Echolocation Methods

Roman Salamon & Henryk Lasota II 2016 – VI 2016

General information [2]

authors: Roman Salamon, Henryk Lasota

translated, modiﬁed, LYXed, and taught by:

Henryk Lasota, Ph.D. (GUT), D.Sc. (UdV), M.Sc.E.E. (GUT) [email protected] room 748 (EA), phone: (58 347) 17 17 & 11 64

consultations: Wednesday 14:00–16:00 (& other terms by appointment)

course slides & script: http://Echolocation Methods – Materials

Supplementary information [3]

Time dimension 30 hours, 2 lecture hours a week

Acceptance requirements Written test with 60% passing threshold

References (bibliography) M. Skolnik (ed.): Radar Handbook, McGraw-Hill, New York 1970, 1998, 2008 (with contributions by 30 world experts). M. Skolnik: Introduction to Radar Systems, McGraw-Hill, New York 1962, 1980, 2001. R. Salamon: Systemy hydrolokacyjne (Sonar Systems), Wyd. GTN, Gdańsk 2006. D. L. Mensa: High resolution radar cross-section imaging, Artech House, Boston 1981, 1984, 1990, 1991. R. Urick: Principles of Underwater Sound, McGraw-Hill, New York 1967, 1975, 1996. D. Martinez et al., High Performance Embedded Computing Handbook: A System Perspective, CRC Press, Boca Raton 2008

1 R. Salamon & H. Lasota 2016-06-08 Echolocation systems I

Course content [4]

For the purpose of the exam, the content of the course is developed in four groups:

• A – I. Echolocation systems,

– II, Radars and sonars, – III. Echolocation signals, Detection

• B – IV, Antenna directivity,

– V. Practical theory of apertures and arrays, – VI. Multibeam system techniques.

• C – VII, Special purpose echolocation,

– VIII. Echolocation system design

• D – IX. MES Dept.- proper sonars,

– X. HPEC: A systems perspective

2 R. Salamon & H. Lasota 2016-06-08 Echolocation systems I

Part I Echolocation systems

1 Generalities

Course philosophy – STEM [5]

• STEM – mix: Remote observation and localization What, and why, do we see and hear? – Science Physical basis, technical parameters, exploitation characteristics (S -> E). – Technology Waves, their spreading - theoretical model of prop- – Engineering agation (M), practical models (S), medium inho- – Maths mogeneities, inhomogeneities in the medium.

• (+Art -> STEAM ) Department of Marine Electronics Systems - sonars for the Polish Navy, echosounders for Meteorology and Water Management Authority etc. System con- Antennas (antennae) - key elements of spatial sys- ception, design (S + E + M), element design and tems (STEM manifests itself in the implementa- development (E + T), system implementation and tion process: The antenna design is an engineering tests (S + E) marine tests and exploitation in real art (E), calculations (M) are founded on the phys- sea conditions (STEM – TRL 7 / TRL 9). ical theory of diﬀraction (S), construction is tech- nologically complex (T).

Course philosophy – Systems, waves, sygnals [6]

Education =6 self-learning Electromagnetic waves (radio waves, microwaves, Lecture = reflection of an expert - experienced en- coherent light). gineer (E+T), - qualified scientist (S + M), offered Acoustic waves (sonars). to younger colleagues („greenhorns”) . Seismic waves (geophysical exploration).

Acquisition of information from the environment Dedicated signal processing Radars, sonars microprocessor systems – active detection, beamforming – passive Dedicated exposition of the space and object infor- Sensor networks mation Passive acquisition systems Synchronized, asynchronous

Course philosophy – Space [7]

Remote interaction with objects in the environmental space: command systems, moving objects automatic control. Objects: land vehicles, aircrafts (ﬂying units), ﬂoating on the surface, under water: car, plane, ship, submarine, autonomous vehicle (drone, UAV, USV, UUV)

Information – the space itself meteorological phenomena - atmosphere underwater phenomena - hydrosphere (navigation obstacles, icebergs) tomography – sequential radio- or ultrasono-graphy: biological objects, technological elements, hydrosphere

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1.1 General working principle General working principle of echolocation system [8]

Working (operation/functioning) principle The transmitter generates a powerful electric pulse. The transmit antenna radiates it into the sur- rounding space as a sounding wave – electromagnetic (radar, lidar) or acoustic (sonar, sodar) probe. The pulse wave travels through the relevant physical space (radio or sound channel) and hits a distant object (target). The reﬂected wave reaches (back) the receiving antenna and the electric echo signal is detected (or not) in the receiver system. The receiver detects the echo signal and measures the time τ elapsed since the moment of sending it until its reception. When the propagation speed c of the signal wave is known, the distance R of the target from the echolocation system is calculated as: cτ τ = 2R/c, meaning: R = 2

2 Basic tasks of echolocation systems

Basic tasks of echolocation systems [9]

Possible tasks 1. Detection of the object/target in the observed space

2. Determination of the target position – localisation

3. Estimation of selected parameters of the target

4. Target classiﬁcation

5. Target identiﬁcation

2.1 Target detection and localisation Target detection and localisation [10]

1. Target detection is to determine whether at a given time receiver receives the echo signal or a noise/interference. The noise occurs in the channel (space, air, water environment) and add/supperpose in the receiver to the echo signal. The determination of the presence of the useful/known signal on the noise background is called detection.

2. Target localisation relative to the echolocation system is mainly performed by measuring its distance and bearing. The latter means the angle between the direction in which the target is detected, and the reference axis. 4 R. Salamon & H. Lasota 2016-06-08 Echolocation systems I

2.2 Target bearing Target bearing [11]

2a. Target bearing can be, for example, an azimuth angle (relative to north) and elevation (relative to the earth surface). Reference system can be, eg, the plane, the ship or any device at which the echolocation system is installed.

2b. Directivity The bearing/direction measurement is performed by making use of directional properties of transmitting and receiving antennae/antennas of the echolocation system.

2.3 Estimation, classification, identification Estimation, classification, identification [12]

3. Parameter estimation consists in determining the size, velocity, direction of movement, etc. Information about these parameters are sometimes included in the echo signal and can be extracted from it.

4. Target classiﬁcation means the recognition in a wide (worse) or narrow (better) class of objects. For example, the detected target is a vessel (wide class) or the detected object is a boat (narrow class).

5. Target identification means an assignment to a very narrow class of objects such as a Boeing 737 or more precisely the specific aircraft (eg. “friend or foe” or “flight number...”). The course will deal with only the first three of the above mentioned tasks (excluding classification and identification)

2.4 General classiﬁcation of echolocation systems General classiﬁcation of echolocation systems [13]

Four kinds of echolocation systems Due to the physical type of applied signal waves, echolocation systems are divided (in historical order) into:

• radiolocation systems that use electromagnetic waves in air (radars),

• underwater acoustic systems (hydroacoustic systems) using acoustic waves in water reservoirs (sonars),

• aerolocation systems using acoustic waves in air (sodars), 5 R. Salamon & H. Lasota 2016-06-08 Echolocation systems I

• geolocation systems using mechanical waves on the Earth surface and underwater,

• laser systems using coherent optical waves in air (lidars).

The choice of speciﬁc waves is mainly due to the size of their absorption/attenuation in the propagation medium. Generally, these waves are selected, that are the least attenuated in the environment of system operation.

2.5 Semantics Semantics [14]

Two classes of “detection, navigation, and ranging”

• radar (RAdio Detection And Ranging),

• sonar (SOund Navigation And Ranging),

• sodar (SOund Detection And Ranging),

• lidar (LIght Detection And Ranging).

Terminology (wording, nomenclature) – echolocation semantics

• transmitter, • transmitting power/pulse energy,

• channel/physical space, • attenuation,

• object/target, • noise/interference,

• receiver, • reﬂection/scattering,

• sounding signal/sounding wave. • detection probability,

• false alarm rate.

General scheme of communication system [15]

General scheme of echolocation system [16]

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Sonar transmitter - basic functionalities [17]

Sonar receiver - basic functionalities [18]

Echolocation devices in every day use [19]

Ultrasound parking sensor Working principle: Determining the distance from the obstacle by measuring the time between the moment of transmitting pulse and receiving the echo signal. Price: 4 sensors + measurer 100 zl.

Ultrasonic rangeﬁnder intellimeasure Working principle: as abowe Measuring accuracy: 0.5% Range 12 m. Price 136 zl.

Echolocation devices in every day use [20]

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Laser rangeﬁnder Leica Disto D210 Working principle: as in ultrasound devices, but light impulses Measuring accuracy: 1 mm Range 80 m. Price 350 zl.

One of the MES Dept. sonars - a poster [21]

MG-89DSP, imaging, parameters, scheme [22]

One of the MES Dept. sonars - block scheme [23]

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MCM sonar - MG-89DSP Operating control Transmitter Receiver HPEC system functionalities:

• data streams,

• signal bundles

Transmitter assembly (Zespół nadajnika) [24]

• High voltage power supplies (Zasilacze wysokiego napięcia)

• Blocks of power ampliﬁers (Bloki wzmacniaczy mocy)

• DDS generators, subordinate computers (Generatory DDS, komputery podrzędne)

• Master computer of transmitter control (Komputer nadrzędny sterowania kontroli nadajnika)

Receiver assembly (Zespół odbiornika) [25]

• Compensation and preampliﬁers block (Blok kompensacji i przedwzmacniaczy)

• Transducer compensation circuits (Układy kompensujące przetworników)

• Transmit/receive switches (Przełączniki nadawanie./odbiór)

• Preampliﬁers (Przedwzmacniacze)

• Test receiver (Odbiornik testowy)

• Analog processing block (Blok przetwarzania analogowego)

• Receiver control computer (Komputer sterowania i kontroli odbiornika)

• Test generator (Generator testowy)

• Time variable gain (TVG) (Zasięgowa regulacja wzmocnienia (ZRW))

Operator’s console (Konsola operatora) [26] • Auxiliary display (A, B, messages) (Monitor zobrazowania pomocniczego (A, B, komunikaty))

• Main display (panorama, settings) (Monitor zobrazowania podstawowego (panorama, nastawy))

• Auxiliary display computer (Komputer zobrazowania pomocniczego)

• Control panel (Pulpit operatora)

• Main display computer (Komputer zobrazowania podstawowego)

• Interface with control computers (Interfejs z komputerami sterowania i kontroli)

• Interface with the ship command systems and other systems (Interfejs z systemami dowodzenia okrętu i innymi systemami)

• Interface of the sound velocity distribution meter (Interfejs miernika rozkładu prędkości dźwięku)

• VME bus (Magistrala VME) 9 R. Salamon & H. Lasota 2016-06-08 Echolocation systems I

• Multiplexer, A / D converters, DSPs (Digital Beamforming) (Multiplekser, przetworniki A/C, Procesory DSP (Beamforming cyfrowy))

• Computer control set of the hydraulic system of antenna stabilization and control ASAC (Zespół sterowania i kontroli hydraulicznego systemu stabilizacji i sterowania anteną KSSA)

• Fiber optic cables (Światłowody)

One of the MES Dept. sonars - parameters [27]

3 Acoustic and electromagnetic waves

3.1 Wave phenomenon Wave phenomenon [28]

Wave is a phenomenon that occurs simultaneously in space and time. Its essence is energy transfer in the form of a disturbance, without transport of matter. Wave disturbance is a temporary and local disruption of the state of rest prevailing, otherwise, in adequate physical space called the wave propagation medium. Lack of matter transport, “obvious” in the case of electromagnetic waves, in the case of acoustic waves means motion of matter particles limited to tiny local deviations.

3.2 Mathematical description Mathematical description of wave phenomena [29]

• Electromagnetic wave is strictly vector phenomenon

• Acoustic wave is a phenomenon of mixed scalar-vector character 10 R. Salamon & H. Lasota 2016-06-08 Echolocation systems I

• The mathematical description of both these phenomena in space is typically reduced to scalar information common to both types of waves

• The validity of analysis of wave phenomena in Euclidean space covers:

– the domain of wireless electromagnetics (called electrodynamics) ∗ radio waves, radar signals, light (especially coherent), radio-astronomy signals of any frequency range – the domain of acoustics ∗ in ﬂuids (eg. air, water) and solids (eg. crystals)

The most formally involved is elastic waves mathematics (ie. analysis of ultrasonic transducers being elements that hydroacoustic antennae are made of)

3.3 Electromagnetic wave – dielectrics Electromagnetic wave – dielectrics [30]

• phenomenon of vacuum or material medium polarisation disturbance, which is described by vectors of:

– electric ﬁeld intensity E, in [V/m], and – magnetic ﬁeld intensity H, in [A/m]

• the density of transmitted energy stream (as well as the direction of transportation in the so-called far ﬁeld) is described by Poynting vector P, in [W/m2]:

P = E × H Electromagnetic waves are of shear character (they are subject to polarisation)

3.4 Acoustic wave – ﬂuids Acoustic wave – ﬂuids [31]

• phenomenon of material medium disturbance consisting in deviations from local rest. It means local appearance of elastic volume strain (or density change) and inert motion:

– a measure of strain/density (eﬀect of scalar nature) is sound pressure p, in [Pa = N/m2] – a measure of motion (eﬀect of vector nature) is acoustic velocity v, in [m/s]

• the density of transmitted energy stream (as well as the direction of transportation in the so-called far ﬁeld) is described by acoustic intensity vector I, in [W/m2]:

I = p v Sound waves are of longitudinal character (L – waves)

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Elastic wave - solid-state bodies [32]

• Particle deviation from equilibrium position has in a solid an additional consequence, namely the appearance of stresses. A disturbance is further described by:

– displacement vector d [m], – stress tensor T [Pa] .

• Elastic waves are traversal ones, and are subject to plarization (T – transversal, or S – shear).

• The "transverse" nature of light and other electromagnetic waves, manifested by the ability to po- larization, inspired to look at Earth and in Space for a propagation medium of solid-like properties .

• The concept of "ether" of mechanical properties has been replaced by the ether of electric-and- magnetic properties. The concept of the etherwaves, however, has been eliminated as "scientiﬁcally incorrect" (temporarily!).

Longitudinal waves (P-primary in seismics) [33]

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Transverse (shear) waves (S-secondary in seismics) [34]

Plate waves SH (Love waves) [35]

Shear horizontal waves – particle movement parallel to plate limiting surfaces (SH) - no coupling to the adjacent ﬂuid

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Plate waves (Lamb) - particle motion [36]

Lamb waves - local deformation (strain) [37]

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Surface wave (Rayleigh) [38]

Wave on the “free” boundary of a solid half space (half-inﬁnite “plate”). Applied since ’60-ties in the SAW (surface acoustic wave) signal processing devices (radar- and TV-ﬁlters, delay lines, convolvers, etc.)

Seismic waves (search for natural resources) [39]

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Echograms for P & S waves (gas reservoir) [40]

Cores from boreholes (geological samples) [41]

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Synthetic echoes (30 Hz) [42]

Polar Empress [43]

The unit provided by Gdynia (Poland) shipyard Crist in 2014 to Norwegian recipient – shipbuilding group Kleven, a hull of seismic ship Polar Empress (No. construction NB 369), mostly equipped. Majority of permanently installed functional equipment was mounted in Gdynia.

Seismic ship [44]

• Seismic vessels tow both air sources that release acoustic waves (air guns) inducing seismic waves in bottom sediments, and streamers that have hydrophones (receivers) embedded at a regular interval, up to several kilometers long. The hydrophones receive, simultaneously, both the waves reﬂected from beneath the seabed and GPS data. Towing a number of streamers in parallel enables a 3D survey by gathering stereographic geological data from beneath the seabed.

• Analysis of the received signal allows to specify whether the location is worth even try to carry out exploratory oil wells.

• The wires are wound on a large drum winch, and all the seismic equipment is located on three diﬀerent decks.

http://Mitshubishi Titan-class seismic vessel.

Working principles of seismic vessel [45]

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Underwater acoustic systems (1) [46]

Applications (1) [47]

• 1) General navigation, now also on n very small vessels

– echosounder, 18 R. Salamon & H. Lasota 2016-06-08 Echolocation systems I

– Doppler speed log.

• 2) Fishery

– echosounder (single- or multi-beam), – head sonar with mechanical or electronic beam sweep – system for estimating ﬁsh stocks (information technology - FAO *) – control of the trawl parameters: ∗ opening (distance sensors) ∗ height above the bottom (sonar) ∗ ﬁlling (sonar - "horizonta echosounderl") ∗ ultrasonic communication (data transmission from underwater acoustics devices of the trawl)

*) FAO – Food & Agriculture Organization, R/S “Prof. Siedlecki” – ‘70 of the XX th century

Underwater acoustic systems (2) [48]

Applications (2) [49]

3. Ocean engineering

• local navigation for dynamic positioning of the ship-base

• local navigation of vehicles and robots (ROV, AUV, ...)

• ultrasonic communication (AUV control and data transmission)

4. Military (1)

• detection of submarines / intruders (ASW - AntiSubmarine Warfare) 19 R. Salamon & H. Lasota 2016-06-08 Echolocation systems I

• passive sonar (circular) mounted on:

– surface ship – submarine

ROV – Remote Operating Vehicle; AUV – Autonomous Underwater Vehicle

Underwater acoustic systems (3) [50]

Applications (3) [51]

• 4. Military (2)

– mine search (MCM - Mine CounterMeasure): ∗ multibeam head sonar, ∗ side-looking sonar towed by: ∗ a) surface ship, ∗ b) helicopter ; – local nawigation, – communication with and between submarines.

• 5. Divers equipment (scuba - self-contained breathing apparatus)

– communications, – local navigation, – sonar FM (distance estimation “on ear”) – monopulse sonar (bearing estimation “on eye”) – ultrasound camera (imaging in opaque waters) 20 R. Salamon & H. Lasota 2016-06-08 Echolocation systems I

3.5 Basic scalar equations First-order relations of dynamic physical phenomena [52]

Acoustics – Euler’s relations of ﬂuids

∂ ∂ gp(x, t) = % vp(x, t) = − grad p(x, t), (1) ∂t ∂t motion variation as the effect ⇐ pressure inhomogeneity as a cause. ∂ ∂ sv(x, t) = κ pv(x, t) = − div v(x, t), (2) ∂t ∂t deformation change as the effect ⇐ flow inhomogeneity as a cause.

[53]

Pressure wave equation and Euler’s dynamic relation – set of double-state formulae

 ∂2 1 1 ∂  pQ(x, t) − div grad pQ(x, t) = Q(t)δ(x)  ∂t2 κ% κ ∂t      (3)  1  vQ(x, t) = − grad pQ(x, t)dt % ´

Physical wave equations [54]

Velocity wave equation and Euler’s continuity relation – set of double-state formulae

 ∂2 1 1 ∂  vF(x, t) − grad div vF(x, t) = F (t)δ(x)ˆıF  ∂t2 % % ∂t   κ    (4)  1  pF(x, t) = − div vF(x, t)dt κ ´ Scalar Laplacian ∇2 = div grad

div grad p = ∇2 p Vector Laplacian ∇2 = grad div −curl curl

curl v ≡ 0

Maxwell relations [55]

Electromagnetics – Maxwell’s relations of dielectrics

∂ ∂ BE(x, t) = µ HE(x, t) = − curl E(x, t), (5) ∂t ∂t change of mg. induct. as an eﬀect ⇐ curly el. intensity as a cause. ∂ ∂ DH(x, t) = ε EH(x, t) = + curl H(x, t), (6) ∂t ∂t change of el. induct. as an eﬀect ⇐ curly mg. intensity as a cause. 21 R. Salamon & H. Lasota 2016-06-08 Echolocation systems I

Basic solutions of electromagnetism [56]

 ∂2 1 1 ∂  EP(x, t) + curl curl EP(x, t) = P (t)δ(x) ˆıP  ∂t2 µ ∂t      (7)  1  HP(x, t) = − curl EP(x, t) dt µ ´

[57]

 ∂2 1 1 ∂  HM(x, t) + curl curl HM(x, t) = M(t)δ(x) ˆıM  ∂t2 µ µ ∂t      (8)  1  EM(x, t) = + curl HM(x, t) dt ´ Vector Laplacian ∇2 = grad div −curl curl

div E ≡ 0

−curl curl E = ∇2 E

div H ≡ 0

−curl curl H = ∇2 H

Acoustic waves [58]

An acoustic wave means changes in time and space of local equilibrium states in an elastic medium. Features conditioning propagation of acoustic waves in a medium are: inertia and elasticity. Acoustic waves are described by:

• acoustic pressure [Pa]

• acoustic (particle) velocity [m/s]

• velocity potential [m2/s]

Acoustic waves in liquids and gases (in ﬂuids) are longitudinal (L), and in solids they can also be transverse (T). Acoustic waves propagate at a speed c, much lower than the speed of electromagnetic waves. Acoustic wave velocity in air: c=340 m / s Velocity of sound in water: c=1500 m / s

Basic relations (equations) of acoustics [59]

Continuity equation of elastic matter Equation of state ∂ρ ∂p + div (ρ~v) = 0 ρ – density kg/m3 p = ρ = c2ρ ∂t ∂ρ Euler’s equation Wave equation ∂~v 1 ∂2p = − grad p = c2∇2p ∂t ρ 22 ∂t2 R. Salamon & H. Lasota 2016-06-08 Echolocation systems I

Acoustic characteristic impedance p Zac = = ρc v

Acoustic wave intensity I, in W/m2 equals the ratio of a power P of the wave incident perpendicularly at a surface to its area S: P p2 I = I = = v2c I = pv S ρc

Acoustic wave power, in [W]: P = (pv) dS = I dS ˆS ˆS Scalar wave equation (mathematics)

2 −2 ∂ 2 c Gf(x, t) − ∇ Gf(x, t) = δ(t)δ(x), (9) f ∂t2

Green’s function: time-space fundamental solution in Euclidean space (geometry):

Gf(x, t) = δ(t − r/cf)/(4πr). (10)

Spread celerity in physical space (amorphous ﬂuid):

h i−1/2 cf(x) = κ(x)%(x) . (11)

2 −2 ∂ 2 c Gd(x, t) − ∇ Gd(x, t) = δ(t)δ(x). (12) d ∂t2

Gd(x, t) = δ(t − r/cd)/(4πr). (13)

h i−1/2 cd(x) = (x)µ(x) . (14)

Green’s functions of wave equations (spatial impulse response) [61]

Harmonic point sources, 1-, 2-, 3-dimensional space:

1 −jkr 0 G1 (r, k) = e (r = |x − x |) 2jk

j (2) G2 (r, k) = − H (kr) 4 0

1 −jkr G3 (r, k) = e 4πr Impulse point sources, 1-, 2-, 3-dimensional space:

c 0 r G1 (r, t) = H t − t − 2 c

− 1 c 0 r h 2 0 2 2i 2 G2 (r, t) = H t − t − c (t − t ) − r 2π c

1 0 r G3 (r, t) = δ t − t − 4πr c

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3.6 Similarities of physical ﬁelds and waves Fields and waves – quantities, energy, parameters [62]

3.7 Wave celerities Propagation speed (celerity) [63] electromagnetic waves (vacuum) 9 1 10 As F 4π Vs H 9 c = √ 0 = = µ0 = = c0 = 0.30 · 10 m/s µ 36π Vm m 107 Am m acoustic waves (ﬂuids)

• in water (liquid):

pY 1 1 √ cliq = /ρ κ = /Y c = / κρ

9 3 3 3 YH2O = 2.25 · 10 Pa ρ = 1.0 · 10 kg/m cH2O = 1.5 · 10 m/s • in air (gas):

pγp 5 0 3 cgas = amb/ρgas patm = 1.0 · 10 Pa ρair = 1.2 · 10 kg/m

3 speciﬁc heat ratio: γ = Cp/Cv = 1.4 cair = 0.34 · 10 m/s

• proportions of celerity values: c0 : cH2O : cair = 200000 : 1 : 0.2

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3.8 Spreading geometry Wave geometry [64]

Plane, cylindrical, and spherical waves

+ + − − • plane wave p (x, t) = p (c0t − x) p (x, t) = p (c0t + x)

1 • cylindrical wave p (r, t) = √ f (c0t − r) r

1 • spherical wave p (r, t) = f (c0t − r) r

Communication transmission losses

• absorption loss = attenuation [1/m], [dB/m] h P (r) i P (r) = P0βr 10 log = −α r P0 • spreading loss (so-called free- space “attenuation”) h P (r) i P (r) = P1/r 10 log = −20 log (r/r1) P1 • transmission loss (total) h P (r) i 10 log = −20 log(r/r1) − α · r P1

“Most natural” (?) plane wave [65]

The most spread, almost exclusive description of waves Harmonic waves (sinusoidal, monochromatic)

+ • plane wave p (x, t) = p0 sin / cos (2πf0t − k0x + φ) (two conventions)

2πf0 2π 2π ω0 • wave number k0 = = = = c0 T0c0 λ0 c0

±j(ωt−~k~r+φ) • complex notation p (~r, t) = p0 (~r) e (another two conventions)

4 Waves and motion

4.1 Doppler eﬀect Moving sound source [66]

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If the transmitter and receiver move relatively to each other or at least one of the propagation paths is associated with the reﬂection from a moving object, the Doppler eﬀect can be observed revealing by a change in the carrier frequency or widening of the signal spectrum. In fact, this is the time-scale of waves and signals that changes, being compressed when the object approaches and expanded when it moves away. Doppler shift: v fD = fT − fR ≈ fT cos αr c

http://en.wikipedia.org/wiki/Doppler_eﬀect http://Doppler-Ballot experiment http://The Doppler Eﬀect and Sonic Booms

Musical tones [67] √ 6 Changing the pitch of the tone up, is equivalent to multiplying its frequency in hertz√ by 2 ≈ 1.122462. 12 Changing by a semitone corresponds to the frequency multiplied by a factor 2 ≈ 1.059463. Changing by one octave corresponds to a frequency multiplying or dividing by 2, for example: A1 is 440 Hz, and A2 corresponds to the frequency 880 Hz. Question: If during the 1845 Ballot experiment musicians on the moving train (40 mph) were playing the A1 note (440 Hz) what was the incoming/outcoming pitch?

