Models for the amplitude fluctuations of narrow-band signals and noise in the sea

Abstract

The sound from a steady distant sinusoidal source in the sea fluctuates in amplitude because of multipath interferences, surface motion, internal waves, microstructure, and other propagation effects. Such fluctuations are found to follow a Rician or modified-Rayleigh distribution having as a parameter the fraction of random power in the received signal. At the output of conventional sonar processor—namely, a narrow-band filter, a squarer, and an integrator—the fluctuation statistics are determined by the propagation processes occurring in the sea between source and receiver. On the other hand, ambient sea noise is found, from analyses of field recordings, to have fluctuation statistics determined by the processor itself; ambient noise samples at the processor output obey a chi-square distribution having a number of degrees of freedom equal to twice the bandwidth-time product of the processor, as would be expected from a Gaussian input. The two distributions—Rician power for signals and chi-square for noise—while formally different, have remarkable similarities in the limits. In short, the output fluctuation statistics of narrow-band signals and Gaussian ambient noise can apparently be predicted from estimates of the degree of randomness introduced by the prevailing propagation conditions, and from a knowledge of the processor, respectively, provided these statistics remain stationary during the analysis period.