Error Performance

  • John B. Anderson
  • Tor Aulin
  • Carl-Erik Sundberg
Part of the Applications of Communications Theory book series (ACTH)

Abstract

For most digital communication systems, it is of vital importance that the transmitted symbols are detected as reliably as possible at the receiver end, given a specific SNR. A natural and commonly used criterion of goodness among communication engineers is the symbol error probability, which should be minimized. The ultimate conditions under which error probability may be reduced to zero were set up by Shannon,(l) and problems of this kind will be further elaborated upon in Chapter 5. What is important here is that Shannon dealt with what are called random codes, whereas we now deal with exact deterministic systems. We also impose the further constraint that the transmitted signal always has a constant envelope.

Keywords

Expense Convolution Aulin 

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References

  1. 1.
    C. E. Shannon, A mathematical theory of communication, Bell. Syst. Tech. J. 27, 379–423 (1948).MathSciNetMATHGoogle Scholar
  2. 2.
    M. G. Pelchat, R. C. Davis, and M. B. Luntz, Coherent demodulation of continuous phase binary FSK signals, Proc. Int. Telemetering Conf., Washington, D.C., pp. 181-190, 1971.Google Scholar
  3. 3.
    W. P. Osborne and M. B. Luntz, Coherent and noncoherent detection of CPFSK, IEEE Trans. Commun. COM-22, 1023–1036 (1974).CrossRefGoogle Scholar
  4. 4.
    R. deBuda, Coherent demodulation of frequency-shift keying with low deviation ratio, IEEE Trans. Commun. COM-20, 429–436 (1972).CrossRefGoogle Scholar
  5. 5.
    T. A. Schonhoff, Symbol error probabilities for M-ary coherent continuous phase frequency-shift keying (CPFSK), IEEE Int. Conf. Commun., Conf. Record, San Francisco, pp. 34.5-34.8, 1975.Google Scholar
  6. 6.
    T. A. Schonhoff, Bandwidth vs. performance considerations for CPFSK, IEEE National Telecommun., Conf. Record, pp. 38.1-38.5, 1975.Google Scholar
  7. 7.
    T. A. Schonhoff, Symbol error probabilities for M-ary CPFSK: Coherent and noncoherent detection, IEEE Trans. Commun. COM-24, 644–652 (1976).CrossRefGoogle Scholar
  8. 8.
    T. Aulin and C.-E. Sundberg, Bounds on the performance of binary CPFSK type of signaling with input data symbol pulse shaping, IEEE National Telecommun., Conf. Record, Birmingham, Alabama, pp. 6.5.1-6.5.5, 1978.Google Scholar
  9. 9.
    T. Aulin and C.-E. Sundberg, M-ary CPFSK type of signaling with input data symbol pulse shaping—Minimum distance and spectrum, IEEE Int. Conf. Commun., Conf. Record, Boston, pp. 42.3.1-42.3.6, 1979.Google Scholar
  10. 10.
    A. Lender, The duobinary technique for high speed data transmission, IEEE Trans. Commun. Electron. COM-11, 214–218 (1963).Google Scholar
  11. H.A. Lender, Correlative level coding for binary data transmission, IEEE Spectrum 3, 104–115 (1966).CrossRefGoogle Scholar
  12. 12.
    P. Kabal and S. Pasupathy, Partial response signaling, IEEE Trans. Commun. COM-23, 921–934 (1975).CrossRefGoogle Scholar
  13. 13.
    T. Aulin, N. Rydbeck, and C.-E. Sundberg, Bandwidth efficient constant-envelope digital signaling with phase tree demodulation, Electron Lett. 14, 487–489 (1978).CrossRefGoogle Scholar
  14. 14.
    T. Aulin, N. Rydbeck, and C.-E. Sundberg, Bandwidth efficient digital FM with coherent phase tree demodulation, IEEE Int. Conf. Commun., Conf. Record, Boston, pp. 42.4.1-42.4.6, 1979.Google Scholar
  15. 15.
    T. Aulin, CPM—A power and bandwidth efficient digital constant envelope modulation scheme, Doctoral Thesis, Telecommun. Theory, Univ. of Lund, Lund, Sweden, November 1979.Google Scholar
  16. 16.
    T. Aulin and C.-E. Sundberg, Continuous phase modulation—Part I: Full response signaling, IEEE Trans. Commun. COM-29, 196–209 (1981).MathSciNetCrossRefGoogle Scholar
  17. 17.
    T. Aulin and C.-E. Sundberg, Continuous phase modulation—Part II: Partial response signaling, IEEE Trans. Commun. COM-29, 210–225 (1981).MathSciNetCrossRefGoogle Scholar
  18. 18.
    H. Miyakawa, H. Harashima, and Y. Tanaka, A new digital modulation scheme—Multimode binary CPFSK, Third Int. Conf. Dig. Satellite Commun., Conf. Record, Kyoto, Japan, pp. 105-112, 1975.Google Scholar
  19. 19.
    J. B. Anderson and R. de Buda, Better phase-modulation error performance using trellis phase codes, Electron. Lett. 12, 587–588 (1976).CrossRefGoogle Scholar
  20. 20.
    J. B. Anderson and D. P. Taylor, A bandwidth-efficient class of signal space codes, IEEE Trans. Inf. Theory IT-24, 703–712 (1978).MathSciNetCrossRefGoogle Scholar
  21. 21.