Moving receiver (subjective eﬀect) [68]

Receiver: vr =6 0, source: vs = 0

Observer moving toward the source observes a subjective eﬀect.

0 1 c λ Fs =6 0, v = 0 fs = = ⇔ T = r T λ c

0 0 c + vr c + vr fr =6 fs fr = = · fs = αr · fs λ c

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0 vr = vr · cos β, vr– radial speed

0 vr =6 0

Moving source (objective eﬀect) [69]

Receiver: vr = 0, source: vs =6 0 0 λr = (c − vs) T 0 c 1. v = 0, fr = = fs, λ = c · T s λ 0 0 0 c c 1 vs vr 2. v =6 0, fr = = fs · = fs · αs, αs = 1 + 1 s λ c − v0 v0 ≈ c c r s 1 − s c

0 vs = vs · cos γ

General remarks [70] vs, vr > 0 object closing in, vs, vr < 0 object moving away. The most important is: v f = |f − f | ∼= f → communication eﬀect D s r s c

fD– Doppler frequency v f ∼= 2f → echolocation D s c 4.2 Applications Doppler log [71]

27 R. Salamon & H. Lasota 2016-06-08 Echolocation systems I

Backscatter effect on the seabed. v0 = v·cos α. When ship is moving, the return angle is slightly different (transmitting angle α, receiving angle β). The frequency shift occurs mainly at the vicinity of the transmitting / receiving transducer (antenna): 1. ship moves relative to water, fD = fs · v0 (cos α + cos β) (v0 – speed relative to water stream), 2. on the wave travel to bottom and back, additional infinitesimal Doppler shifts appear on each passage between subsequent stream layers. fD = fs · v. 3. finally, the cumulative shift is fD h fs · 2v cos α In case of water stream there is a problem of with v – speed relative to bottom. change of wave speed. Doppler effect: speed

relative to water current vp, after all speed is linear relative to seabed/bottom.

fD 2 In hydroacoustics: I = Hz/knot kHz. v 3 1 knot = 1 nautical mile/1 h. 1 NM=10 (minute of arc) =1852 m.

Ultrasonography – blood ﬂow monitoring [72]

Doppler ultrasonography works with obliquely incident rays. It uses hydrodynamic nature of the flow inside blood vessels. Special sounding signals are used susceptible to time compression giving higher range resolution. The effects are shown on display screen in red and blue; pixels are red when the flow occurs in one direction, and blue when the flow is in the opposite direction. One color at an area means laminar flow, two colors – that the flow is turbulent. The latter indication is extremely important for the physician – cardiologist.

Doppler devices in every day use - ultrasonic alarm [73]

28 R. Salamon & H. Lasota 2016-06-08 Echolocation systems I

Microwave motion sensor OR CR 212 (ORNO) Working principle: detection of Doppler deviation of echo signal Power emitted – 10 mW Range – up to 8 m Price 53 zl.

Ultrasound motion sensor (Driveen) Working principle: detection of Doppler deviation of echo signal Car alarm PriceUltrasonic 29 zl. transducers (mainly 40 kHz buzzers) emit and receive acoustic wave inside a closed area with no air movement (closed room, car with closed windows). When any movement occurs in the area – an intruder or just slight air flow, a part of the received signal is Doppler-shifted. The frequency change is immediately, very easily detected at the receiver (even slight nonlinearity at the receiver gives rise to a mixing effect, creating signal component of the Doppler difference frequency.

5 Continuous wave radars and sonars

CW FM radars and sonars [74]

Echolocation systems with a continuous wave (CW) and frequency modulation (FM) are used as “silent radars (sonars)” and without FM (CW only) as Doppler radar to measure the speed of moving objects (famous police “hair dryers”). Working principle of a CW FM radar

Frequency of transmitted signal t f (t) = f0 − B/2 + B T Frequency of the received signal t − τ fe (t) = f0 − B/2 + B T 2R τ = Delay c Frequency diﬀerence F (t) = f (t) − fe (t) τ F = B T

Distance measurement [75]

Difference frequency signal is obtained at the output of a mixer, by multiplying the transmitted signal with the echo signal. The values of the frequency difference are determined by performing the Fourier transform of the “difference” signal.

The distance to the target is calculated by changing the scale of the spectrum (only to the half of maximum frequency). cT R = F 2B

Spectrum of a CW FM sonar diﬀerence signal

29 R. Salamon & H. Lasota 2016-06-08 Echolocation systems I

Moving target [76]

Motion of the target makes the echo frequency changing due to the Doppler eﬀect. The frequency change is ∼ 2v fd = f0 c

As a result, the diﬀerence frequency changes: τ 2v F = F0 + fd = B + f0 T c This causes an error in the evaluation/estimation of the target distance T f0 R = R0 + v B ∆R T f0 f0 v = v = 2 Rz BRz B c http://wiki/Moving_target_indication Furthermore, it reduces the magnitude of spectrum fringes, making their detection more diﬃcult. These errors are important mainly in sonar and aerolocation systems, where v/c is high; in the radiolocation this quotient is very small.

Velocity-induced distance errors [77]

Example 1 – radar ∼ f0/B = 200, range Rz = 30 km, target velocity v= 300 m/s (1080 km/h), v/c = 10−6, −4 0 ∆R/Rz = 4 · 10 = 0.40 /00. Distance estimation error is ∆R =12 m – negligible.

In sonars, the error of distance estimation is much larger, which makes more diﬃcult the use of this type of systems. The reason is the relatively low speed of acoustic wave propagation (in water – 200 000 times smaller than the speed of electromagnetic waves). Example 2 – sonar ∼ f0/B = 20, range Rz = 3 km, target velocity v= 5 m/s (18 km/h = 10 kn) v/c = 3 · 10−3, −1 0 ∆R/Rz = 1, 2 · 10 = 12 /0. Distance estimation error is ∆R= 360 m – unacceptable.

6 Doppler radars

Doppler radars [78]

These are special radars that use the Doppler eﬀect to measure velocity of observed objects. They are made as:

• pulse radars - enable measurement of target velocity and location

• continuous wave (CW) radars – measuring only velocity and direction

• frequency modulated CW (CWFM) - measuring target velocity and location

In pulse radars, the velocity v is determined from the target distance diﬀerence dR in a given time interval dT : v = dR/dT . In a continuous wave radar, the frequency diﬀerence is determined between transmitted and received signal, which is equal to the Doppler deviation that is, in turn, proportional to target velocity.

30 R. Salamon & H. Lasota 2016-06-08 Echolocation systems I

fd v =∼ c 2f0 http://wiki/Doppler_radar

31 R. Salamon & H. Lasota 2016-06-08 Radars and sonars II

Car velocity measurement [79]

Required parameters: δf = 1 Hz – measurement accuracy δv = 1 km/h

km 1000 m m 1 = =∼ 0, 3 c = 3 · 108 h 3600 s s

2v δv fD = fs ; δf = 2fs c c 1

8 cδf 3 · 10 · 1 1 9 fs = = = · 10 = 0.5 GHz δv 2 · 3 · 10−1 2

CW FM systems [80]

In the CW FM systems the frequency modulation is used as illustrated:

In frequency increase phase, the frequency difference is: Fi = F0 + fd In frequency decrease phase, the frequency difference is: Fd = −F0 + fd 1 When calculating the sum of frequencies we have: fd = (Fi + Fd) 2 1 and calculating the difference, we have: F0 = (Fi − Fd) 2 Target velocity and distance can be calculated from the previously discussed formulae.

12v – “to and from” 32 R. Salamon & H. Lasota 2016-06-08 Radars and sonars II

Part II Radars and sonars

[2016_06_08_EchoMeth_script_GD_HL]Radars and sonars [R. Salamon, H. Lasota]Roman Salamon & Henryk Lasota 2016-06-08

7 Wave propagation parameters

7.1 Medium, wave celerity, attenuation Wave parameters [82]

Comparison for a given wavelength – λ=0.1 m

Medium Wave Propagation speed Attenuation Air electromagnetic 300 000 km/s 0.01 dB/km Air acoustic 340 m/s 15-85 dB/km Water electromagnetic 300 000 km/s 107dB/km Water acoustic 1500 m/s 1 dB/km

Wavelength vs. resolution; frequency vs. range In echolocation systems, waves are used of similar lengths.Their frequencies are much diﬀerent. In ultrasonography, waves are used of frequencies of several MHz (milimeter wavelengths). Range is very short but suﬃcient, and resolution is adequate.

7.2 Frequency spectra Electromagnetic spectrum [83]

In radars, microwaves are used with wavelengths between several millimeters up to one meter. Only in long distance HF radars the wavelength reaches 10 m. 33 R. Salamon & H. Lasota 2016-06-08 Radars and sonars II

Frequency bands and space coverage of acoustic systems [84]

geoacoustics from fractions of Hz to a dozen of Hz / 300 Hz 1 000km – 1km /10m passive underwater acoustics from a dozen of Hz to 10 kHz 100km – 100m active underwater acoustics from 100 Hz to 1 MHz 10km – 10m aeroacoustics from 300 Hz to 50 kHz 10km – 100m defectoscopy from 1 MHz to 5 MHz 1m – 1cm ultrasonography from 1 MHz to 10 MHz 1m – 1cm acoustic microscopy from 100 MHz to 2 GHz 1cm – 10µm

Channel absorption losses [85] Distance r, at which transmission loss due to mere absorption, equals 60 dB (plane wave propagation is assumed: TL = α r) wireless systems in air (60 dB) 0,01 dB/km 6000 km 0,1 dB/km 600 km 1 dB/km 60 km 10 dB/km 6 km acoustic systems in water (60 dB) 10−4dB/m 0,1 dB/km 600 km 10−2dB/m 10 dB/km 6 km 100dB/m 103dB/km 60 m 102dB/m 105dB/km 0,6 m 106dB/m 109dB/km 60 µm

7.3 Wave attenuation in air Electromagnetic wave attenuation in air [86]

Electromagnetic wave attenuation in air in dB/km

34 R. Salamon & H. Lasota 2016-06-08 Radars and sonars II

Attenuation of radio waves in air gases (oxygen, water vapor) [87]

Acoustic wave attenuation in air [88]

Sound wave attenuation for diﬀerent values of relative humidity

35 R. Salamon & H. Lasota 2016-06-08 Radars and sonars II

7.4 Wave attenuation in water Absorption of acoustic and electromagnetic in water [89]

36 R. Salamon & H. Lasota 2016-06-08 Radars and sonars II

Acoustic wave attenuation in water (2) [90]

Underwater acoustic wave attenuation in dB/m (1 dB/m = 1 000 dB/km !)

Attenuation of acoustic waves in sea water (3) [91]

37 R. Salamon & H. Lasota 2016-06-08 Radars and sonars II

7.5 Wave attenuation in cables Attenuation of electrical signals in cables – twisted pair, coax [92]

7.6 1-D vs 3-D channels Transmission losses in cables vs underwater acoustic channels [93]

1-D absorption losses and 3-D spreading losses

8 Radars

8.1 Wavelength-depending applications Microwave technique bands [94]

Radars use electromagnetic waves of microwave frequencies. Speciﬁc microwave bands are distinguished/identiﬁed by characteristic letters:

38 R. Salamon & H. Lasota 2016-06-08 Radars and sonars II

L 1–2 GHz 15–30 cm Long range, civil and military radars of area control, airspace monitoring/surveillance military radars. S 2–4 GHz 7,5–15 cm Air traﬃc control radars, weather radars, marine radars, altimeters , aircraft radars aerial, AWACS (Airborne Warning and Control System). C 4–8 GHz 3,75-7,5 cm Satellite transponders, meteo radars. X 8–12 GHz 2,5-3,75 cm Missile control, aviation, marine, and weather radars, radars for medium resolution land/terrain mapping. Ku 12–18 GHz 1,67-2,5 cm High-resolution terrain mapping, satellite altimetry (height measurement).

Microwave technology bands (2) [95]

K 18–27 GHz 1,11–1,67 cm Cloud detection radars, police radars (car velocity measurement).

Ka 27–40 GHz 0,75–1,11 cm Cartography radars, short-range observation radar – for example at airports, photoradars – assigned band 34.300 ± 0.100 GHz. Q 40–60 GHz 7,5–5 mm Military communications V 50–75 GHz 6,0–4 mm Highly absorbed by the atmosphere E 60–90 GHz 6,0–3,33 mm W 75–110 GHz 2,7–4,0 mm Vision sensors, very high resolution radars

The general rule is: the higher operating frequency, the shorter the range.

8.2 Radar classiﬁcation Classiﬁcation of radars due to operation principle [96]

Pulse wave radars Continuous wave (CW) radars

• single-beam radars with a mechanical rota- • for distance measurements, tion of antenna, • for Doppler velocity measurement, • multibeam radars with electronic beam de- ﬂection, • hardly detectable, “silent” radars.

• synthetic aperture radars.

The transmitter emits a signal with linear frequency modulation. The delayed echo signal is compared with the currently emitted signal. The frequency diﬀerence is determined between the two signals, proportional to the distance of the observed object.

39 R. Salamon & H. Lasota 2016-06-08 Radars and sonars II

Time-delay distance measurement [97]

Pulse radar and its “panoramic” exposition with a central, rotating time base

[Skolnik 2008]

Linear frequency modulation (LFM) distance measurement [98]

Methods of determining frequency diﬀer- ence:

• multiplication (mixing of the echo signal with the currently transmitted signal + lowband ﬁltration

• spectrum analysis

8.3 Role of radar antennas General block diagram of a radar [99]

40 R. Salamon & H. Lasota 2016-06-08 Radars and sonars II

Radar antennas [100]

Parabolic multibeam antenna of a long-range radar

Rectangular antenna of a vessel radar

Parabolic single beam antenna of a satellite communication

Flat antennas of a 3D radar with electronic beam deﬂection system

Stanley R. Mickelsen Safeguard Complex [101]

The Perimeter Acquisition Radar (PAR) was a separately sited phased array radar intended to detect incoming targets. The radar and site remain in service today as the Perimeter Acquisition Radar Characterization System (PARCS), located at Cavalier Air Force Station.

41 R. Salamon & H. Lasota 2016-06-08 Radars and sonars II

[102]

http://Unoﬃcial site: www.srmsc.org

8.4 Radar consoles Radar imaging [103]

Marine radar display console exposing coast line and moving targets

42 R. Salamon & H. Lasota 2016-06-08 Radars and sonars II

9 Sonars

Sonar frequency bands [104]

In hydrolocation there are no standard bands for operating systems.The operating frequency depends on the assumed range and resolution of the system. The greater is the expected range, the lower is the frequency, while the better is the required resolution, the higher is the frequency.

Frequency range Type of a system few Hz to 2kHz passive systems few kHz to several kHz long-range sonars for search of submarines (ASW - antisubmarine warfare) 30 kHz–80 kHz navigation and ﬁshing echosounders, ﬁshing sonars, synthetic aperture sonars 70 kHz–100 kHz mine-hunting sonars 100 kHz–200 kHz side-scan sonars, hydrographic echosounders, multibeam echosounders for mapping the bottom of reservoir (cartography sounders) 200 kHz–500 kHz short-range sonars of very high resolution

9.1 Working principle Working principle of sonar systems [105]

Sonars are underwater acoustic systems operating on the same principle as radar systems. To browse the aquatic environment they use acoustic waves. It requires from the system conversion of electrical signals into acoustic wave and vice versa.

This conversion is performed by ultrasonic transducers, that are electromechanical elements of transmitting and receiving antennas. Most hydrolocation systems transducers are made of PZT piezoelectric ceramic (PZT – lead titanate-zirconate).

Alternating voltage applied to the electrodes causes vibration of the transducer’s surfaces. The surface placed in water is the source of acoustic waves.

9.2 Transducers and antennas Hydroacoustic transducers and antennas [106]

Piezoelectric transducers are manufactured in various forms:

• cuboid

• ﬂat cylinder

• thin-walled cylinder

• ring

Multi-element cylindrical antenna of a sonar

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9.3 Sonar system classiﬁcation Classiﬁcation of hydrolocation systems due to the principle of operation [107]

Active sonars (pulse systems)

• single beam with a mechanical rotation of the antenna

• multi-beam with electronic beam deﬂection

• side-looking

• with synthetic aperture

Passive sonars (listening systems)

• with antennas mounted on board of a ship

• with towed antennas

• with antennas mounted on bottom of a reservoir

• sonobuoys (radio-hydro-buoys)

Passive systems determine the bearing of objects that emit sound waves (ships, underwater vehicles, torpedoes, whales).

On-board and in-water sonar elements [108]

sonar console towed antenna console of towed antenna sonar

44 R. Salamon & H. Lasota 2016-06-08 Radars and sonars II

[109]

radio-hydro-buoys (sonobuoys) ﬁshery navigation echosounder

9.4 Space scan methods Space search techniques [110]

10 Laser systems

10.1 Working principle Working principle of optical, laser system [111]

Optical systems work on the radar principle using the optical frequency range of coherent electromagnetic waves. They carry the name of LIDAR (Light Detection And Ranging) or, less frequently, LADAR (Laser Detection And Ranging).

Pulse laser is a source of optical signals. Short pulses of light are sent in a very narrow beam. They reﬂect from observation objects and are collected by telescopes equipped with detectors of the light. The distance is calculated as in radars.

10.2 Applications Distance meter [112]

Simple devices are used as range ﬁnders meaning distance meters, ranging up to several hundred meters. They are used in civil engineering works, land surveying (geodesy) as well as in military, hunting, and police applications. More complex lidars have the range of ten kilometers and more. 45 R. Salamon & H. Lasota 2016-06-08 Radars and sonars II

Range ﬁnding applications [113]

Applications:

• geology

• seismology

• meteorology

• geodesy

Space scanning method • archeology

• remote control

• army

• agriculture

11 Echolocation system parameters

11.1 Functional diagram of echolocation system Functional diagram of echolocation system [114]

11.2 Operating and technical parameters Basic operating parameters of echolocation systems [115]

Operating parameters (or exploitation parameters) characterize a system from the point of view of its user. • Coverage/range

• Distance measurement accuracy 46 R. Salamon & H. Lasota 2016-06-08 Radars and sonars II

• Bearing accuracy

• Range resolution

• Angular resolution

• Observation sector (sector angle)

• Search time

• Probability of detection

• Probability of false alarm

• Power supply, weight, dimensions, environmental conditions, installation conditions, hardiness/endurance/durability/vulnerability conditions, etc.

Technical parameters (or technical speciﬁcation)

characterize it from the point of view of system constructor.

11.3 Range, bearing, measurement accuracy Range [116]

The range of the system means the maximum distance at which the system detects, with an assumed probability, a speciﬁc target in given/prevailing conditions of wave propagation.

The range depends on: • technical parameters of the system,

• parameters of the object to be detected (eﬀective scattering area – radio, target strength – hydro)

• wave propagation conditions in the medium

• assumed probabilities of detection and false alarm.

The above exploitation should not be confused with the maximum distance exposed at the system imaging display. The latter is a technical parameter chosen by the manufacturer/constructor according to expected ranges.

Distance measurement accuracy [117]

cT c – wave velocity in medium, [m/s] R = T – time elapsed between the instant of emission of the 2 sounding pulse and the reception of the echo signal

Causes of errors Factors contributing to errors are:

• local, dynamic changes in the wave propagation speed c in medium,

• propagation along curve lines,

• ambiguity in the evaluation of the moment of arrival of the echo pulse

47 R. Salamon & H. Lasota 2016-06-08 Radars and sonars II

Bearing accuracy [118]

Bearing accuracy is the maximum error between the actual direction and the measured bearing. The error is related, in a typical system, by the width and shape of the directional beam.

The accuracy of bearing depends primarily on the width of antenna directional pattern. It is the better the directivity pattern (the beam) is narrower.

The direction of the beam axis is given as the target bearing. The actual bearing is contained in the nominal width of the beam. In general, we are not able to determine the real bearing precisely in the frame of the antenna beam.

11.4 Range and angular resolution Distance resolution [119]

Distance resolution is the shortest distance between similar point-like objects observed at the same bearing angle, at which it possible to discriminate (distinguish between) their echo signals.

cτ ∆R = 2

We are able to distinguish between pulses delayed by at least their duration τ.

In simpler systems, we identify the time τ with the duration of the sounding pulse.

A more general relation has the form:

c ∆R = 2B

where B is the bandwidth of signal spectrum.

Angular resolution [120]

is the smallest angle between similar point-like objects at which it is possible to discriminate (to distinguish) two separate echoes, at the receiver.

Generally, it is assumed that angular resolution equals the width of the beam.

When targets are at diﬀerent distances, special techniques exist that can improve the angular resolution.

48 R. Salamon & H. Lasota 2016-06-08 Echolocation signals III

11.5 Sector-scanning time Scanning time of observation sector [121]

At a given position of antenna beam we observe conical space of apex (vertex) angles ϑ and ϕ, which are nominal angular beam widths, its volume being determined by the range R.of the system. The time required for observation of possible targets is t = 2R/c. The time needed to scan a wider angular sector (Θ,Φ) is, at least:

ΘΦ T ∼= t 1 ϑ ϕ

The problem of scanning time occurs mainly in acoustic systems due to the relatively low speed of wave propagation (sound velocity).

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Part III Echolocation signals

[2016_06_08_EchoMeth_script_GD_HL]Echolocation Signals [R. Salamon, H. La- sota]Roman Salamon & Henryk Lasota 2016-06-08

12 Echolocation in nature

Echolocation in nature [123]

The method of echolocation is being used by some animals for navigation and hunting. They use acoustic sounding waves/signals. Best known is the mechanism of echolocation of bats and dolphins. https://en.wikipedia.org/wiki/Animal_echolocation

12.1 Bats [124]

Echolocation of bats The order of mammals (ca. 1100 species, in Poland – 25) who can ﬂy. Generally nocturnal, so eyesight is of little use. They emit acoustic signals which, depending on the species, are located in the frequency range from approx. 10 kHz to approx. 200 kHz.

Spectrogram of a bat echosounding signal.

http://.../richarddevine/bat-recordings Sonogram of the recording

[125]

Bats emit a broadband pulses and continuous sounding signals with a frequency modulation (FM). Signal level can exceed 130 dB. This is the highest level of sound produced by animals. The signals are generated by the vocal cords. Signals parameters adapt perfectly to the propagation conditions and method of use. In the brain correlation reception is performed, whereby it is possible to precisely measure the distance to the target and determine the delay between the signals received by the left and right ear, and thus the precise bearing. This also provides an unprecedented opportunity to distinguish between two or more close targets (resolution), even at a distance of 0.5 mm. Thanks to the extraordinary complexity of the emitted signals bats are able to identify targets.

Bats are able to compensate the Doppler eﬀect resulting from their own movement and use this eﬀect to highlight the movement of insects on which they pray.

50 R. Salamon & H. Lasota 2016-06-08 Echolocation signals III

[126]

Interesting fact Some Tiger Moths from Arctiidae family in response to the echolocation calls of bats emit ultrasonic signals that warn the bats that the moths have toxic compounds. Tiger Moth Bertholdia trigona emits acoustic pulses at a frequency of 4.5 kHz, which disrupt the process of echolocation of bats, reducing tenfold the eﬀectiveness of hunting. A. Corcoran "Tiger Moth Jams Bat Sonar" [Science (325) 2009] Video depicting moth jamming the sonar of the bat

12.2 Dolphins & Whales Dolphins and Whales [127]

Marine mammals of the order Cetacea, suborder Odontoceti (toothed) use acoustic signals in the water for echolocation.

They emit complex broadband signals with frequency modulation of carrying frequency up to 100 kHz and a very complex structure, adapting to the conditions of propagation.

Spectrogram of a dolphin echosounding signal.

[128]

Dolphins have no ears, and the generation and reception of acoustic signals is carried out in parts of the anatomy illustrated. The mechanism of generation and reception device is adapted to to a large acoustic impedance of water.

Dolphin brain performs correlation processing of the received signals, providing wide coverage and high resolution.

whale_echolocation.gif

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12.3 Other spieces Shrews [129]

Terrestial echolocation

The shrews of two genera (Sorex and Blarina) emit series of ultrasonic squeaks.The nature of shrew sounds, unlike those of bats, are low amplitude, broadband, multiharmonic and frequency modulated. They contain no “echolocation clicks” with reverberations and would seem to be used for simple, close-range spatial orientation. In contrast to bats, shrews use echolocation only to investigate their habitats rather than additionally to pinpoint food. Except for large and thus strongly reﬂecting objects, such as a big stone or tree trunk, they will probably not be able to disentangle echo scenes, but rather derive information on habitat type from the overall call reverberations.

