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The capacity of wireless networks: information-theoretic and physical limits

Published: 01 August 2009 Publication History

Abstract

It is shown that the capacity scaling of wireless networks is subject to a fundamental limitation which is independent of power attenuation and fading models. It is a degrees of freedom limitation which is due to the laws of physics. By distributing uniformly an order of n users wishing to establish pairwise independent communications at fixed wavelength inside a two-dimensional domain of size of the order of n, there are an order of n communication requests originating from the central half of the domain to its outer half. Physics dictates that the number of independent information channels across these two regions is only of the order of √n, so the per-user information capacity must follow an inverse square-root of n law. This result shows that information-theoretic limits of wireless communication problems can be rigorously obtained without relying on stochastic fading channel models, but studying their physical geometric structure.

References

[1]
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables, 9th ed. New York: Dover, 1972.
[2]
S. Aeron and V. Saligrama, "Wireless ad hoc networks: Strategies and scaling laws for the fixed SNR regime," IEEE Trans. Inf. Theory, vol. IT-53, no. 6, pp. 2044-2059, Jun. 2007.
[3]
S. Ahmad, A. Jovičic, and P. Viswanath, "Outer bounds to the capacity region of wireless networks," IEEE Trans. Inf. Theory, vol. IT-52, no. 6, pp. 2770-2776, Jun. 2006.
[4]
O. M. Bucci and G. Franceschetti, "On the spatial bandwidth of scattered fields," IEEE Trans. Antennas Propag., vol. AP-35, no. 12, pp. 1445-1455, Dec. 1987.
[5]
O. M. Bucci and G. Franceschetti, "On the degrees of freedom of scattered fields," IEEE Trans. Antennas Propag., vol. AP-37, no. 7, pp. 918-926, Jul. 1989.
[6]
T. Cover and J. Thomas, Elements of Information Theory. New York: Wiley, 2006.
[7]
D. W. Browne, M. Manteghi, M. P. Fitz, and Y. Rabmat-Samii, "Experiments with compact antenna arrays for MIMO radio communications," IEEE Trans. Antennas Propag., vol. AP-54, no. 11, pp. 3239-3250, Nov. 2006.
[8]
G. J. Foschini, "Layered space-time architecture for wireless communications in a fading environment when using multi-element antennas.," Bell Labs Tech. J., vol. 1, no. 2, pp. 41-59, 1996.
[9]
M. Franceschetti, "A note on Lévêque and Telatar's upper bound on the capacity of wireless ad-hoc networks," IEEE Trans. Inf. Theory, vol. IT-53, no. 9, pp. 3207-3211, Sep. 2007.
[10]
M. Franceschetti, O. Dousse, D. N. C. Tse, and P. Thiran, "Closing the gap in the capacity of wireless networks via percolation theory," IEEE Trans. Inf. Theory, vol. IT-53, no. 3, pp. 1009-1018, Mar. 2007.
[11]
M. Franceschetti, M. D. Migliore, and P. Minero, "The degrees of freedom of wireless networks: Information theoretic and physical limits," in Proc. Allerton Conf. Commun. Computing Contr., Monticello, IL, Sep. 2008.
[12]
R. Gowaikar, B. Hochwald, and B. Hassibi, "Communication over a wireless network with random connections," IEEE Trans. Inf. Theory, vol. IT-52, no. 7, pp. 2857-2871, Jul. 2006.
[13]
I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, A. Jeffrey, Ed. New York: Academic, 1994.
[14]
P. Gupta and P. R. Kumar, "The capacity of wireless networks," IEEE Trans. Inf. Theory, vol. IT-42, no. 2, pp. 388-404, Mar. 2000.
[15]
R. F. Harrington, Time-Harmonic Electromagnetic Fields. New York: McGraw-Hill, 1961.
[16]
J. D. Jackson, Classical Electrodynamics, 2nd ed. New York: Wiley, 1962.
[17]
A. Jovičic, P. Viswanath, and S. R. Kulkarni, "Upper bounds to transport capacity of wireless networks," IEEE Trans. Inf. Theory, vol. IT-50, no. 11, pp. 2555-2565, Nov. 2004.
[18]
R. A. Kennedy, P. Sadeghi, T. D. Abhayapala, and H. M. Jones, "Intrinsic limits of dimensionality and richness in random multipath fields," IEEE Trans. Signal Process., vol. 55, no. 6, pp. 2542-2556, Jun. 2007.
[19]
S. R. Kulkarni and P. Viswanath, "A deterministic approach to throughput scaling in wireless networks," IEEE Trans. Inf. Theory, vol. IT-50, no. 11, pp. 1041-1049, Jun. 2004.
[20]
O. Lévêque and E. Telatar, "Information theoretic upper bounds on the capacity oflarge, extended ad-hoc wireless networks," IEEE Trans. Inf. Theory, vol. IT-51, no. 3, pp. 858-865, Mar. 2005.
