A Forward Scatter Radar Sea Clutter Model Based on Experimental Data

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UNIVERSITY OF PISA

DOCTORAL THESIS

A Forward Scatter Radar Sea

Clutter Model Based on

Experimental Data

A thesis submitted in fulfilment of the requirements to the

Department of Information Engineering of the University of Pisa for

the degree of Doctor of Philosophy

Author: Supervisors:

Maria Bianca PORFIDO Prof. Marco MARTORELLA

Prof. Fabrizio BERIZZI

October 2017

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Declaration of Authorship

I, Maria Bianca PORFIDO, declare that this thesis titled, ’A Forward Scatter Radar Sea Clutter Model Based on Experimental Data’ and the work presented in it are my own. I confirm that:

 This work was done wholly or mainly while in candidature for a research degree at this University.

 Where any part of this thesis has previously been submitted for a degree or any other qualification at this University or any other institution, this has been clearly stated.

 Where I have consulted the published work of others, this is always clearly attributed.

 Where I have quoted from the work of others, the source is always given. With the exception of such quotations, this thesis is entirely my own work.

 I have acknowledged all main sources of help.

 Where the thesis is based on work done by myself jointly with others, I have made clear exactly what was done by others and what I have contributed myself.

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“Diventa ciò che sei avendolo appreso” “Become what you are, having learned it”

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Abstract

Forward Scatter Radar is a particular configuration of Bistatic Radar, where the transmitter and the receiver are facing each other and the Bistatic angle is close to 180°. Unlike traditional backscatter Radar, where the received signal is the sum of target reflections in Forward Scatter Radar it is formed via the shadowing of the direct signal by the target’s body.

Target detection is a challenging task in Forward Scatter Radar, especially in dynamic sea clutter in maritime system due to absence of range resolution in Continuous Wave. This thesis concerns with simulation of sea clutter return and the mitigation of highest component by the use of Ultra Wide Band.

This thesis considers analysis of sea clutter at very low grazing angle in Forward Scatter Radar. It is done mostly through a mapping for estimation of areas, which would affect performance of Forward Scatter Radar in terms of significant reduction of Signal to clutter ratio.

The thesis gives a useful instrument for the study and the development of Forward Scatter Radar maritime systems. It presents a model able to determine the sea clutter spatial distribution. A sea clutter map is provided to evaluate clutter effects in each area of the illuminated surfaces and detection aspects have been analysed for Ultra Wide Band Forward Scatter Radar.

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Acknowledgements

Firstly, I express my gratitude to Prof. M. Cherniakov and Dr. M. Gashinova for the inspiration, guidance and support they provided me.

I would also like to express my gratitude all those who have not been there. Thanks to them, I understood what kind of person I do not want to be.

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List of Figures

Figure 1.1 Radar systems (a) Monostatic Radar, (b) Bistatic Radar (c) Forward Scatter

Radar ... 21

Figure 1.2 FSR original problem ... 23

Figure 1.3 Maritime FSR at small grazing angle ... 25

Figure 2.1 Generic BR topology ... 33

Figure 2.2 Two-Ray Path propagation model for the leakage signal ... 38

Figure 2.3 Two-Ray Path propagation model for target signal ... 40

Figure 2.4 2D Bistatic Radar Doppler shift ... 42

Figure 2.5 FSR Doppler shift mechanism ... 44

Figure 2.6 Rectangular aperture ... 45

Figure 2.7 Coherent scattering component ... 49

Figure 2.8 Diffuse scattering over sea surface ... 49

Figure 3.1 Wave and water motion ... 56

Figure 3.2 Trochoid ... 57

Figure 3.3 Curve traced out by black point as the moving circle ... 57

Figure 3.4 Simple wave model... 58

Figure 3.5 FSR topology ... 60

Figure 3.6 Fan model ... 61

Figure 3.7 Fan orientation ... 61

Figure 3.8 Grid model ... 63

Figure 3.9 Model topology ... 66

Figure 3.10 Target signal Probability Density Function ... 69

Figure 4.1 Clutter returns map in dBm ... 74

Figure 4.2 Grid model without rotation points on the baseline... 75

Figure 4.3 Grid model with rotation points on the baseline ... 75

Figure 4.4 Clutter map in dBm using grid with rotation points on the baseline ... 77

Figure 4.5 Clutter map in dBm using grid without rotation points on the baseline ... 77

Figure 4.6 Clutter map in dBm using grid with rotation point distance of 0.5m ... 80

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Figure 4.8 Clutter map in dBm at 0.1GHz with rotation point distance of 1m ... 82

Figure 4.9 Clutter map in dBm at 0.1GHz with rotation point distance of 2m ... 82

Figure 4.10 Clutter map in dBm at 0.1GHz with cell dimension of 0.5m ... 84

Figure 4.13 Clutter map in dBm at 1GHz with cell dimension of 0.5m ... 87

Figure 4.19 Doppler signature phase ... 91

Figure 4.20 Clutter map in dBm with tilt angle of 0° ... 93

Figure 4.23 Clutter map in dBm with baseline of 50m ... 95

Figure 4.24 Clutter map in dBm with baseline of 100m... 95

Figure 4.25 Clutter maps with different baseline. (a) with 10m baseline (b) 20m baseline(c) 50m baseline (d) 100m baseline ... 97

Figure 4.26 Receive leakage power versus baseline length ... 98

Figure 4.27 Clutter maps with different antennas height (a) Clutter map with transmitter height of 1m , (b) height of 2m , (c) height of 4m , (d) height of 16m ... 100

Figure 4.28 Clutter map in dBm with 2.5m fan height ... 101

Figure 4.29 Clutter map in dBm with 5m fan height ... 101

Figure 5.1 7.5GHz (a) transmitter and (b) receiver ... 106

Figure 5.2 The omnidirectional antennas ... 107

Figure 5.3 Simulated antenna pattern... 107

Figure 5.4 The antenna on tripods ... 107

Figure 5.5 The fan on tripods ... 107

Figure 5.6 BR Hardware signal processing with added FS section ... 109

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Figure 5.8 Schottky diode characteristic ... 110

Figure 5.9 Estimation of the leakage power... 113

Figure 5.10 Estimation of the target power ... 113

Figure 5.11 First scenario Pritchett’s Road car park ... 114

Figure 5.12 First scenario setup ... 115

Figure 5.13 First scenario points ... 115

Figure 5.14 First scenario human baseline crossing ... 117

Figure 5.15 Second scenario. Pitch in Birmingham B311XN. ... 119

Figure 5.16 Second scenario setup ... 120

Figure 5.17 Second scenario points ... 120

Figure 5.18 Second scenario human baseline crossing ... 122

Figure 5.19 Comparison between real and simulated target power, points from 1 to 10 ... 124

