抄録
For the observation and development of undersea resources reliable transmission of information underwater is a necessary prerequisite. Recently a grate deal of effort has been expended in the design and development of underwater acoustic telephone equipment. It can be foreseen, however, that there will be a demand for the transmission of digital as well as analog information underwater in the near future. The efficient transmission of digital information underwater may be accomplished by using such a specific data transmission system as the PSK system, as is the case with digital data transmission on the ground. An appealing alternative, when the required rate of transmission is not too high, is to utilize acoustic telephone channels as the transmission medium for the digital information. Modulation techniques that can be used for the acoustic telephone system include AM, SSB, FM, PM, PPM, PCM, etc. However, if, in the design of such a system, the important design criteria include low cost and simplicity, as is the case with underwater communications equipment, then PPM is a logical choice for the modulation technique. Although Gaussian noise processes are common sources of interference in communication problems, background noise of impulsive character also occurs frequently in underwater acoustics. The aim of the present paper is to study the effects of the mixtures of Gaussian and impulse noise accompanying acoustic signals on the probability of bit errors that occur when binary data are transmitted via a PPM acoustic telephone channel. A block diagram of the modem that is used for the analysis is shown in Fig. 1. Section 3. 1 presents the derivation of an approximate expression for bit error probability due to impulse noise. A simple noise model for the impulse noise referred to as the Poisson noise model is employed. First, a pdf(probability density function)for the time of occurrence of the anomaly in the i-th frame is obtained and then it is converted to the pdf p(V) of amplitude V of the PAM pulse in the i-th frame (eq. (14)). The pdf p(V^^^~) given in eq. (24) of the demodulator output V^^^~ which is a weighted sum of overlapping filtered PAM pulses is calculated with the help of a characteristic function (20) and semiinvariants (22) Two kinds of error probabilities P_r(e|S) and P_r(e|M) are finally obtained in eq. (28). Section 3. 2 and 3. 3 deal with the bit error probabilities due to Gaussian noise and the mixtures of Gaussian and impulse noises, respectively. The method of analysis is similar to that of Section 3. 1. In Chap. 4 some results of numerical calculation of the error probability expressions are presented graphically (Fig. 10). One can observe the threshold characteristic and the effect of impulse noise on the error probabilities.
