Propagation Modeling

  • Gordon L. Stüber


The design of spectrally efficient wireless communication systems requires a thorough understanding of the radio propagation channel. This chapter emphasizes land mobile radio channels, including those found in cellular land mobile radio systems and mobile ad hoc networks including vehicle-to-vehicle channels. The chapter first treats the characteristics of the complex faded envelope in frequency non-selective (flat) fixed-to-mobile channels that are typically found in cellular land mobile radio systems, including the received envelope and phase distribution, envelope correlation and spectra, level crossing rates and fade durations, and space-time correlation. Afterwards, mobile-to-mobile channels are considered. This is followed by a statistical characterization of frequency-selective fading channels, and treatment of polarized fading channels. The chapter continues with a discussion of simulation techniques for fading channels, including filtered white noise, sum of sinusoid techniques such as the classical Jakes’ technique, and techniques for generating multiple uncorrelated faded envelopes. Advanced simulation methodologies are discussed including wide-band simulation models such as the COST207 and COST259 models, symbol-spaced simulation models, and mobile-to-mobile simulation models. The chapter goes on to discuss modeling and simulation techniques for long term fading or shadowing. Finally, the chapter wraps up with theoretical and empirical path loss models, including the famous Okumura–Hata model, Lee’s model, various COST models, and 3GPP mm-wave path loss models.


  1. 1.
    3GPP, Study on 3D channel model for LTE (2015)Google Scholar
  2. 3.
    A. Abdi, J.A. Barger, M. Kaveh, A parametric model for the distribution of the angle of arrival and the associated correlation function and power spectrum at the mobile station. IEEE Trans. Veh. Technol. 51, 425–434 (2002)CrossRefGoogle Scholar
  3. 9.
    G. Acosta, K. Tokuda, M.A. Ingram, Measured joint Doppler-delay power profiles for vehicle-to-vehicle communications at 2.4 GHz, in IEEE Global Communications Conference, Dallas, TX, November 2004, pp. 3813–3817Google Scholar
  4. 13.
    A.S. Akki, Statistical properties of mobile-to-mobile land communication channels. IEEE Trans. Veh. Technol. 43, 826–831 (1994)CrossRefGoogle Scholar
  5. 14.
    A.S. Akki, F. Haber, A statistical model of mobile-to-mobile land communication channel. IEEE Trans. Veh. Technol. 35, 2–7 (1986)CrossRefGoogle Scholar
  6. 18.
    J.B. Andersen, T. Rappaport, S. Yoshida, Propagation measurements and models for wireless communications channels. IEEE Commun. Mag. 33, 42–49 (1995)CrossRefGoogle Scholar
  7. 19.
    M.R. Andrews, P.P. Mitra, R. deCarvalho, Tripling the capacity of wireless communications using electromagnetic polarization. Nature 409, 316–318 (2001)Google Scholar
  8. 22.
    T. Aulin, A modified model for the fading signal at a mobile radio channel. IEEE Trans. Veh. Technol. 28, 182–203 (1979)CrossRefGoogle Scholar
  9. 35.
    P. Bello, Characterization of random time-variant linear channels. IEEE Trans. Commun. 11, 360–393 (1963)CrossRefGoogle Scholar
  10. 40.
    J.-E. Berg, R. Bownds, F. Lotse, Path loss and fading models for microcells at 900 MHz, in IEEE Vehicular Technology Conference, Denver, CO, May 1992, pp. 666–671Google Scholar
  11. 50.
    G.J. Byers, F. Takawira, Spatially and temporally correlated MIMO channels: modeling and capacity analysis. IEEE Trans. Veh. Technol. 53, 634–643 (2004)CrossRefGoogle Scholar
  12. 57.
    U. Charash, Reception through Nakagami fading multipath channels with random delays. IEEE Trans. Commun. 27, 657–670 (1979)CrossRefzbMATHGoogle Scholar
  13. 59.
    D.K. Cheng, Field and Wave Electromagnetics, 2nd edn. (Addison-Wesley, Reading, 1989)Google Scholar
  14. 61.
    S. Chia, R. Steele, E. Green, A. Baran, Propagation and bit-error ratio measurements for a microcellular system. J. Inst. Electron. Radio Eng. (UK) 57, 255–266 (1987)CrossRefGoogle Scholar
  15. 74.