[21]
K. Liu, V. Raghavan, and A. M. Sayeed, "Capacity scaling and spectral efficiency in wideband correlated MIMO channels," IEEE Trans. Inf. Theory, vol. IT-49, no. 10, pp. 2504-2526, Oct. 2003.
[22]
M. D. Migliore, "On the role of the number of degrees of freedom of the field in MIMO channels," IEEE Trans. Antennas Propag., vol. AP-54, no. 2, pp. 620-628, Feb. 2006.
[23]
D. A. B. Miller, "Communicating with waves between volumes: Evaluating orthogonal spatial channels and limits on coupling strengths," Appl. Opt., vol. 39, no. 11, pp. 1681-1699, Apr. 2000.
[24]
U. Niesen, P. Gupta, and D. Shah, "On capacity scaling in arbitrary wireless networks," in Proc. Inf. Theory and Appl. Workshop (ITA), San Diego, Univ. Calif., Feb. 2007, pp. 5-.
[25]
U. Niesen, P. Gupta, and D. Shah, "Capacity region of large wireless networks," in Proc. Allerton Conf. Commun. Computing and Contr., Monticello, IL, Sep. 2008.
[26]
A. Özgür, R. Johari, D. N. C. Tse, and O. Lévêque, "Information theoretic operating regimes of large wireless networks," in Proc. Int. Symp. Inf. Theory (IEEE-ISIT), Toronto, Canada, 2008.
[27]
A. Özgür, O. Lévêque, and E. Preissmann, "Scaling laws for one and two-dimensional random wireless networks in the low attenuation regime," IEEE Trans. Inf. Theory, vol. IT-53, no. 10, pp. 3573-3585, Oct. 2007.
[28]
A. Özgür, O. Lévêque, and D. N. C. Tse, "Hierarchical cooperation achieves optimal capacity scaling in ad hoc networks," IEEE Trans. Inf. Theory, vol. IT-53, no. 10, pp. 3549-3572, Oct. 2007.
[29]
F. W. J. Olver, "The asymptotic expansion of Bessel functions of large order," Philos. Trans. Roy. Soc. London Ser. A, vol. 247, pp. 328-368, 1954.
[30]
F. W. J. Olver, "Tables for Bessel functions of moderate or large orders," National Physical Laboratory Mathematical Tables, vol. 6, 1962, Dep. Scient. Indust. Res., (Her Majesty's Stationery Office), London.
[31]
F. W. J. Olver, "Asymptotics and special functions" in Reprint., MA: Wellesley, 1997, AKP Classics. A. K. Peters.
[32]
R. Piestum and D. A. B. Miller, "Electromagnetic degrees of freedom of an optical system," J. Opt. Soc. Amer., A, vol. 17, no. 5, pp. 892-902, May 2000.
[33]
A. S. Y. Poon, R. W. Brodersen, and D. N. C. Tse, "Degrees of freedom in multiple antenna channels: A signal space approach," IEEE Trans. Inf. Theory, vol. IT-51, no. 2, pp. 523-536, Feb. 2005.
[34]
O. M. Bucci, C. Gennarelli, and C. Savarese, "Representation of electromagnetic fields over arbitrary surfaces by a finite and nonredundant number of samples," IEEE Trans. Antennas Propag., vol. 46, pp. 351-359, 1998.
[35]
A. M. Sayeed, V. Raghavan, and J. H. Kotecha, "Capacity of spacetime wireless channels: A physical perspective," in Proc. Inf. Theory Workshop (ITW'04), Oct. 2004, pp. 434-439.
[36]
E. Telatar, "Capacity of multi-antenna Gaussian channels," Eur. Trans. Telecommun., vol. 10, no. 6, pp. 585-596, Nov. 1999.
[37]
G. T. di Francia, "Resolving power and information," J. Opt. Soc. Amer., vol. 45, no. 7, pp. 497-501, Jul. 1955.
[38]
G. Toraldo Di Francia, "Directivity, super-gain and information," IRE Trans. Antennas Propag., vol. AP-4, no. 3, pp. 473-478, Jul. 1956.
[39]
L.-L. Xie and P. R. Kumar, "A network information theory for wireless communications: Scaling laws and optimal operation," IEEE Trans. Inf. Theory, vol. 50, no. 5, pp. 748-767, May 2004.
[40]
L.-L. Xie and P. R. Kumar, "On the path-loss attenuation regime for positive cost and linear scaling of transport capacity in wireless networks," IEEE Trans. Inf. Theory, vol. IT-52, no. 6, pp. 2313-2328, Jun. 2006.
[41]
F. Xue, L.-L. Xie, and P. R. Kumar, "The transport capacity of wireless networks over fading channels," IEEE Trans. Inf. Theory, vol. IT-51, no. 3, pp. 834-847, Mar. 2005.

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    Published In

    cover image IEEE Transactions on Information Theory
    IEEE Transactions on Information Theory  Volume 55, Issue 8
    August 2009
    480 pages

    Publisher

    IEEE Press

    Publication History

    Published: 01 August 2009
    Revised: 09 February 2009
    Received: 30 October 2007

    Author Tags

    1. Ad hoc networks
    2. ad hoc networks
    3. capacity
    4. network information theory
    5. scaling laws
    6. wireless networks

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