    T. Aulin and C.-E. Sundberg, On the minimum Euclidean distance for a class of signal space codes, IEEE Trans. Inf. Theory IT-28, 43–55 (1982).CrossRefGoogle Scholar
  22. 22.
    T. Aulin and C.-E. Sundberg, Minimum Euclidean distance and power spectrum for a class of smoothed phase modulation codes with constant envelope, IEEE Trans. Commun. COM-30, 1721–1729 (1982).CrossRefGoogle Scholar
  23. 23.
    J. Wozencraft and I. M. Jacobs, Principles of Communication Engineering, Wiley, New York (1965).Google Scholar
  24. 24.
    A. Viterbi, Principles of Coherent Communication, McGraw-Hill, New York (1966).Google Scholar
  25. 25.
    A. T. Lereim, Spectral properties of multi-h phase codes, M. Eng. thesis, McMaster Univ., Technical Report No. CRL-57, Communications Research Laboratory, Hamilton, Ontario, Canada, July 1978.Google Scholar
  26. 26.
    J. B. Anderson, D. P. Taylor, and A. T. Lereim, A class of trellis phase moduation codes for coding without bandwidth expansion, Int. Conf. on Commun., Conf. Record, Toronto, Ontario, Canada, pp. 50.3.1-50.3.5, June 1978.Google Scholar
  27. 27.
    J. K. Omura and D. Jackson, Cutoff rates for channels using bandwidth efficient modulations, Nat. Telecommun. Conf., Conf. Record, Houston, pp. 14.1.1-14.1.11, November 1980.Google Scholar
  28. 28.
    T. Aulin, Viterbi detection of continuous phase modulated signals, Nat. Telecommun. Conf., Conf. Record, Houston, pp. 14.2.1-14.2.7, November 1980.Google Scholar
  29. 29.
    T. Aulin, Symbol error probability bounds for coherently Viterbi detected continuous phase modulated signals, IEEE Trans. Commun. COM-29, 1707–1715 (1981).CrossRefGoogle Scholar
  30. 30.
    S. G. Wilson, J. H. Highfill, and C.-D. Hsu, Error bounds for multi-h phase codes, IEEE Trans. Inf. Theory IT-28, 660–665 (1982).CrossRefGoogle Scholar
  31. 31.
    S. Lin and D. J. Costello, Error Control Coding: Fundamentals and Applications, Prentice Hall, Englewood Cliffs, New Jersey (1983).Google Scholar
  32. 32.
    F. Hemmati and D. J. Costello Jr., Truncation error probability in Viterbi decoding, IEEE Trans. Commun. COM-25, 530–532 (1977).CrossRefGoogle Scholar
  33. 33.
    T. Aulin, C.-E. Sundberg, and A. Svensson, Viterbi detectors with reduced complexity for partial response continuous phase modulation, Nat. Telecommun., Conf. Record, New Orleans, pp. D8.3.1-D8.3.7, December 1981.Google Scholar
  34. 34.
    A. Svensson, C.-E. Sundberg, and T. Aulin, Distance measure for simplified receivers, Electron. Lett. 19(23), 953–954 (1983).CrossRefGoogle Scholar
  35. 35.
    T. Aulin and C.-E. Sundberg, Detection performance of band-limited continuous phase modulation, Globecom’ 82, Conf. Record, Miami, pp. E7.6.1-E7.6.7, December 1982.Google Scholar
  36. 36.
    T. Aulin and C.-E. Sundberg, Optimum and sub-optimum detectors for band and amplitude limited continuous phase modulation, Int. Conf. on Commun., Conf. Record, Boston, pp. A6.1.1-A6.1.6, June 1983.Google Scholar
  37. 37.
    D. P. Taylor and H. C. Chan, A simulation study of two bandwidth-efficient modulation techniques, IEEE Trans. Commun. COM-29, 267–275 (1981).CrossRefGoogle Scholar
  38. 38.
    I. Korn, OQPSK and MSK systems with bandlimiting filters in transmitter and receiver and various detector filters, Proc. IEE, Part F, 439-447 (1980).Google Scholar
  39. 39.
    H. Singh and T. T. Thjung, Error-rate measurements for SFSK with band limitation, Electron. Lett. 16(2), 64–66 (1980).CrossRefGoogle Scholar
  40. 40.
    F. Amoroso, The use of quasi-bandlimited pulses in MSK transmission, IEEE Trans. Commun. COM-27, 1616–1624 (1979).CrossRefGoogle Scholar
  41. 41.
    M. C. Austin and M. U. Chang, Quadrature overlapped raised-cosine modulation, Int. Conf. on Commun., Conf. Record, Seattle, pp. 26.7.1-26.7.5, June 1980.Google Scholar
  42. 42.
    M. Atobe, Y. Matsumoto, and Y. Tagashira, One solution for consant envelope modulation, 4th Int. Conf. on Diag. Sat. Commun., Conf. Record, Montreal, pp. 45-50, October 1978.Google Scholar
  43. 43.
    A. J. Viterbi and J. Omura, Principles of Digital Communications and Coding, McGraw-Hill, New York (1979).Google Scholar
  44. 44.
    T. Aulin and C.-E. Sundberg, CPM—An efficient constant amplitude modulation scheme, Int. J. Satellite Commun. 2, 161–186 (1984).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • John B. Anderson
    • 1
  • Tor Aulin
    • 2
  • Carl-Erik Sundberg
    • 3
  1. 1.Rensselaer Polytechnic InstituteTroyUSA
  2. 2.Chalmers University of TechnologyGöteborgSweden
  3. 3.AT & T Bell LaboratoriesHolmdelUSA

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