Humans [130]

Some blind people use this abilty for acoustic wayfinding, or navigating within their environment using auditory rather than visual cues. It is similar in principle to active sonar and to animal echolocation. By actively creating sounds – tapping canes, stomping foot, snapping fingers, or making clicking noises with their mouths – people trained to orient by echolocation can interpret the sound waves reflected by nearby objects, accurately identifying their location and size. http://.../ultrasonic-helmet.../ + movie

13 Echolocation signals

Echolocation signals [131]

Signal used in active echolocation systems:

• narrowband signals – sinusoidal signals with rectangular or similar envelope

• broadband signals – signals with frequency modulation or keying

• coded signals, pseudo-random

• broadband signals – sinusoidal signals with a very short duration.

Signal received (listened, intercepted) in passive systems:

• narrowband, harmonic-like, monochromatic signals,

• broadband, random-like signals.

The main diﬀerence between active and passive systems is that the signals are known in active systems and in passive systems – are unknown.

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14 Narrowband signals

14.1 Monochromatic signal Narrowband signal [132]

Harmonic (monochromatic) signal

s(t) = A(t) cos(ω0t − ϕ0)

Requirement: the spectrum bandwidth of signal envelope A(t) is much lower than the carrier frequency f0 .

Signal spectrum 1 S( jω) = {A [ j (ω + ω )] ejϕ0 + A [ j (ω − ω ) e−jϕ0 ]} . 2 0 0

Amplitude spectrum

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14.2 Sinusoidal pulse Signal of rectangular envelope [133]

s (t) = S0Π(t/τ) cos (ω0t − ϕ0)

The product of the signal bandwidth and pulse duration is equal to one.

Bτ = 1 Signal spectrum:

S0 S (jω) = I {Π(t/τ)} ? I {cos ω0t} = 2π S τ n sin [(ω + ω ) τ/2] sin [(ω − ω ) τ/2] o = 0 0 + 0 2 (ω + ω0) τ/2 (ω − ω0) τ/2

15 Autocorrelation function

15.1 Signal autocorrelation and energy [134]

Deﬁnition of correlation function: Deﬁnition of autocorrelation function: ∞ ∞ ? ? r12 (τ) = s1 (t) s (t + τ) dt r11 (τ) = s1 (t) s (t + τ) dt ˆ 2 ˆ 1 −∞ −∞

Autocorrelation function spectrum: Signal energy: 2 I {r11 (τ)} = |S (jω) | E = r11 (0)

15.2 Rectangular pulse Determination of the autocorrelation function of a rectangular pulse [135]

54 R. Salamon & H. Lasota 2016-06-08 Echolocation signals III

15.3 Sinusoidal pulse Determination of the autocorrelation function of a sinusoidal signal with rectangular envelope [136]

16 Special signals

16.1 Linear frequency modulation (LFM) signal Signal with linear frequency modulation (LFM) [137] ( " ∆f # ) s (t) = S Π(t/τ) sin 2π f + (t − τ) · t − ϕ 0 < t < τ 0 0 τ 0

Instantaneous frequency dϕ ωc (t) = 2πfc (t) = dt d ∆f 2 fc (t) f0 1 + t − τt dt τf ∆f = f0 + (2t − τ) τ

LFM signal spectrum [138]

55 R. Salamon & H. Lasota 2016-06-08 Echolocation signals III

B = 2∆f Spectrum bandwidth (spectral width) Bandwidth – time-length product Bτ 1

Spectrum width of LFM signal does not depend on its duration (time-length). Signals of high-value Bτ products are used in echolocation systems with matched ﬁltering (correlation receivers).

Phase of a linearly frequency modulated (LFM) signal [139]

Autocorrelation function of LFM signal [140]

16.2 Hyperbolic frequency modulation (HFM) signal Signal with hyperbolic frequency modulation (HFM) [141]

2π s (t) = A (t) sin ln (1 + kf0t) k

f0 f (t) = 1 + kf0t 1 B k = f0τ f0 − B Doppler-shift resistance HFM signal is more resistant to the Doppler eﬀect than LFM signal. This is important mainly in hydro- and aerolocation where the ratio of target 56 velocity to the propagation velocity of acoustic waves is relatively high. R. Salamon & H. Lasota 2016-06-08 Echolocation signals III

Spectrum of a HFM signal http://www.seaﬂoorsystems.com http://benthos1624.pdf

16.3 Signals with code modulation Code modulation signals [142]

Objective: Obtaining possibly narrow autocorrelation function with minimal side lobes. The most used are binary codes which are sequences of numbers 1 and 0 (or +1 and -1). Modulation process involves assigning the values of rectangular pulse with amplitudes +1 and -1, and the multiplication of such a signal by the sinusoidal carrier signal. This means therefore phase keying of the sinusoidal signal.

Code modulation signal spectrum [143]

The code modulation signal is a narrow band one, as shown in the ﬁgure. The bandwidth depends on the width of the modulating signal, that is, the rectangular pulse train.

Examples of codes [144]

Barker codes give the smallest possible level of side lobe and the smallest width of the autocorrelation function of maximum equal to the number of elements. Unfortunately, the longest Barker code has a length of mere N = 13: 57 R. Salamon & H. Lasota 2016-06-08 Echolocation signals III

1111100110101

Autocorrelation function [145]

Properties: - constant side lobe level, maximum equal to the number of elements

MLS - Maximum Length Sequence [146]

This is a binary periodic sequence the period M of which has 2N−1 elements. The module of its discrete spectrum is ﬂat, and the phase spectrum is uniformly distributed in the interval −π- +π. These properties are very similar to those of white noise.

Single period of a M=31 (L=5) MLS Spectrum modulus of one period of the M=31 MLS signal

M=2047 MLS signal [147]

Phase of M=2047 (L=11) MLS signal spectrum R. Salamon & H. Lasota 2016-06-08 Echolocation signals III

Autocorrelation function of one period

Cyclic autocorrelation function

MLS as a tool for determining impulse responses of linear systems [148]

m (t) – MLS input signal, rmm (t) = m(t) ? m(t) - MLS autocorrelation, h (t) – system impulse response 1. System response to a MLS

ym (t) = h (t) ∗ m (t) 2. MLS-and-system response cross-correlation function

rym(t) = ym (t) ? m (t) = h (t) ∗ m (t) ? m (t)

rym(t) = h (t) ∗ rmm (t) ' h(t) Advantage: input signal has much greater energy than can be achieved with a linear Dirac impulse.

Sampling of echolocation signals [149]

Sampling is the first stage of the analog-to-digital (AD) conversion. The aim is to replace a continuous analog signal with a sequence of very short pulses (Dirac’s impulses in theory) whose values are equal to the values of the analog signal at specific points in time. Time moments are usually chosen with a fixed distance called the sampling period, and the reciprocal of this period is called the sampling frequency. In practice special devices are used for collecting and retaining the value of the analog signal at precise moments in time (sample-and-hold devices). When the moments of sampling need not to be very precise, the sample signal generally refers to the time when the signal aligns with a reference (pattern) value.

59 R. Salamon & H. Lasota 2016-06-08 Echolocation signals III

Sampling techniques [150]

In the second stage of the A/D conversion numerical values are assigned to sampled values (usually in binary notation).

• Sampling methods:

– direct sampling, – quadrature sampling, – direct sampling of baseband signals after quadrature detection.

• Condition of correct sampling:

– Preservation full information about the analog signal in the discrete signal.

• Criterion:

– The possibility to faithfully reproduce the analog signal from samples.

• Warning:

– Sampling operation is nonlinear, therefore the order of operations before and after sampling can not be changed.

60 R. Salamon & H. Lasota 2016-06-08 Echolocation signals III

17 Detection of echolocation signals

Detection of echolocation signals [151]

Goal of the detection processing: Detection of the known signal (transmission signal, useful signal) s(t) in the echo signal x(t).

x(t) = s(t) + n(t) n(t) – noise, interference y(t) = T x(t) y(t) – signal at the receiver output

17.1 Detection conditions Detection conditions [152]

s(t) – useful echo signal - deterministic extreme option 1 – fully known signal intermediate options - signal partially known extreme option 2 – entirely unknown signal

n(t) – non-deterministic interference (stochastic) – noise, reverberation

The sum (superposition) of deterministic and stochastic signals is a stochastic signal x(t) – signal at the receiver input – stochastic y(t) – signal at the receiver output – stochastic

Binary detection

• 1 – useful signal has been received

• 0 – mere interference received

Decisions taken at the receiver output and their probabilities/likelihood [153]

s n Decision Probability Decision Probability

present present 1 – true PD 0 – false 1 − PD

absent present 1 – false PF A 0 – true 1 − PF A PD – probability of detection PFA – probability of a false alarm Primary objective of the system: To ensure (to provide) a maximum value of PD and a minimum value of PFA. These objectives are inherently contradictory – it is necessary to compromise (meaning an optimiza- tion)

61 R. Salamon & H. Lasota 2016-06-08 Echolocation signals III

17.2 Detection of a continuous signal on the background of Gaussian noise Detection of a continuous signal on the background of Gaussian noise [154]

Detection consists in deciding whether there is a constant useful signal in the received signal.

p1(y) – the probability distribution of the signal Neyman-Pearson criterion at the output of the receiver when there is an echo p1(γ) signal at the input (+ noise) ≥ λ p 0(γ) p0(y) – the probability distribution of the signal at " 2 # the output of the receiver when there is only noise 1 (y − y¯1) p1 (y) = √ exp − at the input πσ 2σ2 2 y = γ – " 2 # detection threshold 1 (y − y¯0) η – value of the constant useful signal p0 (y) = √ exp − 2πσ 2σ2

y¯1 =y ¯0 + η

[155]

2 η (2γ − y¯1 − y¯0) η + 2¯y0 σ exp = λ γ = + ln λ 2σ2 2 η

The detection threshold γ can be set so that the N-P criterion have assumed value λ. Signal-to-noise ratio at the receiver output

2 {E [y1] − E [y0]} SNRy = General deﬁnition σ2

E [y1] =y ¯0 + η E [y0] =y ¯0 2 SNRy = η/σ Deﬁnition in a typical speciﬁc case The signal-to-noise ratio is equal to the quotient of the useful signal power and the noise variance.

Detection and false alarm probabilities [156]

∞ ∞ PD = p1 (y) dy PFA = p0 (y) dy ˆγ ˆγ

y¯0 = 0y ¯1 = η = 1 σ = 0.5

62 R. Salamon & H. Lasota 2016-06-08 Echolocation signals III

17.3 Receiver operating curves (ROC) Receiver operating curves (ROC) [157]

ROC curves allow to determine the SNR of assumed PD and PFA. The ﬁgure illustrates the determination of a detection threshold (dashed curve)

17.4 Reception of a stochastic signal on the background of (against) Gaussian noise Reception of a stochastic signal on the background of (against) Gaussian noise [158]

The lower is our knowledge about the signal, the harder is its detection

Example: noise and signal are Gaussian and uncorrelated

2 2 2 σ1 = σ0 + σs p0– noise distribution p1 (y) = p0 (y) ∗ ps (y) ps– signal distribution p1– signal and noise distribution

Distribution of the probability density of a sum of signals is a convolution of their individual probability distributions. A comparison of the detection of a constant value signal (the previous case) and of a stochastic signal of mean value equal to the constant value of the previous signal. The noise in both cases is the same.

63 R. Salamon & H. Lasota 2016-06-08 Echolocation signals III

[159]

Conclusion: The probability of the stochastic signal detection is lower, and the probabilities of a false alarm are the same.

17.5 Detection of a known signal in the Gaussian noise background Detection of a known signal in the Gaussian noise background [160]

This is a case similar to the situation that prevails in echolocation systems in which the received signal is almost a copy of the known sounding signal. The amplitude (magnitude) and the moment of its appearance in the receiver input are unknown. Case of completely known signal (including the magnitude and the moment of reception.

x1 (t) = s (t) + n (t) 1 – a known useful signal s(t) + Gaussian noise n(t) are received x0 (t) = n (t) 0 – mere noise received

Structure of the optimal (optimum) correlation receiver:

τ ∞ y (τ) = x (t) s (t) dt ≥ γ r (τ) = x (t) x (t + τ) dt ˆ xx ˆ 0 −∞ x (t) = s (t) −→ Autocorrelation function τ = 0

64 R. Salamon & H. Lasota 2016-06-08 Echolocation signals III

17.6 Reception of rectangular pulses Reception of a rectangular pulse [161]

18 Matched reception – processing gain

18.1 Statistical properties of the signal at the output of a correlation receiver Statistical properties of the signal at the output of a correlation receiver [162]

Samples of the received signal Histogram – the probability density distribution

Conclusion: We can estimate the probabilities of detection and false alarm with the method given above.

18.2 Signal-to-noise ratio at the input and output of a receiver – “processing gain” Signal-to-noise ratio at the input and output of a receiver – “processing gain” [163]

τ τ 2 E [y1] = E s (t) dt + E s (t) n (t) dt = E (τ) ´0 ´0

E (τ) – signal energy in the time moment τ 65 R. Salamon & H. Lasota 2016-06-08 Echolocation signals III

( τ 2) σ2=E s (t) n (t) dt = NE (τ) ´0

N – noise power spectral density

2 2 {E [y1] − E [y0]} [E (τ)] SNRy = = σ2 NE (τ)

E (τ) SNRy = N Signal-to-noise ratio at the output of a correlation receiver is equal to the ratio of the energy of the signal and the power spectral density of the noise.

[164]

Signal-to-noise ratio at the receiver input

Ps 2 SNRx = 2 , σx = NB,E (τ) = Psτ σx

E (τ) Psτ PsτB Ps SNRy = = = = Bτ 2 = Bτ · SNRx N N NB σx

SNRy = Bτ · SNRx

Correlation receiver improves the input signal-to-noise ratio proportionally to the product of the signal spectrum width and its time length (duration). The comparison concerns direct signal detection with no correlation receiver.

Conclusion: It is preferred to use signals with a large product of time duration and spectrum width. The product has to be increased by lengthening the duration of the signal, because then its energy increases. Spectral width does not aﬀect the SNRy but it determines the range resolution that we will show next.

18.3 Receiver matched to a signal Receiver matched to a signal [165]

k (t) = s (−t)

k (t) – Impulse response of a matched ﬁlter

Equivalence with a correlation receiver ∞ ∞ y (τ) = s (−t) x (τ − t) dt = s (t0) x (t0 + τ) dt0 −∞´ −∞´ We get the correlation function of the transmitted and received signals. If x(t) = s(t), it means the autocorrelation function of the transmitted signal.

66 R. Salamon & H. Lasota 2016-06-08 Echolocation signals III

Implementation of a matched ﬁlter in the frequency domain [166]

Y (jω) = K (jω) X (jω)

y (t) = I−1 {Y (jω)}

The matched ﬁlter transfer function K (jω) = I {k (t)} = I {s (−t)} = S∗ (jω)

Reception of signals within the noise [167] x (t) = s (t) + n (t)

Y (jω) = K (jω) X (jω) = [S∗ (jω) S (jω) + N (jω) S∗ (jω)] = |S (jω) |2 + N (jω) S∗ (jω)

N (jω)– widmo szumu

The useful signal at the output of a matched ﬁlter −1 2 y (t) = I |S (jω) | = rss (t)

Noise variance ∞ N σ2 = |S (jω) |2dω = NE 2π ˆ −∞

Signal-to-noise ratio at the output of a matched ﬁlter 2 2 [rss (0)] E E SNRy = = = NE NE N

18.4 Detection of signals of unknown parameters Detection of signals of unknown parameters [168] Signal appears at the receiver input in an unknown moment y (τ) = [As (t − t0) + n (t)] ∗ s (−t) Signal at the ﬁlter output Implementation in the frequency domain

Y (jω) = AS∗ (jω) S (jω) e−jωτ0 + N (jω) S∗ (jω) = A|S (jω) |2e−jωτ0 + N (jω) S∗ (jω)

0 y (t) = Arss (t − τ0) + σn (t)

We get a delayed autocorrelation function plus noise. The noise is narrowband of the variation shown on the previous page.

67 R. Salamon & H. Lasota 2016-06-08 Echolocation signals III

[169] Example: A ﬁltering matched to the delayed rectangular pulse (two realizations of noise). Rectangular pulse with a duration τ.

Detection of a signal with linear frequency modulation [170]

[171]

68 R. Salamon & H. Lasota 2016-06-08 Echolocation signals III

[172]

[173]

[174]

69 R. Salamon & H. Lasota 2016-06-08 Echolocation signals III

[175]

[176]

70 R. Salamon & H. Lasota 2016-06-08 Echolocation signals III

[177]

18.5 Detection and false alarm probabilities of partly unknown signals Probabilities of detection and false alarm when the moment of appearance of a useful signal is unknown [178]

Signal appears in an unknown moment, in a long observation time T . The signal duration at the receiver output isτ. The detection probability does not depend on the observation time T . The probability of a false alarm concern the time τ. We calculate it as follows:

T τ PF AT = PFA, PFA = PF AT τef T

Example: We allow one false alarm within one hour observation. The duration of the useful signal is 3.6 ms. The probability of false alarm is, by the given criteria :

−3 3.6 · 10 −6 PFA = · 1 = 10 3600

18.6 Reception of sinusoidal signals with unknown parameters Reception of sinusoidal signals with unknown parameters [179]

All parameters known τ 2 2 2 A y (τ) = A sin (ω0t + ϕ0) dt = {sin 2ϕ0 + 2 (ω0τ + ϕ0) − sin [2 (ω0τ + ϕ0)]} ω ´0 4 0

71 R. Salamon & H. Lasota 2016-06-08 Echolocation signals III

Unknown phase [180]

τ 2 2 A y (τ) = A sin (ω0t + ϕ) sin (ω0t) dt = {sin ϕ + 2ω0τ cos ϕ − sin (2ω0τ + ϕ)} ω ´0 4 0

Conclusion: It is impossible to perform a threshold detection.

18.7 Fourier transform as realization of a ﬁlter matched to a sinusoidal signal Fourier transform as a realization of ﬁlter matched to a sinusoidal signal [181]

We receive sinusoidal signal of unknown amplitude A, frequency f0, and phase ϕ. We download N samples of the signal with a frequency fs, and calculate digital spectrum. We have:

N X S (k) =A sin (2πf0n/fs + ϕ) exp (−j2πnk/N) 1 ( N ) X = (A/2j) exp [j (2πf0n/fs + ϕ)] exp (−j2πnk/N) 1 N X − exp [−j (2πf0n/fs + ϕ)] exp (−j2πnk/N) 1

The right-hand, maximum spectrum fringe appears for k0 equal to:

f0 k0 = N fs 72 R. Salamon & H. Lasota 2016-06-08 Echolocation signals III

Periodogram [182]

For this fringe we have: N P Sp (k0) = (A/2j) exp (jϕ) 1 = (A/2j) N exp(jϕ) 1

Squared module of the ﬁnge (the periodogram value for k0):

2 2 2 A N A NTs |Sp (k0) | = N = Nfs 4 4 A2τ E = Nfs = const 4 2 The result is proportional to the energy of the received signal, what is characteristic for the correlation reception. Conclusion: The Fourier transform performs ﬁltering matched to sinusoidal signals, including signals of unknown parameters.

Reception of sinusoidal signal in noise [183]

Example of the reception of an unknown sinusoidal signal on the background of a Gaussian noise.

Amplitude ﬂuctuation due to the noise [184]

A magnitude spread of the sinusoidal signal spectrum fringe due to noise 73 R. Salamon & H. Lasota 2016-06-08 Echolocation signals III

Gaussian distribution [185]

Probability density distribution of the spectrum fringe of a sinusoidal signal and Gaussian noise at high SNR value.

The distribution is Gaussian with mean value equal to the sine wave fringe and variance dependent on the amplitude of the the signal and the noise variance.

Ricean distribution [186]

Distribution of the probability density at low SNR (Rice distribution)

Periodogram of the noise Probability density distribution of the noise fringes is exponential. The average value of noise fringe height (magnitude) in the periodogram is Nσ2 and is equal to the standard deviation of the magnitude (N – number of spectrum fringes). Remark: The noise periodogram does not tend to a constant value with increasing number of spectrum fringes.

19 Signal sampling techniques

Sampling techniques of echolocation signals [187]

Sampling methods:

• direct sampling,

• quadrature sampling,

• direct sampling of baseband signals after quadrature detection.

74 R. Salamon & H. Lasota 2016-06-08 Echolocation signals III

Condition of a good sampling: Preservation (conservaion) in the discrete signal of a complete information about the analog signal.

Criterion (touchstone): The possibility of a faithful reproduction of the analog signal from samples.

Warning: Sampling operation is nonlinear, therefore the sequence of operations before and after the sampling can not be interchanged.

19.1 Direct sampling of signals Direct sampling of signals [188]

Discrete signal spectrum ∞ 1 P I {sn (t)} I {sn (t)} ? I δ (t − nTs) 2π n=−∞ 1 2π P∞ Sn (jω) = S (jω) ? δ (ω − nωs) 2π Ts n=−∞

∞ X Sn (jω) = S [j (ω − nωs)] n=−∞ Mathematical formulation of sampling operation: Spectrum of a discrete signal is continuous ∞ and periodic. Full information about the sig- X nal is contained in each period of the spec- sn (t) = s (t) · δ (t − nTs) n=−∞ trum. ∞ X = s (nTs) δ (t − nTs) n=−∞

Spectrum of sampled signals [189]

Signal spectrum in the result of sampling of an analog signal with limited spectrum (a)

Signal spectrum in the result of sampling of an analog signal with unlimited spectrum(b)

Sampling is proper, when the original analog signal can be perfectly restored from samples. Conditions for a good sampling:

• signal spectrum must be limited in frequency do- 1 Ts < main, 2fM • the sampling rate must meet the Nyquist criterion: Signal spectrum is to be limited with an analog ﬁlter prior to (before) sampling!

19.2 Quadrature sampling of narrowband signals Quadrature sampling of narrowband signals [190]

Quadrature sampling is used to reduce the number of samples. 75 R. Salamon & H. Lasota 2016-06-08 Echolocation signals III

Conditions for the application of quadrature sampling:

• narrowband signal

• knowledge of the carrier frequency

∞ X sˆn (t) = A (t) cos (ω0t − ϕ) · δ (t − nTs) + jδ (t − T0/4 − nTs) n=−∞

∞ X sˆn (t) = cos ϕ A (nmT0) · δ (t − nmT0) n=−∞ ∞ X − j sin ϕ A [T0 (nm + 1/4)] · δ [t − T0 (nm + 1/4)] n=−∞

Signal spectrum after quadrature sampling [191]

Complex notation of the signal after direct sampling ∞ ∼ −jϕ P sˆn (t) = e A (nmT0) · δ (t − nmT0) n=−∞

Signal spectrum after quadrature sampling ∞ ∼ 1 −jϕ X Sn (jω) = e A [j (ω − nωs)] mT 0 n=−∞

Discrete signal after quadrature sampling is a baseband signal. Information is preserved about the envelope and about the phase of the carrier.

Sampling period: of quadrature sampling of direct sampling gain m 1 00 1 TS f0 Ts = mT0 = ≤ TS ≤ 0 =≤ 1 + f0 2fMA 2 (f0 + fMA) TS fMA

[192]

76 R. Salamon & H. Lasota 2016-06-08 Echolocation signals III

Sinusoidal (harmonic, monochromatic) signal with rectangular envelope [193]

Amplitude spectrum of the signal.

[194]

Real and imaginary samples after a quadrature sampling.

The phase of the carrier is calculated as artg of the quotient (ratio) of the values of real and imaginary samples.

77 R. Salamon & H. Lasota 2016-06-08 Echolocation signals III

[195]

Envelope of the signal after quadrature sampling.

Amplitude spectrum of of the signal after quadrature sampling.

Phase changes vs quadrature sampling [196]

Signal with varying phase Condition: ∼ s (t) = A (t) cos [ω0t − ϕ (t)] ϕ (t + T0/4 = ϕ (t)) The phase varies slowly

Signal after quadrature sampling ∞ ∼ P −jϕ(nmT0) sˆn (t) = e A (nmT0) · δ (t − nmT0) n=−∞

Linear phase change – Doppler eﬀect d ωc = (ω0t + 2πfDt + ϕ0) = 2π (f0 + fD) dt Spectrum ∞ ∼ 1 P −jωϕ(t) Sn (jω) = I e ∗ A [j (ω − nωS)] 2πmT0 n=−∞

Samples of sinusoidal signal with Doppler shift [197]

a – without a shift b – pairs of quadtrature samples c – real samples d – imaginary samples

Real and imaginary quadrature samples of a shifted signal are just samples of a sinusoidal signal with the frequency equal to the Doppler frequency shift. 78 R. Salamon & H. Lasota 2016-06-08 Echolocation signals III

[198]

jωD t jϕ0 jϕ0 I e e = 2πe δ (ω − ωD)

∼ jϕ0 S (jω) = (1/mT0) A [j (ω − ωD)] e

Spectrum of Doppler shifted sinusoidal signal with rectangular envelope

19.3 Time delay of signals Time delay of signals [199]

Time-delayed narrowband signal s(t − τ) = A (t − τ) cos [ω0 (t − τ) − ϕ (t − τ)]

Time-shifted signal after quadrature sampling ∞ ∼ −jω0τ P −jϕ(nmT0−τ) sˆn (t − τ) = e e A (nmT0 − τ) · δ (t − nmT0) n=−∞

Spectrum of the delayed signal 1 n o S (jω) =∼ e−jω0τ I e−jϕ(t)A (t) mT0 Approximate relation 1 n o S (jω) =∼ e−j(ω0+ω)τ I e−jϕ(t)A (t) mT0 More accurate formula Information about the delay is contained in the phase characteristics.

