Spread Scattering and Propagation

  • Dennis W. Ricker
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 725)


The sonar environment rarely produces the ideal conditions of point scattering in white (uncorrelated) Gaussian interference because the ocean is not a homogeneous medium. The salinity and temperature vary as a function of depth and location due to weather changes, solar heating, and fresh water influx from rivers and estuaries. These induce density variations that change the refractive index of the water and hence the propagation speed causing sound wave refraction. This is commonly called ray bending for sonars operating at medium to high frequency (1–100kHz) [ 1, 2, 3] and can cause a transmitted pulse and the resulting echo to propagate over several paths with different delays. Multiple boundary reflections from the surface and bottom are possible and the combined phenomenon is called multipath propagation. Figure 6.1 is an example of a summertime near surface downward refracting sound velocity profile (SVP) and raypath plot. The sun warms the surface waters generating a gradient of decreasing temperature with depth to about 100 ft depth. Thereafter temperature slowly increases with depth. Sound speed increases with water temperature causing the acoustic wavefront to refract downward near the surface but upward below creating a “duct” of converging raypaths at about 200 ft depth. Multiple reflections are also occurring at the surface and bottom.


White Gaussian Noise Parameter Domain Ambiguity Function Processing Gain Scattering Function 
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  1. [1]
    W.S. Burdic. Underwater Acoustic System Analysis. Prentice-Hall, 1984.Google Scholar
  2. [2]
    S.C. Clay and H. Medwin. Acoustical Oceanography. Wiley Interscience, 1977.Google Scholar
  3. [3]
    R.J. Urick. Principles of Underwater Sound. McGraw-Hill, 1975.Google Scholar
  4. [4]
    H.L. Van Trees. Detection, Estimation, and Modulation Theory-Part III. Wiley, 1971.Google Scholar
  5. [5]
    L.J. Ziomek. A Scattering Function Approach to Underwater Acoustic Detection and Signal Design. PhD Thesis in Acoustics, Penna. State Univ., Nov. 1981. Applied Research Laboratory TR 81–144.Google Scholar
  6. [6]
    R. Laval. Time-Frequency-Space Generalized Coherence and Scat- tering Functions. In G. Tacconi, editor, Aspects of Signal Processing, Part 1, pages 69–87. D. Reidel, Dordrecht-Holland, 1977.CrossRefGoogle Scholar
  7. [7]
    R. Laval and Y. Labasque. Medium Inhomogenieties: Effects on Spatial and Temporal Processing. In Underwater Acoustics and Signal Processing. D. Reidel, Dordrecht-Holland, 1981.Google Scholar
  8. [8]
    D. Middleton. A Statistical Theory of Reverberation and Similar First Order Scattered Fields, I Waveforms and the General Process. IRE Trans. Info. Theory, IT-13(3):372–412, July 1967.MathSciNetMATHCrossRefGoogle Scholar
  9. [9]
    L.J. Ziomek. Underwater Acoustics, A Linear Systems Approach. Academic Press, Orlando, FL, 1985.Google Scholar
  10. [10]
    L.G. Weiss. Wideband Inverse Scattering and Wideband Deconvolution of Acoustic Signals Using Wavelet Transforms. PhD Thesis in Acoustics, Penna. State Univ., May 1993.Google Scholar
  11. [11]
    L.G. Weiss. Wavelets and Wideband Correlation Processing. IEEE Sig. Proc. Magazine, Jan. 1994.Google Scholar
  12. [12]
    K.L. Hillsley and R.K. Young. Linear Time-Varying System Characterization using Wavelet Transforms. In Proc. Symposium on Progress in Electromagnetic Research, Seattle WA, July 24–28 1995.Google Scholar
