Signal-Design Concepts for Noncoherent Channels

  • Charles L. Weber
Part of the Springer Texts in Electrical Engineering book series (STELE)


All our results thus far apply exclusively to coherent channels. We now consider the more difficult problem of determining optimal signal waveforms for telemetry systems which are still synchronous, that is, where the receiver knows the time interval during which the signal is to arrive but not the carrier-phase angle of the arriving signal. The waveform emitted at the transmitter during the interval [0,T] is still assumed to be one of M equally powered equally likely signals, but after transmission through the channel, coherent phase information of the carrier is assumed to be lost; in addition, we have the previous assumption of corruption of the signal by additive white gaussian noise. The received signal y(t) is then of the form
$$ y(t) = Vs_j (t;\phi ) + n(t) $$
where, as before V 2/2 is the average received signal power and n(t) is the additive white gaussian noise (independent of the transmitted wave-forms).


Additive White Gaussian Noise Signal Structure Coherent System Signal Design Binomial Coefficient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 19.1
    Helstrom, C.: “Statistical Theory of Signal Detection,” Pergamon Press, New York, 1960.Google Scholar
  2. 19.2
    Wainstein, L. A., and V. D. Zubakov: “Extraction of Signals from Noise,” Prentice-Hall, Englewood Cliffs, N.J., 1962.Google Scholar
  3. 19.3
    Middleton, D.: “Introduction to Statistical Communication Theory,” McGrawHill, New York, 1960.Google Scholar
  4. 19.4
    Balakrishnan, A. V., and I. J. Abrams: Detection Levels and Error Rates in PCM Telemetry Systems, IRE Intern. Conv. Record, 1960.Google Scholar
  5. 19.5
    Nuttall, A. H.: Error Probabilities for Equicorrelated M-ary Signals Under Phase-coherent and Phase-incoherent Reception, IRE Trans. Inform. Theory, vol. IT-8, no. 4, July, 1962, pp. 305–315.MathSciNetCrossRefGoogle Scholar
  6. 19.6
    Reiger, S.: Error Rates in Data Transmission, Proc. IRE, vol. 46, May, 1958, pp. 919–920.Google Scholar
  7. 19.7
    Turin, G. L.: The Asymptotic Behavior of Ideal M-ary Systems, Proc. IRE, vol. 47, no. 1, January, 1959.Google Scholar
  8. 19.8
    Helstrom, C. W.: The Resolution of Signals in White Gaussian Noise, Proc. IRE, vol. 43, no. 9, September, 1955, pp. 1111–1118.CrossRefGoogle Scholar
  9. 19.9
    Scholtz, R. A., and C. L. Weber: Signal Design for Non-coherent Channels, IEEE Trans. Inform. Theory, vol. IT-12, no. 4, October, 1966.Google Scholar
  10. 19.10
    Lindsey, W. C.: Coded Non-coherent Communications, IEEE Trans. Space Electron. Telemetry, vol. SET-II, no. 1, March, 1965.Google Scholar
  11. 19.11
    Weber, C. L.: A Contribution to the Signal Design Problem for Incoherent Phase Communication Systems, IEEE Trans. Inform. Theory, vol. IT-14, March, 1968.Google Scholar
  12. 19.12
    Helstrom, C. W.: Scholium, IEEE Trans. Inform. Theory, vol. IT-14, April, 1968.Google Scholar
  13. 19.13
    Schaffner, C. A.: “The Global Optimization of Phase-incoherent Signals,” doctoral dissertation, California Institute of Technology, Pasadena, Calif., April, 1968.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1987

Authors and Affiliations

  • Charles L. Weber
    • 1
  1. 1.Electrical Engineering DepartmentUniversity of Southern CaliforniaLos AngelesUSA

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