Phase errors in quadrature sampling with fast phase changes [200]

Phase of quadrature-sampled time-shifted signal with frequency modulation: a – narrowband approximation, b – without the narrowband approximation. 79 R. Salamon & H. Lasota 2016-06-08 Echolocation signals III

[201]

The case of four times narrower spectrum (4 x smaller frequency deviation) and the same pulse duration (time width).

Conclusion: Too fast changes of the phase manifest themselves in errors of quadrature sampling phase characteristics

19.4 Sampling as frequency transformation Sampling as frequency transformation [202]

Sampling of a narrowband signal ∞ P sn (t) = A (t) cos (ω0t − ϕ) · δ (t − nTs) n=−∞

Spectrum

∞ 1 X Sn (jω) = S (jω) ∗ δ (ω − nωs) T s n=−∞ ∞ jϕ −jϕ 1 X = A [j (ω + ω0)] e + A [j (ω − ω0)] e ∗ δ (ω − nωs) T 2 s n=−∞

∞ ∞ 1 jϕ X 1 −jϕ X Sn (jω) = e A [j (ω + ω0 − nωs)] + e A [j (ω − ω0 − nωs)] T T 2 s n=−∞ 2 s n=−∞

80 R. Salamon & H. Lasota 2016-06-08 Antenna directivity IV

[203]

Conditions for spectrum non-overlapping 4f0 fs = 4N + 1 2f0/B − 1 N ≤ 4 Example: f045 kHz, B = 8 kHz, N ≤ 2.56 So we choose N = 2 and calculate: fs = (4/9) f0 = 20 kHz

81 R. Salamon & H. Lasota 2016-06-08 Antenna directivity IV

Part IV Antenna directivity

[2016_06_08_EchoMeth_script_GD_HL]Antenna directivity [H. Lasota]Henryk La- sota 2016-06-08

20 Radar and sonar antennae

Radar antennae ships, yachts [205] Mobile antenna, mobile casing

Large antenna, narrow beam

Rotary antenna, stationary casing Small antenna, wide beam

Radar antennae PIT 1 [206] Radars of Przemysłowy Instytut Telekomunikacji (PIT) (Industrial Telecomunications Institute)

• classic – distance, azimuth (2-D)

• 3D radars – distance, azimuth, elevation

82 R. Salamon & H. Lasota 2016-06-08 Antenna directivity IV

Radar antennae PIT 2 [207]

Radar antennae marine 3-D radar [208]

Radar antennae stationary 3-D radar [209]

83 R. Salamon & H. Lasota 2016-06-08 Antenna directivity IV

Radar antennae - BMEWS [210] Ballistic Missile Early Warning System Toroidal-parabolic antenna

Radar antennae - OTH (Over The Horizon) [211] Multielement, linear antenna

DUGA [212]

• Type of antenna – dipole wall

• Antenna surface 84

– Transmitter – 210 x 85 m – Receiver – 300 x 135 m

• Range – 3000 km

• Band – HF

• Frequency 4–30 MHz. R. Salamon & H. Lasota 2016-06-08 Antenna directivity IV

https://wiki/Duga_radar

Sonar antenna [213]

Hydroacustic antennae 1 [214]

Antennae

• singlebeam, multibeam

Antenna transducers (aperture)

• stationary, rotary

• singleelement, multielement

Apertures – linear (rods, towed “snakes”)

• ﬂat (rectangular, circular, parabolic)

• cylindrical (tubular, ﬂat on a cylindrical surface)

85 R. Salamon & H. Lasota 2016-06-08 Antenna directivity IV

Hydroacustic antennae 2 [215]

Antennae beams

• stationary, mobile

• shaped, „natural”

Beamforming is carried out in the add-and-delay systems using phase shifters (narrowband), delay lines (broadband)

21 Diﬀraction

21.1 Light diﬀraction Diﬀraction [216]

Wave distribution behind a hole (aperture): diﬀraction – “deﬂection” of light on the aperture edge

Young 1804, Rubinowicz 1917: “original” light waves plus a radiation from the edge

Grimaldi 1665, Huyghens 1670, Fresnel 1804, Helmholz 1859, Kirchhoﬀ 1882: re-radiation (re-emission) from the aperture surface

21.2 Fraunhofer’s diﬀraction Fraunhofer’s diﬀraction; far zone [217]

Bessel’s function (ﬁrst kind, ﬁrst order) dou- Sine over the argument sin α bled, over the argument Sa (α) = J1 (α) α Ja (α) = 2 α How it can be calculated? How such beams can be designed?

86 R. Salamon & H. Lasota 2016-06-08 Antenna directivity IV

21.3 The Kirchhoﬀ-Helmholz integral formula The Kirchhoﬀ-Helmholz integral formula [218]

Mathematically symmetric form 1 ∂ exp (−jkr) ∂ exp (−jkr) P R~ = P ( ~x0) − P ( ~x0) dS ( ~x0) π ∂n r ∂n r 4 S´

P – complex amplitude of pressure (as well as electromagnetic potentials) R~ – observation point at space ~x0– point on the radiating surface S S– radiating surface (should be closed around the point at space) r = r R,~ ~x0 – distance between the points R~ and ~x0

22 Radiation of acoustic and electromagnetic waves

22.1 Surface sources – the Rayleigh formula Radiation and reception of waves – scalar description (acoustics) [219]

v – velocity of vibration of the radiating surface (called aperture) Kirchhoﬀ’s integral formula −1 ejkr ∂~v ejkr p R~ = ρ0 + p grad dS~ 4π ¨ r ∂t r S

Rayleigh’s formula for plane surfaces embedded in an inﬁnite, rigid baﬄe

jkr0 ωρ0 e jk∆r p R~ = Vn (S) e dS Vn– normal component of surface velocity 2jπ r0 ¨ S

22.2 Near and far zone Near zone and far zone (near and far ﬁelds) [220]

a) observation point close to the antenna – we say that it is in the near ﬁeld (better - near zone). b) observation point far away from the antenna – we say that it is in the far zone. In the latter case, the radii r can be considered parallel. 87 R. Salamon & H. Lasota 2016-06-08 Antenna directivity IV

22.3 Rayleigh’s distance Near zone [221]

In near ﬁeld, the main part of the radiated power is contained in a prism with the aperture-shaped cross-section.

A square radiating surface, sides equal to λ0, 3λ0, and 9λ0, constant (uniform) velocity amplitudeVn. Near-zone limit (Rayleigh’s distance)

2 ∼ a db = π ≈ Al 4λ0

A square radiating surface, sides equal to 2λ0, 4λ0,and 5λ0, uniform (constant) velocity amplitudeVn.

[222]

Transition from Fresnel to Fraunhofer diffraction for a slit, (a) Fresnel pattern for edge of infinitely wide slit. (b)-(g) Actual diffraction patterns from slit, at distances indicated in upper diagram, (h) Fraunhofer pattern.

[223]

Diagram of light intensity behind a diﬀraction grating. R. Salamon & H. Lasota 2016-06-08 Antenna directivity IV

Intensity as heatmap for monochromatic light behind a grating. https://.../wiki/Diﬀraction_grating

22.4 Directivity pattern Far zone [224]

0 x = r0 sin θ cos ϕ 0 y = r0 sin θ sin ϕ 0 z = r0 cos θ ∆r =∼ −x sin θ cos ϕ − y sin θ sin ϕ

Rayleigh’s formula

jkr0 ωρ0 e −jkx sin θ cos ϕ −jky sin θ sin ϕ p (r0, θ, ϕ) = Vn (x, y) e e dxdy 2jπ r0 ¨ S

Pressure amplitude depends on the distance from the observation point to the antenna center (spherical wave) and on the angles pointing the observation point.

89 R. Salamon & H. Lasota 2016-06-08 Antenna directivity IV

Directivity pattern [225]

Deﬁnition Pressure on the acoustic axis of antenna jkr0 p (r0, θ, ϕ) ωρ0 e p(r0, 0, 0) = Vn (x, y) dxdy b (θ, ϕ) = | r0 = const jπ r p(r0, 0, 0) 2 0 ˜S A directivity pattern refers to the:

• far zone (far ﬁeld)

• harmonic wave of a deﬁned given frequency The directivity pattern does not depend on the distance from the observation point

Formula for determining a directional pattern

−jkx sin θ cos ϕ −jky sin θ sin ϕ Vn (x, y) e e dxdy b (θ, ϕ) = ˜S Vn (x, y) dxdy ˜S

22.5 Rectangular aperture directivity Directivity pattern of a rectangular aperture with a uniform velocity distribution [226]

lx/2 ly /2 1 b (θ, ϕ) = e−jkx sin θ cos ϕe−jky sin θ sin ϕdxdy S ˆ ˆ −lx/2 −ly /2 lx ly sin k sin θ cos ϕ sin k sin θsinϕ 2 2 b (θ, ϕ) = lx ly k sin θ cos ϕ k sin θsinϕ 2 2

lx – length of one side of the rectangle ly – length of the second side of the rectangle

Directivity pattern in Cartesian coordinates [227]

lx = 3λ0 ly = 2λ0

A = lx/λ0 = 3 B = ly/λ0 = 2 90 R. Salamon & H. Lasota 2016-06-08 Antenna directivity IV

Directivity patterns cross-section views [228]

sin (2π sin θ) b (θ, 90◦) = 2π sin θ

sin (3π sin θ) b (θ, 0◦) = 3π sin θ

b (θ, 34◦) = sin (3π sin θ cos 34◦) sin (2π sin θ sin 34◦) 3π sin θ cos 34◦ 2π sin θ sin 34◦

In practice, we commonly use mere cross-sectional views of a directivity pattern.

22.6 Circular aperture directivity Directivity pattern of circular surface (aperture) [229]

1 r 2π dS = ρdρdϕ ∆r = kρ sin θ cos ϕ b (θ) = ejkρ sin θ cos ϕρdρdϕ πr2 ´0 ´0 r 1 2J1 (kr sin θ) b (θ) = J0 (kρ sin θ) ρdρ = πr2 ˆ kr sin θ 0

Nominal beam width 0.27λ0 θ−3dB = 2 arcsin 2 · 0.54(λ0/2r) = 1.08/R R = 2r/λ r ≈

23 Directivity as space Fourier transform

23.1 Calculations of speciﬁc directivity patterns Application of the Fourier transform to calculations of directivity patterns [230]

The basic formula for calculating a one-dimensional directivity pattern ∞ ∞ −j2π x sin θ x −j2π x sin θ x b (θ) = v (x) e λ dx ⇒ b (θ) = v e λ d ˆ ˆ λ λ −∞ −∞ Normalization of the x dimension relative to the wavelength λ 91 R. Salamon & H. Lasota 2016-06-08 Antenna directivity IV

New variables: u = x/λ – normalized aperture variable ν = sin θ – normalized space frequency ∞ Ω = 2πν – normalized space angular frequency b (ν) = v (u) e−j2πuν du ˆ −1 ≤ ν ≤ 1 − 2π ≤ Ω ≤ 2π −∞ kθ = νk = k sin θ – wavelength-related space frequency

−k ≤ kθ ≤ k ∞ 1 b (k ) = v (x/λ) e−jkθ xdx θ λ ˆ −∞ Expressed in these variables, the directivity pattern is a Fourier transform of the velocity distribution along the line antenna (possibly representing a chosen equivalent cross-section of a surface antenna).

Examples of application of Fourier transforms to directivity pattern calculations [231]

Rectangular aperture

v (x, y) = const. A = lx/λ 1 Q 1 Q v (u) = (u/A) =⇒ v(x) = (x/lx) – velocity distribution along a line A lx sin (ΩA/2) b (Ω) = I {v (u)} = = Sa (ΩA/2) – space spectrum (normalized angular frequency) ΩA/2

sin (kθA/2) b (kθ) = I {v (x)} = = Sa (kθA/2) – space spectrum (“real” angular frequency) kθA/2

lx sin π sin θ sin (πA sin θ) λ b (θ) = = – directivity pattern πA sin θ lx π sin θ λ

Examples of linear velocity distributions at a square antenna aperture [232]

a) cross-section along the symmetry axis b) section along the diagonals c) arbitrary cross-section One-dimensional (linear) distributions are formed as orthogonal projections of Dirac’s distributions onto a selected cross-section Directivity patterns in a selected cross-section is calculated for the corresponding equivalent linear/line distribution.

92 R. Salamon & H. Lasota 2016-06-08 Antenna directivity IV

Distribution along an arbitrary cross-section (other than characteristic ones) [233]

0 xnm = xn cos ϕ + ym sin ϕ

Directivity pattern for a triangular distribution of aperture excitation [234]

Triangular distribution as a space convolution integral of rectangular distributions 1 h 1 i h 1 i 1 h 1 i h 1 i v (u) = Λ(u/2A) = Q (u/A) ∗ Q (u/A) =⇒ v (x) = Λ(x/2l ) = Q (x/l ) ∗ Q (x/l ) 2 2 x x x A A A lx lx lx

Space spectrum n 1 Y o n 1 Y o h sin (ΩA/2) i2 b (Ω) = I (u/A) · I (u/A) = =⇒ b(k ) = Sa2(k A/2) A A ΩA/2 θ θ

The directivity pattern of a triangular distribution is the square of the one related to respective rectangular distribution.

23.2 Space spectrum visible range Space (spatial) spectrum [235]

93 R. Salamon & H. Lasota 2016-06-08 Antenna directivity IV

23.3 Directivity pattern parameters Parameters of a directivity function/pattern [236]

0.44λ 0.44 3-dB beam width: θ−3dB = 2 arcsin = 2 arcsin ≈ 0.88/A lx A π zeros of space spectrum: Ω0n = ±2 n =⇒ ν0n = ±n/A A π 1 ∼ maxima of space spectrum: ΩMn = ± (2n + 1) =⇒ νMn = ±(n + )/A A 2 2 2 ∼ ∼ side-lobe levels: b (ΩMn) = = ΩMn π (2n + 1)

number of side lobes: Nb < 2A − 1 Note:

The level of subsequent side lobes does not depend on antenna length.

23.4 Logarithmic view of directivity Logarithmic graph of the directivity pattern of linear apertures with constant velocity distribution [237]

bdB (θ) = 20 log |b (θ) |

94 R. Salamon & H. Lasota 2016-06-08 Antenna apertures and arrays V

Part V Practical theory of antenna apertures and arrays

[2016_06_08_EchoMeth_script_GD_HL]Practical theory of antenna apertures and arrays [H. Lasota]Henryk Lasota 2016-06-08

24 Space-domain Fourier transform

24.1 Space version of the sampling theorem Space version of the sampling theorem [239]

Time version In order to reproduce (restore) the f(t) with a spectrum limited to ωM , from samples taken at intervals T , the interval has to meet the condition: T < TM , where TM = π/ωM = 1/2fM (half period of the upper spectrum limit). Space version In order to reproduce (restore) the f (ξ) with a space spectrum limited to kθM , from samples taken at distances (space intervals) intervals d, the interval has to meet the condition: d < dM , where dM = π/kθM . Because kθM = k sin θM , hence d < λ/2sinθM . Conclusion (discrete aperture = antenna array) In order to eﬃciently retrieve space signal samples using a matrix of points along the line (or plane), it is necessary to provide spacing between themd < λ/2. If it is certain, that the signal comes from an ◦ angular sector limited by angles +/ − θM , the interval may be smaller (for θM = 30 it gives d < λ).

24.2 Fourier transform space properties Fourier Transform in space radiation and reception problems [240]

R. Bracewell, The Fourier transform and its applications, McGraw-Hill, 1978

• A. Vocabulary – Transform pairs

• B. Grammar – Transform features

Mind the change of functions in Figs.!

i.e. :α = kθa/2 β = kθd/2

v(x) =⇒ f(x)

b(kθ) =⇒ F (kθ)

95 R. Salamon & H. Lasota 2016-06-08 Antenna apertures and arrays V

24.3 Fourier transform pairs A. Fourier transform pairs 1, 2 – Two point sources [241]

1 – in phase

f(x) = +δ(x + d/2) + δ(x − d/2) F (kθ) = 2 cos (kθd/2) = 2 cos β

2 – in antiphase:

f(x) = −δ(x + d/2 + δ(x − d/2) F (kθ) = 2 sin (kθd/2) = 2 sin β

β = kθd/2 d – distance between sources.

A. Fourier transform pairs 1,2 [242]

Here also the well-known associations occurs: ◦ ◦ kθ = k sin θ 90 ≤ θ ≤ +90 − k ≤ kθ ≤ k therefore: kd 2π d d |kθ| ≤ k and |β| ≤ = = π = πD 2 λ 2 2 d where D = – normalized distance between two radiating points λ This is important for the practice of excitation of point sources working in sets (eg. stereo speakers). An incorrect polarity of adjacent speakers can lead to their mechanical damage and destruction of power stage of ampliﬁers (the case of sin β directivity function instead of expected cos β, for D 1).

A. Fourier transform pairs 3 – Single source [243]

f(x) = δ(x) F (kθ) = const.

In this case the ﬁeld is omnidirectional in acoustics (toroidal in electromagnetics)

96 R. Salamon & H. Lasota 2016-06-08 Antenna apertures and arrays V

A. Fourier transform pairs 4 – Cross section of rectangular aperture [244]

( b, x < a/2 f(x) = bΠ(x/a) = =⇒ F (kθ) = ab Sa(kθa/2) = ab Sa(α) 0, x > a/2

α = kθa/2 a – aperture length.

A. Fourier transform pairs 5 – Gauss excitation (no side lobes) [245]

h 2i h 2i f(x) = exp −π (x/d) =⇒ F (kθ) = exp −π (dkθ/2)

When the bell curve of the aperture excitation widens, that of the space spectrum narrows down.

A. Fourier transform pairs 6 – Diﬀraction grating [246]

x P 1 dkθ 1 P f(x) = Ø = δ(x − id) =⇒ F (kθ) = Ø = δ(kθ − i2π/d) d d 2π d

When the emitting point distribution gets scarce, the space spectrum fringes get dense, and more diﬀraction fringes appear in the visible range.

97 R. Salamon & H. Lasota 2016-06-08 Antenna apertures and arrays V

24.4 Fourier transform theorems B. Fourier transform features 1 – similarity (scale) theorem [247]

B. Fourier transform features 2 – superposition and 3 – shifting theorems [248]

2. Superposition theorem:

f (x) = f1 (x) + f2 (x) ←→ F (kθ) = F1 (kθ) + F2 (kθ) quite obvious and very (!) useful.

3. Shifting theorem – beam deﬂection

f (x) · exp (−jkex) ←→ F (kθ − ke)

Phased antenna array [249]

Implementation of the shifting theorem in practice requires the use of multielement apertures (phased arrays), isolated both electrically and mechanically:

P P f(x) = δ(x − id) =⇒ f(x) = δ(x − id) exp(−jkθid)

98 R. Salamon & H. Lasota 2016-06-08 Antenna apertures and arrays V

B. Fourier transform features 4 – convolution/multiplication theorem [250]

4. Theorem of convolution and multiplication:

a) f (x) = f1 (x) ∗ f2 (x) ⇔ F (kθ) = F1 (kθ) · F2 (kθ)

b) f (x) = f1 (x) · f2 (x) ⇔ F (kθ) = F1 (kθ) ∗ F2 (kθ)

Using these principles, it can be shown that the reduction of the infinitely wide diffraction grating to a reasonable size leads to a smearing of each diffraction fringe in the space spectrum. It is also easy to prove that when the weighing excitation applied to the aperture function of a triangular window, a side lobe level decreases twice (measured in dB), at the cost of the main lobe widening.

Multiplication principle of directivity functions/patterns [251]

Directional functions of M ﬁnite sources is equal to the product of the directional radiation of M point sources and the characteristics of a single ﬁnite source:

fMw (x) = fM (x) ∗ fw (x) – excitation distribution

FMw (kθ) = FM (kθ) · Fw (kθ) – directivity function (maths)

DMw (ϑ, ϕ) = DM (ϑ, ϕ) · Dw (ϑ, ϕ) – directivity pattern (physics)

This principle is a manifestation of the theorem of convolution and multiplication.

B. Fourier transform features 5 – derivation/integration theorem [252]

5. Theorem of derivative and integral: d f (x) ↔ jkθF (kθ) dx

F (kθ) f (x) dx ↔ ˆ jkθ

Fourier transform features – application of theorems 4 and 5 in directivity calculations [253]

The distribution f (x) of a trapezoid shape represents a projection of the uniform excitation of a rectangular aperture onto an oblique plane.

It can be represented as the integral of the f1 (x) distribution in the form of two gate function spaced apart with opposite signs. This in turn may be considered as the convolution of a sum of two spaced Dirac pulses with opposite signs f2 (x) and single gate function f3 (x). For the above situation, the following relations are used:

f (x) = f1 (x) dx f1 (x) = f2 (x) ∗ f3 (x) ´

In the space spectrum domain it corresponds to: F1 (kθ) F (kθ) = F1 (kθ) = F2 (kθ) · F3 (kθ) jkθ leading to the known solution of the rectangular aperture directivity in any cross section (not only horizontal or vertical) 99 R. Salamon & H. Lasota 2016-06-08 Antenna apertures and arrays V

25 Aperture functions vs. directivity

25.1 Directivity functions (maths) Directivity function of M = 5 point sources [254] M = 2N − 1 (odd)

100 R. Salamon & H. Lasota 2016-06-08 Antenna apertures and arrays V

Directivity function of M = 6 point sources [255] M = 2N (even)

25.2 Directivity patterns (engineering) 25.2.1 Antenna arrays (discreet apertures) Directivity pattern of M = 6 point sources speciﬁc cases [256] D = 1/6, 1/2, 5/6, and 5/6 + δ

Directivity pattern of M = 7 point sources a speciﬁc case [257] D = 6/7

101 R. Salamon & H. Lasota 2016-06-08 Antenna apertures and arrays V

M = 6 point sources – case of no grating lobes (diﬀraction ones) [258] D = 0.8

M = 7 point sources – case of sparse distribution [259] D = 1.8

102 R. Salamon & H. Lasota 2016-06-08 Antenna apertures and arrays V

25.2.2 Continuous antennae (continuous aperture distributions) Line source a = 3.5λ – directivity function and directivity pattern [260] A = 3.5

Line source a = 7λ – directivity function and directivity pattern [261] A = 7

103 R. Salamon & H. Lasota 2016-06-08 Antenna apertures and arrays V

26 Multielement antennas

26.1 Planar multielement antenna Two dimensional convolution of excitation distributions [262]

Velocity distribution at the antenna surface (in the aperture)

P P V (x, y) = V1 (x − xn, y − yn) = V1 (xy) ∗ δ (x − xn, y − yn) n n

26.2 Principle of beam patterns multiplication Beam pattern multiplication [263]

The principle of directivity pattern multiplication If the antenna is made of identical elements having a directivity pattern b1 (θ), and the directivity pattern of the array of points at which these components are placed is bn (θ), then the antenna directivity pattern b (θ)is the product of the former two patterns: b (θ) = b1 (θ) · bn (θ) Diﬀraction lobes vs visible spectrum range Condition for the absence of diﬀraction lobes in the range of the space spectrum visible angles: d ≤ λ/2

A smoother condition for the absence of diﬀraction lobes - can be applied when the main beam is deﬂected by a small angle: d ≤ λ

The greater distances d ≤ λ can be used when the beam is not deﬂected and the antenna is nearly fulﬁlled with elements.

26.3 Uniformly excited antenna arrays Directivity patterns for uniform distributions of excitation [264]

Vibration distribution N P vn (x) = δ (x − ndx) dx– distance between Dirac impulses −N

Distribution put in the Fourier transform convention 104 R. Salamon & H. Lasota 2016-06-08 Multibeam technique VI

N ∞ P 1 Q P vn (u) = δ (u − nd) = (u/L) · δ (u − nd) L – antenna length −N L −∞

Space spectrum ∞ 1 Q 2π P bn (Ω) = I { (u/L)} ∗ δ (Ω − nΩs)Ω s = 2π/d 2π d n=−∞

Directivity pattern ∞ ∞ 1 P 1 P bn (Ω) = Sa (Ω · L/2) ∗ δ (Ω − nΩs) = Sa [(Ω − nΩs) L/2] d n=−∞ d n=−∞

26.4 Array of point sources Space spectrum of a linear array of point sources [265]

sin [Mπ (d/λ0) sin θ] sin (Mβ) b (θ) = = – directivity pattern/function of M = 2N + 1 or M = 2N M sin [π (d/λ0) sin θ] M sin β element antenna (above – M = 6)

26.5 Multi-element antenna array Directivity pattern of a multi-element antenna [266]

M = 7 d/λ = 2 l/λ = 1, 8

105 R. Salamon & H. Lasota 2016-06-08 Multibeam technique VI

Part VI Multibeam system technique

[2016_06_08_EchoMeth_script_GD_HL]Multibeam system technique [H. Lasota]Henryk Lasota 2016-06-08

27 Single- and multibeam sector observation

27.1 Methods of volume scanning Multibeam system technique [268]

Methods of area (observation sector) scanning:

• single, immobile beam – motion of the antenna or a system carrier (mechanical)

• single, rotating beam – electronic scanning (immobile antenna)

• multiple simultaneously generated, deﬂected beams – beamforming (immobile antenna)

The main task of the multibeam systems is to reduce the search time of a given area. Beamforming is performed in receivers exclusively. „Irradiation” of the angular sector covered by the receiving beams is performed by a broad transmitting beam or by a scanning method. Applications:

• underwater acoustic systems (because of low propagation speed)

• radar systems (to avoid mechanical rotation of big antennae)

• ultrasonic diagnostics (to avoid mechanical rotation of a transducer)

27.2 Simultaneous multibeam observation Space arrangement of beamformer beams [269]

Area/sector search time: 2Rz Θ Φ tp = c θ3dB φ3dB For an assumed range and preserved resolution, the search time of an angular sector is reduced as many times as is simultaneously produced beams – in relation to a single beam system.

