Sonar Principles Asw Analysis

1
Lecture I
The Sonar Equation
and
Signal Detection
Dr. Nicholas C. Nicholas
Applied Technology Institute
349 Berkshire Drive
Riva, Maryland 21140
888-501-2100/410-956-8805
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10 – Vol. 95 Register online at www.ATIcourses.com or call ATI at 888.501.2100 or 410.956.8805
Sonar Principles & ASW Analysis
Off The Course Tuition."
Summary
This course provides an excellent introduction to underwater sound and highlights how sonar principles are
employed in ASW analyses. The course provides a solid understanding of the sonar equation and discusses in-
depth propagation loss, target strength, reverberation, arrays, array gain, and detection of signals.
Physical insight and typical results are provided to help understand each term of the sonar equation. The
instructors then show how the sonar equation can be used to perform ASW analysis and predict the performance of
passive and active sonar systems. The course also reviews the rationale behind current weapons and sensor
systems and discusses directions for research in response to the quieting of submarine signatures.
The course is valuable to engineers and scientists who are entering the field or as a review for employees who
want a system level overview. The lectures provide the knowledge and perspective needed to understand recent
developments in underwater acoustics and in ASW. A comprehensive set of notes and the textbook Principles of
Underwater Sound will be provided to all attendees.
Instructors
Dr. Nicholas Nicholas received a B. S. degree from
Carnegie-Mellon University, an M. S.
degree from Drexel University, and a
PhD degree in physics from the Catholic
University of America. His dissertation
was on the propagation of sound in the
deep ocean. He has been teaching
underwater acoustics courses since
1977 and has been visiting lecturer at the U.S. Naval
War College and several universities. Dr. Nicholas has
more than 25 years experience in underwater acoustics
and submarine related work. He is working for Penn
State’s Applied Research Laboratory (ARL).
Dr. Robert Jennette received a PhD degree in
Physics from New York University in
1971. He has worked in sonar system
design with particular emphasis on long-
range passive systems, especially their
interaction with ambient noise. He held
the NAVSEA Chair in Underwater
Acoustics at the US Naval Academy
where he initiated a radiated noise measurement
program. Currently Dr. Jennette is a consultant
specializing in radiated noise and the use of acoustic
monitoring.
Course Outline
1. Sonar Equation & Signal Detection. Sonar
concepts and units. The sonar equation. Typical active
and passive sonar parameters. Signal detection,
probability of detection/false alarm. ROC curves and
detection threshold.
2. Propagation of Sound in the Sea.
Oceanographic basis of propagation, convergence
zones, surface ducts, sound channels, surface and
bottom losses.
3. Target Strength and Reverberation. Scattering
phenomena and submarine strength. Bottom, surface,
and volume reverberation mechanisms. Methods for
modeling reverberations.
4. Elements of ASW Analysis. Fundamentals of
ASW analysis. Sonar principles and ASW analysis,
illustrative sonobuoy barrier model. The use of
operations research to improve ASW.
5. Arrays and Beamforming. Directivity and array
gain; sidelobe control, array patterns and beamforming
for passive bottom, hull mounted, and sonobuoy
sensors; calculation of array gain in directional noise.
6. Passive Sonar. Illustrations of passive sonars
including sonobuoys, towed array systems, and
submarine sonar. Considerations for passive sonar
systems, including radiated source level, sources of
background noise, and self noise.
7. Active Sonar. Design factors for active sonar
systems including transducer, waveform selection, and
optimum frequency; examples include ASW sonar,
sidescan sonar, and torpedo sonar.
8. Theory and Applications of Current Weapons
and Sensor Systems. An unclassified exposition of the
rationale behind the design of current Navy acoustic
systems. How the choice of particular parameter values
in the sonar equation produces sensor designs
optimized to particular military requirements. Generic
sonars examined vary from short-range active mine
hunting sonars to long-range passive systems.
What You Will Learn
• Sonar parameters and their utility in ASW Analysis.
• Sonar equation as it applies to active and passive
systems.
• Fundamentals of array configurations, beamforming,
and signal detectability.
• Rationale behind the design of passive and active
sonar systems.
• Theory and applications of current weapons and
sensors, plus future directions.
• The implications and counters to the quieting of the
target’s signature.
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2
What is Sound?
Sound is a mechanical wave motion propagating in an elastic
medium. Associated with this wave motion are changes in the
local pressure and density.
Sonar, an acronym for SOund NAvigation and Ranging, uses
sound energy (generally underwater) to transmit information.

