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underwater acoustic communications systems operating in a coastal shallow waters scenario. Ambient noise; non-Gaussian statistics; high frequency.
Simulation of non-White and non-Gaussian Underwater Ambient Noise F. Traverso and G. Vernazza

A. Trucco

Dynatech, University of Genoa, Genova, Italy [email protected]

Dynatech, University of Genoa, Genova, Italy Istituto Italiano di Tecnlogia (IIT) , Genova, Italy

Abstract—Noise in the ocean is the result of many contributions. Sources emitting sound in open sea as well as in a coastal area can be placed both in the sea surface and underwater. Excluding the self-noise, the noise impinging a sonar system is called ambient noise and usually is split in two groups: anthropic and natural. In this paper we focus in modeling noise produced by ship transit, which falls in the anthropic category, and noise due to sea surface agitation, that is classified as a natural source. In particular we aspire to simulate the acoustic noise radiated by the machinery of a vessel once the rotational speed of the propeller induces the cavitation effect. Further, we take account of the wind speed action in the sea state and its contribution to the actual underwater ambient noise. An algorithm based on a nonGaussian approach allows to generate sequence of samples representative of a noise realization having specified kurtosis level and to reproduce the desired source spectrum. The results of the simulation suggest that the surface ship transit can be thought as a major factor in limiting the performance of a underwater acoustic communications systems operating in a coastal shallow waters scenario. Ambient noise; non-Gaussian statistics; high frequency.

I.

INTRODUCTION

Acoustically speaking the ocean is changeling environment subject to constant changing. Chemically and physical reactions, meteorological and oceanic processes and a widespread biological life are natural fonts of diversity in seawaters. Moreover, the anthropic activity in the ocean complicates the global scenario. Commercial and cruise lines have grow up in the last century, together with an increasing of industrial interest in offshore oil and gas extraction. Locally, the harbours become even more efficient and coastal shipping is becoming of the most important sources of ocean traffic [1]. This complex environment contributes to create a very noisy underwater ambient, that, apart the self-noise, often limits the performance of a sonar systems [2]. The presence of the ambient noise makes the acoustic channel unaffordable for such systems, especially when an estimation of the different sources contribution is hard to perform. The solution is to design a sonar whose performance are robust enough, by considering the noise effect adopting a model for the sources [3]. Usually, in modeling the ambient noise in the ocean, one consider a white-Gaussian process jointly with a white spectrum, representative for an sum of independent sources. Even if this assumption can hold for many of the marine scenarios, often just few sources are active in the environment

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and the white-Gaussian hypothesis is not applicable. Since each noise source contributes to the local sound pressure by an amount that depends on its physical characteristics and the attenuation between the source and receiver, it is common to find that just one predominates in a given frequency band [4] and characterizes the noise spectral level (NSL) and the probability density function (PDF) of the local ambient noise. Often, a sonar system, designed for underwater acoustic communications, works with frequencies between 1 kHz and 10 kHz [6],[7]. Within this frequency range the acoustic noise due to the ship transit and produced by the sea surface agitation prevails over the effect of the other sources [4]. Measurements of ocean noise shown that both the noises can be characterized by non-white spectrum [7]-[10] and non-Gaussian statistic [11],[12]. However, in literature a gap regarding underwater ambient noise statistics in the kHz decade has not been covered yet. In particular, the characterization of ship–radiated noise is usually limited to the traditional case of deep waters and long range, which is often performed by semi-empirical model for frequencies below 1 kHz [8]-[10], where, once present, it is the dominant source of ambient noise. Recently few examples of high frequency statistics of ambient noise have been proposed in the literature [13], a complete understood of the broadband ship’s noise characteristics is not yet achieved. In this paper we aim to contribute in filling this gap, by focusing in a specific marine scenario, littoral shallow waters, and by discussing the effect of the considered noise sources in the spectrum and statistic of the actual ambient noise. Ship transit noise is probably the main contributors to underwater noise in harbour approaches or coastal waters. Ship transit is to be intended as the noise radiated by the transit of a single surface vessel in the vicinity of the receiver. It differs from shipping traffic noise, which accounts for a number of vessels radiating at the same time in the same location [2], i.e. a shipping density. A noise model for shipping traffic aims to reproduce a mean noise level corresponding to a distribution of ships in a well-defined ocean area. A simulator of ship transit noise generates a signal representative for the radiation of a single ship sailing in free water, i.e. without a significant noise contribution of other surface vessels nearby. The second is the subject of this paper. The radiated noise from a vessel can be depicted as generated by several sub-sources, however in the 1 kHz to 10 kHz interval the NSL is dominated by propeller cavitation [7]. The acoustic noise generated by cavitation exhibits a broadband continuous spectrum, peaking in a frequency range depending on the ship machinery, with