Figure 5.20 Comparison between real and simulated target power, points 11,12,13,14,15,16,19 ... 124

Figure 5.21 Comparison between real and simulated target power points from 21 to 24 ... 125

Figure 5.22 Point 19 calibration curve ... 125

Figure 5.23 Point 19 spectrogram ... 126

Figure 5.24 Third scenario ... 127

Figure 5.25 Third scenario setup ... 127

Figure 5.26 Homemade blade ... 128

Figure 5.27 Homemade blade RCS ... 128

Figure 5.28 Third scenario clutter map ... 129

Figure 5.29 Third scenario human baseline crossing ... 130

Figure 5.30 Third scenario points ... 130

Figure 5.31 Simulated received target power for points 1,5,6,7. Point 1 red line, Point 5 green line, Point 6 brown line and Point 7 blue line ... 132

Figure 5.32 Real received target power for points 1,5,6,7 Point 1 red line, Point 5 green line, Point 6 brown line and Point 7 blue line. ... 132

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Figure 5.34 Simulated Power Spectral Density in Point 7 ... 135

Figure 5.35 Real Power Spectral Density in Point 7 ... 136

Figure 5.36 Total Power Spectra Density at 7.5GHz with 0.5mblade ... 136

Figure 5.37 Total Power Spectra Density at 7.5MHz with 0.5mblade ... 137

Figure 5.38 10m baseline isophase surfaces ... 138

Figure 5.39 1000mbaseline isophase surfaces ... 138

Figure 5.40 Total Power Spectra Density of 0.1m blade ... 139

Figure 6.1 UWB FSR simplified block diagram ... 141

Figure 6.2 3D Shell Resolution ... 142

Figure 6.3 Intersections between ellipsoids and surface ... 144

Figure 6.4 Clutter surfaces for different τ ... 144

Figure 6.5 Sea clutter map FSR CW indBm with 100mbaseline ... 145

Figure 6.6 Clutter for _min100m baseline 2D view ... 146

Figure 6.7 Clutter for _max100m baseline 2D view... 146

Figure 6.8 Percentage of power received on total power and hidden space ... 148

Figure 6.9 Clutter map indBmwith 500mbaseline ... 150

Figure 6.10 Clutter surface varying  and 500mbaseline ... 150

Figure 6.11 Clutter for  and _min 500m baseline (a) 3D view, (b) 2D view ... 150

Figure 6.12 Clutter for _max and 500m baseline (a) 3D view, (b) 2D view ... 150

Figure 6.13 Clutter map in dBmwith 1000mbaseline ... 151

Figure 6.14 Clutter surface varying  and 1000mbaseline ... 151

Figure 6.16 Clutter for _max and 1000m baseline (a) 3D view, (b) 2D view... 151

Figure 6.17 Clutter map dBmwith 1500mbaseline ... 152

Figure 6.18 Clutter surface varying  and 1500m baseline ... 152

Figure 6.20 Clutter for _max and 1500m baseline (a) 3D view, (b) 2D view... 152 Figure 6.21 Percentage of power received and the hidden space with 500m baseline . 153 Figure 6.22 Percentage of clutter received and the hidden space with 1000mbaseline 154

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Figure 6.23 Percentage of clutter received and the hidden space with 1500mbaseline 154

Figure 6.24. FSR target in the middle ... 155

Figure 6.25 Signal target to Clutter Ration in CW mode, target in the middle ... 157

Figure 6.26 Signal target to Clutter Ration in pulse mode, target in the middle ... 157

Figure 6.27 Signal target to Clutter Ration in CW mode, target 100m far from the receiver ... 158

Figure 6.28 Signal target to Clutter Ration in pulse mode, target 100m far from the receiver ... 158

Figure 6.29 Hidden space versus pulse width ... 159

Figure 7.1 FSR topology ... 163

Figure 7.2 Multiple fan (a) xz plane (b) xy plane ... 165

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List of Tables

Table 2.1 Douglas Sea State scale... 46

Table 3.1 Simulation parameters... 68

Table 3.2 Continuous distributions BIC ... 70

Table 4.1 Simulation parameters to build clutter map ... 73

Table 4.2 First analysis simulation parameters ... 75

Table 4.3 Second analysis simulation parameters... 78

Table 4.4 Third analysis simulation parameters ... 81

Table 4.5 Fourth analysis simulation parameters ... 83

Table 4.6 Fifth analysis simulation parameters... 86

Table 4.7 Sixth analysis simulation parameters ... 89

Table 4.8 Seventh analysis simulation parameters ... 92

Table 4.9 Eighth analysis simulation parameters ... 94

Table 4.10 Ninth analysis simulation parameters ... 96

Table 4.11 Tenth analysis simulation parameters ... 99

Table 5.1 Radar Specifications ... 108

Table 5.2 First scenario, system physical specifications ... 116

Table 5.3 First scenario results ... 118

Table 5.4 Second scenario, system physical specifications ... 121

Table 5.5 Second scenario results ... 123

Table 5.6 Third scenario, system physical specifications ... 131

Table 5.7 Third scenario results ... 133

Table 6.1 Pulse FSR simulation parameters ... 147

Table 6.2 Pulse FSR simulation parameters multiple baseline ... 149

Table 6.3 Simulation parameters for target detection ... 156

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Abbreviations

BR: Bistatic Radar ... 20

CW: Continuous Wave ... 35

DRC: Doppler Receiver Channel ... 108

FS: Forword Scatter ... 20

FSCS: Forward Scatter Cross Section ... 32

FSR: Forward Scatter Radar ... 20

PDF: Probability Distribution Function ... 25

PSD: Power Spectral Density ... 51

PTD: Physical Theory of Diffraction ... 44

RCS: Radar Cross Section ... 32

RF: Radio Frequency ... 108

SCR: Signal to Clutter Ratio ... 24

TRP: Two Ray Path ... 36

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Chapter 1 Introduction

Background

Radar is an acronym for Radio Detection and Ranging, and it is clear that its main goal is to detect targets and to measure their range. Modern Radar systems have advanced in functions as tracking, automatic target classification, kinematic parameters estimation and imaging.

Radar is basically an electromagnetic system which consists of a transmitter and a receiver and related antennas, plus a signal processor. Based on the transmitter and receiver topology we can identify different types of Radar systems. When the transmitter and the receiver share a common antenna we talk about Monostatic Radar [1], as shown in Figure 1.1 (a). This is the most common type of Radar.

