Statistical characteristics of digital hydroacoustic signal with sweep-spread carrier in the receiver predetection point

Abstract

After matched filtering of receive signal with continuously spread carrier (sweep-spread carrier, S2C), the ratio between the signal and environmental noise increases. With increase of the ratio the influence of environmental noise on the probability of error in determining the discrete values of the signal rapidly decreases. However, the ratio of other kind - between the signal energy and the energy of delayed multipath components with random parameters - remains unchanged, since the amount of energy reflected by boundaries of underwater acoustic channels, layers and different objects is proportional to energy of transmitted signal. Thus it is more important to investigate the influence of random multipaths on the characteristics of the received signal, rather than the influence of Gaussian noise. There was determined that the interference of random multipath components of the sweep-spread signal causes a normal distribution of its quadrature components. There was made the quantitative assessment of the probability distribution of these components, in particular, the analytical expressions for variances of the distributions as functions of amplitude, base of the signal, Rice coefficient and the amount of multipaths. These expressions show that with increase of the signal base B the variance of the distribution at the output of the optimal demodulator decreases inversely proportional to B. In Rayleigh channels the most probable value of the signal with sweep-spread carrier is square root B times smaller than the most probable value of the signal with a frequency-constant carrier. In Rician channels the most probable value of the demodulator output signal is equal to the amplitude of the dominant multipath component. Taking into account B times smaller distribution variance of the signal with sweep-spread carried the amplitude of such signal was more often situated in close vicinity of the most probable value than the amplitude of the signal with frequency-constant carrier. To verify the analytical expressions, there were carried out numerical experiments. The results of verification demonstrated good agreement between analytical model and numerical experiment.