magnitude level that increase with increased velocity. Roughly, in standard water-air weather conditions, sea surface agitation noise is governed by the wind, which blowing over the surface augments the wave height and the corresponding breaking effect [4]. Depending on the actual wind speed, a sea state level can be defined to establish the equivalent NSL [14]. Since acoustic noise is essentially a sequence of values that has random characteristics, to produce a simulator, a randomnumber generator is frequently used [15]. If the algorithm generates sequences that repeat over time it is a pseudo-random number generator. The proposed procedure for simulating ambient noise is based on the properties of the Gaussian process moments. A normal distribution is characterized by the value of its kurtosis that is equal to 3. Any shift from this value corresponds to a PDF different from the normal distribution. Typical kurtosis value for ocean noise PDFs lies between 2 and 4, a considerably departure from the Gaussian case [12],[16],[17],[18]. The adopted method generates the pseudorandom sequence following the algorithm proposed in [15]. Trough this technique it is possible to assign a desired power density spectrum jointly with a kurtosis value to the target stochastic process. In the algorithm, low kurtosis values are associated to a sinusoidal like source, that is well suited for noise generated by the hydrodynamic process known as propeller cavitation. High kurtosis values, instead, are distinctive of an impulsive source and more appropriate for noise produced by breaking waves. Adopting the considered NSL models for ship noise and sea surface agitation noise, the goal is to simulate both the sources and discuss the effect of their contribution to the local ambient noise. This paper is organized as follows. In Section 2 the considered ambient noise scenario is described while Section 3 resumes the adopted models for the noise sources spectra. In Section 4 is presented the adopted generator of non-Gaussian noise and the results for several scenarios having different characteristics are discussed in Section 5. Finally, in Section 6, some conclusions are drawn. II.

CARACTERISTICS OF THE AMBIENT NOISE SCENARIO

Traditionally, in underwater acoustic communication systems [19],[20] there was only limited attention for modeling of ambient noise, as the focus was on reproduction of highSNR channel measurements with the channel simulator, and only a basic noise model, with a white or coloured spectrum and a Gaussian probability density function (PDF), was added to decrease the SNR afterwards. Instead, in state-of-the-art systems [19], several types of low-SNR simulations are desired for the derivation of representative channel statistics, so realistic noise modeling at the receiver becomes crucial. To this end, some specifications are typically addressed for the ambient noise which will be used to define in the simulated scenario. Excluding self-noise, a typical noisy underwater environment can be depicted as the result of the co-existence of several sources. Each active noise source in the environment contributes to the local ambient noise level by an amount that depends on its spectrum and its impact to the SNR is governed by its statistics. Consequently, only a few noise sources

dominate a specific scenario for a given frequency range. In this paper, the focus is on shallow littoral waters with medium distance to the coastline. A. Noise Sources In a shallow water scenario, within a coastal area, shipping is most probably the dominant source of underwater noise [21]. Acoustic radiation by a ship is an important underwater noise source and is usually considered as the main source in harbours and harbour approaches. Depending in the actual scenario the ship’s noise can be assumed as produced by shipping traffic or a ship transit. While shipping traffic represents an average ambient noise level due to many ships, ship transit is a local noise source. In this paper we consider the ship’s noise as the noise radiated by a ship sailing in the sea surface nearby the receiver. Moreover, under severe weather condition wind blowing over the sea surface could induce wave breaking and augment the level of ambient noise [13]. However, even if the sea surface may appear perfectly calm it is subject to an agitation that is cause of the increasing of the mean isotropic ambient noise spectrum level. B. Freqency band In a coastal area of shallow waters, the absolute distance between a sonar system working underwater and the noise sources is limited to few kilometers. It follows that the dominant source will be close to the receiver. A short range permits to high frequency components of the noise sources to propagate between the two and then to affect the receiver performance [13]. This consideration is of importance especially for underwater acoustic systems working in the range between 1 and 10 kHz, for which the prediction of ambient noise is often reduced to the white-Gaussian hypotesis and the traditional deep waters models, often available just for low frequencies [12], are non sufficiently accurate [4]. Moreover, this frequency range further limits the noise sources that could have impact on the SNR at the receiver to those that have a significant spectrum level in this band. In the frequency band from 1 to 10 kHz ship transit and surface agitation represent the major sources of noise as shown in [22],[23]. C. Statistics Whereas some of the ambient noise sources have spectral characteristics that, over the operating bandwidth of a typical sonar system, might well be described as uniform or “white” and statistics that can be easily approximated by the Gaussian case, the same cannot necessarily be said of the acoustic emanations originating in vessel machinery and propellers or from the sea surface. Furthermore, even though the sum of independent sources is generally considered a Gaussian process, the ambient noise is generally far from Gaussian, especially when the scenario limits the ambient noise to a few sources. It follows that for the ambient noise model adopted in the considered scenario it is appropriate to describe the selected sources with non-Gaussian statistics. In Table I the general scenario is described in terms of significant characteristics for ambient noise modeling.

