Adding DecibelsAdding Decibels

The Passive Sonar Equation

Will the sensor detect the red submarine?

Signal to Noise Ratio

Signal

Noise (quiet) Noise (Loud

Signal Signal Intensity

Noise Noise Intensity

The higher the SNR, the more likely you are to hear (detect) the signal.

Source Level and Transmission Loss

S

0

ISL 10log

I

SL

TL

RL SL TL

S

R

ITL 10log

I

S/ N R0 0

Signal Noise Intensity Noise IntensityL 10log L 10log SL TL 10log

Noise I I

Sources of Noise

• Shipping Noise

• Wind and Weather

• Marine Life – Biologic Activity

• Self Noise– Flow of Water– Machinery

Omni directional Noise

Isotropic Noise

IN

IN

IN

IN

IN

IN

IN

Receiver

Detector

Directivity Factor• Some detectors are only able to provide a voltage proportional to all

incident sound from all directions. (non-directional = ND)• Other detectors use more sophisticated signal processing and form

beams thereby providing a voltage proportional to sound incident from a particular direction. (directional = D)

IN

IN

IN

IN

IN

IN

IN

Receiver

Detector

IS

ND

D

Nd

N

DN Electrical power generated by actual directional receiver

NDN Electrical power generated by equivalent non-directional receiver

The Passive Sonar Equation

S/ N R0 0

Signal Noise Intensity Noise IntensityL 10log L 10log SL TL 10log

Noise I I

S/ N R N Received

SignalL 10log L L SL TL NL DI

Noise

S/ NL SL TL NL DI

S

0

ISL 10log

I

S

R

ITL 10log

I

N

0

INL 10log

I

DI 10log d

Figure of Merit• Often a detection threshold is established such that a

trained operator should be able to detect targets with that LS/N half of the time he hears them. Called “Recognition Differential.” (RD)

• Passive sonar equation is then solved for TL allowable at that threshold. Called “Figure of Merit.” (FOM)

TLallowable = Figure of Merit = SL- LS/N Threshold - (NL-DI)

• Since TL logically depends on range, this could provide an estimate of range at which a target is likely to be detected. Called “Range of the Day.” (ROD)

• Any LS/N above the Recognition Differential is termed “Signal Excess.” (SE) Signal Excess allows detection of targets beyond the Range of the Day.

Example• A hostile submarine with a

Source Level, SL = 130 dB re 1 Pa is near a friendly submarine in a part of the ocean where the Noise Level from all sources, NL = 70 dB re 1 Pa. The directivity factor is 3000 for the friendly submarine’s sonar. If the Recognition Differential for the friendly submarine is 20 dB, what is the Figure of Merit?

• If the actual Transmission Loss is 50 dB, what is the Signal Excess.

Signal to Noise Level

S/ N0 0

Signal Intensity Signal Intensity Noise IntensityL 10log 10log 10log

Noise Intensity I I

But we will be measuring the signal intensity level at the receiver/detector, IR

(in the frequency band of the detector)

This is different from the signal intensity level leaving the target, IS (in the frequency band of the detector)

S

S 0R R

S0 0 S

R

I

I II III I II

Fraction of emitted intensity reaching receiver

S SR

0 0 R

I II10log 10log 10log

I I I

RL SL TL

OR

Noise Level and Directivity Index

IN

IN

IN

IN

IN

IN

IN

Receiver

Detector

IS

ND

D

Nd

N

DN Electrical power generated by actual directional receiver

NDN Electrical power generated by equivalent non-directional receiver

N Received N

0 0

I I 1

I I d N Received N

N Received0 0

I IL 10log 10log 10log d

I I

OR

N

0

INL 10log

I

DI 10log d

N ReceivedL NL DI