Statistical Description of Wireless Multipath Channel

  • Joachim SpeidelEmail author
Part of the Signals and Communication Technology book series (SCT)


In the following, we are going to describe the time variance of a multipath channel by statistical parameters. We assume a multipath channel with delay spread function \(g_{c}(t,\tau )\) given in ( 7.3) and neglect the receiver noise in the following. For the receive signal ( 7.12), then holds with ( 7.13) and \(u_{a}(t)=x(t)\).
$$\begin{aligned} q_{R}(t)=\sum _{\nu =1}^{N_{P}}x(t)\circledast \left[ \tilde{\alpha }_{\nu }(t)g_{I}\left( \tau -\tau _{\nu }(t)\right) \right] \circledast g_{R}(\tau ) \end{aligned}$$
As can be seen, even for a constant transmit signal \(x(t)=const.\)


  1. 1.
    A. Papoulis, S.U. Pillai, Probability, Random Variables, and Stochastic Processes, 4th edn. (McGraw-Hill, Boston, 2002)Google Scholar
  2. 2.
    A. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions (Dover Publications Inc, New York, 1974)zbMATHGoogle Scholar
  3. 3.
    M. Nakagami, The m-distribution - a general formula for intensity distribution of rapid fading, in Statistical Methods in Radio Wave Propagation, ed. by W.G. Hoffman (Pergamon, New York, 1960)Google Scholar
  4. 4.
    M. Alouini, J. Goldsmith, A unified approach for calculating the error rates of linearly modulated signals over generalized fading channels. IEEE Trans. Commun. 47, 1324–1334 (1999)CrossRefGoogle Scholar
  5. 5.
    K.M. Simon, M.-S. Alouini, Digital Communication Over Fading Channels: A Unified Approach to Performance (Wiley, New York, 2000)CrossRefGoogle Scholar
  6. 6.
    G.L. Stueber, Principles of Mobile Communication (Kluwer, Dordrecht, 2001)Google Scholar
  7. 7.
    R.H. Clarke, A statistical theory of mobile radio reception. Bell Syst. Tech. J. 47, 957–1000 (1968)CrossRefGoogle Scholar
  8. 8.
    W. Jakes, Microwave Mobile Communications (Wiley, New York, 1975)Google Scholar
  9. 9.
    P. Dent, G.E. Bottomley, T. Croft, Jakes fading model revisited. Electron. Lett. 29, 1162–1163 (1993)CrossRefGoogle Scholar
  10. 10.
    A.F. Molisch, Wireless Communications (Wiley and IEEE press, New York, 2009)Google Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of TelecommunicationsUniversity of StuttgartStuttgartGermany

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