  13. [13]
    P. Maas. Wideband Radar: the Hyp (hyperbolic) Transform. Inverse Problems, 5:849–857, 1989.MathSciNetCrossRefGoogle Scholar
  14. [14]
    D.M. Drumheller and D.W. Ricker. Receiver-Transmitter Optimization for Detection in Doubly Spread Channels. Journ. of the Acoust. Soc. Amer., 89(4):1714–1723, April 1991.MathSciNetCrossRefGoogle Scholar
  15. [15]
    W.C. Knight, G.G. Pridham, and S.M. Kay. Digital Signal Processing for Sonar. Proceedings of the IEEE, 69(11):1451–1507, Nov. 1981.CrossRefGoogle Scholar
  16. [16]
    J.J. Kisenwether. The Characterization of Delay Spread Channels Using Cross Correlation Processing. PhD Thesis in Acoustics, Penna. State Univ., Aug. 1998.Google Scholar
  17. [17]
    D.W. Ricker and A.J. Cutezo. Estimation of Coherent Detection Performance for Spread Scattering in Reverberation-Noise Mixtures. Journ. of the Acoust. Soc. Amer., 107(4):1978–1986, April 2000.CrossRefGoogle Scholar
  18. [18]
    L.J. Ziomek and L.H. Sibul. Broadband and Narrowband Signal-to- Interference ratio Expressions for a Doubly Spread Target. Journ. of the Acoust. Soc. Amer., 72(3):804–819, 1982.MATHCrossRefGoogle Scholar
  19. [19]
    S.T. McDaniel and A.D. Gorman. Acoustic and Radar Sea Surface Backscatter. Journ, Geophys. Res., 87:4127–4136, 1982.CrossRefGoogle Scholar
  20. [20]
    S.T. McDaniel. Sea Surface Reverberation: A review. Journ. of the Acoust. Soc. Amer., 94:1905–1922, 1993.CrossRefGoogle Scholar
  21. [21]
    R.P. Goddard. The Sonar Simulation Toolset. In Proc. Oceans ‘89, The Global Ocean, volume 4, pages 1217–1222, 1989. IEEE Pub. no. 89CH 2780–5.Google Scholar
  22. [22]
    W.S. Hodgkiss. An Oceanic Reverberation Model. IEEE Journ. of Oceanic Engineering, OE-9(2), April 1984.Google Scholar
  23. [23]
    G.R. Valenzuela and M.B. Laing. A Study of Doppler spectra of Radar Sea Echoes. Journ. Geophys. Res, 75:551–563, 1970.CrossRefGoogle Scholar
  24. [24]
    R.L. Swarts and C.J. Eggen. Simplified Model of the Spectral Characteristics of High Frequency Surface Scatter. Journ. of the Acoust Soc. Amer., 59(4):846–851, April 1976.CrossRefGoogle Scholar
  25. [25]
    S.O. McConnel. Remote Sensing of the Air-Sea Interface using Mi- crowave Acoustics. In Proc. Oceans ‘83, pages 85–92. IEEE and Marine Tech. Soc, 1983.CrossRefGoogle Scholar
  26. [26]
    H. Weinberg. Generic Sonar Model. Technical report, Naval Underwater Syst. Center, 1985. TR 5971D.Google Scholar
  27. [27]
    J.P. Hermand and W.H. Roderick. Acoustic Model-Based Matched Filter Processing for Fading time-Dispersive Ocean channels: Theory and Experiment. IEEE Journ. of Oceanic Engineering, 18(4):447–465, October 1993.CrossRefGoogle Scholar
  28. [28]
    L.H. Sibul and E.L. Titlebaum. Signal Design for Detection of Targets in Clutter. Proceedings of the IEEE, 69(4):481–482, April 1981.CrossRefGoogle Scholar
  29. [29]
    Altes R.A. Suppression of Radar Clutter and Multipath Effects for Wideband Signals. IEEE Trans. Info. Theory, 17:344–345, May 1971.MATHCrossRefGoogle Scholar
  30. [30]
    D.M. Drumheller. Receiver Optimization for Detection in Doubly Spread Communication Channels. Technical report, Applied Research Lab., Penna. State Univ., Dec. 1984. TM-84–185.Google Scholar
  31. [31]
    D.K. Barton. Radars: Frequency Agility and Diversity, volume 6. Artech House, Dedham, Mass., 1977.Google Scholar
  32. [32]
    J.V. DiFranco and W.L. Rubin. Radar Detection. Artech House, Dedham, MA, 1980.Google Scholar
  33. [33]