106 R. Salamon & H. Lasota 2016-06-08 Multibeam technique VI

28 Multibeam systems structure

28.1 Antenae of multibeam systems Multielement antenna [270]

In multi-beam systems, it is necessary to use multielement antennae. The aperture of multielement antennae can be planar, cylindrical, or spherical.

28.2 Multibeam system receiver Structure of a multibeam system receiver [271]

The number of independent APB channels is equal to the number of independent elements of the antenna. The number of independent beams at the beamformer output is diﬀerent (lower) than the number of the antenna elements.

107 R. Salamon & H. Lasota 2016-06-08 Multibeam technique VI

29 Beamformer technology

29.1 Technology classiﬁcation criteria Beamformer classiﬁcation [272]

Due to method used: Due to type of processed signals:

• delay-and-sum beamformers • narrowband,

• space spectrum estimators • broadband.

Due to technology: Due to domain of signal processing:

• analogue, • working in the time domain,

• digital. • working in the frequency domain.

29.2 Delay-and-sum beamformers Working principle of a narrowband, delay-and-sum beamformer [273]

Beamformer producing beams in one plane

Signal at the output of n-th antenna element sn (t, θ) = S0 sin {2πf0 [t − τgn (θ)] + ϕ}

“Geometric” delay nd τgn (θ) = − sin θ c

In order to produce one deﬂected beam, the signals in each channel signal are delayed in such a way that total delay in each channel is equal. All such delayed signals are summed to give the signal of a tilted/deﬂected beam.

108 R. Salamon & H. Lasota 2016-06-08 Multibeam technique VI

Delay-and-sum processing [274]

Signal at the output of the k-th summator/adder – k-th beam signal N P s (t, θ, θk) = S0 sin {2πf0 [t − τgn (θ) − τn (θk)] + ϕ} −N The condition of phase compli- Electrically induced delay ance/conformity nd τn (θk) = τs + sin θk τgn (θk) + τn (θk) = τs c

Deﬂected beams [275]

Signal at the k-th adder output N P nd s (t, θ, θk) = S0 sin 2πf0 t + (sin θ − θk) + ϕ − ϕs −N c

sin [Mπ (d/λ0) (sin θ − sin θk)] s (t, θ, θk) = S0M sin (2πf0t + ϕ − ϕs) M sin [π (d/λ0) (sin θ − sin θk)]

Directivity pattern of the k-th beam

sin [Mπ (d/λ0) (sin θ − sin θk)] b (θ, θk) M sin [π (d/λ0) (sin θ − sin θk)] Beam width ∼ λ0 1 θ−3dB = 50.4 Md cos θk

The beam deﬂects by a given/speciﬁed angle and is widening. Conclusion: It is advised not to use a too wide sector of simultaneous observation.

◦ θk = 30

109 R. Salamon & H. Lasota 2016-06-08 Multibeam technique VI

29.3 Multiple directivity patterns Beamformer directivity patterns [276]

Typically, the beams are deﬂected by an angle equal to an integer multiple of the width of the central beam.

29.4 Finite dimensions of antenna elements Inﬂuence of limited dimensions of antenna elements on beamformer directivity patterns [277]

Principle of pattern multiplication.

(M = 11, d/λ = 0.6, l/λ = 0.55, deflection angle 9◦)

110 R. Salamon & H. Lasota 2016-06-08 Multibeam technique VI

Comparison with multipoint array [278]

◦ (M = 11, d/λ = 0.8, l/λ = 0.75, θ1 = 7 )

Note: In point arrays, an excessive distance between the points results in appearance of diffraction lobes in deflected beams. The individual element directivity patterns reduces the level of diffraction lobes.

29.5 Aperture weighing (apodization) Inﬂuence of amplitude weighing on beamformer directivity pattern [279]

Amplitude weighing – symmetric case N P nd s (θ, θk) = Wn cos 2π (sin θ − sin θk) Wn– amplitude weighing function. −N λ0

Note: Amplitude weighing do not reduce the level of diﬀraction lobes.

29.6 Analog phase beamformers Narrowband, analog phase beamformers [280]

For sinusoidal signals, delays can be replaced by phase shifts.

nd nd ϕn (θk) = 2πf0 sin θk = 2π sin θk c λ0

A technical problem: to realize phase shifting devices operating in full range (from 0 to 2π), basing on RLC circuits.

The technical solution: Beamformer with quadrature detection: sxn (t, θ) = Sn sin {2πf0 [t − τgn (θ)] + ϕ} sin (2πf0t) 111 R. Salamon & H. Lasota 2016-06-08 Multibeam technique VI

syn (t, θ) = Sn sin {2πf0 [t − τgn (θ)] + ϕ} cos (2πf0t) After baseband ﬁltration: 1 1 xn (t, θ) = Sn cos [ϕgn (θ) − ϕ] yn (t, θ) = − Sn sin [ϕgn (θ) − ϕ] 2 2

Scheme of signal processing in a single channel for a selected beam deﬂection angle [281]

Number of beamformer processing circuits: U= NK

After performing the operations shown at the diagram: 1 1 yn (t, θ, θ ) = Sn sin [ϕgn (θ) + ϕn (θ ) − ϕ] xn (t, θ, θ ) = Sn cos [ϕgn (θ) + ϕn (θ ) − ϕ] k 2 k k 2 k sn (t, θ, θk) = xn (t, θ, θk) sin (2πf0t) − yn (t, θ, θk) cos (2πf0t)

1 sn (t, θ, θk) = Sn sin [2πf0t − ϕgn (θ) − ϕn (θk) + ϕ] 2

29.7 Digital beamformers Digital beamformers [282]

Classiﬁcation:

• Bemformers operating in time domain:

– with oversampling, – with interpolation.

• Bemformers operating in frequency domain:

– narrowband, – broadband.

• Beamformers with a space spectrum estimation.

The time and frequency domain digital beamformers realize digitally the above mentioned methods/techniques of delay-and-sum processing of signals. The space spectrum estimation is realized numer- ically.

112 R. Salamon & H. Lasota 2016-06-08 Multibeam technique VI

29.8 Time-domain beamformers Time-domain beamformers [283] Beamformers perform direct delay of arbitrary signals – narrowband and broadband.

Signal at the input of n-th antenna element

sn (t, θ) = S0s [t − τgn (θ)]

sn (i, θ) = S0s {∆t [i − τgn (θ) /∆t]} – sampling τgn (θ) sn (i, θ) = S0s [i − in (θ)] – discrete signal in (θ) = ∆t n (d/c) sin (θk) Tg in (θk) = = n sin (θk) ∆t 2∆t

Tg = d/c for upper frequency limit

According with Nyquist’s theorem

1 Tg ∆t <= = 2fg 2

in (θk) = n sin (θk) The required delay is not an in- ∼ 180 fs = fsN teger number – it is necessary to πθ1 increase the sampling frequency .

29.9 Interpolation beamformers Interpolation beamformer [284]

Interpolation beamformers are used for decreasing the sampling frequency to Nyquist’s frequency and limiting beamformer memory.

Interpolation:

• zero padding (insertion)

• digital baseband ﬁltration

Interpolation or oversampling coeﬃcient

Fs 180 I = = FsN πθ1 The sampling frequency must be at least I times higher than the Nyquist frequency.

29.10 Nyquist frequency sampling Narrowband digital beamformers with the Nyquist frequency sampling [285]

Signal samples in the n-th channel xn (i, θ) = An (i − ign) cos [2πai − ϕgn + ϕ0] Signal after the Hilbert transformation yn (i, θ) = An (i − ign) sin [2πai − ϕgn + ϕ0]

Calculation algorithm of the signal in the k-th deﬂected beam N N X X b (i, k) = x (i, n) cos [ϕ (n, k)] − y (i, n) sin [ϕ (n, k)] n=1 n=1 113 cos [ϕ (n, k)] = cos [ϕn (θk)] R. Salamon & H. Lasota 2016-06-08 Multibeam technique VI

sin [ϕ (n, k)] = sin [ϕn (θk)] Result: N ∼ X b (i, k) = NA (i) cos [2πai − ϕg (n) + ϕ (n, k) + ϕ0] n=1 The amplitude of b(i, k) is proportional to the above given beamformer directivity pattern.

Operating scheme of digital phase beamformer [286]

The Hilbert transformer can be replaced by 90◦phase-shift circuits, but this deteriorates beamformer parameters, especially when the signal spectrum is relatively wide.

29.11 Quadrature detection Narrowband digital beamformer with quadrature detection [287]

Signal in n-th channel sn (t, θ) = An (t, θ) sin [2πf0t + ϕgn (θ)] Signal samples after quadrature detection yn (i, θ) = An (i, θ) sin [ϕgn (θ)] xn (i, θ) = An (i, θ) cos [ϕgn (θ)] Complex samples sˆ(i, θ) = xn (i, θ) + jyn (i, θ) = An (i, θ) exp {j [ϕgn (θ)]}

sˆ(i, n) = An (i, θ) exp [jϕn (θ)] Beamformer algorithm N X S (k, i) = w (k, n) s (n, i) W (k, n) = exp [−jϕn (θk)] n=1

Beamformer algorithm matrix [288]

d ϕn (θk) = 2πf0 (n − 1) sin θk c

 S (1)   w (1, 1) w (1, 2) . . . w (1, n) . . . w (1,N)   s (1)   S (2)   w (2, 1) w (2, 2) . . . w (2, n) . . . w (2,N)   s (2)         .   ......   .   .   ......   .    =   ·    S (k)   w (k, 1) w (k, 2) . . . w (k, n) . . . w (kN)   s (n)         .   ......   .   .   ......   .  S (K) w (K, 1) w (K, 2) . . . w (Kn) . . . w (K,N) s (N)

S = ws 114 R. Salamon & H. Lasota 2016-06-08 Multibeam technique VI

30 Space spectrum estimation

30.1 Angle of signal arrival vs space frequency Space spectrum estimation [289]

Basics of the technique

Acoustic pressure at a straight line: h x i p (x, t) = pk sin ω0 t + sin θk + ϕ0k c

Pressure distribution at a given moment t = t0 (ω0t0 = ϕ0) – sampling in the time domain x x p (x, t0) = pk sin ω0 sin θk + ϕ0 + ϕ0k ; p (x, t0) = pk sin 2π sin θk + ϕ0 + ϕ0k c λ0

New variable (space counterpart of the time) – quotient x/λ0. The frequency of the pressure distribution is Fk = sin θk – space frequency. Angular frequency Ωk = 2πFk – space angular frequency. These relations are made use of when the directivity patterns are determined with the Fourier transform technique.

30.2 Space sampling Sampling in the space domain [290]

Space sampling means a placement of point elements of a receiving antenna, at a straight line, with a constant distance d between them.

Nyquist’s criterion

d 1 ≤ λ0 2Fkmax

Values of the pressure distribution samples at the moment t = t0 : nd s (n) = Snpk sin 2πFk + ϕ0 + ϕ0k λ0

Antenna elements should be distant no more than half a wavelength ( d/λ0 ≤ 1/2 ) one from another.

30.3 Quadrature sampling in the time domain Complex samples [291]

Quadrature sampling in the time domain x (n) = S0pk cos (πnFkn + ϕk) t = t0 y (n) = S0pk sin (πnFkn + ϕk) t = t0 + T0/4 Complex form of samples

j(πFkn+ϕk) sˆ(n) = x (n) + jy (n) = S0pke In the case of a single wave incident on the antenna from a certain direction, the angle of wave incidence and wave amplitude can be determined from the following formulas:

1 1 p 2 2 Fk = ln [exp (jπFk)] pk = x (n) + y (n) jπ S0 115 R. Salamon & H. Lasota 2016-06-08 Multibeam technique VI

Practical case: Let us assume k waves of the same frequency impinging from diﬀerent angles:

K X sˆ(n) = S0 pk exp [j (πnFk + ϕk)] – sample values k=1 Continuous spectrum of sample series ∞ K jω P P S e = S0 pk exp [j (πnFk + ϕk)] exp (−jnω) n=−∞ k=1

Spectrum fringes [292]

K ∞ jΩ P P S e = S0 pk exp (jϕk) exp [jπn (Fk − F )] k=1 n=−∞ ∞ P sin [πM (Fk − F ) /2] exp [jπn (Fk − F )] = lim = δ (Fk − F ) n=−∞ M→∞ sin [π (Fk − F ) /2]

K Spectrum fringes determine the space frequencies jΩ X S e = S0 pk exp (jϕk) δ (Fk − F ) (angles of arrival) and amplitudes of the received k=1 waves.

30.4 Spectrum measured by ﬁnite antenna Finite antenna length [293]

Finite antenna length – K elements K jΩ P sin [πM (F − Fk) /2] S e = S0M pk exp (jϕk) k=1 M sin [π (F − Fk) /2]

With a ﬁnite number of antenna elements, we receive the same directivity patterns as in a beamformer cooperating with such an antenna.

116 R. Salamon & H. Lasota 2016-06-08 Multibeam technique VI

30.5 Digital space spectrum estimation Digital realization of space spectrum estimation [294]

Discrete Fourier transform N Sˆ (k) = P sˆ(n) exp [−j2π (n − 1) (k − 1) /N] n=1

sin {πN [Fm/2 − (k − 1) /N]} Sˆ (k) = S0pmN N sin {π [Fm/2 − (k − 1) /N]}

(M = 32, d/λ0 = 0, 5 p1 = 1P a, ◦ ◦ θ1 = −30 , p2 = 1P a, θ2 = 32 ) The Fourier technique is more eﬀective in numerical calculations than beamforming, for bigger number of antenna elements (starting fromN ≥ 32)

30.6 Space spectrum of wideband signals Inﬂuence of signal spectrum width on the directivity pattern shape of phase beamformers [295]

Phase beamformers compensate precisely geometric phases only for the middle (or center) frequency. The wider is a spectrum, the higher are errors. N 1 P sin [πn (fg/f0) g (θ, θk)] b (θ, θk) = cos [πng (θ, θk)] g (θ, θk) = sin θ − sin θk M n=−N πn (fg/f0) g (θ, θk)

Beamformer directivity patterns: a – for wideband signal, b – for narrowband signal of frequency f0 (M = 19, fg/f0 = 0.2, dλ0 = 0.5)

117 R. Salamon & H. Lasota 2016-06-08 Multibeam technique VI

Percentage increase in the width of the beam due to incomplete compensation of phase [296]

◦ (B = 2fg, θk = 30 )

Increase in the width of the beam caused by an incomplete compensation of phase [297]

◦ ◦ ◦ (fg/f0 = 0.2; θk = 15 , 30 and 45 )

Transients in phase beamformers [298]

Phase beamformers do not compensate geometric delays arising from diﬀerent times of arrival (TOA) of the wave front at antenna elements.

Envelope of a received rectangular pulse vs. time and angle ◦ (M = 7, d/λ = 0.5, θk = 30 , pulse length equal to the antenna length) 118 R. Salamon & H. Lasota 2016-06-08 Multibeam technique VI

31 High-resolution methods of space spectrum estimation

31.1 Linear prediction technique High-resolution methods of space spectrum estimation [299]

In the above discussed conventional beamformers and Fourier method the angular resolution depends on the length of the antenna. The high-resolution methods make it possible to obtain to very good resolution without increasing the antenna length. Basic idea - an apparent increase of the antenna length by generation of additional signals "received" by apparent antenna elements. Linear prediction technique: By a proper selection of coeﬃcients ap, we determine the value of signal sample s(n), having measured samples s(n − 1), s(n − 2), . . . , s(n − P ). The sample s(n) equals:

P X s (n) = − aps (n − p) p=1 Idealistic hypothesis: s(n) – calculated sample is equal to the actual sample sr(n).

It is the so-called parametric autoregresive (AR) model of a linear system of P th-order.

Estimation errors [300]

Realistic hypothesis: calculated sample diﬀers from the actual one by an error e(n): s (n) − sr (n) = e (n)

Causes of errors:

• measured samples diﬀer from the actual ones by the noise and measurement errors

• coeﬃcients ap have been determined incorrectly (they are determined on the basis of erroneous values of samples and, additionally, the calculation method itself can be burdened with error.

P X s (n) + aps (n − p) = e (n) p=1 With an unlimited number of distribution samples, the space spectrum can be determined by the above-described Fourier transform - with, theoretically, an inﬁnitely good resolution.

[301]

With the system model (the coeﬃcients ap), the space frequencies (coordinates) can be determined much easier using the method shown below. The Fourier transform of a diﬀerence equation: ( P ) P I s (n) + aps (n − p) = I {e (n)} p=1

From the shifting theorem: " P # P S (k) 1 + ap exp (−j2πpk/P ) = e0 for the white noise p=1 119 R. Salamon & H. Lasota 2016-06-08 Multibeam technique VI

Power density (energy) spectrum: σ2 |S k |2 ( ) = 2 P P 1 + ap exp (−j2πpk/P ) p=1 2 The poles of |S (k)| determine the space frequencies (sines of angles of incidence).

[302]

The coeﬃcients ap are determined by one of several common methods used for spectrum estimation. They can be found in the literature. In the MATLAB environment, there are functions performing the estimation with certain methods. Major drawbacks and limitations of the spacel spectrum estimation methods:

• high sensitivity to low signal to noise ratio, that manifests itself by errors in the determination of space frequency, by appearance of false space frequencies, etc.

• diﬃculties in proper selection of the model order; when it is too small (smaller than the number of incident waves) the determined frequencies are lost, merged and shifted; at too high the model order, false spectrum fringes appear that might be misinterpreted as coming from actual targets.

General conclusion: Methods of space spectrum estimation have not replaced the beamforming methods in hydro- and radiolocation, and are optionally used as complementary ones. They can be used in echolocation systems in automatic control, where the signal to noise ratio is good (high).

Burg’s method [303]

%The program calculates the PSD with the Burg method, for three sinusoidal signals downloaded/retrieved in quadrature from 32 antenna elements % Model of the 8th order % SNR=12 dB for the s2 sinusoid (15 dB for the biggest, 9dB for the smaller) C=zeros(10,256); % Memory reservation for m=1:100; % 100 realizations x=1:32; s1=1.4*exp(i*(pi*x*sin(pi*30/180))); s2=1*exp(i*(pi*x*sin(pi*60/180))); s3=0.7*exp(i*(-pi*x*sin(+pi*45/180))); % Generation of signals s=s1+s2+s3+0.25*randn(1,32)+i*0.25*randn(1,32); %Signal received with noise P=pburg(s,8)’; % The function determining spectrum fringes by the Burg method A=P(1:128); % The left half of spectrum fringes B=P(129:256); % The right half of spectrum fringes C(m,:)=[B A]; % Switching the halves of the spectrum. Building a matrix of 100 realizations end Y=sum(C); % Total of 100 spectra YA=Y.^0.5; % Square root of the power spectrum density MY=max(YA); % Maximum value skala=-1+1/128:1/128:1; plot(skala,YA/MY,’k’) %Graph of the power spectrum density square root

120 R. Salamon & H. Lasota 2016-06-08 Special purpose systems VII

Burg’s method spectrum – 100 snapshots averaged (1) [304]

SNR= +20 dB SNR= +12 dB SNR= +6 dB

SNR= +2.5 dB SNR= 0 dB SNR= −6 dB

Burg’s method spectrum – 100 snapshots averaged (2) [305]

SNR= −9.5 dB SNR= −12 dB SNR= −14 dB

“Power” of averaging Results as good as in the case of one snapshot with 20 dB lower noise level (0.025 instead of 0.25).

121 R. Salamon & H. Lasota 2016-06-08 Special purpose systems VII

Part VII Special purpose echolocation systems

[2016_06_08_EchoMeth_script_GD_HL]Special purpose echolocation systems [H. Lasota]Henryk Lasota 2016-06-08

32 Beam focusing

Special echolocation systems [307]

Focused beam The purpose of focusing is to improve the angular resolution by concentrating the beam in a small area in the near ﬁeld (near zone) of the antenna.

Focusing is carried out by a proper delaying the signals transmitted and/or received by individual antenna elements. 2 ∆r (n) [(n − 1) d] Delay: τ (n) = =∼ Quadratic dependence! c 2r (0) c

Focused beams [308]

Beamformer compensates the delay with one of the methods described above in the time or frequency domain. Remarks: Focusing is effective in the mere near field. Focus can be shifted dynamically throughout the entire area of the near field. Focusing is mainly used in medical diagnostic ultrasound.

Field distribution of a focused beam Standard near-ﬁeld distribution of line aperture (without focusing)

122 R. Salamon & H. Lasota 2016-06-08 Special purpose systems VII

Hologram as amplitudes-and-phases recorded at a plane surface [309]

Close-up photograph of a hologram’s surface. The object in the hologram is a toy van. It is no more possible to discern the subject of a hologram from this pattern than it is to identify what music has been recorded by looking at a CD surface. Note that the hologram is described by the speckle pattern, rather than the “wavy” line pattern (wikipedia.org). http://en.wikipedia.org/wiki/Holography

33 CW FM radars and sonars

CW FM radars and sonars [310]

Distance measurement [311]

The distance to the target is calculated by changing the scale of the spectrum (only to the half of maximum frequency). cT R = F 2B

Spectrum of a CW FM sonar diﬀerence signal 123 R. Salamon & H. Lasota 2016-06-08 Special purpose systems VII

Moving target [312]

Motion of the target makes the echo frequency changing due to the Doppler effect. The frequency change is ∼ 2v fd = f0 c As a result, the difference frequency changes: τ 2v F = F0 + fd = B + f0 T c This causes an error in the evaluation/estimation of the target distance T f0 R = R0 + v B ∆R T f0 f0 v = v = 2 Rz BRz B c Furthermore, it reduces the magnitude of spectrum fringes, making their detection more difficult. These errors are important mainly in sonar and aerolocation systems, where v/c is high; in the radiolocation this quotient is very small.

Velocity-induced distance errors [313]

34 Quiet radars

Quiet radars [314]

How a CW FM radar can be “quiet” or “silent”, meaning more difficult to be detected by a third party receiver that listen/intercept radar signals? The CW FM radar receiver performs matched filtering (here the Fourier transform). Signal to noise ratio is thus proportional to the energy of the emitted signal. In the CW FM radars, the signal duration is extended and its power is proportionally reduced, while retaining enough energy to detect a target. The receiver of an enemy is not matched to our radar signal (it is not known to him!). The signal-to-noise ratio at such a receiver is thus proportional to the received signal power, and this is very small. Detection is, therefore, much more difficult or even impossible.

Quiet radars 2 [315]

The spectrum of the CW FM radar signal is broad, making it diﬃcult to detect with spectrum analysis techniques. The CW FM radar signal is continuous that makes it diﬃcult to be observed by an increase of the instantaneous power of the received signal (noise). The latter is natural in typical pulse radars. 124 R. Salamon & H. Lasota 2016-06-08 Special purpose systems VII

PIT quiet radar [316]

CRM 203 radar – power 1mW – 2 W, beam width 0.7deg, range up to 48 Mm Quiet (“silent”) marine radars have been manufactured in Poland by PIT* (the Telecommunications Research Institute) in Gdańsk (shortly Bumar Electronics, now PIT-Radwar). *)Przemysłowy Instytut Telekomunikacji – Industry Institute of Telecommunications (Warsaw, Gdańsk, Wrocław).

35 Synthetic aperture radars and sonars

Synthetic aperture radars and sonars [317]

Synthetic aperture radars (SAR) and sonars (SAS) are used to increase the lateral (transversal) resolution, which depends in common radars and sonars on the beam width and deteriorates with the distance from the system antenna.

The general working principle of SAR and SAS involves collecting, recording and processing of the echo signals by a small antenna with a wide beam in subsequent points of the trajectory traveled by the antenna installed on a plane (underwater vehicle, satellite) moving in a straight line. Thus the antenna is apparently extended in space, that reduces the beam width and thereby improves the lateral resolution of the system (azimuthal in the ﬁgure).

