Understanding Directivity: AVS vs Hydrophone Arrays

Directivity Comparison Between AVS Arrays and Hydrophone Arrays

Underwater acoustic sensing plays an important role in applications such as marine exploration, underwater communication, sonar systems, and target tracking. To detect acoustic signals in water and determine their direction of arrival, engineers commonly use sensor arrays.

Two widely used sensing technologies are hydrophone arrays and Acoustic Vector Sensor (AVS) arrays. Although both can detect underwater sound, their ability to determine the direction of incoming signals differs significantly.

In this article, we explore how these two sensing approaches compare in terms of directivity, which is a key parameter describing how well a sensor focuses on signals coming from a particular direction while suppressing signals from other directions.

Understanding Directivity

The performance of an acoustic sensor or array is often evaluated using a metric called directivity. In simple terms, directivity indicates how selective a sensor is with respect to the direction of incoming sound waves.

A highly directive sensor concentrates its sensitivity toward a specific direction and reduces interference from other directions. This property is extremely useful in underwater environments where background noise and reflections are common.

To quantify this behavior, we use a parameter known as the Directivity Factor (DF). It represents the ratio of the acoustic power received from a particular direction to the average power received from all possible directions.

DF = 4π |B(θ, φ)|² / ∫∫ |B(θ, φ)|² sinθ dθ dφ

In this expression:

• θ (theta) represents the elevation angle
• φ (phi) represents the azimuth angle
• B(θ, φ) describes the beam pattern of the sensor or array

The beam pattern essentially describes how sensitive the sensor is to signals arriving from different spatial directions.

Engineers often convert the directivity factor into decibel form using the Directivity Index (DI), which makes it easier to compare systems.

DI = 10 log10 (DF)

For a simple omnidirectional hydrophone, sound is received equally from every direction. Because of this uniform response, its directivity factor is 1.

DI_p = 0 dB

This means a single hydrophone does not provide any directional gain.

Directivity of Acoustic Vector Sensors (AVS)

Unlike hydrophones that measure only acoustic pressure, an Acoustic Vector Sensor measures both pressure and the particle velocity components of the acoustic wave.

Because particle velocity contains directional information, vector sensors are able to estimate the direction of incoming sound much more effectively than conventional pressure sensors.

To understand this behavior, consider a simple uniaxial sensor that measures only the x-component of the particle velocity vector.

B(θ, φ) = (sinθ cosφ)²

Using this beam pattern, the directivity factor becomes:

DF = 3 sin²θ cos²φ

If the sensor measures velocity along other axes, similar expressions are obtained.

DF_y = 3 sin²θ sin²φ

DF_z = 3 cos²θ

These equations indicate that velocity sensors can achieve a directivity factor up to three times greater than a standard omnidirectional hydrophone. This corresponds to an improvement of roughly 4.8 dB in directivity index.

However, the exact directivity depends on the arrival angle of the acoustic signal. For certain directions, the directivity may become lower than that of a pressure sensor.

Beam Pattern of a General Vector Sensor

A complete vector sensor measures acoustic pressure along with particle velocity in three orthogonal directions (x, y, and z). These measurements can be combined using weighting coefficients to produce a directional beam pattern.

B(θ, φ) = (wp + a(θ,φ)wx + b(θ,φ)wy + c(θ,φ)wz)²

The directional coefficients are defined as:

• a(θ, φ) = sinθ cosφ
• b(θ, φ) = sinθ sinφ
• c(θ, φ) = cosθ

The parameters wp, wx, wy, and wz represent weights applied to the pressure channel and the velocity channels respectively.

When calculating the directivity factor, cross-terms appearing in the denominator cancel out because they involve sinusoidal integrals evaluated over complete cycles.

DF = (1 + a wx + b wy + c wz)² / (1 + wx² + wy² + wz²)

To obtain the maximum directivity, we assume the pressure weight wp = 1 and solve the resulting equations.

a(θ, φ)(3 + wx² + wy² + wz²) = wx(1 + a wx + b wy + c wz)

b(θ, φ)(3 + wx² + wy² + wz²) = wy(1 + a wx + b wy + c wz)

c(θ, φ)(3 + wx² + wy² + wz²) = wz(1 + a wx + b wy + c wz)

Solving these equations provides the optimal weighting values:

wx = 3a(θ, φ)
wy = 3b(θ, φ)
wz = 3c(θ, φ)

Substituting these values back into the directivity expression yields:

DF = 1 + 3(a² + b² + c²)

Since the direction cosines satisfy the identity:

a² + b² + c² = 1

the directivity factor becomes:

DF = 4

Finally, converting this to the directivity index gives:

DI = 10 log10(4) = 6 dB

This result shows that a single acoustic vector sensor that measures both pressure and particle velocity can achieve a maximum directional gain of 6 dB. Compared with a simple hydrophone, vector sensors provide significantly better directional sensitivity, making them highly useful for applications such as underwater communication, target localization, and sonar signal processing.