TABLE I.

AMBIENT NOISE SCENARIO

reference value of range for underwater noise sources is 1 m. Usually the SLnoise is obtained measuring the noise signal far from the source and than carried back to the standard reference range by considering the actual loss due to the propagation occurred during the measurement. Following the SLnoise, for the considered ambient noise sources, will be assumed as a power density spectrum and measured in dB re 1 μPa2/Hz at 1 m.

Noise Caracteristics

Enviroment

Source

Statistics

Frequencies

Non-Gaussian

1 to 10 kHz

Ship transit

Shallow waters; coastal area

Sea surface agitation

III.

NOISE SPECTRAL MODELING

Underwater acoustic systems inevitably involve the detection of signals. The study of acoustic noise is of importance because one or more of these sources will set the limit to sonar and communication system performance. The sonar equation [24] is an equation of energy conservation that is typically used for the evaluation of the performance of a sonar system operating under specific conditions. For this reason, the sonar equation provides guidelines rather than exact results. The core of the sonar equation is the signal-to-noise ratio (SNR) at the input of the receiver. Expressed in logarithmic scale, i.e. dB, the SNR is: SNR = SPL − SPLnoise ,

(1)

where SPL and SPLnoise are respectively the sound pressure level of the signal and of the noise impinging on the sonar receiver, measured in dB re 1 μPa2. SPLnoise is obtained by summing the contributions of ambient noise and self-noise. It depends on the receiver bandwidth B, and the noise spectral level (NSL). The NSL represent the level of spectral density of the noise at the receiver and is measured in dB re 1 μPa2/Hz. For a standard reference value of frequency of 1 Hz SPLnoise is:

SPLnoise = NSL + 10 log (B ) .

(2)

The overall noise spectral level, NSL, is the power sum of the noise spectrum levels attributable to the predominant sources of noise. The whole NSL can be computed as follows: Q

NSL =

∑10 log[NSL

q

q =1

]

10 ,

PLnoise = PLα − PLg ,

(5)

where PLα accounts for the absorption loss, while the PLg represents the geometrical loss. The weight of each term in (5) depends on the considered noise source and on the actual environment scenario. Finally a noise source is typically characterized by a specific radiation pattern RP that distributes the amount of power radiated in each direction. For isotropic sources the power is equally radiated in all the directions and the RP, measured in dB, is:

RPiso = 0 .

(6)

On the contrary, once noise source has a privileged direction of emission, i.e. a non-flat isotropic pattern, the corresponding RP is a gain with magnitude determined by the physical process radiating sound. Concluding, an ambient noise source having source level SLnoise subjected to a propagation loss PLnoise and emitting sound with the radiation pattern RPnoise, will have the following NSL at the receiver:

NSL = SLnoise + RPnoise − PLnoise .

(7)

(3)

where Q is the number of predominant noise sources in the sonar system bandwidth B. The NSL at the sonar receiver is the difference between the source level (SL) of the noise SLnoise and the propagation loss PLnoise:

NSL = SLnoise − PLnoise .