    S.C. Schwartz. The Estimator-Correlator for Discrete Time Problems. IEEE Trans. Info. Theory, IT-23:93–100, 1977.MATHCrossRefGoogle Scholar
  34. [34]
    J.A. Tague. Estimation-Correlation, Modeling, and Identification in Adaptive Array Processors. PhD Thesis in Electrical Engineering, Penna. State Univ., Univ. Park, PA, Dec. 1987.Google Scholar
  35. [35]
    L.L. Sharf. Statistical Signal Processing. Addison-Wesley, 1991.Google Scholar
  36. [36]
    M.J. Roan and L.H. Sibul. Performance Quantification for the Wavelet Transform Domain Estimator-Correlator. In Proc. 32nd Intnl. Conf., Princeton Univ., March 1998. 32nd Intnl. Conf. on Info. Sciences and Systs.Google Scholar
  37. [37]
    D.W. Ricker and A.J. Cutezo. A Model Based Estimator Correlator (EC) Structure. IEEE Trans. Sig. Proc., 48(10):2733–2742, Oct. 2000.CrossRefGoogle Scholar
  38. [38]
    T. Kailath. Correlation Detection of Signals Perturbed by a Random Channel. IRE Trans. Info. Theory, IT-6:361–366, 1960.MathSciNetCrossRefGoogle Scholar
  39. [39]
    L.H. Sibul, L.G. Weiss, and R.K. Young. Group theoretic Aspects of Signal Processing in the Time-frequency and Time-Scale Domains. In Proc. 30th Ann. Conf., Princeton Univ., March 1996. 30th Ann. Conf. on Info Sciences and Systems.Google Scholar
  40. [40]
    L.H. Sibul, L.G. Weiss, and T.L. Dixon. Wavelet Transform Domain Implementation of the Estimator Correlator for Detection of Distributed Objects in Stochastic Media. In Proc. 1997 Conf., Johns Hopkins Univ., March 1997. 1997 Conf. on Info. Sciences and Systs.Google Scholar
  41. [41]
    L.H. Sibul and J.A. Tague. Estimation-Correlation, Modeling and Identification in Adaptive Array Processors. In Proc. 2nd IF AC Workshop, Lund Sweden, July 1986. 2nd IFAC Workshop on Adaptive Systems.Google Scholar
  42. [42]
    A.D. Whalen. Detection of Signals in Noise. Academic Press, 1971.Google Scholar
  43. [43]
    A. Papoulis. Probability, Random Variables, and Stochastic Processes. McGraw-Hill, New York NY, 1965.MATHGoogle Scholar
  44. [44]
    G. Strang. Linear Algebra and its Applications. Academic Press, 1980.Google Scholar
  45. [45]
    C.F. Van Loan G.H. Golub. Matrix Computations, volume 6. Johns Hopkins Press, Baltimore, MD, 1983.MATHGoogle Scholar
  46. [46]
    D.W. Ricker and A.J. Cutezo. Detection by Incoherent Recombination with Partial Information. IEEE Trans, on Aerosp. and Elect. Systs., 37(l):2733–2742, Jan. 2001.Google Scholar
  47. [47]
    C.W. Helstrom. Elements of Signal Detection and Estimation. Prentice-Hall, Englewood Cliffs N.J., 1995.MATHGoogle Scholar
  48. [48]
    P. Swerling. Probability of Detection for Fluctuating Targets. Technical report, Rand Corp., April 1954.Google Scholar
  49. [49]
    J.I. Marcum. A Statistical Theory of Target Detection by Pulsed Radar. IRE Trans. Info. Theory, IT-6(2):59–267, April 1960.MathSciNetCrossRefGoogle Scholar
  50. [50]
    D.K. Barton. Simple Procedures for Radar Detection Calculations. IEEE Trans, on Aerosp. and Elect Systs., aes-5(5):837–846, Sept. 1969.CrossRefGoogle Scholar
  51. [51]
    Irving Kanter. Exact Detection Probability for Partially Correlated Rayleigh Targets. IEEE Trans, on Aerosp. and Elect. Systs., aes-22(2): 184–196, March 1986.MathSciNetCrossRefGoogle Scholar
  52. [52]
    M.A. Weiner. Detection Probability for Partially Correlated Chi-Square Targets. IEEE Trans, on Aerosp. and Elect. Systs., 24(4):411–416, July 1988.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Dennis W. Ricker
    • 1
  1. 1.The Pennsylvania State UniversityUSA

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