Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-22T07:48:37.870Z Has data issue: false hasContentIssue false

A generalisation of the study of sum and square law signal processors with multiple clipped inputs

Published online by Cambridge University Press:  17 February 2009

R. G. Keats
Affiliation:
Department of Mathematics, University of Newcastle, Newcastle, Australia.
V. K-K. Yu
Affiliation:
Department of Mathematics, University of Newcastle, Newcastle, Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The recent work of Cheng and Stokes on the processing of clipped signals from two or three receivers is extended and generalised by removing a number of restrictions. In particular, there is no restriction on the number of receivers and the restrictions on the statistical properties of the signal and noise processes have been considerably relaxed.

Mathematically—Plackett's result is used to expand the orthant proabilities involved in increasing powers of the input signal to noise ratio.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Birdsall, T. G. and Kaye, G. T., ‘SCAR—the MPT scattering array’, Proceedings of Conference on Signal Processing for Arrays held at the Weapons Research Establishment, Salisbury, South Australia, 1975.Google Scholar
[2]Cheng, M. C., ‘On a class of non-linear transformations of Gaussian random processes’, Ph.D. Thesis, University of Adelaide (1968).Google Scholar
[3]Cheng, M. C., ‘The clipping loss in correlation detectors for arbitrary input signal to noise ratios’, I.E.E.E. Trans. on Information Theory, IT–14 (1968), 382389.Google Scholar
[4]Cheng, M. C., ‘The orthant probabilities of four Gaussian variates’, Ann. Math. Stat., 40 (1969), 152161.Google Scholar
[5]Edelblute, D. J., Fisk, J. M. and Kinnison, G. L., ‘Criteria for optimum signal detection for arrays’, J. Acoust. Soc. Amer., 41 (1967) 199205.Google Scholar
[6]Ekre, H., ‘Polarity coincidence correlation detection of a weak noise source’, I.E.E.E. Trans. on Information Theory, IT–9 (1963), 1823.Google Scholar
[7]Faran, J. J. Jr, and Hills, R. Jr, The Application of Correlation Techniques to Acoustic Receiving Systems, (Technical Memo No. 28, Acoust. Res. Lab., Harvard, 1952).Google Scholar
[8]Helstrom, C. W., Statistical Theory of Signal Detection, (London, Pergamon Press, 2nd ed., 1960).Google Scholar
[9]Kailath, T., ‘A general likelihood formula for random signals in Gaussian noise’, I.E.E.E. Trans. on Information Theory, IT–15 (1969) 350361.Google Scholar
[10]Kailath, T., ‘The innovations approach to detection and estimation theory’, Proc. I.E.E.E. 58 (1970), 680695.Google Scholar
[11]Kailath, T., ‘Some extensions of the innovations theorem’, B.S.T.J. 50 (1971), 14871494.Google Scholar
[12]Kanefsky, M., ‘Detection of weak signals with polarity coincidence arrays’, I.E.E.E. Trans. on Information Theory IT–12 (1966), 260268.Google Scholar
[13]Keats, R. G., ‘Sum and square law signal processors with multiple clipped inputs’, Proceedings of Conference on Signal Processing for Arrays held at Weapons Research Establishment, Salisbury, South Australia, 1975.Google Scholar
[14]Laning, J. H. and Battin, R. H., Random Processes in Automatic Control, (McGraw-Hill, 1956).Google Scholar
[15]Lewin, L., Dilogarithms and Associated Functions (London, MacDonald Press, 1958).Google Scholar
[16]Plackett, R. L., ‘A reduction formula for normal multivariate integrals’, Biometrika 41 (1954), 351360.Google Scholar
[17]Schultheiss, P. M. and Tuteur, F. B., ‘Optimum and suboptimum detection of directional Gaussian signals in an isotropic Gaussian noise field, Part II: degradation of detectability due to clipping’, I.E.E.E. Trans. on Military Electronics MIL–9 (1965), 208211.Google Scholar
[18]Stokes, B. J., ‘Signal detection using infinite clipping: A survey and an application’, M. Math. Thesis, University of Newcastle (1973).Google Scholar
[19]Thomas, J. B. and Williams, T. R., ‘On the detection of signals in nonstationary noise by product arrays’, Journal of Acoust. Soc. of America 31 (1959), 453462.Google Scholar
[20]Usher, T. Jr, ‘Signal detection by arrays in noise fields with local variations’, Journal of Acoust. Soc. of America 36, No. 8 (1964), 14441449.Google Scholar
[21]Van Trees, H. L., Detection, Estimation and Modulation Theory – Part III: Radar-Sonar Signal Processing and Gaussian Signals in Noise, (New York, Wiley, 1971).Google Scholar