The PLnoise represents the power loss due to the propagation of the signal (i.e. noise) trough the medium (i.e. water) between the source and the sonar receiver. PLnoise is calculated in dB re 1 μPa2. Essentially, it is function of two terms: the geometrical loss, that considers the geometrical spreading of the sound wave, and the absorption loss, that is the effect of the absorption coefficient of the medium, and can be defined as follows:

(4)

The SLnoise represents the sound radiated underwater by the noise source and always referred to a standard range from a presumed acoustic centre of the source. The adopted standard

A. Sea surface agitation Usually ocean sound in the band 0.5-20 kHz is called “wind noise”, “sea state noise” or “Knudsen noise” [23]. The noise sources in that case are explained by microsources theory for dipoles near the ocean surface, each having individual peak source pressures of 0.1 to 1 Pa [24]. These microsources are oscillations of bubbles, created by the breaking of the waves that immediately radiate sound. Departures from the average NSL up to ±10 dB are common for surface agitation noise, particularly in case of shallow water and for small depths, close to the surface [26],[27]. For its physical nature the surface agitation is characterized by a diffuse noise field, it follows that the corresponding

radiation pattern RPsea, measured in dB, can be modeled as an isotropic source, and by adopting (6): RPsea = 0 .

(8)

The magnitude of the SL depends on the surface conditions and is governed by the wind speed. For a wind blowing at certain speed a sea state can be defined, and a behaviour of the corresponding SL can be obtained by employing ad hoc equations. An empirical computation of SLnoise for surface agitation is also possible, for instance by using the equation proposed [14]: SLsea ( f ) = 50 + 7.5 w + 20 log( f ) − 40 log( f + 0.4) ,

(9)

where f is the frequency in kHz and w is the wind speed in meters per seconds [m/s]. The validity of (9) is for frequency from 100 Hz to 100 kHz and for wind speed as reported in [14]. As first approximation, the relative NSL can be calculated by considering the surface agitation noise not subjected to geometrical and absorption loss, because of the plane wave propagation, without attenuation with range, and the shallow waters scenario, which limits the receiver depth [27]. It follows that: NSLsea ( f ) = SLsea ( f ) .

(10)

Nevertheless, once the water depth becomes very low, i.e. a shallow water environment, one must consider the effect of the seabed absorption and the multipath structure of the noise signal in the channel. In [28]-[30] shown that in a shallow water channel the surface generated noise is affected by propagation loss. In [30] is proposed some interesting channel model case for dominating boundary that could be used as reference for the surface agitation PLsea. However, for short range between noise source and sonar receiver, as for the considered scenario, one can adopts a negligible absorption loss and use (10). B. Ship Transit The radiated noise from a vessel, i.e. the SLship, can be depicted as generated by several sources. However, the underwater noise spectrum of a radiating vessel is dominated by two principal sources: machinery and propellers. Experiencing some radiated noise is common to all rotating machinery. When the engine is not isolated from the ship, its vibration drives the hull and the sound is radiated in accordance to the modes of vibration of the hull panel. Propeller cavitation is the major cause of noise generated by surface ships [7]. Propeller noise can be produced by a purely hydrodynamic mechanism such as cavitation or by mechanical vibration. Propeller cavitation results from pressure fluctuations in the water near the blade tips. When these fluctuations fall below ambient pressure, dissolved air is forced to leave and forming the cavitation wake [31]. The acoustic