    R. Clarke, A statistical theory of mobile radio reception. Bell System Tech. J. 47, 957–1000 (1968)CrossRefGoogle Scholar
  16. 78.
    COST 207 Digital Land Mobile Radio Communications (Commission of the European Communities, Brussels, 1989)Google Scholar
  17. 79.
    M. Failli, COST 207 Management Committee, TD(86)51-REV 3 (WG1), Proposal on channel transfer functions to be used in GSM tests late 1986 (1986)Google Scholar
  18. 80.
    COST 231 TD(91)109, 1800 MHz mobile net planning based on 900 MHz measurements (1991)Google Scholar
  19. 81.
    COST 231 TD(973)119-REV 2 (WG2), Urban transmission loss models for mobile radio in the 900- and 1,800-MHz bands (1991)Google Scholar
  20. 89.
    W.B. Davenport, W.L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1987)CrossRefzbMATHGoogle Scholar
  21. 90.
    G.W. Davidson, D.D. Falconer, A.U.H. Sheikh, An investigation of block adaptive decision feedback equalization for frequency selective fading channels, in IEEE International Conference on Communications, Philadelphia, PA, June 1988, pp. 360–365Google Scholar
  22. 93.
    P. Dent, G.E. Bottomley, T. Croft, Jakes fading model revisited. Electron. Lett. 7, 1162–1163 (1993)CrossRefGoogle Scholar
  23. 107.
    E. Eleftheriou, D.D. Falconer, Adaptive equalization techniques for HF channels. IEEE J. Sel. Areas Commun. 5, 238–247 (1987)CrossRefGoogle Scholar
  24. 110.
    V. Erceg, P. Soma, D. Baum, S. Catreux, Multiple-input multiple-output fixed wireless radio channel measurements and modeling using dual-polarized antennas at 2.5 GHz. IEEE Trans. Wirel. Commun. 3, 2288–2298 (2004)Google Scholar
  25. 111.
    V. Erceg, H. Sampath, S. Catreux-Erceg, Dual-polarization versus single-polarization MIMO channel measurement results and modeling. IEEE Trans Wireless Commun. 5, 28–33 (2006)CrossRefGoogle Scholar
  26. 113.
    ETSI TR 125 943, Univeral Mobile Telecommunications System (UMTS), Deployment aspects 3GPP TR 25.943 version 7.0.0 Release 7 (2007)Google Scholar
  27. 127.
    R.C. French, Error rate predictions and measurements in the mobile radio data channel. IEEE Trans. Veh. Technol. 27, 214–220 (1978)CrossRefGoogle Scholar
  28. 128.
    R.C. French, The effect of fading and shadowing on channel reuse in mobile radio. IEEE Trans. Veh. Technol. 28, 171–181 (1979)CrossRefGoogle Scholar
  29. 140.
    A.A. Giordano, F.M. Hsu (eds.), Least Square Estimation with Applications to Digital Signal Processing (Wiley, New York, 1985)Google Scholar
  30. 142.
    A.J. Goldsmith, L.J. Greenstein, A Measurement-based model for predicting coverage areas of urban microcells. IEEE J. Sel. Areas Commun. 11, 1013–1023 (1993)CrossRefGoogle Scholar
  31. 143.
    A.J. Goldsmith, L.J. Greenstein, G.J. Foschini, Error statistics of real time power measurements in cellular channels with multipath and shadowing, in IEEE Vehicular Technology Conference, Secaucus, NJ (1993), pp. 108–110Google Scholar
  32. 147.
    I. Gradshteyn, I. Ryzhik, Tables of Integrals, Series, and Products (Academic Press, San Diego, 1980)zbMATHGoogle Scholar
  33. 149.
    O. Grimlund, B. Gudmundson, Handoff strategies in microcellular systems, in IEEE Vehicular Technology Conference, Saint Louis, MO, May 1991, pp. 505–510Google Scholar
  34. 150.
    M. Gudmundson, Analysis of handover algorithms, in IEEE Vehicular Technology Conference, Saint Louis, MO, May 1991, pp. 537–541Google Scholar
  35. 151.
    M. Gudmundson, Analysis of handover algorithms in cellular radio systems. Report No. TRITA-TTT-9107, Royal Institute of Technology, Stockholm, Sweden, April 1991Google Scholar
  36. 152.
