M.Afsar Ali In underwater acoustic communication, you can calculate the received signal strength (RSS) and range between a transmitter and receiver using various factors and formulas. One common formula for calculating the received signal strength in dB is based on the inverse square law, which states that the power of a signal decreases with the square of the distance from the source. The formula is as follows:

**RSS (dB) = SL - 20 * log10(R) - TL + DI - NL - TS**

Where:

- **RSS (dB)** is the received signal strength in decibels.

- **SL** is the source level, which represents the initial transmitted acoustic power level in dB.

- **R** is the range between the transmitter and receiver in meters.

- **TL** is the transmission loss, which accounts for the loss of signal power due to spreading and absorption in the water medium.

- **DI** is the directivity index, which represents the gain or loss of the signal due to the directionality of the transmitter and receiver transducers.

- **NL** is the noise level in the environment, often given in dB re 1 µPa (microPascal).

- **TS** is the target strength, which accounts for the reflectivity of the target (e.g., AUV or ROV).

Now, let's break down each component:

1. **Source Level (SL):** This is the power level at which the signal is initially transmitted. You need to know the source level of your transmitter in dB.

2. **Transmission Loss (TL):** Transmission loss accounts for the attenuation of the signal as it propagates through the water. It depends on various factors such as frequency, water temperature, salinity, and depth. You can use empirical models or software tools to estimate TL for your specific scenario.

3. **Directivity Index (DI):** This factor accounts for the directional properties of the transducers used in the transmitter and receiver. It can be positive or negative depending on whether the transducers focus or disperse the acoustic energy. You may need to consult the specifications of your transducers.

4. **Noise Level (NL):** This represents the background noise in the underwater environment. It's typically measured in dB re 1 µPa and can vary depending on the location and frequency band of interest.

5. **Target Strength (TS):** TS accounts for how well the target (e.g., AUV or ROV) reflects the acoustic signal. It depends on the target's shape, size, and composition. TS values can often be found in literature or measured experimentally.

By plugging in the values for SL, R, TL, DI, NL, and TS into the formula, you can calculate the received signal strength (RSS) in dB at the receiver's location. This RSS value gives you an indication of the signal's strength relative to the initial source level. Keep in mind that underwater acoustic communication is a complex field, and accurate modeling requires consideration of various environmental and equipment-specific factors.

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Source Level (SL): 180 dB re 1 µPa at 1 meter

Range (R): 3,000 meters (3 km)

Transmission Loss (TL): 40 dB

Directivity Index (DI): 5 dB (indicating some directional gain)

Noise Level (NL): 120 dB re 1 µPa

Target Strength (TS): -30 dB (indicating a weak target reflection)

RSS (dB) = SL - 20 * log10(R) - TL + DI - NL - TS

RSS (dB) = 180 - 20 * log10(3000) - 40 + 5 - 120 - (-30)

Calculate each part of the equation:

- 20 * log10(3000) ≈ 87.99 dB

- -(-30) = 30 dB

Plug these values back into the main equation:

RSS (dB) = 180 - 87.99 - 40 + 5 - 120 + 30

Calculate:

RSS (dB) ≈ 86.01 dB

To calculate the received signal strength in underwater acoustic communication in decibels (dB), you can use the following formula:

Received Signal Strength (RSS) in dB = Transmit Power (in dB) - Path Loss (in dB) + Antenna Gain (in dB) - System Losses (in dB)

Here's a breakdown of each component:

Once you have all these values, you can plug them into the formula to calculate the received signal strength in dB. Keep in mind that underwater acoustic communication is a complex field with many environmental variables to consider, so accurately estimating path loss can be challenging and may require specialized modeling or measurements for your specific scenario. Additionally, real-world underwater communication systems often have to contend with issues like multipath propagation and interference, which can further affect signal strength.

You need to calculate the theoretical linear range of sound attenuation at the selected frequency using Natalia Kucherenko's formula (see preprint "REGULARITY OF THE WAVE ENERGY ABSORPTION PROCESS AS AN EXAMPLE OF THE PROPAGATION OF ACOUSTIC WAVES IN WATER") and then carry out amplitude modulation of the sound propagation data using the 2D program calculation of refraction. To do this, you need to set the actual bottom topography between the emitter and the receiver, the depth of the emitter and the depth of the receiver.

In the future, you can perform amplitude modulation using 3D refraction calculations using the program http://oalib.hlsresearch.com/Rays/

Dear all, there is an important element which is the depth and seafloor nature (in terms of absorption and reflexivity).

The conventional "sonar equation" detailed by Kaylin embeds the assumption of depth>range but 3km is far more than the depth in most maritime areas, so the problem becomes far more complex with multipath transmissions interfering together (bottom/surface successive reflections); furthermore, the sound speed is varying with the depth, curving the acoustic rays, but you can neglect this bathymetry influence if the range is only few km; conversely, you need to factor that the acoustic telemetry is using high frequency signal carriers (several hundred KHz) to augment the data rate , making the absorption on the seabed far from being negligible but however not always sufficient to neglect the reflected waves; the sea surface reflection is also very weather-dependant; to mitigate this "multipath" situation, you have to make the right choice of waveform for the transmitted signal to be robust again these interferences... As a result, the real range will vary with the depth of the ROV/UUV. With a rocky seafloor (eg Baltic sea) or rocky outcrops area, the acoustic propagation turns highly reverberant and augmenting the source level will not help to increase the range.

To make things worse, if the support vessel is not at a full standstill, you have to introduce its own noise signature, and the one of the ROV, as additional elements to the ambient noise level, and also their respective speeds as inducing flow noise on the transmitter arrays...

In short, it is impossible to calculate the effective transmission range without knowing the carrying frequency band, waveform, seafloor absorption, UUV depth, own noise signatures and speeds of the platforms, 3D seafloor geometry if not flat and horizontal etc. - such complex acoustic propagation models exist (3D ray tracing) but you will not find them on-line!

Alternatively just trust the telemetry manufacturer's data as an average but keep some margin if your deployment theatre is less favourable...

Note that the unit is not really dB but it is db//1𝜇pa. We may think of 𝑑𝐵// 1 𝜇𝑃𝑎 in acoustics as playing the role of 𝑑𝐵𝑚 in RF. When referring to the Tx/Rx (acoustic) power it is customary to specify the acoustic intensity value in decibel (dB) relative to the intensity due to 1 micro-pascal (𝜇𝑃𝑎) root mean square (RMS) pressure

The received signal strength can be calculated using the passive sonar equation 𝑆𝑁𝑅 = 𝑆𝐿 − 𝑇𝐿 − 𝑁𝐿 Where 𝑆𝐿 is the source level, 𝑇𝐿 is the transmission losses, and 𝑁𝐿 is the noise level.

Calculation of the TL and NL is complex and is explained in section 3.1.3 and 3.1.4 of https://www.tetcos.com/downloads/v13.3/UWAN.pdf