noise generated by cavitation exhibits a broadband continuous spectrum, peaking in a frequency range depending on the actual ship speed with magnitude that in general increase with increased vessel velocity. As secondary consequence of cavitation, the spectrum may experience a tonal effect due to blade-rate, with a frequency which is the proportional to the number of he propeller blades [30]. The blade-rate line series is generally the dominant feature of the low-frequency spectrum of ship-generated sounds. Finally, in some case, a poorly designed propeller may exhibit “singing” when, typically, one blade-edge enters a high-frequency state of vibration whilst running. Therefore, the lower frequency end of the noise spectrum is dominated by machinery lines and blade-rate lines of the propeller. These lines die away with increasing frequency and become hidden in the continuous spectrum, that increasing vessel speed, augments in intensity and extends over the lower frequency band. It is possible to separate the contribution of the radiators in the ship noise spectrum, pointing attention to the ship speed in which the noise components become significant. When the vessel reaches a speed inducing appearance of the propeller cavitation effect, a crossover frequency may be said to exist, below which the tonal components dominate the spectrum, and above which the spectrum is in large part the broadband noise spectrum of a cavitating propeller. For ships and submarines, this frequency is said to lie roughly between 0.1 and 1 kHz [7]. This empirical property of the noise spectrum allow to consider a SLnoise model of ship transit noise that is dependent only on the broadband cavitation effect of the propellers, with a magnitude governed by the vessel speed. The propeller blades are rotating twisted wigs that produce strong hydrodynamic forces. Previous studies revealed three distinctive regimes of blade-surface cavitation [7]. Each regime depends on the ratio between the blade rotational speed, that determines the vessel velocity, and the corresponding cavitation inception speed, that is peculiar of the propeller design. For increasing blade rotational speed, the corresponding spectrum exhibits initially a rounded peak that becomes sharply and, for the higher cavitation regime, assumes a broadband shape, losing its tonality. It follows that for a vessel transiting at low speed, it is possible to approximate the cavitation noise, assuming a radiated spectrum, i.e. the SLship, following the low regime cavitation curve shown in [7]. Once the speed increases, one takes advantage on using an empirical equation to model the corresponding NSL with a simple shape. For medium ship speed, the adopted expression for the radiated SL of a transit ship is the following equation [27]: SL ship ( f ) = RNL

1kHz

− 20 log ( f 1000

).

(11)

where RNL1kHz is the radiated noise level in dB re 1 μPa2/Hz at 1 kHz, generally obtained by measurement campaign data, and represents the reference for the derivation of the SLship at the desired frequencies. Unlike surface agitation noise, ship noise is a local nonstatic noise source in the sense that the vessel radiates as a

point-like source, i.e. a spherical wave, which is changing its position dynamically inside the scenario. This means that the relative distance between the noise source and the receiver changes accordly to the vessel movements and can increase quickly. To account for this dynamic source position the PLnoise has to be considered, by taking into account the contribution of both the terms in (5). The first one, PLα, depends on the acoustic absorption coefficient α that is related to the temperature, salinity and depth of the considered water mass. Many ad-hoc formulas for a specific channel scenario can be found in the literature, e.g. in [19], however, for the considered scenario the François-Garrison model represents an appropriate choice [27] and is the adopted choice for the absorption loss in the ship noise case. An approximation for α, acceptable within the considered frequency band, is:

the radiating vessel. The pressure contours are close to the dipole behaviour and the radiated energy is generally greatest abeam, appearing to come principally from the propeller [7]. The propeller noise power astern is reduced by being absorbed and scattered by the bubbly wake and it is reduced forward by the ship body. The total net effect is that the behaviour of ship radiation shows typically a “butterfly” pattern along the heading vessel axis [7]. Consequently, considering a shallow water channel, the angle between the vessel axis and receiver can be projected into the horizontal plane, assuming for ship noise a dipole-like source radiation pattern. The adopted equation for the ship transit noise radiation pattern RPship in dB is then the following:

α( f ) = 0.05 ⋅ f 1.4 .

where θ is the angle of radiation in deg respect to the vessel main axis.

(12)

The contribution of the absorption loss to the whole transmission loss is proportional to the spatial range. For ship noise, it is the absolute distance r between the considered vessel and he sonar receiver: PLα = α ( f ) ⋅ r .

(13)

The second contribution in (5), PLg, is a function of the geometrical propagation, that depends on the environment geometry. For large distances in shallow water, the waveguide propagation model is well suited [27] to describe the geometrical loss, since it takes into account the reflection of the acoustic waves at the seabed and the sea surface, representing a multi-path structure. The net effect of the geometrical loss for waveguide propagation depends on the transition range r0, which is the distance from the source where the spherical propagation becomes cylindrical propagation. This propagation transition is due to the environment geometry and r0 is equal to: r0 =

H , 2 tan β 0

(14)

where H is the channel depth and β0 is the maximum grazing angle imposed by the fluid. Considering the contributions of both the propagation loss, the whole PLship is: ⎧20logr + α( f ) ⋅ r, r < r0 . (15) PLship = PLα + PLg = ⎨ ⎩20logr0 +10log(r r0 ) + α( f ) ⋅ r, r ≥ r0

After the propagation characterization of the noise radiated underwater by passing ships, now attention is given to the directional properties of the source. The dynamic position of a surface noise source with respect to the underwater receiver is established by the reciprocal distance and angle. Propeller noise is not radiated uniformly in all directions, but has a characteristic directional pattern in the horizontal plane around

RPship = 10 log (sin (θ )) ,

(16)

Finally, the adopted model for the NSLship is the following: NSLship ( f ) = RNL1kHz − 20 log( f 1000) + ⎧20 log r + α( f ) ⋅ r , r < r0 . (17) ⎪ + 10 log(sin(θ )) − ⎨ ⎛r ⎞ ⎪20 log r0 + 10 log⎜⎜ r ⎟⎟ + α( f ) ⋅ r , r ≥ r0 ⎝ 0⎠ ⎩

IV.