Synthetic aperture working principle [318]

Time-correlated pulse compression & space-correlated focusing

Complex amplitude is “naturally” recorded in subsequent positions. The amplitude-and-phase knowledge of the received signals makes the SA technique to be a holography on the radio waves. 125 R. Salamon & H. Lasota 2016-06-08 Special purpose systems VII

Lateral and range resolution [319]

It can be shown that the phase of the received signals varies quadratically along the path traveled by the antenna. The frequency varies linearly, and so we get a signal with linear frequency modulation (LFM). The use of matched ﬁltering causes at the output of the ﬁlter a very short pulse coming from point target, similarly as in the case of ordinary reception of chirp signals. (Such signals are used in such systems in order to improve the depth/distance resolution and are processed in the usual manner). Lateral (azimuth) resolution of the system: λ δ =∼ R 2L R – distance, L – apparent length of the antenna (of the synthetic aperture) The length of the synthetic aperture depends on the beam width: ∼ λ L = Rθ−3dB = R D – actual length of the antenna D D δ =∼ 2 Lateral resolution does not depend on the distance and is the better the shorter is the antenna.

Resolution in SAR systems [320]

Lateral resolution of SAR radars reaches 10 cm and in experimental broadband radars even about 1 mm. Radar of Terra SAR satellites resolution: 1 m at a ﬁeld 5 km x 10 km 3 m at a surface 30 km x 50 km Works at a frequency 9.65 GHz (wavelength ca 3 cm) Orbit 514 km.

Diﬃculties:

• the accuracy of the ﬂight path ca 0.1λ

• great computational complexity of signal processing (two-dimensional Fourier transform, etc. – not so long ago performed opti- cally). SAR image of Pentagon

Signal processing in SAR and SAS [321] Sounding signal with linear frequency modulation s (t, x)

Distance compression – by time (matched ﬁltering)

S (f, x) = It {s (t, x)} B = 15 kHz Depth resolution Y f, x S f, x S∗ f, x ∼ |S f, x |2 ( ) = ( ) p ( ) = ( ) δr = 5 cm −1 y (t, x) = I {Y (f, x)} = rss (t, x) Pulse duration y (t, x) T = 1/B

Azimuthal (lateral) compression – by path x (space focussing)

126 R. Salamon & H. Lasota 2016-06-08 Special purpose systems VII

Z (t, u) = Ix {y (t, x)} The frequency of the y(t, x) signal is changing linearly as a result of Doppler eﬀect. The longer the ∗ ∼ 2 Q (t, u) = Z (t, u) Zp (t, u) = |Z (t, u)| pathway, the wider is the bandwidth and the better −1 q (t, x) = I {Z (t, u)} = ryy (t, x) is the resolution. Azimuthal resolution = half actual length of the antenna.

36 Side scan sonar

Side scan sonar [322]

√ Nonlinear distance scale: x = r2−d2. Usually Scan/search method linearised in the receiver.

Towed vessel/container (a “towﬁsh”) with a side scan sonar (SSS)

Benthos Side Scan Sonar [323]

Acoustic Source Level: + 225 dB re µPa @ 1 meter Range: 25 to 500 meters each channel Frequency Range (TTV-196): Sweeps 190 kHz to 210 kHz band Chirp Frequency Range (TTV-196D): Simultaneously sweeps in the 110 kHz to 130 kHz and 370 kHz to 390 kHz bands CW Frequency (TTV-196) 200 kHz CW Frequency (TTV-196D) Simultaneous 123 kHz and 383 kHz Transducer Radiation (TTV-196) 0.5◦ horizontal, 55◦ vertical Transducer Radiation (TTV-196D) 0.5◦ horizontal, 55◦ vertical (110 kHz to 130 kHz band), 0.5◦ horizontal, 35◦ vertical (370 kHz to 390 kHz band) Receiver Gain User adjustable from 0 to 21 dB in 3 dB increments; time varied – from -20 to 40 dB

127 R. Salamon & H. Lasota 2016-06-08 Special purpose systems VII

37 Multibeam echosounder

Multibeam echosounder [324]

Many narrow beams in the cross section perpendic- Multibeam sonar image of the bottom with a ular to the movement of the vessel (towﬁsh) wreck

38 Passive sonars

Passive sonar with a towed antenna [325]

Sonar detects acoustic signals emitted by ships, determines their spectrum and determines the direction of the wave source using beamforming algorithms.

Scheme of a towed antenna (above).

Submarine with a towed antenna sonar (Lockheed Martin)

128 R. Salamon & H. Lasota 2016-06-08 Special purpose systems VII

MES Dept. passive sonar [326]

Console of the SQR-19 towed antenna sonar (De- partment of Marine Electronic Systems) Antenna at the production hall

39 Sonobuoys

System of sonobuoys [327] Buoys are thrown from an airplane or helicopter for receiving/intercept acoustic noise emitted by submarines. The signals are than transmitted by radio to the aircraft. The sonobuos are, in fact, radiohydrobuoys

Sonobuoys (ULTRA company) Deployment of sonobuoys at a sea

Working principle of a directional buoy [328]

The bearingα is read from the ratio of spectrum fringes. 129 R. Salamon & H. Lasota 2016-06-08 Underwater acoustics, principles VIII

Display system of the SEM Dept. sonobouoys [329]

Displaying system for HYD 10 buoys (Department of Marine Electronic Systems)

130 R. Salamon & H. Lasota 2016-06-08 Underwater acoustics, principles VIII

Part VIII Principles of underwater acoustics

[2016_06_08_EchoMeth_script_GD_HL]Principles of underwater acoustics [H. La- sota]Henryk Lasota 2005 – 2016

40 Underwater environment

Operating environment of hydroacoustic systems [331] • type of reservoir

– inland ∗ lake ∗ river – sea ∗ oﬀshore ∗ continental shelf (depth up to 200 m) ∗ deep ocean

40.1 Propagation conditions Propagation conditions [332] • refraction

– „curvilinear” propagation: ∗ shadow zones ∗ propagation channels

• rebound (reﬂection/scattering) from the bottom and water surface

– multiple paths of wave/signal propagation water surface motion (waves, rip- ples) causing fast signal fluctuations: ∗ deep changes in signal level – destructive interference ∗ change of signal – the Doppler effect by reflection – daily volatility of propagation properties – extremely low frequency fluctuations – internal waves – relating to weather

• absorbtion

• scattering (reverberation)

• high level of noise

– natural – of civilization origin 131 R. Salamon & H. Lasota 2016-06-08 Underwater acoustics, principles VIII

40.2 (Hydro)acoustic waveguides Water reservoirs as (hydro)acoustic waveguides [333] The reservoir, as a medium of acoustic wave propagation in infrasound, sound, and ultrasound range, can be treated as a waveguide with a very heterogeneous “ﬁller”. The main phenomena aﬀecting the wave wandering in it are:

• reﬂection/scattering – at medium borders

• refraction – deﬂection on the heterogeneity of distribution of sound velocity – in the sense of changing the direction of the wave front of plane waves

• attenuation – the eﬀect of shear and volume viscosity of water and the relaxation of magnesium ions contained in MgSO4 (frm = 59.2 kHz) and boron ions contained in boron acids (frb = 0.9 kHz)

• dispersion – on small heterogeneity of the medium, in terms of diﬀerent acoustic characteristic impedance, suspended in the depths

41 Sound modes

Sound modes [334] • Shallow reservoir (relatively!) as a waveguide:

– wave equation for steady states (Helmholtz equation), – harmonic sollutions are assumed, with separable dependence on r and z, – boundary conditions are introduced (surface, bottom)

The solutions are waves (propagation modes) with „periodic" amplitude distributions between boundaries and diﬀerent phase and group velocities! Modes are also called speciﬁc values of the problem (eigenvalues). Mode propagation concerns low frequencies (depth comparable to the wavelength).

132 R. Salamon & H. Lasota 2016-06-08 Underwater acoustics, principles VIII

[335]

42 Refraction

Sound velocity distribution [336] • The speed of sound in water depends on:

– temperature T – salinity S

– pressure/depth Ph/z

• These parameters are diﬀerent in diﬀerent places:

– the type of water reservoir (lake, river, sea, ocean) – climate zone

• In given waters the distribution of T and S it is heterogeneous and varies in long, medium and short-terms (eg. internal waves):

– season of the year (seasonal changes), – time of the day (diel – 24 h) [diurnal, nocturnal],

– phase of tides (tidal – 12.5 h) https://en.wikipedia.org/wiki/Tide (https://pl.wikipedia.org/wiki/Plywy_morskie) – (wind, insolation)

133 R. Salamon & H. Lasota 2016-06-08 Underwater acoustics, principles VIII

42.1 Propagation velocity Propagation velocity [337] Empiric formula [Medwin]

2 3 −6 c = 1449.2 + 4.6T − 0.55T + 0.00029T + (1.34 − 0.01T ) · (S − 35) + 1.58 · 10 Ph

c – sound velocity in water [m/s] T – temperature [◦C] S – salinity [ppt = 10−3] Ph – hydrostatic pressure [N/m2] Aproximate formula

c = 1449 + 4.6T + (1.34 − 0.01T )(S − 35) + 0.016z

where: z – depth [m]

42.2 Sound rays Sound rays [338] • Geometric approach – rays

– Assumptions: ∗ channel dimensions are signiﬁcant in relation to the wavelength and furthermore, in the wavelength scale: ∗ the speed of sound propagation can be considered constant (not changing signiﬁcantly) ∗ the wave intensity changes are also negligible

Snell’s law [339]

sin ϑ sin ϑi dz ds dz = = a, ds = , dt = = , dr = dz tan ϑ. c (z) c (zi) cos ϑ c (z) c (z) cos ϑ

134 R. Salamon & H. Lasota 2016-06-08 Underwater acoustics, principles VIII

Radius of ray path: [340] d [c (z)] c = b = gradzc, r = 1/ab, r = dz gradzc · sin ϑ

Positive and negative curvature radius [341]

135 R. Salamon & H. Lasota 2016-06-08 Underwater acoustics, principles VIII

Shadow zones [342]

42.3 Sound channels Refraction in ocean [343]

136 R. Salamon & H. Lasota 2016-06-08 Underwater acoustics, principles VIII

Multipath propagation [344]

42.4 Oceanic sound channel Layered structure of oceanic waters [345]

137 R. Salamon & H. Lasota 2016-06-08 Underwater acoustics, principles VIII

Oceanic sound channel [346]

Oceanic sound channel II [347] Sound velocity distribution in deep (?) oceanic waters has a minimum favoring cylindrical energy spread .

Deepwater sound channel – SOSUS [348]

138 R. Salamon & H. Lasota 2016-06-08 Underwater acoustics, principles VIII

42.5 Sound attenuation Sound attenuation in water – fresh water [349]

Sea water [350]

139 R. Salamon & H. Lasota 2016-06-08 Underwater acoustics, principles VIII

Relaxation-induced attenuation [351]

Reminder [352]

140 R. Salamon & H. Lasota 2016-06-08 Underwater acoustics, principles VIII

42.6 Sea noise Sea noise [353]

Knudsen noise curves [354]

141 R. Salamon & H. Lasota 2016-06-08 Underwater acoustics, principles VIII

43 Refraction in sonar systems

Acoustic wave refraction [355] Forecast of sound rays in natural waters for sonar range estimation [R. Salamon, Sonar systems]

Typical proﬁle of acoustic wave velocity in ocean [356]

Equiphase surfaces and sound rays [357]

142 R. Salamon & H. Lasota 2016-06-08 Underwater acoustics, principles VIII

Sound rays due to positive velocity gradient [358]

Sound rays proper to negative velocity gradient [359]

143 R. Salamon & H. Lasota 2016-06-08 Underwater acoustics, principles VIII

Surface channel [360]

Acoustic channel [361]

144 R. Salamon & H. Lasota 2016-06-08 Underwater acoustics, principles VIII

Sound intensity distribution [362]

Depth distributions of sound velocity [363] Left chart – Wdzydze lake, spring season, right chart – Baltic Sea, summer season

145 R. Salamon & H. Lasota 2016-06-08 Underwater acoustics, principles VIII

Sound intensity distribution in Wdzydze lake [364]

Acoustic channel in Southern Baltic [365]

146 R. Salamon & H. Lasota 2016-06-08 Technology progress IX

Intensity distribution [366] Wave emitted by an antenna of deﬁned directivity pattern under a negative gradient of sound speed.

147 R. Salamon & H. Lasota 2016-06-08 Technology progress IX

Part IX Technology progress in modern hydrolocation systems

[2016_06_08_EchoMeth_script_GD_HL]Modern technology and techniques in hydrolocation systems [R. Salamon, H. Lasota]R. Salamon, H. Lasota 2016-06- 08

Overview [368]

Traditional solution New approach 1. Envelope detection (see part III, sec. 17) Matched ﬁltering (see part III, sec. 18) 2. Single beam echosounder (see part VI, sec. 26) Multibeam echosounder (see part VI, sec. 27-28) 3. Low frequency echosounder (see part II, sec. 6, part IV sec 20-21) Parametric echosounder 4. Side scan sonar (see part VII, sec. 36) Synthetic aperture sonar (see part VII, sec. 31,35) 5. High power sonar Quiet sonar (see sec. 41)

44 Matched ﬁltering

Matched ﬁltering [369]

Disadvantages of envelope detection

• range depends on the power of sounding signal (limited transmitter power, cavitation)

• distance resolution depends on the duration of the sounding pulse (for short pulses bandwidth of the receiver must be broad – the noise level increases)

• need to use excessively wide bandwidth of the receiver due to the Doppler eﬀect

Example:

• operating frequency f = 15 kHz

• speed of observation object (target) v = 10 m/s

• duration of the sounding pulse τ = 100 ms

• optimum bandwidth of the receiver B = 1/τ = 10 Hz

• Doppler shift ∆f = (2v/c)f = 200 Hz

• necessary bandwidth B = 400 Hz

• increase of the noise level in the receiver ∆SNR = 10 log 40 = 16 dB

The principle of matched ﬁltering (correlation reception) [370]

1. The transmitter emits a sounding signal with a linear or hyperbolic frequency modulation s (t)

Bt s (t) = S0 sin 2π f − t T

2. The receiver calculates the Fourier transform of the echo signal

X (jω) = F {x (t)} and S (jω) = F {s (t)} 148 R. Salamon & H. Lasota 2016-06-08 Technology progress IX

3. The spectrum X (jω) is multiplied by the spectrum S∗ (jω) and the inverse Fourier transform y (t) = F −1 {X (jω) S∗ (jω)} is calculated

−1 n 2o 4. If X (jω) = S (jω), than y (t) = F |X (jω)| = rxx (t) – autocorrelation function of the sounding signal.

[371]

Noise in the 30 kHz frequency band

Matched ﬁltering advantages [372]

• the range depends on the energy of sounding signal (long pulse with a limited power provides high energy) • E SNR0 = = BτSNRi M

• distance resolution depends on the spectrum width of the sounding pulse (∆R = c/2B – does not depend on the pulse duration, therefore the sounding signal can be very long)

• Doppler eﬀect reduces the output signal with linear frequency modulation and does not reduce the signal with hyperbolic frequency modulation

Example:

• operating frequency f = 15 kHz

• speed of observation object (target) v = 10 m/s

• sounding pulse width τ = 1 s

• receiver bandwidth B = 3 Hz

• Doppler shift ∆f = (2v/c)f = 200 Hz – a slight inﬂuence of the Doppler eﬀect

• Bτ = 3000 (35 dB)

• range increases approximately 6 times with the same transmitter power! 149 R. Salamon & H. Lasota 2016-06-08 Technology progress IX

45 Multibeam echosounder

45.1 Beamforming Multibeam echosounder [373]

Disadvantages of single beam echo sounder

• small scanned volume (contained in a single, narrow beam)

• distance measurement only in the direction of the beam axis

• two-dimensional cross-section image of the scanned volume

Advantages:

• Simple construction, low cost.

Working principle of a narrowband, delay-and-sum beamformer [374]

Beamformer producing beams in one plane

Signal at the output of the n-th antenna element sn (t, θ) = S0 sin {2πf0 [t − τgn (θ)] + ϕ}

“Geometric” delay nd τgn (θ) = − sin θ c

In order to produce one deﬂected beam, the signals in each channel signal are delayed in such a way that the total delay is equal in each channel. All thus delayed signals are summed to give the signal of a tilted/deﬂected beam.

[375]

150 R. Salamon & H. Lasota 2016-06-08 Technology progress IX

Operating scheme of a digital phase beamformer [376]

The Hilbert transformers can be replaced by 90◦phase-shift circuits, but this deteriorates beamformer parameters, especially when the signal spectrum is relatively wide.

[377]

Advantages of a multibeam Disadvantages echosounder • Extensive design (hence high costs): • wide angle of simultaneous observation (the number of deﬂected beams exceeds one hun- – a multi-element antenna, dred) – a multi-channel receiver, • high (good) angular resolution (the width of – high performance computation system, a single beam – a few degrees) – electronic stabilization of beam position • possibility of three-dimensional exposition

45.2 Acoustic camera Adaptive Resolution Imaging Sonar (Sound Metrics) [378] http: ARIS camera http: Seeing with sound http: High-resolution sonar-images

151 R. Salamon & H. Lasota 2016-06-08 Technology progress IX

Side-looking camera images [379]

152 R. Salamon & H. Lasota 2016-06-08 Technology progress IX

Acoustic camera parameters [380]

46 Parametric echosounder

Parametric echosounder [381]

Purpose Examination of the internal structure of seabed (sea bottom)

Basic requirement Sounding pulse frequency as low as possible to ensure deep penetration of acoustic waves into sediments.

Disadvantages of low-frequency echosounder

• very large dimensions of the antenna (Example:f = 7.5 kHz, wavelength λ = 0.2m, beamwidthi Θ = 10 deg, antenna length L =∼ 1 m)

• multi-element antenna built of the sandwich-type transducers

• large wieght of antenna

• large cost

The operating principle of parametric echosounder [382]

The transmitting transducer emits, within a narrow beam, sounding pulses filled with a superposition of sine waves of high frequencies, f1 and f2, with a very high amplitude of acoustic pressure. In the near-field of the trancducer, the wave is almost plane, thus its pressure does not decrease. It is so high that it falls within the range of medium nonlinearity. Due to the nonlinear phenomena, a low frequency sine wave is effectively created within the beam, of frequency F = f1 − f2, being the difference of the original ones. 153 R. Salamon & H. Lasota 2016-06-08 Technology progress IX

Features of parametric echosounder [383]

• Positive

– low diﬀerence frequency (a few kilohertz) – small antenna size – beam width equal to the width of the beam at high frequencies (typically a few degrees) – lack of side lobes (in conventional systems the side lobe level is reduced by amplitude weighing in multi-element antennas) – possibility of obtaining a relatively broad spectrum of diﬀerence signal – possibility of using high-power primary signals (higher cavitation threshold at high frequencies)

• Negative

– low eﬃciency of power conversion of high frequency signals into the signal of low, diﬀerence frequency

[384]

Echosounder f = 100 kHz

Parametric echosounder f = 5 kHz

Courtesy of Professor. G. Grelowska and Professor E. Kozaczka 154 R. Salamon & H. Lasota 2016-06-08 Technology progress IX

47 Synthetic aperture sonar

Synthetic aperture sonar [385]

Drawbacks of side scan sonar (SSS)

• lateral resolution worsening with distance (resulting from a constant angular resolution)

• nonlinear scale of bottom-projected object position vs. sounding distance: p x = r2 − d2

where r – measured distance , d – depth (can be linearized in the receiver)

Synthetic aperture radars and sonars [386]

In common radars and sonars, the lateral resolution depends on the beam width and deteriorates with the distance from the system antenna. Synthetic aperture radars (SAR) and sonars (SAS) are used to increase the lateral (transversal) resolution.

The general working principle of SAR and SAS involves collecting, recording and processing of the echo signals by a small antenna with a wide beam, in subsequent points of the trajectory traveled by the antenna installed on a platform (airplane, underwater vehicle, satellite) moving in a straight line. Thus the antenna is apparently extended in space, that reduces the beam width and thereby improves the lateral resolution of the system (azimuthal in the ﬁgure).

Synthetic aperture working principle [387]

155 R. Salamon & H. Lasota 2016-06-08 Technology progress IX

Time-correlated pulse compression & space-correlated focusing Complex amplitude is “naturally” recorded in subsequent positions. The amplitude-and-phase knowledge of the received signals makes the SA technique to be a holography on the radio waves.

Signal processing in SAR and SAS [388] Sounding signal with linear frequency modulation s (t, x) Distance compression – by time (matched ﬁltering)

S (f, x) = It {s (t, x)} B = 15 kHz Distance resolution ∗ ∼ 2 Y (f, x) = S (f, x) Sp (f, x) = |S (f, x)| δr = 5 cm −1 y (t, x) = I {Y (f, x)} = rss (t, x) Pulse duration y (t, x) T = 1/B Azimuthal (lateral) compression – by path x (space focussing)

[389]

Advantages: • constant, very good (“high”) lateral resolution

• constant, very high longitudinal (distance, depth) resolution Disadvantage: • High cost resulting from complex design and high performance computing 156 R. Salamon & H. Lasota 2016-06-08 Signal levels X

48 Silent sonar CW FM

Silent sonar CW FM [390]

Purpose: Hindering an opponent the detection of sounding signal by an intercepting sonar. Factors hindering the detection by an intercept sonar:

• possibly low power

• continuous signal (constant wave)

• widest possible spectrum

Linear frequency modulation: B B fl (t) = sin 2π f0 − + t t 2 2T

Hiperbolic frequency modulation: f1fh B fh (t) = sin 2π T ln 1 − t B fhT .

[391]

Signal processing in the receiver – matched ﬁltering

−1 ∗ y (n) = I {F (k) X (k)} y (n) = X0rff (n − n0)

The inﬂuence of the Doppler eﬀect when observing moving targets

∼ f0 1 Distance measurement error: ∆Rm = −vT + B 2

157 R. Salamon & H. Lasota 2016-06-08 Signal levels X

Part X Signal levels in physical space

[2016_06_08_EchoMeth_script_GD_HL]Levels of wave signals in physical space; logarithmic scales [H. Lasota]Henryk Lasota

Sound levels, izophonic curves, spreading „loss” [393]

Values vs. levels – SPL [394]

SPL Sound Pressure Level

• logarithmic measure of the eﬀective value of the sound pressure in airprms

−6 • "surplus" above the reference value pref = 20 × 10 Pa

p SPL = 20 log rms pref

SIL Sound Intensity Level −12 2 measure of sound intensity I referred to Iref = 10 W/m

I SIL = 10 log Iref

SWL Sound Power Level −12 measure of the sound power P referred toPref = 10 W

P SWL = 10 log Pref

158 R. Salamon & H. Lasota 2016-06-08 Signal levels X

Medium characteristic impedance vs. SPL and SIL [395]

Acoustic impedance of the medium for a plane acoustic wave: Zak = p/v Acoustic wave intensity: 2 I = p · v = p /Zak Characteristic impedance medium of the medium: q Zak = ρc = ρ/κ

3 Air: ρ = 1.2 kg/m ; c = 340m/s; Zak = 400rayl

It can be calculated that in air the pressure p = 2 × 10−5 Pa corresponds to the intensity I = 10−12 W/m2, or reference values are equivalent. This means that SPL = SIL (only in air !)

SWL & SIL [396]

A dependence of SWL and SIL on the distance is illustrated by the following formulae: P SWL = 10 log Pref

I = P/4πr2 2 2 Pref = Iref · 1 m = Iref · (r1) Whence: SWL = 10 log 4π + 20 log r/r1 or otherwise: SIL = SWL − 10 log 4π − 20 log r/r1

Range of communication systems [397]

• Energy balance of a system with isotropic antenna

– lossless medium – lossy medium

• Antenna directivity

– transmission directivity – receiving directivity

• Energy balance with directional antennae

• Range equation

– power of acoustic noise – receiver electrical noise

159 R. Salamon & H. Lasota 2016-06-08 Signal levels X

Energy balance [398]

• comparing the acoustic power of the signal emitted by the transmitting antenna (or rather of the radiated wave) with the acoustic power of the signal received by the receiver antenna (segment of the wave reaching the area of the antenna), or else

• weakening of the received signal with increasing the distance between the transmitter T and the receiver R

• simplifying assumptions:

– propagation medium is : ∗ unlimited, continuous, homogeneous, isotropic, lossless – the source of the wave is a hypothetical transmitting antenna radiating acoustic wave omni- directionally (isotropic) - this means small size of the antenna a relative to the wavelength λ

– the receiving antenna has a ﬁnite equivalent surface (aperture) ΣR

Logarithmic scales [399]

Transmission Loss (TL) [400]

Spreading loss Plain wave – no loss (0 dB) Cylindrical wave – TL= 10 log r/r1 Spherical wave – TL = 10 log r/r1 (In wireless communication and radiolocation it is being called "free space attenuation" - horror!)

Absorption loss Actual attenuation (conversion of wave energy into heat) – α [dB/m]

Depending on the channel, the transmission loss is being calculated according to one of the following formulas: TL= α · r

TL= 10 log r/r1 + α · r

TL= 20 log r/r1 + α · r

160 R. Salamon & H. Lasota 2016-06-08 Signal levels X

Directivity Index (DI) [401]

For suﬃciently large aperture:

P DI = 10 log 4π λ2

Therefore: For a rectangular aperture of relative sides A × B: DI = 10 log 4π + 10 log A + 10 log B = 10 log AB + 11 dB.

For a circular aperture with a relative radius R: DI = 20 log 2π + 20 log R = 20 log R + 16 dB.

For a linear aperture having a relative length A: DI = 10 log 2A = 10 log A + 3 dB.

