The effect of Doppler on long-range sound propagation

Abstract

In this sound propagation study of the effect of Doppler on source and/or receiver motion has been developed. It is based on modifying the inputs to existing normal-mode software so that the source and/or receiver trajectory and consequent Doppler effects of the given ocean experiment are properly modeled without requiring direct changes in the static softward. From this the effects of the received signal after long-range, multipath sound propagation from a moving source can be modeled and interpreted.

Impact of the ocean acoustic transfer function on the coherence of undersea propagations

“…where the indicated smoothing is computed over the analysis interval T. This relation indicates that four discrete correlation peaks (independent of sidelobes) will occur in the twin dual-path situation, provided the two-dimensional correlation pulsewidth is sufficiently narrow to resolve the peak separations over the 76 (ambiguity) plane. For narrow-band signals, y (7,6) will take the form [4] y(7,S) = x ( 7 , 6 ) cos 77 (2 + 6)f,7…”

“…For a linear delay-difference variation during T, the optimum correlator delay modulation is also linear in time during T, so that one receiver output is time scaled (compressed or expanded) by a constant factor before cross correlating [ 2 ] . For a narrow-band signal, this compensation can be approximated by a constant frequency shift [ 3 ] , [6], [7].…”

Impact of the ocean acoustic transfer function on the coherence of undersea propagations

“…The two-dimensional correlation function between the two sensor channels may be written simply as + %7(7 + 7 2 , 6 -62) …”

“…For a narrow-band signal, this compensation can be approximated by a constant frequency shift [ 3 ] , [6], [7].…”

“…where y (7,6) is the ambiguity function of u(t) (that is, the autocorrelation of the signal over the time-delay and Dopplershift dimensions). It can be seen that when the secondary signal is widely separated from the primary signal (in the 7-6 plane), the ambiguity function will be near zero and the average power of the received signal will be essentially 1 t @' .…”