Otherwise, when the receiver and the transmitter are separately located we have BR as shown in Figure 1.1 (b). If the system has a single transmitter and few receivers separated in space we talk about Multistatic Radar [2], while if the system has a variable number of transmitters and receivers we talk about Multisite Radar [3]. In both Multistatic Radar and Multisite Radar all the collected data from different sensors are jointly processed.

A Bistatic Radar (BR) is characterized by the angle formed between the transmitter and the receiver, the Bistatic angle β. When the Bistatic angle is close to 180° we are in Forward Scatter (FS) configuration, as shown in Figure 1.1 (c). BR and Forward Scatter Radar (FSR) have different scattering mechanism. Unlike BR, to guarantee the FSR operation the presence of the leakage signal it is necessary, which is the direct signal from the transmitter to the receiver.

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In a conventional BS Radar, the leakage signal is often present but it is not significant as in FS [4]. It is typically unwanted and several techniques are used to suppress it, such as: physical shielding, Doppler processing, high gain antennas, side lobe cancellation, adaptive beamforming and adaptive filtering [5].

(a) (b)

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Figure 1.1 Radar systems (a) Monostatic Radar, (b) Bistatic Radar (c) Forward Scatter Radar

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In 1908, Mie reported for first the time the electromagnetic wave scattering from a target in FS region [6]. Ufimtsev clarified the physical phenomenon at the base of this in the second half of 1900 with the introduction of the Physical Theory of Diffraction [7], that was introduced for the study of diffraction related to objects with larger or comparable size with respect to the impinging wavelength. When an opaque object, with larger or comparable size with respect to wavelength is illuminated by an electromagnetic wave directly beyond the object a shadow region is determined. In this zone, there is a very small electromagnetic field because the incident field is eliminated from the field generated by the currents induced on the object. This field, defined as shadow radiation, is the physical phenomenon at the base of the Forward Scatter. Shadow radiation is the component of the scattered field in the shadow region, which does not depend on the shape of the body [8]. As discussed in [9] it is determined by the shadow contour of the illuminated object shown in Figure 1.2.

In [10], Ufimtsev demonstrated this result for black bodies, the well know shadow contour theorem, which more recently in [11] it has been demonstrated also for targets made by perfect electric conductor. Here, the gap between the Babinet principle, which states that the diffraction pattern from an opaque body is equal to that from a hole of the same size and shape except for the overall forward beam intensity, and the physical optics approximation has been exceeded. In [12] for a 2D problem in far field conditions it is provided that the forward contribution is strictly related to the scattering field obtained through the Babinet principle. An extension of this approach in near field conditions has been proposed in [13].

The first comprehensive study for the prediction of the performance of FSR that involves electromagnetic phenomena is provided in [14]. Two classes of objects with the same shadow contour have been evaluated in near field and far field conditions. The scattered field can be obtained by classical modal solutions for few relatively simple cases. In [15] a comparisons of methods that can be used for calculations of FS.

According to [16] the Forward Scatter is the shadow radiation component that does not depend on the whole shape of the scattering object and onits electromagnetic

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properties. It is completely determined by the size and the geometry of the shadow contour. This result defines the major characteristic of FSR, the robustness to a stealth target’s shape and coating.

The interest in FSR grew with the Cold War and the necessity to develop Radars capable of detecting stealth aircraft [17].

In FSR systems all the conventional functions of Radar can be accomplished [18], [19], such as target detection [20], kinematic parameters estimation [21], automatic target classification [22] and imaging [23]. In [24] experimental data and models for maritime Forward Scatter Radar are presented, with particular attention about sea at very low grazing angles, when there is an intermittent loss of signal in case of high sea states, because direct and reflected rays are shown by the sea surface [25]. Techniques and signal processing developed for ground application systems cannot be used for maritime application due to the different propagation modes of electromagnetic waves.

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Motivation

The aim of this work is to develop a model of Forward Scatter sea clutter at very small grazing angle. Using a geometrical approach a sea clutter map has provided. The map shows clutter effects in the each area of the illuminated surface and it could be a useful instrument for the study and the development of FSR maritime systems. In particular is provided that the design of waveform Ultra Wide Band pulse can result in increase of Signal to Clutter Ratio (SCR).

There is a specific problem of target detections against dynamic sea clutter in maritime FSR due to some inherent limitations as the absence of range resolution in CW FSR [19] and a very narrow target detection corridor [26]. Moreover, other issues appear at low grazing angle where the effect of waves shields part of the sea surface and changes the clutter area.

An UWB FSR system for the detection of small marine targets with low Radar reflectivity such as jet-ski, inflatable boats, was presented in [27]. A rough estimation of signal to clutter ratio was made in [28] and in [29] a target cross section estimation has been made. Target visibility estimation in a buoy mounted maritime FSR has been proposed in [30] and target observability improvement in multi-static solution has been investigated in [31]. In the last two studies, a germinal model based on wave spectral formulation has been used to carry out sea surfaces for higher sea states.

A necessary step to examine fully a maritime FSR system is to provide a sea clutter model at very small grazing angle. There is a lack of study about signal propagation model above the sea surface, in Figure 1.3 but some experimental measurements have been made [25]. This study lays the foundations of the thesis work.

Clutter is a significant factor limiting the performance of any Doppler Radar system as it masks the useful target signal and, therefore complicates target detection. To determine the characteristics of the clutter is necessary in order to differentiate the target from the clutter signal. Usually, this is achieved by performing measurements of clutter returns to get the clutter signal pattern and by developing a model based on characteristics of the measured clutter signal. Due to the uncertainty of the environment, the probabilistic

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approach is more diffuse, several methods to model clutter signal use Probability Distribution Function (PDF).

Figure 1.3 Maritime FSR at small grazing angle

A correct model is one that is validated through an accurate match with real data. Many distributions have been proposed for describing the statistics of the clutter for various environments [32]. Depending on the Radar applications, sea clutter properties vary quite widely. Usually the clutter is described through its spatial distribution and its magnitude, which is proportional to the illuminated area.

The clutter issue becomes more critical in the case of FSR because this kind of Radar does not have range resolution [19] and clutter power is collected from the whole surface illuminated by the Radar antennas unlike for BR. In literature there are many works that define clutter characteristics and close formula in conventional Monostatic Radar while is not the same for Bistatic Radar. Where seen a more complex geometry is difficult to obtain an accurate Bistatic clutter model. These are often approximations of Monostatic models [33] which are described in terms of the Radar cross section[34]. An overview about the work in Bistatic sea clutter is presented in [35, 36].

