Post on 27-Mar-2015
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…