NON-GAUSSIN NOISE GENERATION

The acoustic noise is a random process assuming value corresponding to a pressure signal. In the ocean the characteristics of the underwater ambient noise come as result of process that is not predictable, like the generation of breaking waves in the sea surface or the propeller cavitation of a transit ship. From a signal processing point of view the outputs of such sources are realization of a stochastic process with specific PDF and power spectrum, and can be considered as sequence of random numbers. For simulation and laboratory tests, random-number generator functions are frequently used to produce continuous sequences or finite sets of random numbers. Many of the algorithms generate sequences that repeat, and these algorithms are known as pseudo-random number generators. The first option for simulation of the ambient noise is then to employ a pseudo-random generator. However, the produced sequence of numbers should have the characteristics of the noise source that it represents, in terms of spectrum and statistics. In order to fully accomplish the requirements of the selected ambient noise models, the approach proposed in [15] is adopted. This technique is based on an algorithm that generates sequences of random numbers, which are realizations of a stochastic process. During the initialization of the algorithm, it is possible to assign a desired power density spectrum jointly with an a priori value of the kurtosis to the target process. The value of the kurtosis of a random variable is a common method to determine how far its PDF is from a Gaussian shape. The Gaussian process has a kurtosis equal to 3, and any shift from this value corresponds to a PDF with a

non-Gaussian shape. In conclusion, the Webster technique is able to reproduce noise realizations with a specific kurtosis value and arbitrary power spectral density, allowing simulation of the stochastic process representative of the actual underwater noise. As described, the ambient noise is the sum of a number of different acoustic sources having different distributions. In [15] a sampled waveform, having a logarithmic envelope, is employed to characterize the ambient noise. The generation of the noise is focused to produce a sequence of random values that posses a kurtosis with value higher or lower than 3 depending on the noise source simulated. The generation is carried out trough the random sampling, with uniform distribution, of the above mentioned waveform. The random numbers generated by the Webster technique are statistically independent, this means that they are representative of white noise. With the aim of assign the desired spectral shape, i.e. the right NSLnoise, to the generated noise realization, an appropriate FIR filter can be designed and used to filtering the generated sequence. Since filtering is an additive process and tends makes the statistic of the output sequence "more Gaussian", as stated by the central limit theorem, in [15] is adopted a relationship between the kurtosis of the sequences at the filtering ends, involving the coefficients of the designed FIR filter. It is possible to express the kurtosis β2{y} of the filtered noise samples ym as function of the L+1 coefficients wl of the FIR filter and the kurtosis β2{x} of the generated number xm as follows: L

β 2 {y m } = 3 + [β 2 {x m } − 3]

∑w

4 l

l =0

⎛ ⎞ ⎜ wl2 ⎟ ⎜ ⎟ ⎝ l =0 ⎠ L

∑

2

.

(18)

Therefore one can specify the kurtosis β2{y}, i.e. the departure from the Gaussian statistics, of the output sequence independently by the filter coefficients wl, whose values allow to filter the samples xm and obtain the desired NSLnoise, by requiring the kurtosis β2{x} of the input sequence to satisfy (18). This corresponds to imposing a desired non-Gaussian behavior to the noise statistics and designing an appropriate FIR filter whose frequency response reproduces the desired NSLnoise. Low kurtosis values are well suited for ship transit noise [12],[21], whereas in [15] high values are more appropriate for sea surface agitation noise. The so produced sequence can be assigned to a time series by considering the numbers as samples of a sampling process with a desired frequency sampling. Obviously, the FIR filter has to be designed to work with the same frequency. The pressure time series, expressed in μPa, representing the acoustic noise at the receiver, is converted to NSL using a standard signal processing method [32], and the resulting units for spectral density are dB re 1 μPa2/Hz. Once the two noise sources, ship transit and sea surface agitation, are jointly simulated, the conversion procedure from

pressure levels to spectral levels is performed after the sum of the two time series contributions. V.