Between 1996 and 1977 were published first results from maritime experiments with C-band and X-band Bistatic Radar, by Pidgeon [37] and GEC Electronics [38]. These

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results provoked big interest in the scientific community and they have been discussed in many work [34, 39, 40].

In [41] Ewell and Zehner performed low grazing angle sea clutter measurements at X-band using pulsed land based Bistatic Radar. They showed that the amplitude distribution of both the Monostatic and Bistatic sea clutter were close to the lognormal distribution and Monostatic clutter amplitude was higher than the Bistatic one.

In [42] low grazing Bistatic sea clutter backscatter experiments with X-band CW land based are presented. Measurements were performed over a variety of the receiver angles. They showed that the smaller of the transmitter and the receiver grazing angle tend to prevail the resulting normalized Radar cross section.

In [43] Yates performed experiments with simultaneous Monostatic and Bistatic synthetic aperture Radar and showed that results was reasonable agreement with the compound K-distribution model.

In [36] Griffiths examined the possibility of using models developed for Monostatic sea clutter and the compound K-distribution for amplitude statistics.

In [44] continuation of Griffiths work is presented a comparison between measurement and simulation of Monostatic and Bistatic sea clutter.

Monostatic and Bistatic are backscattering Radars where the received signal is the sum of target reflections. They have different parameters of electromagnetic scattering but for both the electromagnetic scattering from the sea clutter cell area is reflected towards the receiver. Unlike the FSR where the received signal is shadowing from the sea clutter surface in direction the receiver.

Models defined for backscattering Radars cannot be applied for FSR seen the different characteristics and scattering mechanism. Rregarding FSR sea clutter model the literature has some gaps.

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Some studies about FSR ground clutter and creation mechanism have been presented in [45-47].

Computer simulation and analytical approaches of the time-spatial scattering processes have been used for estimation of radio propagation characteristics over a sea surface [48-53]. A great number of papers present the estimate of received power reduction, thus they focus on average characteristics as average specular reflection coefficient and average power scattered [48, 51, 54]. In [54, 55] some discussions about the suitability of statistics of FS coherent reflection, presented from Amet [56] and Miller-Brown-Vegh [57] is given.

Sea clutter modelling in high grazing low resolution Radars has been performed since the early ages of FSR. Simple models such as Gaussian model and Kirchoff approximation have been used [58].

As mentioned in [30] and [31] two models based on wave spectral formulation has been used to carry out sea surfaces for higher sea states. Both models are based upon the idea that the sea surface is the sum of many sinusoids of certain amplitudes, directions and phases. The sum is performed by the inverse fast Fourier transform [59] and the surface elevation is considered a Gaussian random process [60]. In [30] Pierson-Moskowitz [61] wave spectrum has been chosen for the simulations while in [31] JONSWAP spectra [62]. There is rather limited number of researches on experimental observation of FSR at low grazing angles. In [49] the results of different propagation experiments had in San Francisco across the Golden Gate. Sea wave spectral analysis in X-band for different grazing angle was estimated. In [63] several of low grazing angle Radar measurements were conducted over a pool where waves were artificially produced. The experimental study worked in X-band and the roughened water simulated a surface at sea states 0, 3, and 5. In the method, the wave height is 1 / 10th scaled and there are no wind effects. It showed that increasing sea state the dominant scattering mechanisms change. In chapter 4 details of scattering mechanisms will be illustrated.

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In [55] is presented a direct numerical simulations of near zero grazing angle Forward Scatter. The study has been performed for 1GHz shipboard communication system. Spectral and statistical properties of clutter were discussed and they suggest a useful explanation of expected coherent and incoherent scattering mechanism. Coherent and incoherent power estimations at various angles have been valuated.

Analysis of spectral and statistical properties about sea clutter data at very low grazing angle are presented in [25]. FS clutter data has been recorded at frequencies of 7.5GHz and 24GHz . These results will be used to validate the sea clutter model presented in the thesis. Many details will be given in the Chapter 4. The original contributions in this research thesis are:

 To development a light simulation model for Forward Scatter Radar sea clutter  To made a clutter mapping by simulating the scatter return from a rotating

ground target

 To provide signal model for rotating ground target in Forward Scatter Radar  To demonstrate the effectiveness of the proposed model on simulated and real

data

 To show that design of UWB pulse can result in increased SCR.

The following papers have been produced during the research activities:

 Porfido, M. B., De Luca, A., Martorella, M., Gashinova, M., & Cherniakov, M. (2017, June). Simulation method of Forward Scatter Radar sea clutter based on experimental data. In Radar Symposium (IRS), 2017 18th International (pp. 1-9). IEEE.

 Porfido, M. B., Martorella, M., Gashinova, M., & Cherniakov, M. (2018). Sea Clutter Power Reduction in Pulse Forward Scatter Radar. In Radar Symposium (IRS), 2018 19th International. IEEE.

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Thesis structure

This thesis is organized as follows: Chapter 2

The chapter focuses on FSR system, his peculiarities and capabilities. It provides the reader details about FSR geometry, principles and basic equations, emphasizing the important aspects that the reader needs to know and understand. The equation of FSR is the same as for Bistatic Radar but is no longer valid in the case of ground-based target, where the Two Ray Path propagation model well describes the wave propagation, which considers direct signal and the ground reflections signal. The direct signal is essential in the target signature formation. The latter is formed via the shadowing of the direct signal by the target’s body, its formulation is given and the knowledge of the Forward Scatter Cross Section is necessary. It contains the moving target silhouette information at each time and analytical solutions are only available for few convex shapes. About target with complex shape, the Forward Scatter Cross Section could be rough estimated using an equivalent rectangular shape. Finally, the sea clutter issue in FSR is discussed, in particular spectral and statistical properties about sea clutter at near zero grazing angle are given.

Chapter 3

The core of this chapter is the definition of sea clutter model. It starts with an overview of water waves observed in the ocean and background knowledge about sea waves models. A description of sea surface and of mechanical movement of the point of sea wave is given, with the mathematical description of a specific class. It is shown as a rotating fan can be used to approximate a dynamic model of progressive sea waves. The physical model and the signal model used in the simulation technique are provided and the choice of parameters is justified. Finally, sea clutter characteristics such as power spectral density and clutter signal distribution are estimated with evaluation of best fit Probability Density Function by BIC.

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This Chapter and the Chapter 3 are the thesis core. It focuses on estimation of parameters affecting mapped clutter. The grid model is investigated and the grid cell dimensions are defined, considering that they depend on the wavelength, the baseline and blade length. Furthermore, they are investigated influences of the baseline, the fan tilt angle, and the antennas and fan heights.

