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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)
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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 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.
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Approach
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. . .
Approach
. . .. . .
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Information flow decomposition
ADV
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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 operatorG
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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…