MASSIMO FRANCESCHETTIUniversity of California at San

Diego

Information-theoretic and physical limits on the capacity of wireless

networks

P. Minero (UCSD), M. D. Migliore (U. Cassino)

Standing on the shoulder of giants

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) ?

Scaling approach

• All pairs must achieve the same rate• Consider the limit

IEEE Trans-IT (2000)

Information-theoretic limits

• Provide the ultimate limits of communication

•Independent of any scheme used for communication

• 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

Information theoretic “truths”

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

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.

Approach

. . .

Approach

. . .. . .

Information flow decomposition

ADV

First flow component

. . .. . .

Second flow component

. . .. . . . . .

Second flow component

D

O

M

Singular values have a phase transition at the critical value

Hilbert-Schmidt decomposition of operator

G

Singular values of operatorG

Degrees of freedom theorem

O

The finishing touches

O

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

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

A different configuration

Distribute nodes in a 3D volume of size

Nodes are placed uniformly on a 2D surface inside the volume

Different configurations

The endless enigma (Salvador

Dali)

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

To be continued…