Transmitting and receiving gain of an antenna [402]

It can be shown that for a transmitting - receiving antenna with a given aperture, the coeﬃcients K and κ are equal. For this reason, there is a practice to use a concept of the gain G as a numerical parameter characterizing the antenna directivity:

G = K = κ = 4π/Ω0

In the logarithmic measure

DIR = 10 log K

DIR10 log κ

Glog = 10 log G [dB] Energetic gain - applies to the electric power. Directivity gain - applies to the power stream on the side of the ﬁeld, does not take into account the conversion eﬃciency of the antenna

Power level (SWL) [403]

SWL – power level (water – re 1W; air – re 1 pW)

PTel SWLel = 10 log Pref

PTak PTel · ηea SWLak = 10 log = 10 log Pref Pref

SWLak = SWLel + EF

EF = 10 log ηea – logarithmic measure of electric/acoustic conversion eﬃciency (negative value)

161 R. Salamon & H. Lasota 2016-06-08 Signal levels X

SIL in water [404]

Sound intensity level: I SIL = 10 log Iref

For sound in water Iref has been adopted corresponding to pressure: −6 pref = 10 Pa = 1 µPa or pref = 1 Pa and since 2 6 Iref = (pref ) /Zak Zak = %c = 1.5 · 10 rayl,

so: 2 6 2 −18 2 Iref = (1 µPa) /1.5 · 10 W/m = 0.67 · 10 W/m Iref 10 log = −182 dBre1 W/m2 1 W/m2

or: 2 6 2 −6 2 2 Iref = (1 Pa) /1.5 · 10 W/m = 0.67 · 10 W/m ≈ 1 µW/m Iref 10 log = −62 dBre1 W/m2 1 W/m2

Madness of the civilization, [405]

The diﬀerence of 120 dB - in a simple and obvious matter of a technical standard A reasonable reference value of 1 µW/m2 0.67 · 10−6 W/m2 is being pushed by a value of10−6pW/m2(60 dB below the threshold of hearing 1 pW/m2!

Euro – the common currency of ambiguously sounding name juro, ojro, orro, jewro, euro and Asians can easily come up with the names of cars (almost) equally sounding in all European languages!

Source Level (SL) 1 [406]

SIL1 – Sound pressure level of an isotropic quasi-point source measured in a unit distance r1

IT 1 PT SIL1 = 10 log = 10 log 2 Iref 4π · r1Iref

SL – Source Level = SIL1 directive source

IT 1 PT · K SL = 10 log = 10 log 2 Iref 4πr1Iref

DI – Directivity Index EF – logarithmic measure of conversion eﬃciency SL = SIL1 + DIT (+EF )

Source Level (SL) 2 [407]

In view of the large number of possible reference values, numerous forms of SL. formula can be found Most often it is SL [dBre1µPa] = SWLel [dBre1W]+EF +182−10 log 4π+DIT = SWLel [dBre1W]+10 log ηea+171+DIT

162 R. Salamon & H. Lasota 2016-06-08 Signal levels X

Distance measurement [408]

Echo signals arrive at the receiver with a delay TR from the time of emission of the sounding signal, resulting from the ﬁnite wave propagation speed c in the medium:

TR = 2R/c, hence the distance R to the heterogeneity of/in the resort which is the source of the echo signal is: R = cT R/2

In the case of simple detection of a signal of time length (duration) Ti, the distance resolution (longitudinal, range resolution) δR is: δR = cTi/2 in the case of correlation reception of special wideband signals with TiB 1, the range resolution is: δR = c/2B

Direction measurement [409] • 1) Rotating antenna or a directional beam sweeping the observation sector

– measurement of the direction from which the echo comes means a search, in subsequent sounding signal transmissions, for its maximum level – the same principle applies to passive listening systems – the direction is determined with a precision (accuracy) ∆θ equal to the beamwidth Θ – also the angular resolution δθ is equal to the width of the beam Θ – a sweep with the beam narrower to the size of the object leads to determine its contour (shape) • 2) Two receiving points

– the direction θ from which the echo comes is determined from the time diﬀerence ∆TR between its arrival to two points spaced at a distance d one from another (or, in the case of monochromatic signals, from the phase diﬀerence ∆ϕ between two points):

∆TR = d sin θ/c θ = arc sin(∆TRc/d) θ = arc sin(∆ϕλ/2πd) (very good measurement precision bur poor angular resolution equal Θ )

Speed measurement [410]

Waves generated by a moving object have in the medium the frequency displaced relative to the original one. The frequency diﬀerence fD between that of a source moving at a radial speed vR, and the received frequency fR is called the Doppler shift:

fR ≈ fS(1 + vR/c)

fD = fS–fR ≈ fSvR/c Waves reﬂected from a moving object have Doppler shift doubled:

fD ≈ 2fSvR/c

Radial velocity vR of the object, means the projection of its velocity vector v onto the axis pointing towards the observer:

vR = v cos α where α- angle between the motion vector and the direction to the observer.

Sonars vs radars [411] 163 R. Salamon & H. Lasota 2016-06-08 Signal levels X

3 9 cha = 1.5 · 10 m/s cem = 0.3 · 10 m/s

The waiting time for echo (and the rate of space scan) diﬀers 200 000 times!

TR ha = 1.3 s/km of range TR em = 6.7 µs/km of range (6.7 ms / 1000 km of range)

Very diﬀerent sounding pulse repetition frequency Tp > 3TR ⇒ Fp ha < 1 Hz Fp ha = 1 − 5 Hz for a given size of the antenna, sonar achieves the same directivity as radar, with much lower fre- −6 quencies: fha = fem · 5 · 10 at the same frequency, acoustic systems have a much better resolution (acoustic microscope)λha = −6 λem · 5 · 10 usually fha fem and λha λem

Speciﬁcity of sonar technology - easiness [412] much lower frequency

fha = 500Hz − 300kHz ⇔ fem = 100MHz − 30GHz

λha = 3m − 5mm ⇔ λem = 3m − 10mm

longer durations of pulses Ti (LF technology vs. nanosecond technology)

Ti ha = 20 µs − 20 ms ⇔ Ti em = 0.1 ns − 10 ns good resolution achieved with relatively small aperture diameters:

• angular resolution δθ ≈ 1/A = λ/a

• the potential transversal resolution δx ≈ λ

Speciﬁcity of sonar technology - diﬃculties [413]

• long time to wait for an echo, hence special methods of time- and space processing to reduce time of space search:

– acquiring maximum information from the observed sector within a single transmission of sounding pulse: ∗ monopulse techniques ∗ multi-beam technology – use of accumulated information from numerous soundings: ∗ complex techniques of imaging / exposure ∗ recording of echo signals from multiple soundings ∗ multidimensional analysis (time, frequency, statistics) ∗ multimonitor, multiple observation posts

164 R. Salamon & H. Lasota 2016-06-08 Signal levels X

Operating area search time – head sonar [414]

• Exemplary requirements

– sonar range: RM = 150 m ⇒ waiting time for echo: TR = 0.2 s – safety factor (time reserve): n = 3 ◦ ◦ – dimensions of the search area: ΘSH × ΘSV = 60 × 20 ◦ ◦ – beam width: ΘH × ΘV = 5 × 5 – number of transmissions at one direction: 1

• Search time

– number of transmissions into the area: N × M = ΘSH /ΘH × ΘSV /ΘV = 12 × 4 = 48

– time of area search (scan, inspection): TS = TR · N · M ≈ 10 s

– search time with a margin of safety: TΣ = n · TS = 0.5 min

– extension of the range to do RM = 1 500 m increases search time TΣ to 5 min, the use of a 16-beam sonar reduces it to about 20 s

Monostatic, bistatic, and multistatic echolocation [415]

• Transmitter and receiver of echolocation system (its transmitting and receiving antennae) can be, in general, in two diﬀerent locations. We are dealing with bistatic echolocation. If the receiver receives signals coming from several transmitting antennae of diﬀerent locations, the system works as multistatic..

• Classical radar / sonar operate in a monostatic conﬁguration using the same transmitting and receiving antenna, or two diﬀerent antennae in a common location (eg. a common mast).

• Transmitting antenna emits a wave that "illuminates" whole the chosen sector of observation within a single transmission.

• Receiving antenna working with a multi-channel receiver can "generate" simultaneously a number of narrow beams covering the sector. The aperture of such an antenna is much larger than the aperture of the sector antenna.

Sonar energy balance 1 [416]

• The energy balance of an echolocation system is performed in two stages, according to the scheme of a cascade of two communication conﬁgurations:

– from the transmitting antenna to the area of the “illuminated” heterogeneity, – from the heterogeneity as an isotropic secondary source to the receiving antenna.

• IntensityISi of the incident wave in the area of heterogeneity equals:

PT eηeaK ISi = exp (−nr) 4πr2

• Equivalent power PS of the secondary point source is: PS = ISiσS

165 R. Salamon & H. Lasota 2016-06-08 Signal levels X

Sonar energy balance 2 [417]

• Intensity IR of the wave reaching the receiving antenna:

PS IR = exp (−nr) 4πr2

• Power PR of the secondary point source is: PR = IRΣR hence:

PT eηeaK PR = 2 σSΣR exp (−2nr) (4π) r4

• Energy balance of a sonar as a surplus of the radiated acoustic power over the power perceived by the receiving antenna 2 PT (4π) = r4 exp (2nr) PR KσSΣR

Eﬀective scattering area of a target [418]

Effective scattering area σS of an object, known also as its “radar cross-section”, is defined as the ratio of the power PS radiated isotropically from the scattering element (target), to the intensity ISi of a plane wave incident on the element: PS σS = ISi In the general case of bistatic configuration and a target (object, heterogeneity) of complex shape, σS it depends both on the direction (ϑST , ϕST ) of the object exposure relative to its proper reference system, ie. selected axis and reference plane, and the direction of observation (ϑSR, ϕSR). For objects with spherical symmetry (ball), the effective scattering surface is only a function of the difference between the angle of observation and angle of exposure:

σS (ϑST ϕST ; ϑSRϕSR) = σs (ϑSR − ϑST )

Scattering, reﬂection σs (ϑSR = ϑST ) [419]

Radar cross-section of a ball σS (a/λ), monostatic obsewrvation: 4 2 σS → 9π (ka) for k → 0 σS → π (a) for ka → ∞

Scattering cross-sections – addendum [420] 166 R. Salamon & H. Lasota 2016-06-08 Signal levels X

Air bubble in water at resonance 2 σS ≈ 400πa !! Scattering of acoustic wave in aerated water causes an increase in attenuation (multiple reﬂections)

Rigid ball 4 – σS → 9π (ka) for ka → 0 2 – σS → πa for ka → ∞

Scattering, reﬂection [421]

σS (ϑSR − ϑST )

Bistatic observation of dielectric spheres in linearly polarized light

Radar cross section of a plane [422]

σS (ϑS)

167 R. Salamon & H. Lasota 2016-06-08 Echolocation system design XI

Target strength of a submarine [423]

TS (ϑS)

168 R. Salamon & H. Lasota 2016-06-08 Echolocation system design XI

Part XI Echolocation system design

[2016_06_08_EchoMeth_script_GD_HL]Echolocation system design [H. Lasota]Henryk Lasota 2016-06-08

49 Range equation

Echolocation system parameter planning [425]

Purpose of the range equation Determination of the technical speciﬁcation of the system to ensure the detection of a given object with assumed probabilities PDi PFA Model of an echolocation system:

In radar design, an algebraic form of the range equation is used, and in underwater acoustic (hydrolocation) – a logarithmic form introduced by R. Urick.

49.1 Logarithmic form of the range equation Logarithmic form of the range equation [426]

I0 Starting equation: = SNRx , where: In I0 – echo signal intensity – wave incident normally onto the receiving antenna surface In – noise intensity at the input of the receiver (in its passband) It – transmitted signal intensity related to the reference distance of 1 m, measured at the antenna far zone (spherical wave conditions) Ii – incident signal intensity measured at target surface related to the target center Ir – reﬂected/scattered signal intensity related to the reference distance of 1 m from the target center, measured at the scatterer/reﬂector far zone

Relative measures [427]

Reference pressure/intensity in underwater acoustics: −18 2 I1 = 0.67 · 10 W/m – acoustic intensity corresponding to the reference pressure pref = 1 µPa in a plane wave −6 2 or (better but rarely) pref = 1 Pa , meaning I1 = 0.67 · 10 W/m (in a plane wave)

I0 I1 I0 In SNRx = =⇒10 log − 10 log = 10 log SNRx I1 In In I1 169 R. Salamon & H. Lasota 2016-06-08 Echolocation system design XI

The basic form of logarithmic range equation:

EL − NL = DT

I0 In where: EL = 10 log – Echo level, NL = 10 log – Noise level, and I1 I1

DT = 10 log SNRx – Detection threshold

Deﬁnitions (technical - with measurement procedure indications) [428]

The echo level EL is the intensity of the signal plane wave incident perpendicularly on the surface of the receiving transducer, expressed in dB.

Noise level NL is an equivalent intensity of an interfering plane wave incident perpendicularly to the surface of the receiving transducer, that gives at the receiver output the same signal level as is observed at its output when receiving actual electric and acoustic noise and interference in the system, expressed in dB.

Detection threshold DT is the expressed in dB ratio of intensities of the signal and interference plane waves incident normally onto the surface of the receiving transducer, which assures that at the receiver output the assumed criteria for target detection are met.

Determination of the echo level [429] I0 I0 Ir I0 Ir Ii I0 Ir Ii It = = = I1 Ir I1 Ir Ii I1 Ir Ii It I1

Let take the logarithm of both sides of the above equation: I0 I0 Ir Ii It 10 log = 10 log + 10 log + 10 log + 10 log I1 Ir Ii It I1

Ir It TL = 10 log Unilateral transmission loss TL = 10 log I0 Ii

Ir It TS = 10 log Target strength SL = 10 log Source level Ii I1 EL = −TL + TS − TL + SL

EL = SL − 2TL + TS

If the transmitter and receiver of the system are located at the same place, the transmission losses in both directions are the same.

170 R. Salamon & H. Lasota 2016-06-08 Echolocation system design XI

More deﬁnitions (technical, meaning engineering) [430]

The source level SL: is a normalized value of intensity, expressed in decibels, of the acoustic wave at a distance of one meter from the surface of the radiating transducer on its acoustic axis.

It SL = 10 log I1

Transmission loss TL: The unilateral transmission loss TL is the intensity ratio, expressed in decibels, of the wave radiated by the transmitting transducer, measured on its acoustic axis at a distance of one meter from its surface, and of the plane wave incident perpendicularly onto the surface of the receiving transducer. In the so-called multi-static configurations, with receiver situated in another place than the transmitter, the transmitter – target “forward” distance differs from the target – receiver “backward” distance. Hence the unilateral transmission losses differ:

Ir It TLf = 10 log TLb = 10 log I0 Ii

Formulae for calculating range equation parameters [431]

Source level of an underwater system transmitter working in water

SL = 171 + 10 log Pt/P1 + 10 log η + DIt [dB]. Sometimes you will ﬁnd 51 replacing 171 (why? what does it mean?)

Pt – transmitter electric power, P1 = 1W η – electro-acoustic eﬃciency of antenna transducers DIt – directivity index of transmitting antenna

Example: Pt = 1 kW, η = 0.5, 4πab a = b = 10λ dIt = = 4π100 = 400π ' 1250 λ2 DIt = 10 log (dIt) = 31 dB SL = 171 + 30 − 3 + 31 = 229 dB

Transmission loss TL [432]

Transmission loss depends on how the wave propagates:

plane wave TL = 0 + αR [dB]

cylindrical wave TL = 10 log R/R1 + αR

spherical wave TL = 20 log R/R1 + αR

R – distance from the antenna to the target, R1 = 1m α – absorption coeﬃcient [dB/m]

Example: R = 1 km, α = 0.01 dB/m, spherical spreading

TL = 20 log 1000 + 0.01·1000 = 60 + 10 = 70 dB Acoustic wave attenuation depends on the chemical composition of the water, frequency, temperature and other factors (see earlier lecture). Electromagnetic wave attenuation in radars is generally very small and is often dropped. For a wavelength of less than 1 cm, the attenuation does not exceed 0.01 dB/km. For shorter wavelengths it grows very quickly. Water vapor and rain make the attenuation growing in a narrow frequency band (for wavelengths of about 1 cm). 171 R. Salamon & H. Lasota 2016-06-08 Echolocation system design XI

Target strength [433]

Target strength depends on the size of the object, its shape, material, position in relationship with the direction(s) of waves incidence and reﬂection, scattering properties, etc. Examples of the target strength in hydrolocation: ﬁsh TS = 19.1 log L (cm) − 0.9 log f (kHz) − 62 L = 30cm, f = 30 kHz, TS = −35.1 dB (herring)

Submarines TS = +10... + 45 dB Surface ships TS = +15... + 25 dB Mines TS = +10... + 15 dB Torpedoes TS = −20 dB (from the bow)

Perfectly reﬂecting sphere: σ πr2 r TS = 10 log 2 = 10 log 2 = 20 log = 20 log [r (m) /2] 4πr1 4πr1 2r1 A wave of intensity I is incident on a sphere (or ball) of a cross-section σ. The power of the wave passing through this surface is P = Iσ. We assume that the ball reﬂects the wave equally in all directions. The power on the surface of a 2 sphere of radius r1 is P , and the intensity is Ir = P/4πr1 .

172 R. Salamon & H. Lasota 2016-06-08 Echolocation system design XI

Noise level [434]

NL = SPL + 10 log(B/B1) − DIo SPL – spectral noise level SPL = 10 log(In1/I1) B – frequency band width [Hz], B1 = 1 Hz DIo – directivity index of the receiving antenna Detection threshold DT = 10 log(SNRo) = 10 log d SNRo – signal to noise ratio at the receiver input as to fulﬁll the conditions of detection at the receiver output. It is determined from the operation curves of the type of detector taking into account Spectral noise level at sea. the possible eﬀect of the receiver on possible noise reduction.

Signal level at the receiver input [435]

UL = EL + VR U – voltage at the receiver input [V]

UL = 20 log(U/U1) signal level at the input (U1 = 1V) VR = 20 log(S) voltage response (S – antenna transducer sensitivity)

S = (U/U1)/(p/p1) p1 = 1 µPa or p1 = 1Pa (!)

VR is usually determined experimentally

p – acoustic pressure of the plane wave incident normally onto the antenna.

System range in a medium without absorption loss [436]

XL = SL − NL − DT

173 R. Salamon & H. Lasota 2016-06-08 Echolocation system design XI

System range in a medium with absorption loss [437]

XL = SL − NL − DT

Mind the distance scale change compare to the former ﬁgure!

50 Echosounder design procedure

50.1 Assumptions Design process of a simple ﬁshery echosounder [438]

Goal: Determination of basic technical parameters of ﬁshery echosounder with following exploatation parameteres:

• range R = 200 m

• target – ﬁsh L=30 cm

• angular resolution 9◦× 9◦

• range resolution ∆R = 75 cm

• probability of detection PD = 0.8

• probability of false alarm: one false alarm per 0.1 h

• sea state ss = 6

• working frequency f = 50 kHz

• piezoelectric transducers sensitivity VR= - 69 dB or - 189 dB (?)

First steps: pulse length, receiver bandwidth, SPL, DI [439]

Design calculations: Remark: we assume reference value p1 = 1 Pa

• 1. Sounding pulse duration:

τ = 2∆R/c τ = 2 · 0.75 m : 1500 m/s = 1.5 m : 1.5 · 103 m/s = 10−3 m/s = 1 m/s 174 R. Salamon & H. Lasota 2016-06-08 Echolocation system design XI

• 2. Receiver bandwith: B = 1/τ B = 1 kHz

• 3. Spectral noise level

Empirical formula: SPL = −64 + 19 log 6 − 17 log 50 = −64 + 15 − 29 = −78 dB

• 4. Directivity index

4πab 41253 41253 DI = 10 log = 10 log = 10 log = 10 log 509 = 27 dB λ2 θϕ 9 · 9

Subsequent steps: NL, PFA [440] • 5. Noise level:

NL = SPL + 10logB − DI = −78 + 30 − 27 = −75 dB

• 6. False alarm probability:

Tt = 2R/c = 400/1500 = 0.27 s – delay of echo signal

Tr = 0.23 s – time needed for distant echo extinction. T = Tt + Tr = 0.5 s transmission period n = 2 two pulses per second Number of transmissions with one false alarm altogether: L = 360 ∗ 2 = 720 transmissions False alarm probability in single transmission: PFA = 1/720 False alarm probability in single pulse:

∼ −6 PFA = PFA1 (τ/Tt) = (1/720)(1 ms/270 ms) = 5 · 10

Receiver operating curves (reminder) [441]

ROC curves allowing to determine the SNR of assumed PD and PFA.

• 7. Resulting signal to noise ratio:

d = 25(from ROC curves)

• 8. Detection threshold required: SNRx = SNRy = DT = 10 log d = 10 log 25 = 14 dB

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Subsequent steps: EL required, corresponding UL , ULn (receiver electric noise) [442]

• 9. Echo level: EL = NL + DT = −75 + 14 = −61 dB

VL = −69 dB re 1V/Pa – measured in calibration procedure of piezoelectric transducer.

• 10. Echo voltage level at the receiver input:UL = EL + VL = −61 − 69 = −130 dB

With so small electrical equivalent value of the acoustic noise, the electrical noise can dominate! Veriﬁcation: R = 1 kΩ – measured value of transducer electrical impedance, T = 283◦ K 2 −23 3 3 −17 −14 2 Un = 4 kT RB = 4 · 1.38 · 10 · 283 · 10 · 10 = 1600 · 10 = 1.6 · 10 V Un = 0.13 µV, −6 ULn = 20 log(0.13 · 10 ) = −17 − 120 = −137 dB ELn = ULn − VL + DT = −137 + 69 + 14 = −54 dB

Conclusion: electrical noise dominates.

Subsequent steps: EL (DT) modiﬁed, TS, TL [443]

Taking into account possible additional interference, it is advised to increase the minimum voltage to U = 3 µV, meaning 20 dB more EL = −61 dB + 20 dB = −41 dB , it corresponds to an increase of DT to 34 dB relative to acoustic noise

• 11. Target strength

TS = 19.1 log L (cm) − 0.9 log f kHz − 62 TS = 19.1 log 30 − 0.9 log 50 − 62 = 28.2 − 1.5 − 62 = −35

• 12. Transmission loss – spherical spread

– absorption coeﬃcient α = 10 dB/km 2TL = 40 log R + 2αR = 40 log 200 + 2 · 10 · 0.2 = 92 + 4 = 96 dB

Final calculations: SL, electric power, antenna diameter [444]

• 13. Source level

EL = SL − 2TL + TS SL = EL + 2TL − TS = −41 + 96 + 35 = 90 dB

• 14. Transmitter electric power

SL = 51 + 10 log P + 10 log η + DI 10 log P = SL − 10 log η − DI − 51 = 90 + 3 − 27 − 51 = 15 dB =1.5 B P = 1015/10 = 101.5 = 30 W

• 15. Antenna design

0.44λ lx 0.44 sin (θ−3 dB/2) = = = 5.6 lx λ sin 4.5 λ = c/f = 1500 [m/s]/50000 [1/s] = 0.03 m = 3 cm

lx = 5.6 · 3 cm = 16.8 cm 176 R. Salamon & H. Lasota 2016-06-08 Echolocation system design XI

50.2 Results Antenna aperture [445]

Echosounder antenna elements

Antenna directivity pattern [446]

Echosounder antenna directivity pattern

Technical parameters of the designed echosounder [447]

Nominal frequency 50 kHz Transmitter power 30 W Source level re 1 Pa @ 1 m 90 dB Source level re 1 µPa @ 1 m 210 dB Sounding pulse length 1 ms Minimum echo signal voltage 3 µV Maximium noise voltage 0.6 µV Receiver bandwidth 1 kHz Antenna beamwidth 9◦× 9◦ 177 R. Salamon & H. Lasota 2016-06-08 HPEC XII

Warning: Both SL values are correct!

178 R. Salamon & H. Lasota 2016-06-08 HPEC XII

Part XII High Performance Embedded Computing

[2016_06_08_EchoMeth_script_GD_HL]High Permormance Embedded Comput- ing [I. Kochanska]Iwona Kochanska

High Performance Embedded Computing (HPEC) [449]

One of the major goals of HPEC: to deliver ever greater levels of functionality to embedded signal and image processing (SIP) applications.

High performance SIP algorithms demand throughputs ranging from hundrads of millions of operations per second (MOPS) to trillions of OPS (TOPS).

HPEC challenges [450]

HPEC is particularly challenging:

• high throughout requirements,

• real-time deadlines

• form-factor constraints.

HPEC is a juggling act that must deal with all three challenges at once.

HPEC latencies [451]

HPEC latencies:

• milliseconds for high pulse repetition frequency (PRF) tracking radars

• a few hundred milliseconds in surveillance radars

• minutes for sonar systems

The best designs will satisfy both latency and throughput requirements while minimizing:

• hardware resources

• software complexity

• form factor (HPEC systems must ﬁt into spaces ranging from less than a cubic foot to a few tens of cubic feet, and must operate on power budgets of a few watts to a few kilowatts)

With these size and power constraints, achievable computational power eﬃciency, measured in operations per second per unit power (OPS/watt), and computational density, measured in operations per second per unit volume (OPS/cubic foot), determine the overall technology choice.