Chapter 5

The Chapter is dedicated to confirmation of clutter mapping model by measurements in specified location. Test experimental equipment and methodology of experiment are described. At the end of chapter, simulation and experimental results are discussed.

Chapter 6

In this Chapter, the application of the proposed sea clutter model is discussed and detection aspects have been analysed for UWB FSR.

Chapter 7

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Chapter 2 Forward Scatter Radar

Introduction

In this chapter are discussed peculiarities and capabilities of FSR and details about geometry, principles and basic equations are given. The sea clutter issue is introduced and in particular, spectral and statistical properties about sea clutter at near zero grazing angle are given.

In FSR systems, the transmitter and receiver antennas are facing each other and the FS effect is observable within a narrow area. Unlike traditional backscatter Radar systems, where the received signal is the sum of target reflections, in FSR it is formed via the shadowing of the direct signal by the target’s body.

The key feature of the Forward Scatter effect for Radar applications is its fundamental independence on the radio absorbent coating of a target. It is an efficient counter-stealth system, independences on target’s material or shape, but only on it contour [64].

The basic advantage of the FSR is the essential increase in the power budget in the directions close to a given baseline, it provide larger target Radar Cross-Section (RCS) in forward direction compared to that backscatter when it operates in optical scattering regime [29, 65]. RCS for bistatic angle equal to 180° is provided in (2.1) and it is defined as Forward Scatter Cross Section (FSCS):

2 4 FSMax A     (2.1)

with A the physical target area and  the wavelength. Optical region is region, irrelevant to the target nature, is where RCS enhancement is always observed in the FS main lobe.

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Considering D the maximum target dimension and  the wavelength, three scattering regions are defined. The Rayleigh region where D/   the Mie region where 1

/ 1

D   and the optical region where / D   . FS main lobe is equivalent to the 1 main lobe of an antenna with an aperture that corresponds to target silhouette. Its width in radiant is in (2.2). FS K D    (2.2)

where K is a factor between 1 and 4, which depends on the target shape and the reference level of the FS main lobe [65]. As shown in Figure 2.1 a system is referred to as FSR if

2 FS

 _{  }_{  }

, the main lobe points to the receiver.

Figure 2.1 Generic BR topology

Another advantage of FSR is reduction in fluctuations of Forward Scattered signal. Signal fluctuation is noticeable distortions produced by the phase interference of reflections from more scatters, which worsen the Radar’s characteristics of target

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detection and tracking. When the size of a target exceeds the wavelength of radiation, also a small target angle variation gives rise to sharp fluctuations of signal. In the FSR this effect is essentially reduced [66] because in it the magnitude and phase of the signal scattered by a target is defined by the shadow contour which insignificantly varies even with appreciable changes in the target aspect angle. As result, the maximum coherent analysis time in FSR may be equal to the target visibility time. There is an excellent frequency resolution provided in equation (2.3) with v_tgtarget speed.

0 2 FS tg R Dv     (2.3)

It is accurate for many practical scenarios to assume that target trajectory is linear and speed is constant, because the FS effect is observed within narrow spatial angles from the baseline.

FSR system has ability to measure very low Doppler frequencies, in [4] is shown it is capable of measuring frequencies lower than 1Hz .This is because the system to produce the Doppler output uses the direct signal as a pseudo local oscillator to mix with the received target. Self mixing converts any transmitter noise in direct current and removes any modulation of the transmitting signal than a universal signal processing algorithms can be used.

FSR has also inherent drawbacks and limitations [24, 67] the main are :

 The operational area is restricted to a relatively narrow spatial viewing angle along the transmitter-receiver baseline, the FRCS will not be observed if the target does not pass near the baseline

 Absence of range resolution [19]. Doppler frequency is zero when the target crosses the baseline due to the Radar loses its ability to measure range. The bistatic Doppler shift caused by target motion as define in [34] is provided in equation (2.4). When  180 the Doppler frequency becomes zero. The FSR Doppler shift will be investigated later in target signature paragraph.

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35 cos cos( / 2) tg d v f     (2.4)

In FSR system there are essential technical problems such as: the presence of very strong direct signal at the receiver input that may be exceed the receiver dynamic range and put it into the saturation mode, problems about synchronization of the transmitter and the receiver separated by a long distance.

In general, about probing signal, there are two main approaches. The first one involves using an impulse signal, while the second one uses a Continuous Wave (CW). The last one is preferred because the use of an impulse probing signal leads to the need for the development and implementation of a transmitter and receiver operating with a very wide band signal. Assume to use an impulse signal for the measurement of the transmitter–target–receiver range sum. It is the difference between delays of the target return and the direct transmitter signal. The target return with respect to the direct transmitter signal measured is small due to the FS effect region being stretched along the baseline. Hence, the signal bandwidth should be sufficiently wide [67].

Wide band Radar is much more complicated in comparison with the case of a CW FSR and it requires much power. The problem of power budget and precise synchronization requirements could be overcome using a quasi-harmonic CW signal and a low/gain at the transmit side, a monopulse antenna is used at the receive side.

Forward Scatter Radar equation

When the transmitter-to-target and target-to receiver distances as well as target’s height are much larger than target dimensions [19] the target can be consider as a point and the FSR equation is the same as for Bistatic Radar [68]:

2 4 R T T R Tx tg tg Rx P P G G  L L     (2.5)

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36

with P the receiver power and_R P the transmitter power, _T G and _T G the transmitter _R

and the receiver antenna gains in the target direction.



is the target RCS,  is the wavelength and L_{Tx tg} and Ltg Rx the transmitting and receiving losses respectively. Where

T

R and R are the distances between the transmitter-to-target and the target-to-receiver. _R

2 4 tg Rx R L R           (2.6) 2 4 Tx tg T L R           (2.7)

The equation (2.5) is no longer valid in the case of ground and sea based target. Where the Two Ray Path (TRP) propagation model well describes the wave propagation [68]. This model will be thoroughly described in the next paragraph.

Two Ray Path propagation model

When transmitting and receiving antennas and target are placed on the ground, the wave reflected from the ground has practically zero grazing angle. Thus, the propagation loss increases as the distance from the transmitter and the receiver increases. The FSR equation will be:

2 4 TRP TRP R T T R Tx tg tg Rx P P G G  L L     (2.8)

Where LTRP_{Tx tg} and LTRPtg Rx are the transmitting and receiving TRP propagation losses respectively. 2 2 4 T tg TRP Tx tg T h h L R   (2.9) 2 2 4 tg R TRP tg Rx R h h L R   (2.10)

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37

They depend on distances to target R and _T R , the transmitting antenna heights _R h , _T

the receiver antenna heightsh and the target height _R h . The equations (2.9) and (2.10) _R

are approximate assuming that the distance between the transmitter and the receiver denoted by BL is more bigger than h and _R h , and the ground is a perfect conductor. _T

As provided in [68] the FSR equation (2.8) comes from the application of the TRP model, which is a well know model used in the analysis of the propagation loss. It considers direct signal and the ground reflections signal.