3
Longitudinal Waves
COMPRESSIONS AND RAREFACTIONS OF LONGITUDINAL WAVES
λ = WAVELENGTH
f = FREQUENCY
c = SPEED OF SOUND

4
Terminology
Psycho/Physiological Physical
Pitch Frequency
(Nominal) Audible Range: 20 –20,000 Hz
Speech Range : 100 – 4,000 Hz
Infrasonic : Below audible range
Ultrasonic : Above audible range
Loudness Intensity
Intensity = 10 LOG10 I1/I0 = 20 LOG10 P1/P0 Decibels (dB)
Quality Waveform
Spectrum, Relative
amplitudes/phases

5
Nominal Speed of Sound
Material Speed of Sound (m/s) Density (g/cm3)
Aluminum (rolled) 6420 2.7
Stainless Steel 5790 7.9
Rubber, Gum 1550 0.95
Fresh Water (25oC) 1498 0.998
Sea Water (25oC) 1531 1.025
Air 331 0.0012
Sea Water 1430→1530

6
Acoustic Wavelength versus Frequency
Wavelength = sound speed/ frequency
λ = c/f

7
Sensitivity of the Human Ear
0 dB = 0.0002 dyne/ sq. cm
Shortly & Williams (53)

8
Doppler Shift (Passive Sonar)
When a sound source is moving with respect to an acoustic observer, the frequency
of the sound is shifted.
f0 = fs c + V0
c - Vs
f0 = observed frequency
fs = frequency at the source
c = speed of sound
V0 = speed of observer approaching sound source = V1 cos Θ
Vs = speed of source approaching observer = V2 cos Θ
Θ = bearing angle
Doppler shift is about 0.35 Hz per knot, about 1% at 30 knots

9
Doppler Shift (Active Sonar)
In active sonar, the approaching target received a signal which is shifted higher in
frequency (up-Doppler), then reradiates as a moving source approaching the
receiver, causing a doubling of the Doppler shift.
f = 0.69 Hz/(knot) (KHz) [ACTIVE]
REMEMBER
Approaching target produces an up-Doppler.
Receding target produced a down-Doppler.
Active sonar Doppler shift is double that of passive sonar
(about 2% at 30 knots)

10
Lofargram of Simulated Aircraft Overflight

11
Decibel (dB)
Decibels are 10 times the logarithm (to base 10) of
the ration of a power or power-related quantity
divided by a reference level.
I (dB re 1 watt/cm2) = 10 log I (watts/cm2)
Iref
(watt/cm2)
Remember the following properties of logarithms:
log 10X = X
log [10X 10Y] = log 10(X+Y) = X+Y
To convert from dB to linear units
i (linear ratio) = 10(0.1)I
Where i = linear ration normalized by reference unit
I = dB value.

12
Intensity/Pressure/Acoustic Impedance
Intensity is the (sound) power flow per unit area
I = P2 / ρc
where P = pressure amplitude
ρc = acoustic impedance
ρ = density
c = speed of sound
Intensity = 10 log I/Iref
= 10 log (P/Pref )2
= 20 log P/P2

13
Pressure Units
- Force per unit area
- MKS units:
1 Pascal = 1 Newton/m2
- CGS units:
1 µbar = 1 dyne/cm2
-New reference unit
1 µPascal = 10-6 Newton/m2

14
Power Addition
It is sometimes necessary to sum powers of two numbers which are expressed
by dB. The numbers cannot be simply summed in dB form, as that would
correspond to multiplication. In order to sum power, first convert from dB to
the original units, add, and then express the result in dB. Alternately, the
following curve can be used.