    M. Gudmundson, Correlation model for shadow fading in mobile radio systems. Electron. Lett. 27, 2145–2146 (1991)CrossRefGoogle Scholar
  37. 158.
    K. Haneda, J. Zhang, L. Tian, G. Liu, Y. Zheng, H. Asplund, J. Li, Y. Wang, D. Steer, C. Li, T. Balercia, S. Lee, Y. Kim, A. Ghosh, T. Thomas, T. Nakamura, Y. Kakishima, T. Imai, H. Papadopoulas, T.S. Rappaport, G.R. MacCartney Jr., M.K. Samimi, S. Sun, O. Koymen, S. Hur, J. Park, C. Zhang, E. Mellios, A.F. Molisch, S.S. Ghassemzadeh, A. Ghosh, 5G 3GPP-like channel models for outdoor urban microcellular and macrocellular environments, in IEEE Vehicular Technology Conference, Nanjing, China, May 2016Google Scholar
  38. 160.
    P. Harley, Short distance attenuation measurements at 900 MHz and 1. 8 GHz using low antenna heights for microcells. IEEE J. Sel. Areas Commun. 7, 5–11 (1989)Google Scholar
  39. 161.
    M. Hata, T. Nagatsu, Mobile location using signal strength measurements in cellular systems. IEEE Trans. Veh. Technol. 29, 245–251 (1980)CrossRefGoogle Scholar
  40. 164.
    M.-J. Ho, G.L. Stüber, Co-channel interference of microcellular systems on shadowed Nakagami fading channels, in IEEE Vehicular Technology Conference, Secaucus, NJ, May 1993, pp. 568–571Google Scholar
  41. 165.
    P. Hoeher, A statistical discrete-time model for the WSSUS multipath channel. IEEE Trans. Veh. Technol. 41, 461–468 (1992)CrossRefGoogle Scholar
  42. 170.
    K. Imamura, A. Murase, Mobile communication control using multi-transmitter simul/sequential casting (MSSC), in IEEE Vehicular Technology Conference, Dallas, TX, May 1986, pp. 334–341Google Scholar
  43. 171.
    W.C. Jakes, Microwave Mobile Communication (IEEE Press, New York, 1993)Google Scholar
  44. 173.
    M. Kaji, A. Akeyama, UHF-band propagation characteristics for land mobile radio, in International Symposium on Antennas and Propagation, University of British Columbia, Canada, June 1985, pp. 835–838Google Scholar
  45. 181.
    C. Komninakis, A fast and accurate Rayleigh fading simulator, in IEEE Communications Conference, San Francisco, CA, December 2003, pp. 3306–3310Google Scholar
  46. 182.
    I.Z. Kovacs, P.C.F. Eggers, K. Olesen, L.G. Petersen, Investigations of outdoor-to-indoor mobile-to-mobile radio communication channels, in IEEE Vehicular Technology Conference, Vancouver, Canada (2002), pp. 430–434Google Scholar
  47. 184.
    S. Kozono, T. Suruhara, M. Sakamoto, Base station polarization diversity reception for mobile radio. IEEE Trans. Veh. Technol. 33, 301–306 (1984)CrossRefGoogle Scholar
  48. 185.
    A. Kuchar, J.P. Rossi, E. Bonek, Directional macro-cell channel characterization from urban measurements. IEEE Trans. Antennas Propag. 48, 137–146 (2000)CrossRefGoogle Scholar
  49. 188.
    J. Kunisch, J. Pamp, Wideband Car-to-Car Radio Channel Measurements and Model at 5.9 GHz, in IEEE Vehicular Technology Conference, Calgary, Canada (2008)Google Scholar
  50. 189.
    S.-C. Kwon, G.L. Stüber, Polarized channel model for body area networks using reflection coefficientsGoogle Scholar
  51. 191.
    M. Landmann, K. Sivasondhivat, J.-I. Takada, I. Ida, R. Thoma, Polarisation behaviour of discrete multipath and diffuse scattering in urban environments at 4.5 GHz. EURASIP J. Wirel. Commun. Netw., 2007, 60 (2007), Article ID 57980Google Scholar
  52. 192.
    B. Larsson, B. Gudmundson, K. Raith, Receiver performance for the North American digital cellular system, in IEEE Vehicular Technology Conference, Saint Louis, MO, May 1991, pp. 1–6Google Scholar
  53. 194.
