The objective of this chapter is to illustrate the basic principles of sonar performance modeling. This is achieved by deriving the most important passive and active sonar equations, each accompanied by a worked example. These worked examples are intended to be didactic rather than realistic: enough realism is included in them to illustrate the underlying principles, but no more—where there is a conflict between simplicity and realism then simplicity is preferred, except at the expense of the principle itself.1
3.1.1 Objectives of sonar performance modeling
The objective of sonar performance modeling is to quantify sonar performance, enabling a decision-maker to:
— predict the likelihood that a given sonar task, such as the detection of a submerged object, will be carried out successfully;
1More realistic examples are provided in Chapter 11.
— compare the effectiveness of different sonar designs in carrying out a given task;
— compare the effectiveness of different strategies for carrying out a given task.
Examples of possible sonar tasks, in addition to detection, are localization, classification, evasion,2surveillance, and communication. Irrespective of the applica- tion, sonar effectiveness must depend on the probability of making a successful detection each time the sonar is used. Less obvious, but equally important, is the observation that sonar effectiveness also depends on the number of false alarms,3 because of the time and other resources wasted on investigating these. Much of sonar performance modeling, and the main thrust of this book, is concerned with the calculation of the probabilities of detection and false alarm for a given scenario or scenarios.
3.1.2 Concepts of ‘‘signal’’ and ‘‘noise’’
A sonar receiver is a complicated piece of equipment, typically comprising
— a hydrophone, or an array of hydrophones, to convert an underwater pressure disturbance into an electronic one;
— a suite of signal-processing algorithms,4to enhance the signal-to-noise ratio;
— a display unit, to help the sonar operator determine whether an object of interest (a target) is present.
Pressure fluctuations5at the receiver can be thought of as a linear sum of two different kinds:
— those caused by the presence of the target (the signal);
— all other pressure fluctuations (the noise).
The ‘‘target’’ is any object that we wish to detect.
The above definitions of signal and noise are necessarily vague, as the distinction between them depends on details of the signal processing that have not yet been specified. The noise definition as ‘‘all sound that is not part of the signal’’ means that
2Although the task of evasion is not performed directly by the sonar, the modeling of evasion and the development of evasion tactics are nevertheless an important application of sonar performance modeling.
3Fluctuations in noise levels alone can result in a sonar detection system erroneously reporting the presence of a target. Such an event is known as a ‘‘false alarm’’.
4The algorithms can be implemented either in hardware or software.
5Strictly speaking, what matters is the voltage in an electrical or electronic circuit, after filtering. For simplicity we assume for now that, to within a multiplying constant, the pressure and voltage fluctuations are identical. The validity of this assumption requires the hydrophone sensitivity and filter response (or at least their product) to be independent of frequency, within the bandwidth of interest.
many different potential sound sources need to be taken into account.6Each case is different, and knowledge of which noise sources to include in a model is acquired by experience. Common sources ofambient noiseare wind and shipping. Also important isself-noise, especially from thesonar platform.
A special kind of noise that is unique to active sonar, known asreverberation, is the sound originating from the sonar transmitter and subsequently scattered by underwater boundaries and obstacles other than the target, before arriving back at the receiver. The combined effect of ambient noise, self-noise, and reverberation is known as thebackground.
The sonar equation is an expression for the signal-to-noise ratio (or more generally signal-to-background ratio) written as a product of energy ratios, and usually expressed in decibels. The conversion to decibels turns the product of ratios into a sum of the logarithms of these ratios.
3.1.3 Generic deep-water scenario
For the purpose of the present chapter, attention is restricted to a specific deep-water scenario, in which the following simplifying assumptions and approximations are made:
— reflections from the seabed are neglected, equivalent to assuming an infinite water depth;
— density and sound speed are assumed to be uniform everywhere in the sea;
— all background noise (including reverberation) is assumed to originate at the sea surface.
The scenario resulting from these assumptions is not a realistic one, but it contains enough realistic features (the reflecting sea surface, a source of reverberation, and some basic signal processing) to illustrate the main principles involved. More realistic applications, without these simplifying assumptions, are described in Chapter 11.
A sonar equation is derived for each main category of sonar, followed by a worked example. These examples make some additional assumptions that serve to simplify the calculations. For example, for passive sonar the background noise is assumed to arise only from wind; and the target is assumed to be located in the broadside beam of ahorizontal line array(a sequence of hydrophones placed along a straight horizontal line).
3.1.4 Chapter organization
The remainder of this chapter is divided into two main sections, one on passive sonar (Section 3.2) and one on active sonar (Section 3.3). These sections are further divided into sub-sections concerned with coherent and incoherent processing. In each of the 3.1 Introduction 55 Sec. 3.1]
6In some situations non-acoustic sources of noise can also be important.
four sub-sections the relevant sonar equation is derived, and illustrated by means of a worked example.
3.2 PASSIVE SONAR