Presentation on theme: "MASSIMO FRANCESCHETTI University of California at San Diego Information-theoretic and physical limits on the capacity of wireless networks TexPoint fonts."— Presentation transcript:
MASSIMO FRANCESCHETTI University of California at San Diego Information-theoretic and physical limits on the capacity of wireless networks TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A AAAA 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
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 Maxwells physics and by Shannons theory of information. It is independent of channel models and cannot be overcome by any cooperative communication scheme.
Information flow decomposition A D V
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 operator G
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
The endless enigma (Salvador Dali) A hope beyond a shadow of a dream (John Keats) To be continued…