# sonareqsnr

Compute SNR using the sonar equation

## Description

example

SNR = sonareqsnr(SL,NL,DI,TL) returns the received signal-to-noise ratio, SNR, from the source level, SL, received noise level, NL, receiver directivity index, DI, and transmission loss, TL. SNR is computed using the Sonar Equation. Use this syntax to evaluate passive sonar system performance.

example

SNR = sonareqsnr(SL,NL,DI,TL,TS) returns SNR taking into account the target strength TS. Use this syntax to evaluate active sonar system performance, where the transmitted signal is reflected from a target.

## Examples

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Estimate the SNR of a signal arriving from a source with a source level of 200 dB. The noise level is 75 dB, the receive array directivity index is 25 dB, and the transmission loss is 140 dB.

SL = 200.0;
NL = 75.0;
DI = 25.0;
TL = 140.0;
SNR = sonareqsnr(SL,NL,DI,TL)
SNR = 10

Estimate the SNR of a signal transmitted by a source with a source level of 130 dB//1 μPa and reflected from a target with 25 dB//1 ${m}^{2}$ target strength. The noise level is 45 dB//1 μPa, the receive array directivity is 25 dB, and the one-way transmission loss is 60 dB.

SL = 130.0;
NL = 45.0;
DI = 25.0;
TL = 60.0;
TS = 25.0;
SNR = sonareqsnr(SL,NL,DI,TL,TS)
SNR = 15

## Input Arguments

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Sonar source level, specified as a scalar. Source level is the ratio of the source intensity to a reference intensity, converted to dB. The reference intensity is the intensity of a sound wave having a root-mean-square (rms) pressure of 1 μPa. Units are in dB//1 μPa.

Example: 90

Data Types: double

Received noise level, specified as a scalar. Noise level is the ratio of the noise intensity to a reference intensity, converted to dB. The reference intensity is the intensity of a sound wave having a root-mean-square (rms) pressure of 1 μPa. Units are in dB//1 μPa.

Example: 70

Data Types: double

Receiver directivity index, specified as a scalar. Units are in dB.

Example: 30

Data Types: double

Transmission loss (TL), specified as a positive scalar. Transmission loss is the attenuation of sound intensity as the sound propagates through the underwater channel. Transmission loss is defined as the ratio of sound intensity at 1 m from a source to the sound intensity at distance R. For active sonar, TL represents one-way transmission loss.

$TL=10\mathrm{log}\frac{{I}_{\text{s}}}{I\left(R\right)}$

Units are in dB.

Example: 120

Data Types: double

Target strength, specified as a scalar. Target strength is the ratio of the intensity of a reflected signal at 1 m from a target to the incident intensity. Target strength is the sonar analog to radar cross section. Units are in dB//1 m2.

Example: 5

Data Types: double

## Output Arguments

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Received signal-to-noise ratio, returned as a scalar.

Data Types: double

## References

[1] Ainslie M. A. and J.G. McColm. "A simplified formula for viscous and chemical absorption in sea water." Journal of the Acoustical Society of America, Vol. 103, Number 3, 1998, pp. 1671--1672.

[2] Urick, Robert J, Principles of Underwater Sound, 3rd ed. Peninsula Publishing, Los Altos, CA, 1983.