Considering that to guarantee FSR system operating there are always two signals. The direct signal from the transmitter and the receiver (the leakage signal) and the target signal. Thus, it is necessary to provide two signals description using the TRP model one for the leakage signal and one for the target signal.

TRP propagation model for the leakage signal

In the Figure 2.2 the TRP propagation model for the leakage signal is shown. The transmitted power arrives at the receiver following two paths. A direct path form the transmitter to the receiver denoted by R and a reflected path from the ground denoted ₁

with R . ₂ 2 2 1 ( T R) R  BL  h h (2.11) 2 2 2 ( T R) R  BL  h h (2.12)

The total direct signal u is the sum of the direct wave and the reflected wave. _L

1 2

( ) j j

L

u t U e  U e (2.13)

The direct wave is the first addend of the equation (2.13), where U₁ / 4 R₁ is the free space loss and _ej1_{the associated phase with}

1 2 R1/

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receiving point is proportional to path lengths. The phase at the transmitting antenna is supposed equal to zero.

The reflected wave is the second addend of the (2.13), where U₂  / 4 R₂ is the free space loss and _ej2_{the associated phase with}

2 2 R2/

   , moreover there is the complex ground reflection  (2.14) which change amplitude and phase signal.  depending on ground grazing angle ₂(2.15), wavelength and antennas’ polarization.

2 2 2 2 2 2 sin( ) ( cos( )) sin( ) ( cos( )) g g g g               (2.14) 2 arctan((hT hR) /BL)    (2.15)

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The ground properties are specified with complex relative dielectric permittivity of the ground . _g 0 ( ) 2 g r j f        (2.16)

Where _r is the relative dielectric constant,



is the conductivity and ₀is the dielectric constant. Thus the leakage signal power is:

2

L L

P  u (2.17)

Considering a generalized free space propagation model assuming that the transmitter radiates unit power and the transmitting and receiving antennas are isotropic the propagation loss will be equal to the leakage power:

L

L P (2.18)

Taking BLh h_t, _r and considering a perfect conductive ground the propagation loss reduces to 2 2 4 T R h h L BL

 . It is an approximation and it depends only on the geometry, it becomes frequency dependent in the case of real ground conditions.

TRP propagation model for target signal

In the Figure 2.3 the TRP propagation model for the target signal is shown. The target is seen as an antenna. It receives the transmitting signal from the transmitter and transmits the receiver waves towards the receiver. Due to the TRP propagation model is applied two times, one is considering the couple transmitter and target and the other one is considering the couple target and receiver. The transmitted power arrives at the target following two paths. A direct path form the transmitter to the target denoted by R and a ₅

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40 2 2 2 5 ( x x) ( y y) ( r tg) R  Rx tg  Rx tg  h h (2.19) 2 2 2 6 ( x x) ( y y) ( r tg) R  Rx tg  Rx tg  h h (2.20)

The scattered waves arrive at the receiver following two paths. A direct path form the target to the target denoted by R and a reflected path from the ground denoted with₃ R . ₄

2 2 2 3 ( x x) ( y y) ( t tg) R  Tx tg  Tx tg  h h (2.21) 2 2 2 4 ( x x) ( y y) ( t tg) R  Tx tg  Tx tg  h h (2.22)

Whit Tg[Tg Tg h_x, _y, _tg] the target position and Tx[Tx Tx h_x, _y, _t] and

[ _x, _y, _r]

Rx Rx Rx h the transmitter and receiver locations respectively. The total target signal u_tgis the sum of the direct wave and the reflected wave.

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41 3( ) 4( ) 5( ) 6( ) 3 4 4 5 6 6 2 4 ( ) F ( ) j k ( ) ( ) j t ( ) j t ( ) j t tg u t  U t e t U t e U t e U t e       _   __   _ (2.23)

with_F the target FSCS. The first brackets contain the TRP model for the system target- receiver and the second one the TRP model for the system transmitter-target. As defined in the previous paragraph: U_3,4,5,6 / 4 R_3,4,5,6 are the free-space losses,

3,4,5,6 2 R3,4,5,6/

    are the path phase shifts, ₄and ₆the viewing angles and,  and ₄

6

 the complex ground reflection coefficients.

4 arctan((htg ht) /R4)    (2.24) 6 arctan((htg hr) /R6)    (2.25) 2 4 4 4 ₂ 4 4 *sin( ) ( cos( )) *sin( ) ( cos( )) g g g g               (2.26) 2 6 6 6 ₂ 6 6 *sin( ) ( cos( )) *sin( ) ( cos( )) g g g g               (2.27)

Whit  defined in equation (2.16). _g The target signal power is:

2

tg tg

P  u (2.28)

Considering the equation (2.8) and assuming that the transmitter radiates unit power and the transmitting and receiving antennas are isotropic, the target power is:

2 4 TRP TRP tg Tx tg tg Rx P  L L     (2.29)

Target signature

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As mentioned in FSR system the total received signal s t is formed via the _r( ) shadowing of the direct signal by the target’s body.

( ) ( ) ( )

r L tg

s t u t u t (2.30)

When an observer moving relative to the source of wave is produced a change in wave frequency, this is the Doppler effect. In a Radar system, it is a frequency shift of received wave in comparison to a radiated wave frequency .

The Doppler shift in Bistatic Radar [19] can be described as in (2.4) or as in (2.31).

( ) ( ) ( ) ( ) 2 ( ) sin sin 2 2 T R T R d t t t t v f t              _  _ _ _     (2.31)

Where _Tis the angle between the baseline and the transmitter-target line on the plane xy , _R is the angle between the baseline and the receiver-target line on the plane

xy .v is the target speed and



the angle with the target crosses the baseline.