15
EXAMPLE FOR THE COMBINATION OF
SHIPPING NOISE AND WIND WAVE NOISE
EXAMPLE FOR DETECTION THRESHOLD = -5 dB
(S/N)REQ = -5 dB
[(S+N/N)]REQ = 1.2 dB

16
More Examples
If the acoustic pressure in a plane wave is increased by a
factor of 3, what is the change in level of the sound?
If the acoustic intensity in a plane wave is increased by a
factor of 3, what is the change in level of the sound?
If the acoustic pressure in a plane wave is reduced to 1/4,
what is the change in level of the sound?
If the acoustic intensity in a plane wave is reduced to
1/10, what is the change in level of the sound?

17
Yet More Examples
At a certain location the noise level due to oceanic
turbulence is 70 dB, the noise level due to distant
shipping is 73 dB, and the self-noise level is 73 dB.
What is the total noise level?

18
Bathymetry
Illustration of bathymetrically unimpeded ray paths emanating from Herd Islands with the
indicated launch angles. All rays are refracted geodesics along the surface containing the sound
channel axis. White boxes indicate locations of oceanographic research stations capable of receiving
acoustic signals. (Munk and Forbes, 1989; J. Phys. Oceanography, No. 19, 1965-78; copyright by
the American Meteorological Society)

19
Generalized Shipping Routes

21
Bathymetry and Sound Speed Structure

22
Ambient Noise Measurements
Paul C. Etter, Underwater Acoustic
Modeling, E & F SPON,
New York, NY, Second Edition, 1996

23
Bathymetric and Sound Speed Structure
(North Pacific)

24
Ambient Noise Measurements

25
Directionality of Ambient Noise

26
Ambient Noise Near Compact Ice Edge

27
Radar Equation Definitions
SNR = Signal-to-noise ratio
PT = Transmitter power
GT = Transmitter directional gain
r = Range to target
= Attenuation coefficient
= Effective target scattering cross-section
AR = Effective area of receiver
KBT = Thermal noise power
Pamb = Ambient noise power
Prev = Reverberation backscattered power
Convert equation to dB by taking 10 log of both sides of
the equation.

28
The Radar/Sonar Equation
SNR = Signal Power
Noise Power
= Gain Against Noise or reverberation

29
Sonar Equations (dB Values)
Active Sonar – Ambient Noise Background
[SL - 2TL - + TS] = [NL – DT] + DT + SE
Active Sonar – Reverberation Background
[SL - 2TL - + TS] = (RL) + DT + SE
Passive Sonar
[SL - TL] = (NL – DI) + DT + SE
Signal Level = Effective + Required + Signal
Masking Signal Excess
Noise to Noise Relative
Ratio to DT

30
Solving the Sonar Equation
The sonar equation expresses the signal-to-noise
ration as function of the sonar and environmental
parameters. At the maximum detection range, the
received signal power divided by the noise power is
equal to the detection threshold. (Signal excess is
zero.) Uncertainties in some of the parameters,
especially TL and NL, limit the accuracy of prediction
to a few dB.

31
Figure of Merit
FOM equals the maximum allowable one-way transmission
loss in passive sonar or the maximum allowable two-way
transmission in active sonar.
Passive FOM = TL = SL - [NL – DI + DT]
Active FOM = 2TL = SL + TS – [NL – DI + DT]
Note:
Including TS in active FOM disagrees with Urick, but is a
common practice.
FOM is not useful for reverberation limited ranges.

32
Passive Sonar Prediction
[SL – TL] - [NL – DI] = DT
Received - Background = Detection
Signal Level Masking Noise Threshold
Urick [75]

33
Active Sonar Prediction
Urick [75]

34
Active Sonar Parameters
Parameter Symbol Important Factors
Source Level SL Input Power
Conversion Efficiency
Directivity Index
Cavitation Limitations
Target Strength TS Target Area
Target Aspect
Pulse Duration
Frequency
Reverberation Level RL Source Level
Beam Width
Pulse Length
Boundaries
Scattering Layers
Frequency

35
Detection Threshold
DT = 10 log Req Signal Power for a Spec. Performance
Noise Power per Hz at the Receiver Input
Detection Threshold (DT) is defined as the ratio (in decibels) of
the signal power in the receiver bandwidth to the noise ower
spectrum level (in a 1 Hz band) measured at the receiver
terminals, required for detection at some specified level of
correctness of the detection decision [i.e., p(D) and p(FA)].
Typical requirements per decision (or per look):
p(D) = 0.5 or 0.9
p(FA) = 10-6
Urick [75]