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HPC latencies (2) [452]

The front-end and back-end latency allowances are determined by the overall latency requirement and must be traded oﬀ against each other. For example, tracking radars may have to close the tracking loop in a few milliseconds.

• he amount of time the radar has to detect the target, update its track, generate a new position prediction, and then direct its antenna to point in a new direction (to keep the target in the radar beam) must not exceed a few milliseconds

• This update rate is driven by the dynamics of the target being tracked. For a slow-moving target, a few hundred milliseconds or even a few seconds may be appropriate. For a highly maneuverable target such as a ﬁghter aircraft, ﬁrecontrol radars may need to operate with millisecond latencies

HPEC canonical architecture [453]

HPEC processing stages [454]

Front-end signal and image processing stage extract information from a large volume of input data (performs stream-based signal and image processing).

• removal of noise and interference from signals and images

• detection of targets

• extraction of feature information from signals and images back-end data processing stage Further reﬁne the information so that an operator, the system itself, or another system can then act on the information to accomplish a system-level goal (knowledge-based processing).

• parameter estimation

• target tracking 180 R. Salamon & H. Lasota 2016-06-08 HPEC XII

• fusion of multiple features into objects

• object classiﬁcation and identiﬁcation

• other knowledge-based processing tasks

• display processing

• interfacing with other systems

HPEC technology [455]

The technology choices for front-end processors:

• full-custom very-large-scale integration (VLSI)

• application speciﬁc integrated circuits (ASICs)

• ﬁeld-programmable gate array (FPGAs)

• programmable digital signal processors (DSPs)

• microprocessor units (MPUs)

• hybrid designs that incorporate a combination of these technologies

The technology chosen for the back-end data processing:

• programmable multicomputer composed of DSPs or MPUs

• shared memory multiprocessor

Typically, front-end processing requires signiﬁcantly greater computational throughput, whereas back-end processing has greater program complexity. Throughput is usually measured in terms of OPS.

• front-end algorithms can require anywhere from a few billion OPS to as many as a few trillion OPS

• back-end algorithms tend to require an order of magnitude or two fewer OPS

HPEC data rates [456]

• Front-end computations perform operations that transform raw data into information.

• The analog-to-digital converters (ADCs) are themselves highly sophisticated components that set limits on the precision and bandwidth of the signals that can be digitally processed.

• SIP algorithms remove noise and interference, and extract higher level information, such as target detections or communication symbols, from a complex environment being sensed by a multidimensional signal, image, or communication sensor.

• In phased-array radars, for example, signals with data rates in the 100s of millions of samples per second (MSPS) arrive at the front-end of the digital signal processor from tens of receiver channels. This results in an aggregate sample rate of billions of samples per seconds (GSPS)

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Data reduction in front-end stages [457]

ECCM (electronic counter-countermeasures): beamforming operation in which the channels are combined to form a small number of beams Detection stage – algorithm rejects noise and identiﬁes the range gates that contain targets. The number of targets is signiﬁcantly less than the total number of range gates. Front-end output/input data rate is typically less than 0.5%.

(Source: Martinez, D. R., Bond, R.A., Vai, M.M.,High Performance Embedded Computing Handbook: A Systems Perspective, CRC Press 2008.)

Surface moving-target indication (SMTI) surveillance radar example [458]

• SMTI radars are used to detect and track targets moving on the earth’s surface

• Radar signal consisting of a series of pulses from a coherent processing interval (CPI) is transmitted

• The pulse repetition interval (PRI) determines the time interval between transmitted pulses. Mul- tiple pulses are transmitted to permit moving-target detection

• The pulsed signals reflect off targets, the earth’s surface (water and land), and man-made structures such as buildings, bridges, etc.; a fraction of reflected energy is received by the radar antenna

• The goal of the SMTI radar is to process the received signals to detect targets (and estimate their positions, range rates, and other parameters) while rejecting clutter returns and noise. The radar must also mitigate interference from unintentional sources such as RF systems transmitting in the same band and from jammers that may be intentionally trying to mask targets

(SMTI) surveillance radar [459]

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(Source: Martinez, D. R., Bond, R.A., Vai, M.M.,High Performance Embedded Computing Handbook: A Systems Perspective, CRC Press 2008.)

SMTI analog processing [460]

• The radar antenna typically consists of a two-dimensional array of elements (1000s of elements)

• The signals from these elements are combined in a set of analog beamformers to produce subarray receive channels, thereby reducing the number of signals that need to be converted to the digital domain for subsequent processing. For example: 20 vertical subarrays are created that span the horizontal axis of the antenna system. Employed in an airborne platform, the elevation dimension is covered by the subarray analog beamformers, and the azimuthal dimension is covered by digital beamformers

• The channel signals subsequently proceed through a set of analog receivers that perform downcon- version and band-pass ﬁltering

• The signals are then digitized by analog-to-digital converters (ADCs) and input to the high performance digital front-end

SMTI digital processing [461]

• Channelizer process divides the wideband signal into narrower frequency subbands

• Filtering and beamformer front-end mitigates jamming and clutter interference, and localizes return signals into range, Doppler, and azimuth bins

• Constant-false-alarm-rate (CFAR) detector (after the subbands have been recombined)

• Post-processing stage that performs such tasks as target tracking and classiﬁcation

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Part XIII MES Department sonars

[2016_06_08_EchoMeth_script_GD_HL]MES Department sonars [MES Dept.]Marine Electronic Systems Department 2016-06-08

51 Operational and technical parameters in underwater sounding

51.1 Polish Navy sonars (developed by the MES Department, ETI Faculty, GUT) Sonars developed by the MES Department, ETI Faculty, GUT [463]

All the MES sonar systems are in a fully operational service on board of Polish Navy anti-submarine warfare (ASW) and mine counter-measure (MCM) ships of both US and Soviet origin, meeting critical requirements of the highest technology readiness level (TRL 9).

I Long-range active ASW sonar II Medium-range MCM sonar III Helicopter dipping ASW sonar for submarine detection and tracking IV Passive ASW towed-array sonar V Side-scan MCM sonar

51.2 Long-range active ASW sonar I Long-range active ASW sonar [464]

The hull-mounted anti-submarine warfare (ASW) long-range, multi-beam sonar systems with full angular range of target tracking are designed for the detection, localization and tracking of ships and other objects.

The long-range active ASW system is equipped with a cylindrical acoustic antenna cooperating with a beam-former, which allows simultaneous observation of the targets at all bearings around the ship. Automatic position stabilization of the antenna enables conducting a continuous survey of targets and determining their position with a good accuracy even at stormy weather. Very high energy, frequency- modulated sounding pulses used in sonar, combined with the correlation detection, assure a long range (up to 32 km), even in diﬃcult propagation conditions with a high level of acoustic noise and reverberation. The system is equipped with a modern, ergonomic imaging assembly with 4 color display screens and control panels, operated by two operators.

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Long-range active ASW sonar – operating consoles [465]

Long-range active ASW sonar – parameters 1 [466] Transmitter Operation frequency (nominal) 8,5 kHz Sweep frequency range 7,75 ÷ 9,25 kHz Transmitting beam horizontal width 360° Transmitting beam vertical width 12° ± 2,5° Number of transmitting channels 30 In-pulse electric power ≥ 10 kW Source level in dB re 1 Pa @ 1m ≥ 95 dB Antenna Ultrasonic transducer sensitivity 500 µV/Pa Receiving beam horizontal width 12° ± 2,5° Receiving beam vertical width 12° ± 2,5° Observation sector width 360°

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Long-range active ASW sonar – parameters 2 [467] Receiver Receiving band (3dB) 7,5 ÷ 9,5 kHz Number of receiving channels 30 Processing Beamforming technology digital, in the frequency-domain with second-order sampling Number of beams 90 Post-beamforming filtering for “chirp” signals digital correlation filtering in the time domain Post-beamforming filtering for “ping” signals envelope detection with digital low-pass filtering Operational range 1, 2, 4, 8, 16, 32 km Time-width of sounding pulses 50, 100, 200, 400, 800, 1600 ms Precision of distance measurement 1% of nominal range Precision of bearing measurement 1° Number of simultaneously tracked targets max. 12

51.3 Medium-range MCM sonar II Medium-range MCM sonar [468]

The mine counter-measure (MCM) sonar systems are designed for searching, detecting, and localizing bottom and contact mines, speciﬁcally in shallow waters with strong bottom reverberations and substantial deﬂection of acoustic wave propagation routes.

The MCM sonar is a multi-transmitting and multi-receiving beam systems designed using real-time microprocessor technology. On the transmitting side, the RDT technique of electronically rotated beam is used. The generation of sounding signals and rotation of electronic beam rotation is implemented using the direct digital synthesis (DDS) controlled by single-chip microprocessors. On the receiving side, a multi-processor DSP system is used for the algorithmic implementation of a beam-former. The latter is implemented in the frequency domain with the second order sampling and 14 bit resolution. A signiﬁcant reduction of beam pattern side lobes both on the transmitting and receiving side is achieved. Two LCD monitors are used for supporting the console operators in detection, identiﬁcation and tracking of objects. Information exchange between the sonar and other on-board systems is also provided.

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Medium-range MCM sonar – operating consoles [469]

Medium-range MCM sonar – parameters 1 [470] Transmitter Operation frequency 41 ÷ 46 kHz Transmitting beam horizontal width 60° Transmitting beam vertical width 9° ± 1° Number of transmitting channels 36 In-pulse electric power ≥ 10 kW Source level in dB re 1 Pa @ 1m ≥ 110 dB Antenna Angular range of antenna declination (vertical) +5 lub -55° Angular range of antenna deﬂection (horizontal) ± 60° Receiving beam horizontal width 3° Receiving beam vertical width 9° ± 1° Angular width of simultaneous observation sector 60° Overall observation sector width 180°

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Medium-range MCM sonar – parameters 2 [471] Receiver Receiving band (3dB) 41 ÷ 46 kHz Number of receiving channels 36 Processing Beamforming technology digital, in the frequency-domain with second-order sampling Number of beams 61 Nominal operation ranges 100, 200, 400, 800, 1600 m Precision of distance measurement 0,5% of nominal range Precision of bearing measurement 1° A-type display target resolution 15, 37.5, 75 cm relative to the pulse-width after compression

51.4 Helicopter dipping ASW sonar III Helicopter dipping ASW sonar [472]

The dipping sonar for helicopters are new systems designed for detection and tracking submarines in both active and passive modes, equipped with an additional gradient passive array and a meter of speed velocity distribution in water. All electronic systems in the transducer, receiver and imaging system are designed using real-time microprocessor technology. The on-deck transmitter using a direct digital synthesis (DDS) modulator generates a broadband, frequency-modulated sounding signal. The sonar receives echo signals from a revolving ultrasonic transducer operating in the active mode and 4 signals from hydrophones of the passive array. After the first stage of preliminary magnification and analog filtering the received signals is subject to analog-to-digital conversion. Consequently, computer-aided processing and imaging is applied. The pulse compression technique used the in active mode significantly improves detection performance and increases the maximum range of detecting and tracking submarines, which can be displayed at console monitor.

Helicopter dipping ASW sonar – operating consoles [473]

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Helicopter dipping ASW sonar – parameters 1 [474] Transmitter Center frequency of the sounding signal 15,5 kHz Sounding signal modulation linear frequency modulation (LMF) Sounding signal sweep range 14 to 17kHz Transmitting beam horizontal width 15° Transmitting beam vertical width 15° Number of transmitting channels 1 In-pulse electric power ≥ 1 kW Sounding pulse maximum energy 0.5 kJ Antenna Receiving beam horizontal width 15° Receiving beam vertical width 15° Observing sector angular range 360° Scanning technique mechanical rotation Receiver 3dB receiver band 14 to 17 kHz Number of receiving channels 1

Helicopter dipping ASW sonar – parameters 2 [475] Processing Number of beams 1 Filtering for a “chirp” signal digital correlation ﬁltering in the frequency domain Filtering for a “ping” signal envelope detection with digital low-pass ﬁltering Operational range 1.5, 3, 6, 12 km Time-width of sounding pulses 50, 125, 250, 500 ms Precision of distance measurement 1% of nominal range Precision of bearing measurement < 5° Number of simultaneously tracked targets max. 4 Passive operation (intercept) Listening band 5 ÷ 300 Hz Listening time 1, 2, 4 s Bearing accuracy: SNR > 20dB, f = 100 Hz 1° SNR > 10dB, f = 100 Hz 3° Spectrum resolution 1, 0.5, 0.25 Hz

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51.5 Towed-array passive sonar IV Towed-array passive sonar [476]

The SQR-19PG is a passive anti-submarine warfare (ASW) towed- array side-scan sonar system designed for detecting and tracking submarines.

The SQR-19PG sonar is a low-frequency, broadband, passive real-time system designed using digital microprocessor technology. Increased angular resolution has been achieved by generating more receiving beams using eﬀective methods of digital signal processing. New eﬀective beam-forming algorithms for broadband signals, as well as methods for high-resolution spectrum estimation were developed and applied. This results in a precise measurement of the incoming acoustic wave bearing. Novel algorithms for automatic tracking of selected targets were developed and applied. The adequate data transmission rate from the transducer array, thru the towing cable-line is assured by using the VDSL (Very High Speed Digital Subscriber Line) transmission technique.

Towed-array passive sonar [477]

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Towed-array passive sonar – parameters 1 [478] Maximum operation depth 610 m Antenna modules filling liquid ISOPAR M Number of intercept bands 4 Frequency range of intercept bands: I: 10 – 175 Hz II: 175 – 350 Hz III: 350 – 700 Hz IV: 700 – 1400 Hz Effective antenna diameter in the specific bands: I: 195 m II: 97,5 m III: 48,8 m IV: 24,4 m Number of processed acoustic channels 120 Non-acoustic data transferred from the antenna immersion depth magnetic heading water temperature Number of beams formed 91 Observation sector 360°

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Towed-array passive sonar – parameters 2 [479] Bearing ambiguity port side / starboard ability to determine the heading side after a change of the course Target bearing accuracy from ± 2° in orthogonal axis up to ± 4° in sectors Motion parameters being measured current bearing bearing rate of change Listening time 1s, 2s, 4s Frequency resolution in speciﬁc bands for a given listening time: I: 1, 0,5, 0,25 Hz II: 1, 0,5 , 0,25 Hz III: 2, 1, 0,5 Hz IV: 4, 2, 1 Hz Resolution of analog-to-digital conversion 16 bis Sampling frequency of acoustic signals 4096 Hz Data transmission down-link band (to antenna) 1 ÷ 3,5 MHz Data transmission up-link band (from antenna) 3,8 ÷ 6 MHz Modulation scheme of digital signal transmission VDSL – QAM Number of simultaneously tracked targets max.. 16

51.6 Side-scan MCM sonar V Side-scan MCM sonar [480]

The side-scan mine counter-measure sonar systems use a very eﬀec- tive underwater acoustic method for detecting and localizing mo- tionless underwater objects.

The side scan sonar is an active system designed using real-time microprocessor technology. Multi- element ultrasonic transducers are towed behind the ship above the bottom in a so-called tow ﬁsh. The beam patterns are diagonally directed to the bottom, on the right and left. The dynamic beam width control ensures constant linear resolution throughout the entire search operation. The echo signals from the towed transducers are converted into the digital form and sent to the on-board device using the VDSL (Very High Speed Digital Subscriber Line) data transmission technology. The survey results and other information are displayed on two-monitor operator console with such functions as zoom, short-term memory, dimensioning, multiple windows, etc. The side-scan method is used eﬀectively in deep water and on the bottom (e.g. contact and bottom mines, shipwrecks, underwater structures). It enables identifying the bottom topography (for hydrographic purposes – making seabed maps) on the area of several hundred meters wide on both sides of the sounding vessel.

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Side-scan MCM sonar – towﬁsh and sounding exposition [481]

Side-scan MCM sonar – parameters [482] Side-scan sonar: Source level (dB re 1 Pa @ 1m) ≥ 90 dB Time-width of sounding pulses 0.2, 0.5, 1, 2 ms Operation frequency on the left side of the towﬁsh 154 ± 5 kHz on the right side of the towﬁsh 175 ± 5 kHz Angular resolution in the horizontal plane dynamically varying with the range: 1° for 200 m constant 4° Linear resolution in the horizontal plane with dynamically varying beam width: ca. 3.5 m Range resolution: switched 0,5 or 1,5 m Vertical width of observation beam 50° Display exposition range 150 or 300 m Reservoir depth 5 to 100 m Towing speed max. 6 knots Echosounder: Operation frequency 200 kHz Reservoir depth 5 to 100 m

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Contents

I Echolocation systems 3

1 Generalities 3 1.1 General working principle ...... 4

2 Basic tasks of echolocation systems 4 2.1 Target detection and localisation ...... 4 2.2 Target bearing ...... 5 2.3 Estimation, classification, identification ...... 5 2.4 General classification of echolocation systems ...... 5 2.5 Semantics ...... 6

3 Acoustic and electromagnetic waves 10 3.1 Wave phenomenon ...... 10 3.2 Mathematical description ...... 10 3.3 Electromagnetic wave – dielectrics ...... 11 3.4 Acoustic wave – ﬂuids ...... 11 3.5 Basic scalar equations ...... 21 3.6 Similarities of physical ﬁelds and waves ...... 24 3.7 Wave celerities ...... 24 3.8 Spreading geometry ...... 25

4 Waves and motion 25 4.1 Doppler eﬀect ...... 25 4.2 Applications ...... 27

5 Continuous wave radars and sonars 29

6 Doppler radars 30

II Radars and sonars 33

7 Wave propagation parameters 33 7.1 Medium, wave celerity, attenuation ...... 33 7.2 Frequency spectra ...... 33 7.3 Wave attenuation in air ...... 34 7.4 Wave attenuation in water ...... 36 7.5 Wave attenuation in cables ...... 38 7.6 1-D vs 3-D channels ...... 38

8 Radars 38 8.1 Wavelength-depending applications ...... 38 8.2 Radar classiﬁcation ...... 39 8.3 Role of radar antennas ...... 40 8.4 Radar consoles ...... 42

9 Sonars 43 9.1 Working principle ...... 43 9.2 Transducers and antennas ...... 43 9.3 Sonar system classiﬁcation ...... 44 9.4 Space scan methods ...... 45 194 R. Salamon & H. Lasota 2016-06-08 MES Department sonars XIII

10 Laser systems 45 10.1 Working principle ...... 45 10.2 Applications ...... 45

11 Echolocation system parameters 46 11.1 Functional diagram of echolocation system ...... 46 11.2 Operating and technical parameters ...... 46 11.3 Range, bearing, measurement accuracy ...... 47 11.4 Range and angular resolution ...... 48 11.5 Sector-scanning time ...... 49

III Echolocation signals 50

12 Echolocation in nature 50 12.1 Bats ...... 50 12.2 Dolphins & Whales ...... 51 12.3 Other spieces ...... 52

13 Echolocation signals 52

14 Narrowband signals 53 14.1 Monochromatic signal ...... 53 14.2 Sinusoidal pulse ...... 54

15 Autocorrelation function 54 15.1 Signal autocorrelation and energy ...... 54 15.2 Rectangular pulse ...... 54 15.3 Sinusoidal pulse ...... 55

16 Special signals 55 16.1 LFM signal ...... 55 16.2 HFM signal ...... 56 16.3 Signals with code modulation ...... 57

17 Detection of echolocation signals 61 17.1 Detection conditions ...... 61 17.2 Continuous signal – Gaussian noise ...... 62 17.3 Receiver operating curves (ROC) ...... 63 17.4 Stochastic signal – Gaussian noise ...... 63 17.5 Known signal – Gaussian noise ...... 64 17.6 Reception of rectangular pulses ...... 65

18 Matched reception – processing gain 65 18.1 Statistical properties – correlation receiver ...... 65 18.2 Signal-to-noise ratio ...... 65 18.3 Receiver matched to a signal ...... 66 18.4 Detection of signals of unknown parameters ...... 67 18.5 Detection and false alarm probabilities ...... 71 18.6 Reception of sinusoidal signals ...... 71 18.7 Fourier transform as realization of a ﬁlter ...... 72

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19 Signal sampling techniques 74 19.1 Direct sampling of signals ...... 75 19.2 Quadrature sampling of narrowband signals ...... 75 19.3 Time delay of signals ...... 79 19.4 Sampling as frequency transformation ...... 80

IV Antenna directivity 82

20 Radar and sonar antennae 82

21 Diffraction 86 21.1 Light diffraction ...... 86 21.2 Fraunhofer’s diffraction ...... 86 21.3 The Kirchhoff-Helmholz integral formula ...... 87

22 Radiation of acoustic/electromagnetic waves 87 22.1 Surface sources – the Rayleigh formula ...... 87 22.2 Near and far zone ...... 87 22.3 Rayleigh’s distance ...... 88 22.4 Directivity pattern ...... 89 22.5 Rectangular aperture directivity ...... 90 22.6 Circular aperture directivity ...... 91

23 Directivity as space Fourier transform 91 23.1 Calculations of speciﬁc directivity patterns ...... 91 23.2 Space spectrum visible range ...... 93 23.3 Directivity pattern parameters ...... 94 23.4 Logarithmic view of directivity ...... 94

V Practical theory of antenna apertures and arrays 95

24 Space-domain Fourier transform 95 24.1 Space version of the sampling theorem ...... 95 24.2 Fourier transform space properties ...... 95 24.3 Fourier transform pairs ...... 96 24.4 Fourier transform theorems ...... 98

25 Aperture functions vs. directivity 100 25.1 Directivity functions (maths) ...... 100 25.2 Directivity patterns (engineering) ...... 101 25.2.1 Antenna arrays (discreet apertures) ...... 101 25.2.2 Continuous antennae (continuous aperture distributions) ...... 103

26 Multielement antennas 104 26.1 Planar multielement antenna ...... 104 26.2 Principle of beam patterns multiplication ...... 104 26.3 Uniformly excited antenna arrays ...... 104 26.4 Array of point sources ...... 105 26.5 Multi-element antenna array ...... 105

VI Multibeam system technique 106

196 R. Salamon & H. Lasota 2016-06-08 MES Department sonars XIII

27 Single- and multibeam sector observation 106 27.1 Methods of volume scanning ...... 106 27.2 Simultaneous multibeam observation ...... 106

28 Multibeam systems structure 107 28.1 Antenae of multibeam systems ...... 107 28.2 Multibeam system receiver ...... 107

29 Beamformer technology 108 29.1 Technology classiﬁcation criteria ...... 108 29.2 Delay-and-sum beamformers ...... 108 29.3 Multiple directivity patterns ...... 110 29.4 Finite dimensions of antenna elements ...... 110 29.5 Aperture weighing (apodization) ...... 111 29.6 Analog phase beamformers ...... 111 29.7 Digital beamformers ...... 112 29.8 Time-domain beamformers ...... 113 29.9 Interpolation beamformers ...... 113 29.10Nyquist frequency sampling ...... 113 29.11Quadrature detection ...... 114

30 Space spectrum estimation 115 30.1 Angle of signal arrival vs space frequency ...... 115 30.2 Space sampling ...... 115 30.3 Quadrature sampling in the time domain ...... 115 30.4 Spectrum measured by ﬁnite antenna ...... 116 30.5 Digital space spectrum estimation ...... 117 30.6 Space spectrum of wideband signals ...... 117

31 High-resolution methods 119 31.1 Linear prediction technique ...... 119

VII Special purpose echolocation systems 122

32 Beam focusing 122

33 CW FM radars and sonars 123

34 Quiet radars 124

35 Synthetic aperture radars and sonars 125

36 Side scan sonar 127

37 Multibeam echosounder 128

38 Passive sonars 128

39 Sonobuoys 129

VIII Principles of underwater acoustics 131

197 R. Salamon & H. Lasota 2016-06-08 MES Department sonars XIII

40 Underwater environment 131 40.1 Propagation conditions ...... 131 40.2 (Hydro)acoustic waveguides ...... 132

41 Sound modes 132

42 Refraction 133 42.1 Propagation velocity ...... 134 42.2 Sound rays ...... 134 42.3 Sound channels ...... 136 42.4 Oceanic sound channel ...... 137 42.5 Sound attenuation ...... 139 42.6 Sea noise ...... 141

43 Refraction in sonar systems 142

IX Technology progress in modern hydrolocation systems 148

44 Matched ﬁltering 148

45 Multibeam echosounder 150 45.1 Beamforming ...... 150 45.2 Acoustic camera ...... 151

46 Parametric echosounder 153

47 Synthetic aperture sonar 155

48 Silent sonar CW FM 157

X Signal levels in physical space 158

XI Echolocation system design 169

49 Range equation 169 49.1 Logarithmic form of the range equation ...... 169

50 Echosounder design procedure 174 50.1 Assumptions ...... 174 50.2 Results ...... 177

XII High Performance Embedded Computing 179

XIII MES Department sonars 184

51 Operational & technical parameters 184 51.1 Polish Navy sonars ...... 184 51.2 Long-range active ASW sonar ...... 184 51.3 Medium-range MCM sonar ...... 186 51.4 Helicopter dipping ASW sonar ...... 188 198 R. Salamon & H. Lasota 2016-06-08 MES Department sonars XIII

51.5 Towed-array passive sonar ...... 190 51.6 Side-scan MCM sonar ...... 192

199