#### Noise Level (NL)

Noise level (NL) is the ratio of the noise intensity at the receiver to the same reference intensity used for source level.

### Active Sonar Equation

The active sonar equation describes a scenario where sound is transmitted from a source, reflects off a target, and returns to a receiver. When the receiver is collocated with the source, this sonar system is called monostatic. Otherwise, it is bistatic. Phased Array System Toolbox models monostatic sonar systems. The active sonar equation is

SNR=SL−2TL−(NLDI)+TS

where 2TL is the two-way transmission loss (in dB) and TS is the target strength (in dB). The transmission loss is calculated by computing the outbound and inbound transmission losses (in dB) and adding them. In this toolbox, two-way transmission loss is twice the one-way transmission loss.

#### Target Strength (TS)

Target strength is the sonar analog of radar cross section. Target strength is the ratio of the intensity of a reflected signal at 1 m from a target to the incident intensity, converted to dB. Using the conservation of energy or, equivalently, power, the incident power on a target equals the reflected power. The incident power is the incident signal intensity multiplied by an effective cross-sectional area, σ. The reflected power is the reflected signal intensity multiplied by the area of a sphere of radius R centered on the target. The ratio of the reflected power to the incident power is

IincσIreflIinc=Irefl4πR2=σ4πR2.

The reflected intensity is evaluated on a sphere of 1 m radius. The target strength coefficient (σ) is referenced to an area 1 m2.

TS=10log10Irefl(1 meter)Iinc=10log10σ4π

 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.

“A simplified formula for viscous and chemical absorption in sea water.”