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## Inhaltsverzeichnis

### Chapter 1. Basic Signal Theory

Abstract
The purpose of this chapter is to establish the basic definitions and terminology to be used throughout this book and to briefly review material required for the understanding of echo-location from an engineering and mathematical perspective. Accordingly, this chapter contains standard signal processing material that would be covered at the senior under-graduate or early graduate level in electrical engineering. Most of it may be found in standard texts some of which are listed in the references. It is assumed that the reader has some background in linear systems, probability and stochastic processes, vector matrix notation, and is familiar with the conventions used to denote random variables and vectors.
Dennis W. Ricker

### Chapter 2. Echo Energy and Time Base

Abstract
The concept of echo-location, that is the transmission of acoustic or electromagnetic energy and the subsequent reception of energy reflected from physical objects or scatterers, is primarily motivated by (1.) the desire to detect their presence, and (2.) to estimate associated parameters such as size, range, speed, and bearing. Secondary objectives which relate to these may involve identification, discrimination, and tracking of specific scattering objects in the presence of competing backscatter sources and noise.
Dennis W. Ricker

### Chapter 3. Detection and Estimation

Abstract
The concepts of echo detection and parameter estimation are introduced in this chapter by considering point scattering which is the simplest scattering model. It results from signal propagation in a homogeneous non-dispersive medium and reflection from a single distant point that may be moving at constant speed with a velocity component along the line of sight. The resulting echo is a Doppler dilated and delayed signal with the same fundamental form as the transmitted waveform (2.26). An understanding of approaches to its detection and the estimation of its constituent parameters is fundamental to an understanding of the signal processing required for the more complex echos treated in later chapters. Common examples are those that are delay and/or Doppler spread because of multiple propagation paths (multipath) especially in shallow water, boundary reverberation, and scattering from fish schools.
Dennis W. Ricker

### Chapter 4. Ambiguity Functions

Abstract
Ambiguity functions and their associated uncertainty functions, play a central role in echo-location as they relate signal characteristics to system and parameter estimation performance. Estimation performance as measured by the CR bound was shown in the previous chapter to be proportional to the resolution or “peakedness” of the ambiguity function (AF). This in turn depends upon the characteristics of the transmitted signal. As will be discussed in later chapters, detection performance in complex (non point-like) backscatter depends strongly on the distributions of signal and interference energy relative to the AF in the space defined by the parameter set p. When the parameters are the usual delay and Doppler parameters associated with sonar or radar, the parameter space is often referred to as the phase space/plane because the parameters are directly related to range (delay) and velocity (Doppler). Range (r), delay (τ), velocity (v), and Doppler (ø, β) are related by $$r \approx c\tau /2$$ and $$v \approx \emptyset c/2{f_0}$$ or $$v \approx (\beta - 1)c/2$$ for the narrow and wideband representations respectively and a monostatic line of sight geometry. In this context, an uncertainty function (UF) is a complex two dimensional function and its associated real ambiguity function (AF) represents a surface.
Dennis W. Ricker

### Chapter 5. Waveforms

Abstract
Waveform specification is an integral part of the overall echo-location system design process because the transmitted waveform represents the “voice” of the system and its properties largely determine the amount and quality of information obtained from an active interrogation. The waveform ambiguity properties that are determined by the amplitude and phase/frequency modulation functions define both the detection performance and the parameter estimation characteristics of systems based upon coherent matched or mismatched filter processing.
Dennis W. Ricker

### Chapter 6. Spread Scattering and Propagation

Abstract
The sonar environment rarely produces the ideal conditions of point scattering in white (uncorrelated) Gaussian interference because the ocean is not a homogeneous medium. The salinity and temperature vary as a function of depth and location due to weather changes, solar heating, and fresh water influx from rivers and estuaries. These induce density variations that change the refractive index of the water and hence the propagation speed causing sound wave refraction. This is commonly called ray bending for sonars operating at medium to high frequency (1–100kHz) [ 13] and can cause a transmitted pulse and the resulting echo to propagate over several paths with different delays. Multiple boundary reflections from the surface and bottom are possible and the combined phenomenon is called multipath propagation. Figure 6.1 is an example of a summertime near surface downward refracting sound velocity profile (SVP) and raypath plot. The sun warms the surface waters generating a gradient of decreasing temperature with depth to about 100 ft depth. Thereafter temperature slowly increases with depth. Sound speed increases with water temperature causing the acoustic wavefront to refract downward near the surface but upward below creating a “duct” of converging raypaths at about 200 ft depth. Multiple reflections are also occurring at the surface and bottom.
Dennis W. Ricker

### Chapter 7. The Spatial Representation

Abstract
In addition to the estimation of Doppler and delay, bearing or angle with respect to the sonar’s orientation is crucial for scatterer localization. Acoustic energy at the transmitter is usually introduced into the medium by a distributed source (projector array) and echo energy is received via a distributed array of individual transducer elements that convert the acoustic energy back into an electrical signal. Sonar arrays are spatially distributed and when in a line, plane, on the surface of a body, or when distributed throughout a volume, they are called line, planar, conformal, and volumetric arrays respectively. The process of summing the weighted responses of the individual receive array elements or more generally integrating the response over a continuous array is called beam formation. The integrated receive array response to acoustic energy depends upon the direction from which the energy arrives and is described by a beam or pattern function. Likewise the transmit pattern function describes the directional distribution of transmitted intensity from a projector array.
Dennis W. Ricker

### Backmatter

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