36
Detection Decision
Decide “Signal Present” when the input exceeds the expected value of
noise by more than a bias level; otherwise, decide “Signal Absent.”
Decision
True Input
Signal Present Signal Absent
Signal Present Correct
DETECTION p(D)
False Dismissal
1-p(D)
Signal Absent FALSE Alarm
p(FA)
Correct Dismissal
1-p(FA)
Urick [75]

37
Signal Detection Experiment
GAUSSIAM NOISE GENERATOR
Average noise level N
15-second sections
STEADY SINUSOIDAL SIGNALS
Duration T
Average Power S
THE EXPERIMENT
Signals embedded in half the 15-second noise sections
(or echo cycles)
Listeners push button when “signal present”
LISTENER TRAINING
Easily detected signals
Signal levels gradually reduced

38
Data Collection
• “HIT” SCORED WHEN LISTENER RESPONDED
WITHIN 1 SEC. AFTER SIGNAL OCCURRENCE
• “FALSE ALARM” SCORED WHEN LISTENER
RESPONDED TO NOISE
• LISTENERS WERE NOT RESTRICTED TO ONE
RESPONSE PER NOISE SECTION
• SCORES WERE TABULATED USING LAST
RESPONSE IN EACH SECTION

39
Estimates of PD and PFA
PD = ____________NUMBER OF “HITS” ___________________
NUMBER OF NOISE SECTIONS WITH SIGNALS
PFA = NUMBER OF “EMPTY SECTIONS” IN WHICH RESPONSES WERE MADE
NUMBER OF “EMPTY” NOISE SECTIONS
“EMPTY” NOISE SECTION IS NOISE SECTION WITH NO EMBEDDED SIGNAL.

40
Experiment Results
♦LISTENED TO SEVERAL HUNDRED NOISE SECTIONS
•Different days
•Different instructions on strictness about responding
♦PD PLOT AGAINST PFA GROUPED AROUND THEORETICALLY COMPUTED S = 0 dB Curve
N
♦WHEN AVERAGE S/N CHANGED TO ±2 dB, MEASUREMENTS CLUSTERED
AROUND S/N = ±2dB CURVES, ETC.
NOTE: log10(1) = 0 means <S> = <N>

Receiving Operating Characteristics (ROC) Operating Curves
41

42
Interpretation of Results
• PD increases with S/N
• PFA decreases as S/N increases
• Visual detection
– Noise sections written out as pen recordings (such as
time bearing plots)
– Observers detect signal by viewing recorder plots
– Different set of PD vs. PFA curves
– Eye not as good (for detection) as ead

43
Concept Leading to Construction of ROC Curves
Output Levels:
•Energy detector – Mean square amplitude of power
•Voltmeter
•Oscillate about (B) when no signal present
•Oscillate about (A) when signal present

44
Gaussian Distribution (Model of Random Noise)
Central Limit Theorem: The random selection of values from any
distribution (Gaussian or not) tends to a Gaussian distribution with the same
mean and standard deviation as was in the original distribution.

45
Normal Distribution Probability Density and Cumulative
Distribution Functions
Cumulative Distribution FunctionNormal Distribution Density

47
Computing ROC Curves
DETECTABILITY
INDEX:
P(y/N) = Prob. Density of output y, given N as input
P(y/SN) = Prob. Density of output y, given S+N as input
IDEAL ENERGY DETECTOR
E = Total signal energy received during time T in band W
S = Signal power in band W (note: E = ST)
T = Sample time of detector
W = Input bandwidth of the detector system

48
Evaluation of P(D) and P(F)
(Prob. density of noise)
(Prob. density of signal and noise)

49
ROC Curves for an Energy Detector

50
Required signal-to-noise (visibility factor) at the input terminals of a linear-rectifier
detector as a function of probability of detection for a single pulse, with the false-alarm
probability (PFA) as a parameter, calculated for a non-fluctuating signal
Blake [69]
Visibility Factor (Radar)

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Sonar Principles Asw Analysis

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