# sonareqsl

Compute source level using the sonar equation

## Syntax

``SL = sonareqsl(SNR,NL,DI,TL)``
``SL = sonareqsl(SNR,NL,DI,TL,TS)``

## Description

example

````SL = sonareqsl(SNR,NL,DI,TL)` returns the source level of a signal, `SL`, required to achieve a specified received signal-to-noise ratio, `SNR`. Source level is computed using the Sonar Equation. Specify the received noise level, `NL`, receiver directivity index, `DI`, and the transmission loss, `TL`. Use this syntax to evaluate passive sonar system performance.```

example

````SL = sonareqsl(SNR,NL,DI,TL,TS)` returns the source level 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. `TL` represents one-way transmission loss.```

## Examples

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Estimate the source level of a signal arriving from a source with an SNR of 10 dB. The noise level is 75 dB, the receive array directivity index is 25 dB, and the transmission loss is 140 dB.

```SNR = 10; NL = 75.0; DI = 25.0; TL = 140.0; SL = sonareqsl(SNR,NL,DI,TL)```
```SL = 200 ```

Estimate the source level of a signal transmitted by a source with SNR of 15 dB 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 index is 25 dB, and the one-way transmission loss is 60 dB.

```SNR = 15.0; NL = 45.0; DI = 25.0; TL = 60.0; TS = 25.0; SL = sonareqsl(SNR,NL,DI,TL,TS)```
```SL = 130 ```

## Input Arguments

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Received signal-to-noise ratio, specified as a scalar. Units are in dB.

Example: `10`

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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Sonar source level, returned 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 an rms pressure of 1 μPa. Units are in dB//1 μPa.

## 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.