. . .


Information flow decomposition
Information flow decomposition wireless networks

A

V

D

d


First flow component
First flow component wireless networks

. . .

. . .


Second flow component
Second flow component wireless networks

. . .

. . .

. . .


Second flow component1

O wireless networks

Second flow component

M

D


Hilbert schmidt decomposition of operator
Hilbert-Schmidt decomposition of operator wireless networks

G

Singular values have a phase transition at the critical value


Singular values of operator
Singular values of operator wireless networks

G


Degrees of freedom theorem

O wireless networks

Degrees of freedom theorem


The finishing touches

O wireless networks

The finishing touches


Understanding the space resource
Understanding the space resource wireless networks

Space is a capacity bearing object

Geometry plays a fundamental role in determining the number of degrees of freedom and hence the information capacity


Geometrical configurations
Geometrical configurations wireless networks

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


A different configuration
A different configuration wireless networks

Distribute nodes in a 3D volume of size

Nodes are placed uniformly on a 2Dsurface inside the volume


Different configurations
Different configurations wireless networks


To be continued… wireless networks

The endless enigma (Salvador Dali)

A hope beyond a shadow of a dream (John Keats)


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