    W.C.Y. Lee, Mobile Communications Engineering (McGraw Hill, New York, 1982)Google Scholar
  54. 196.
    W.C.Y. Lee, Mobile Communications Design Fundamentals (SAMS, Indianapolis, 1986)Google Scholar
  55. 198.
    W. Lee, Y. Yeh, Polarization diversity system for mobile radio. IEEE Trans. Commun. 20, 912–923 (1972)CrossRefGoogle Scholar
  56. 199.
    W.C.Y. Lee, Y.S. Yeh, On the estimation of the second-order statistics of log-normal fading in mobile radio environment. IEEE Trans. Commun. 22, 809–873 (1974)Google Scholar
  57. 202.
    Y.X. Li, X. Huang, The simulation of independent Rayleigh faders. IEEE Trans. Commun. 50, 1503–1514 (2002)CrossRefGoogle Scholar
  58. 206.
    F. Ling, J.G. Proakis, Adaptive lattice decision-feedback equalizers – their performance and application to time-variant multipath channels. IEEE Trans. Commun. 33, 348–356 (1985)CrossRefGoogle Scholar
  59. 208.
    J.-P.M. Linnartz, Exact analysis of the outage probability in multiple-user mobile radio. IEEE Trans. Commun. 40, 20–23 (1992)CrossRefGoogle Scholar
  60. 209.
    J.M.G. Linnartz, R.F. Fiesta, Evaluation of radio links and networks. California PATH Program (1996) [Online]. Available:
  61. 210.
    F. Lotse, A. Wejke, Propagation measurements for microcells in central Stockholm, in IEEE Vehicular Technology Conference, Orlando, FL (1990), pp. 539–541Google Scholar
  62. 214.
    M.B. Madayam, P.-C. Chen, J.M. Hotzman, Minimum duration outage for cellular systems: a level crossing analysis, in IEEE Vehicular Technology Conference, Atlanta, GA, June 1996, pp. 879–883Google Scholar
  63. 216.
    M. Marsan, G. Hess, Shadow variability in an urban land mobile radio environment. Electron. Lett. 26, 646–648 (1990)CrossRefGoogle Scholar
  64. 221.
    I. Mathworks, Filter design toolbox for use with MATLAB, User’s Guide (2005)Google Scholar
  65. 222.
    J. Maurer, T. Fügen, W. Wiesbeck, Narrow-band measurement and analysis of the inter-vehicle transmission channel at 5.2 GHz, in IEEE Vehicular Technology Conference, Birmingham, AL, pp. 1274–1278, 2002.Google Scholar
  66. 225.
    L.B. Milstein, D.L. Schilling, R.L. Pickholtz, V. Erceg, M. Kullback, E.G. Kanterakis, D. Fishman, W.H. Biederman, D.C. Salerno, On the feasibility of a CDMA overlay for personal communications networks. IEEE J. Sel. Areas Commun. 10, 655–668 (1992)CrossRefGoogle Scholar
  67. 226.
    S. Mockford, A.M.D. Turkmani, Penetration loss into buildings at 900 MHz, in IEE Colloquium on Propagation Factors and Interference Modeling for Mobile Radio Systems, London, UK, pp. 1/1–1/4 (1988)Google Scholar
  68. 227.
    S. Mockford, A.M.D. Turkmani, J.D. Parsons, Local mean signal variability in rural areas at 900 MHz, in IEEE Vehicular Technology Conference, Orlando, FL, May 1990, pp. 610–615Google Scholar
  69. 228.
    P.E. Mogensen, P. Eggers, C. Jensen, J.B. Andersen, Urban area radio propagation measurements at 955 and 1845 MHz for small and micro cells, in IEEE Global Communications Conference, Phoenix, AZ, December 1991, pp. 1297–1302Google Scholar
  70. 232.
    R. Muammar, S.C. Gupta, Cochannel interference in high-capacity mobile radio systems. IEEE Trans. Commun. 30, 1973–1978 (1982)CrossRefGoogle Scholar
  71. 233.
    A. Murase, I.C. Symington, E. Green, Handover criterion for macro and microcellular systems, in IEEE Vehicular Technology Conference, Saint Louis, MO, May 1991, pp. 524–530Google Scholar
  72. 238.