RESULTS

As example of ambient noise simulation, we proposed a set of different scenarios of underwater ambient noise in a coastal area of shallow waters. The NSLs are simulated considering the noise received by an underwater acoustic communication system working at 50 m depth over a band of 6 kHz with central frequency 5 kHz. The bottom depth was set to 100 m. The simulated sequence consists on 105 samples, generated by using the proposed procedure. The samples are sampled with sampling frequency 20 kHz and frequency limited in the band from 2 kHz to 8 kHz. The amplitudes of the generated samples are pressure values measured in μPa. Each sequence represents a noise realization of 5 s. We set a kurtosis value consistent with the considered case of source and then we have designed a FIR filter whose response follows the corresponding NSL shape. The kurtosis value was set to 2.5 for ship transit noise and to 3.5 for sea surface agitation. The NSL for sea surface agitation, is derived by (10) using the values in Table 5.2. The NSL for ship transit noise, is obtained by (17) with RNL1kHz value from [1] in case of medium-high vessel speed, i.e. higher than 8 knots, and by reproducing the shapes of the cavitation regime in [1] in case of low vessel speed, i.e. lower than 8 knots. The corresponding spectra were obtained by filtering the produced sequences with a FIR filter reproducing the desired NSL of the considered noise source and scenario condition, i.e. bottom depth and ship position. A. Single noise source Three case of ambient noise due to a single source has been simulated and the samples sequences are plotted in Fig. 1. Concerning sea surface agitation noise, we considered the simple case of a wind blowing at 5 m/s, e.g. a light breeze, corresponding to the sea state 2 in [14]. Usually, the NSL of sea state 2 is the reference used in defining the performance specifications of sonar systems. In Fig. 2 (up) it is shown the NSL corresponding to the generated noise sequence. For a light breeze, the wave height is small and the breaking effect produces a surface agitation noise with limited magnitude, having the classic spectral shape observed by Wenz and reaching the maximum value of 55 dB at 2 kHz. Let us now focus on the case of ship transit noise. Two different scenarios have been simulated. Firstly, we consider a merchant ship sailing at 13 knots, e.g. at cruise velocity, just above the sonar system. As second example, we set a harbour approach scenario in which a cargo ship is transiting at 6 knots 500 m far from the sonar system, with a horizontal angle of 60 deg between vessel heading and receiver. In Fig. 2 (middle and down) it is compared the NSL of ship transit noise in the two scenarios. Once the vessel sails at mild velocity the NSL, in Fig. 2 (middle), assumes high level in the whole frequency band, with increasing magnitude from 95 dB at 8 kHz to 110 dB at the lower frequency end.

both the sources were active. The effect is to limit severely the performance of a sonar system designed for a standard ambient noise. In the second example of ship transit noise, the vessel speed lower and the source is now 500 m far from the receiver. Under such conditions, the propeller cavitation dominates the radiated noise spectrum imposing the characteristics broad peak lightly attenuated by the propagation loss, which falls below 50 dB at 2 kHz. Reducing the speed and increasing the range from the sonar receiver the NSL, in Fig. 2 (down), loose energy and diminishes its level of about 50 dB over the whole frequency range. Despite a lower spectral magnitude, the contribution of the propeller cavitation becomes significant if compared with the action of the surface agitation noise having NSL in Fig. 2 (up). With the aim to analyze the statistics of the simulated ambient noise realizations, in Fig. 3 are shown the PDF corresponding to the sequence of ship transit noise and sea surface agitation noise in Fig. 1. Since the generated sequence are single realization of the stochastic process, only one density is sufficient to represent the PDF of the considered noise source. However in Table II are reported the obtained value of kurtosis for each noise sequence. TABLE II.

KURTOSIS VALUE OF THE SIMULATED NOISE SOURCES Noise Source

Desired

Kurtosis Obtained

Ship transit

2.5

2.48, 2.51

Sea surface agitation

3.5

3.52

-

2.66

Ship transit + Sea surface agitation

In Fig. 3 (down) it is shown the PDF corresponding to a Gaussian process of 105 samples as reference. One notes how the probability densities of the simulated noises depart from the Gaussian case once the respective kurtosis value in Table II is set far from 3. In order to compare the resultant density in a common scale, the data values in Fig. 3 are the noise samples in Fig. 1 normalized respect to their maximum own value.