The Doppler shift as defined for Bistatic Radar is not applicable in FSR, than from [69] the Doppler phase shift of the moving target can be described as:

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43 ( ( ) ( ) ) 2 T R d R t R t BL t        (2.32)

whit R t and _T( ) R t the target distance from the transmitter and the receiver _R( ) respectively. The FSR Doppler shift mechanism is shown in Figure 2.5. Following [70] we can see the equation (2.30) as:

0 0 ( ( ) ) ( ) ( ) j t L ( ) j t ttg r L tg s t U e   U t e   (2.33) Where U is the leakege signal magnitude, _L U_tgis the target signal magnitude, ₀ is the Radar carrer frequency and _Land  are the leakege and target phases. The target _tg magnitude and phase depend on the time. Using the equation (2.32) we can write:

2 ( ) ( ( ) ( ) ) tg t dt R tT R tR BL          (2.34)

Usually the leakege signal magnitude is around 40dB greater than the target signal magnitude [68] thus the equation (2.33) can be expressed as:





0 0 ( ( ) ) ( ) ( ) ( ) ( ) 1 1 ( ) tg L L L j t tg j t j t r L L L U t e s t U e U e m t U             _  _      (2.35)

Whit m t ( ) 1 is the modulation index. We can see a small modulation created by the moving target. In the Figure 2.5 this mechanism is shown. When the target is on the baseline the path difference from the leakage signal and the target signal is null thus U_r

the total receiver magnitude is U_r U_LU_tg.When the target moves the path difference change. With a path difference equal to π the total receiver magnitude becomes

r L tg U U U .

Considering (2.18) and (2.29) the receiver magnitudes can be expressed as

L

U  L and U_tg( )t 4₂

 

t LTRP( )t _{Tx tg}LTRP( )t _{tg Rx}

  

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44

In the description of the target signature, the last element that we need to consider is the RCS 

 

t , which we refer, we dedicate the next paragraph.

Forward Scatter Cross Section

In FSR analytical solutions for the RCS or better FSCS are only available for few convex shapes. These solutions obtained with Physical Theory of Diffraction (PTD) regard optical and sub-optical scattering regions [22, 71]. Thus for target FSCS estimation approximated models [34, 71, 72] or 3D EM simulation methods [29] are used.

In [73] a rough classification based on FSCS comparison with the database of known targets. The FSCS contains the moving target silhouette information at each time.

The FSCS lobe peak intensity is directly proportional to the squared of the frequency and it will be greater than backscattering lobe in some point. This reflects change of the scattering mechanism from Rayleigh, Mie and to optical scattering [29].

As described in [69] the FSCS about a target with complex shape could be rough estimated using an equivalent rectangular shape. According to Babinet’s [74] principle

Figure 2.5 FSR Doppler shift mechanism

π 2π 3π

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and shadow contour theorem [16], the shadow radiation in the optical case is completely determined by the size and geometry of the shadow contour. Thus scattering on the target with the rectangular cross-section is equivalent to the radiation by a rectangular aperture antenna, as shown in Figure 2.6.

The FSCS for the rectangular aperture is:

2 2

sin(

sin )

sin(

sin )

( , ) 4

sin

eff eff eff fs eff eff

l

h

A

l

h









  



_



_

_





 





 





 







 





 





 



(2.36)

where A_effis the rectangular aperture area l_eff the rectangular aperture length and eff

h the rectangular aperture height of target all viewed from the Rx.

Forward Scatter Sea clutter

The sea clutter is the scattered signal from the sea surface, which Radars operating in maritime conditions detect. It is unwanted signal and since the development of Radar system, it has produced problems to Radar expert.

Figure 2.6 Rectangular aperture z

x y

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The sea clutter properties vary quite widely for different Radar applications. The continually time-changing sea surface makes the modelling of sea return extremely complex and a relationship between sea echo measurements and environmental factors is not fully understood.

In [39] are presented some basic definitions which describe the sea surface, as wind waves, gravity waves and capillary waves. Wind waves are produced from the wind action over the sea surface. Gravity waves are bigger than 5cm and they speed of propagation is mainly controlled by the gravity. Capillary waves are smaller than 2.5 and they speed of propagation is mainly controlled by the liquid surface tension. A wave height standard estimate is used to describe the sea state, the Douglas Sea State scale [75]. It describes the sea surface roughness with a degree, a number between 0 and 9, as shown in Table 2.1. In the case of FSR due to the absence of range resolution, the clutter issue becomes more critical. As mentioned in Chapter 1 scattering signal over sea surface has coherent and incoherent components. In [24] FS sea clutter is described as time varying modulation of the average coherent power due to the incoherent component.

Next paragraphs provide the main scattering mechanisms above the sea surface. A particular focus is about FSR sea clutter at near zero grazing angles where the effect of the shadowing by dominant sea waves is an issue. The spectral and statistical properties of sea clutter at near zero grazing angles are shown.

Table 2.1 Douglas Sea State scale

Degree Height (m) Description

0 no wave Calm (Glassy)

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47 2 0.10–0.50 Smooth 3 0.50–1.25 Slight 4 1.25–2.50 Moderate 5 2.50–4.00 Rough 6 4.00–6.00 Very rough 7 6.00–9.00 High 8 9.00–14.00 Very high 9 14.00+ Phenomenal

Forward Scattering above the sea surface

In FSR maritime application is required a particular attention on the scattering conditions. As published in [25] there are three well defined scattering mechanisms above sea surface, then three kinds of components can be distinguished:

 Coherent scattering component, it is the specular scattering comes from the illuminated smooth surface when sea is relatively calm. The coherent component depends mainly on the geometry of FS Radar link. It is expressed by:

COH DIR SP CE

E E E (2.37)

Where E_DIF is the line of sigh direct wave and E_SPE is the specular reflected wave, it is shown in the Figure 2.7.

 Diffuse scattering componentE_DIF, it is the reflection occurs in all direction in the case of higher sea state but with the line is sight sill present. It is shown in the Figure 2.8. It is the sum of the diffuse scattered signal from a large number N of independent scattersE . It is expressed by: _n

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48 n DIF N n E 



E (2.38)

It is the field incoherent componentE_INC.

 Shadow component with intermittent loss of signal, which occurs in the case of very high sea state. The sea surface shadows direct and reflected electromagnetic signal, due to there is an intermittent loss of signal.

The coherent scattering mechanism is dominant when sea is calm. With the presence of ripples on the sea surface, the diffuse scattering mechanism appears and the amount of coherent signal energy decreases. Above sea state 3 of the Douglas scale, for low grazing angle the coherent scattering signal is dominant.

The diffuse scattering mechanism above the sea surface is dominant with higher sea state and strong wind. This is mostly true in the case of big grazing angle. When the sea states are high, the coherent power is negligible.

With very high sea states, the shadow component is dominant and the loss of signal is a problem in the target detection for all grazing angle.

Following [25] the coherent power P_COH is defined as the mean value of the received signal and the incoherent power P_INCas the mean received signal variance.

( )

COH TOT

P  mean E (2.39)

2

( ( ) )

INC TOT TOT

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Figure 2.7 Coherent scattering component

It has been shown that the expected coherent power Pˆ_COHcan be calculated with TRP.