    M. Nakagami, The m distribution; a general formula of intensity distribution of rapid fading, in Statistical Methods in Radio Wave Propagation, ed. by W.G. Hoffman (Pergamon Press, New York, 1960), pp. 3–36CrossRefGoogle Scholar
  73. 245.
    C. Oestges, V. Erceg, A.J. Paulraj, Propagation modeling of MIMO multipolarized fixed wireless channels. IEEE Trans. Veh. Technol. 53, 644–654 (2004)CrossRefGoogle Scholar
  74. 250.
    Y. Okumura, E. Ohmuri, T. Kawano, K. Fukuda, Field strength and its variability in VHF and UHF land mobile radio service. Rev. ECL 16, 825–873 (1968)Google Scholar
  75. 255.
    J.D. Parsons, The Mobile Radio Propagation Channel (Wiley, New York, 1992)Google Scholar
  76. 257.
    J.D. Parsons, A.M.D. Turkmani, Characterisation of mobile radio signals: model description, in IEE Proceedings I, Communications, Speech and Vision, vol. 138 (1991), pp. 549–556Google Scholar
  77. 259.
    C.S. Patel, G.L. Stüber, T.G. Pratt, Comparative analysis of statistical models for the simulation of Rayleigh faded cellular channels. IEEE Trans. Commun. 53, 1017–1026 (2005)CrossRefGoogle Scholar
  78. 260.
    M. Pätzold, Mobile Fading Channels (Wiley, West Sussex, 2002)CrossRefGoogle Scholar
  79. 261.
    M. Pätzold, U. Killat, F. Laue, Y. Li, On the statistical properties of deterministic simulation models for mobile fading channels. IEEE Trans. Veh. Technol. 47, 254–269 (1998)CrossRefGoogle Scholar
  80. 264.
    M.F. Pop, N.C. Beaulieu, Limitations of sum-of-sinusoids fading channel simulators. IEEE Trans. Commun. 49, 699–708 (2001)CrossRefGoogle Scholar
  81. 267.
    R. Prasad, A. Kegel, Spectrum efficiency of microcellular systems. Electron. Lett. 27, 423–425 (1991)CrossRefGoogle Scholar
  82. 272.
    J.G. Proakis, M. Salehi, Digital Communications, 5th edn. (McGraw-Hill, New York, 2007)Google Scholar
  83. 276.
    R.I.-R. M.1225, Guidelines for evaluation of radio transmission techniques for IMT-2000 (1997)Google Scholar
  84. 280.
    T. Rappaport, L. Milstein, Effects of path loss and fringe user distribution on CDMA cellular frequency reuse efficiency, in IEEE Global Communications Conference, San Diego, CA, December 1990, pp. 500–506Google Scholar
  85. 283.
    S. Rice, Statistical properties of a sine wave plus noise. Bell Syst. Tech. J. 27, 109–157 (1948)MathSciNetCrossRefGoogle Scholar
  86. 286.
    A. Rustako, N. Amitay, G. Owens, R. Roman, Radio propagation at microwave frequencies for line-of-sight microcellular mobile and personal communications. IEEE Trans. Veh. Technol. 40, 203–210 (1991)CrossRefGoogle Scholar
  87. 299.
    M. Shafi, M. Zhang, A. Moustakas, P. Smith, A. Molisch, F. Tufvesson, S. Simon, Polarized MIMO channels in 3-D: models, measurements, and mutual information. IEEE J. Sel. Areas Commun. 24, 514–527 (2006)CrossRefGoogle Scholar
  88. 301.
    W.H. Sheen, G.L. Stüber, MLSE equalization and decoding for multipath-fading channels. IEEE Trans. Commun. 39, 1455–1464 (1991)CrossRefzbMATHGoogle Scholar
  89. 306.
    P. Soma, D.S. Baum, V. Erceg, R. Krishnamoorthy, A.J. Paulraj, Analysis and modeling of MIMO radio channel based on outdoor measurements conducted at 2.5 GHz for fixed BWA applications, in IEEE International Conference on Communications, April 2002, pp. 272–276Google Scholar
  90. 307.
    K. Steiglitz, Computer-aided design of recursive digital filters. IEEE Trans. Audio Electroacoust. 18, 123–129 (1970)CrossRefGoogle Scholar
  91. 320.