Figure 1. Noise samples simulated by the proposed procedure. Sea surface agitation for sea state 2 (up). Ship transit noise for a ship sailing at 13 knots 50 m far from the receiver (middle) and for a ship transiting at 6 knots 500 m far from the receiver with an horizontal angle of 60 deg (down).

By comparing the current NSL the contribution of the sea surface agitation noise in Fig. 2 (up), it is easy to verify that the ship transit source would dominate an ambient noise where

B. Combination of noise sources In the previous examples, a single noise source has been simulated each time. Nevertheless, one can consider a scenario where both the sources, ship transit and sea surface agitation, are active simultaneously. In this case the ambient noise could be thought as a combination of two of the NSLs shown in Fig. 2. In particular we would like to simulate the case in which the NSL for sea state 2 is added to the NSL of the ship transit in Fig. 2 (down). The resulting NSL and the corresponding PDF are shown in Fig. 4. Looking at Fig. 4 (up) one note how the spectral characteristics of the cavitation in ship transit noise are modified by the contribution of the sea surface agitation noise. The broad cavitation peak in Fig. 2(down) is attenuated and spread over the lower frequencies because of the higher magnitude levels in the NSL of Fig.2 (up).

Figure 2. Noise spectral level simulated by the proposed procedure.The three spectra are for the three noise signals in Fig. 1, maintaining the same order.

Further, the mix of the two sources produces an increasing of the ambient noise in the whole frequency band respect to the levels in Fig. 2 (up), with a maximum of about 15 dB at 5 kHz, the central frequency of the considered underwater acoustic communication system.

Figure 3. Probability denstity function for the two noise sources simulated by the proposed procedure. Sea surface agitation noise (up) and ship transit noise (middle). The Gaussian case (down) is plotted for comparison.

Moreover, the noise spectrum at 2 kHz is 5 dB higher if compared to the one in Fig. 2 (down). This could affect the receiver performance even in case of a mild contribution of ship transit noise.

source of noise nearby an underwater acoustic communication system working with frequencies between 1 and 10 kHz. The spectra of the sources were modeled by selecting empirical models in the literature, with specific attention to the cavitation effect of the ship propeller. Once a limited number of noise sources coexist in a unique environment the Gaussian model is not yet valid to modeling the ambient noise and the specific source statistics should be considered. Ship transit noise and surface agitation noise are known to be non-Gaussian processes and to simulate both the sources a technique to generate random sequence with arbitrary statistics was employed. The selected noise models together with the adopted random numbers generator were combined to form a simulator that is well suited to reproduce the ambient noise for different underwater acoustic scenarios. Four case of ambient noise were simulated and the resulting noise spectral level and PDF representative of the noise sources was shown and compared. The results shown that in a shallow waters area close to the coastal line, the noise radiated by a ship could affect the performance of a high frequency underwater acoustic system working nearby. REFERENCES [1] [2] [3] [4] [5]

[6] Figure 4. Ambinet noise simulated by the combination of sea state agitation noise in Fig. 1 (up) and ship transit noise in Fig. 1 (down). The noise spectral level (up) and the probabuility density function (down) were obatined after the sum of the two noise sequnces.

Finally, concerning the ambient noise statistics, the PDF resulting form the combination of the two noise sources is shown in Fig. 4 (down). By comparing the PDF in Fig. 4 (down) with the normal distribution in Fig. 3 (down), one note that the ambient hold a non-Gaussian statistic even if both the contributions of the two independent sources are considered. The kurtosis value for the PDF in Fig. 4 (down) is reported in Table II.

[7] [8]

[9] [10]

[11] [12]

[13]

VI.

CONCLUSIONS

Acoustic noise in the sea may come from many sources. Whilst it is true that various sources of interference can coexist, it is most common to find that one of them will predominate in a specific scenario. Surface agitation and ship transit are often the major sources of ambient noise, especially at high frequencies. Once the ship’s noise is the dominant source and the wind speed produces significant breaking waves in the sea surface, the ambient noise increase considerably. In this paper we considered a coastal scenario with shallow waters in which both ship transit and sea surface agitation are active

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