2 2 4 ˆ t r COH t t r h h P PG G d  (2.41)

In fact, using the TRP definitions the coherent component corresponds to the leakage signal and the incoherent component to the target signal.

Forward Scatter Sea clutter at near zero grazing angles

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As mentioned the EM reflection by the sea surface at low grazing angles Radar introduce many issues, for low grazing angle we consider angles between 0.1 and 0.8 on the sea surface. In particular sea waves shields some parts of the surface changing the clutter area [29]. There is rather limited number of researches on experimental observation of FSR at low grazing angles [52, 76]. In order to develop FSR system a fundamental understanding of the operating environment is required, for this scope, experimental FS data are essential. Thanks to a huge program of experiment performed in Birmingham University, a comprehensive database of sea clutter measurements at almost zero grazing angles has been established [24]. The database utility is in to understand the clutter generation mechanism and to validate on-going modelling.

In [24] spectrum and statistics analysis of the sea clutter are provided, considering different environmental condition, carrier frequency, signal transmission mode and antenna properties. Clutter data has been recorded at different sites providing a set of environmental condition such as lake water, littoral water and deep water. Over the Radar operational area, the atmospheric effects have been assumed negligible due to the short baselines used.

Regarding Forward Scatter sea clutter has been concluded that:

 The clutter distribution is close to Rayleigh. It is different from traditional backscatter Radar

 The spectrum is independent of the baseline but it depends strongly on path geometry and the sea state. The right sea state is between 1 and 3 on Douglas scale. For high sea state at low grazing angle there are different effects on wave propagation

 The spectrum is independent of the Radar frequency over a range of microwave frequencies within 1GHz and 37.5GHz

 The spectrum is independent of the transmission modes, antenna heights, beamwidths and polarization (vertical and horizontal). Transmission mode used

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are continuous and pulse (100Mhz , 1GHz , 3GHz ). The antennas height considered are 1.31m and 2.05m while the beamwidths are ±6°, ±10°, ±30°;  The clutter Power Spectral Density (PSD) is concentrated below 1Hz spectral

region with a roll off about 35 40dB per decade. It is the maximum invers fort part of Doppler frequency.

Conclusion

In this chapter a survey about FSR system has been presented, peculiarities, capabilities, geometry, principles and basic equations have been provided.

Among basic advantages of FSR there are: larger target RCS than backscatter when operates in optical scattering regime, reduction in fluctuations of Forward Scattered signal, excellent frequency resolution, ability to measure Doppler frequencies below 1Hz .

Main FSR drawbacks and limitations are: restricted operational area and absence of range resolution, moreover the presence of very strong direct signal at the receiver could put it into the saturation mode.

The equation of the Bistatic Radar is not valid in the case of FSR ground-based target where the power budget estimation is based on the TRP. The TRP model in FSR has been introduced and his application, in the moving target signature estimation, has been underlined.

The moving target signature is seen as a modulation of the leakage signal, modulation due to time-varying scattering geometry. When the target is moving the path length from the transmitter-to-target and target-to-receiver rays vary, so the phase of the target signal varying as well. In particular, the moving target signature is described as a Doppler signature of a point-like target modulated according to FSCS. The Doppler signature contains the target trajectory and speed information while the FSCS contains the target silhouette information at each time. Analytical solutions of Forward Scatter Cross

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Section are only available for few convex shapes it could be rough estimated for target with complex shape.

In the last paragraphs, the sea clutter issue in FSR is discussed, in particular spectral and statistical properties about measured sea clutter at near zero grazing angle has been presented. At very low grazing angles, over a range of 0.1 37.5 GHz , with different antenna polarization, in different locations and for sea states between 1 3 of the Douglas scale have been concluded that the clutter distribution is close to Rayleigh, it does not depend on the considered parameters and it is concentrated below the 1Hz spectral region.

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Chapter 3 Sea clutter model

Introduction

In modelling is necessary to have in account that there is a difference between theory and characterization. The theory relates the received signal to the sea surface physical scattering properties, while the characterization provides a sea clutter description in term of statistical model. As mentioned a relationship between sea echo measurements and environmental factors is not fully understood due to the proposed model is based on sea clutter characterization.

For many years now, the industry of computer graphic are dedicated to the realization of sea surface visual models for use in film animation and computer games. The fundamental method used to generate the sea surface model is based on the concept that the sea surface is composed of the sum of many sinusoids, each with a certain amplitude, direction and phase [59].

The chapter provides background knowledge about sea waves models. The description of mechanical movement of the point of sea wave is given, with the mathematical description of some classes. A practical approach based on the characteristics of measured sea clutter is use to generate a signal with the same spectral and statistical properties of sea clutter at very low grazing angles.

Sea surface

Sea state is a general condition on the free space of large water bodies with respect to wind condition. Francis Beaufort, an Irish Royal Navy officer, provided the first sea state classification in 1805. The Beaufort Sea scale is an empirical measure that relates wind speed to sea state [77]. Wind is the primary generator of sea waves but many other

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variables play a role in it. In our study we consider the sea state below 3 of Douglas Sea scale [75]. It links different heights of the waves to different sea states, as shown in Table 2.1.

The sea surface is a superposition of waves with different features originating from different points. A rich body of theory and observation exists about waves behaviour, water waves in particular in [78, 79].

In [80] an overview of water waves observed in the ocean which can be categorized based on their formation and behaviour. Different types of waves are:

 Breaking waves: formed when the wave collapses on top of itself

 Deep water waves: made up of a number of waves of different lengths superimposed on each other

 Destructive waves: high waves of short wavelength with powerful backwash  Inshore waves: the length is less than the depth of the water they enter

 Internal waves: formed between two water masses of different density  Kelvin waves: formed due to lack of winds in the Pacific Ocean

 Progressive waves: have a steady speed can be capillary waves (formed when wind creates pressure over the surface) or orbital progressive waves (formed at the boundary of two liquids with different density)

 Refracted waves: travel in shallow water when they approach the shore

 Shallow water waves : formed due to the earthquakes or gravitational pull of the sun and the moon on the ocean

 Swell waves: formed from the center of a storm.

Generally, a wave transfers a disturbance from one part of a material to another. The disturbance is propagated through the material without any substantial overall motion of the material itself. The motion of the wave must be distinguished from the motion of the water through which the wave is propagating. The wave moves past a given point, the water at that point moves in an approximately circular orbit as shown in Figure 3.1. The

A Forward Scatter Radar Sea Clutter Model Based on Experimental Data

UNIVERSITY OF PISA

DOCTORAL THESIS