    R.J. Tront, J.K. Cavers, M.R. Ito, Performance of Kalman decision-feedback equalization in HF radio modems, in IEEE International Conference on Communications, Toronto, Canada, June 1986, pp. 1617–1621Google Scholar
  92. 323.
    A.M.D. Turkmani, Probability of error for M-branch selection diversity. IEE Proc. I. 139, 71–78 (1992)Google Scholar
  93. 324.
    A.M.D. Turkmani, J.D. Parsons, F. Ju, D.G. Lewis, Microcellular radio measurements at 900,1500, and 1800 MHz, in 5th International Conference on Mobile Radio and Personal Communications, Coventry, UK, December 1989, pp. 65–68Google Scholar
  94. 329.
    F. Vatalaro, A. Forcella, Doppler spectrum in mobile-to-mobile communications in the presence of three-dimensional multipath scattering. IEEE Trans. Veh. Technol. 46, 213–219 (1997)CrossRefGoogle Scholar
  95. 330.
    R.G. Vaughan, Polarization diversity in mobile communications. IEEE Trans. Veh. Technol. 39, 177–185 (1990)CrossRefGoogle Scholar
  96. 338.
    J.-F. Wagen, Signal strength measurements at 881 MHz for urban microcells in downtown Tampa, in IEEE Global Communications Conference, Phoenix, AZ, December 1991, pp. 1313–1317Google Scholar
  97. 339.
    E.H. Walker, Penetration of radio signals into buildings in cellular radio environments. Bell Syst. Tech. J. 62, 2719–2734 (1983)CrossRefGoogle Scholar
  98. 345.
    R. Wang, D. Cox, Channel modeling for ad hoc mobile wireless networks, in IEEE Vehicular Technology Conference, Birmingham, AL (2002), pp. 21–25Google Scholar
  99. 351.
    A. Williamson, B. Egan, J. Chester, Mobile radio propagation in Auckland at 851 MHz. Electron. Lett. 20, 517–518 (1984)CrossRefGoogle Scholar
  100. 358.
    H. Xia, H. Bertoni, L. Maciel, A. Landsay-Stewart, Radio propagation measurements and modeling for line-of-sight microcellular systems, in IEEE Vehicular Technology Conference, Denver, CO, May 1992, pp. 349–354Google Scholar
  101. 359.
    C. Xiao, Y.R. Zheng, A statistical simulation model for mobile radio fading channels, in Wireless Communications and Networking Conference, New Orleans, LA, March 2003, pp. 144–149Google Scholar
  102. 360.
    C. Xiao, Y.R. Zheng, N. Beaulieu, Statistical simulation models for Rayleigh and Rician fading, in IEEE International Conference on Communications, Anchorage, AK, May 2003, pp. 3524–3529Google Scholar
  103. 361.
    Y. Yamada, Y. Ebine, N. Nakajima, Base station/vehicular antenna design techniques employed in high capacity land mobile communications system. Rev. Electr. Commun. Lab. NTT 35, 115–121 (1987)Google Scholar
  104. 369.
    D.J. Young, N.C. Beaulieu, The generation of correlated Rayleigh random variates by inverse discrete Fourier transform. IEEE Trans. Commun. 48, 1114–1127 (2000)CrossRefGoogle Scholar
  105. 371.
    A.G. Zajić, G.L. Stüber, A new simulation model for mobile-to-mobile Rayleigh fading channels, in Wireless Communications and Networking Conference, Las Vegas, NV, April 2006, pp. 1266–1270Google Scholar
  106. 372.
    A.G. Zajić, G.L. Stüber, Efficient simulation of Rayleigh fading with enhanced de-correlation properties. IEEE Trans. Wirel. Commun. 5, 1866–1875 (2006)CrossRefGoogle Scholar
  107. 376.
    Y.R. Zheng, C. Xiao, Improved models for the generation of multiple uncorrelated Rayleigh fading waveforms. IEEE Commun. Lett. 6, 256–258 (2002)CrossRefGoogle Scholar
  108. 377.
    Y.R. Zheng, C. Xiao, Simulation models with correct statistical properties for Rayleigh fading channels. IEEE Trans. Commun. 51, 920–928 (2003)CrossRefGoogle Scholar

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© Springer International Publishing AG 2017

Authors and Affiliations

  • Gordon L. Stüber
    • 1
  1. 1.Georgia Institute of TechnologyAtlantaUSA

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