IEEE Communications Magazine • June 2017

198

0163-6804/17/$25.00 © 2017 IEEE

A

bstract

In warm shallow waters, the ambient noise

process is found to be impulsive. This phenom-

enon is attributed to the collective snaps creat-

ed by snapping shrimp colonies inhabiting such

regions. Each snap essentially creates a pressure

wave, and the resulting noise process dominates

the acoustic spectrum at medium-to-high fre-

quencies. Consequently, if not addressed,

snap-

ping shrimp noise

is severely detrimental to the

performance of an

acoustic

communication sys-

tem operating nearby. This article briefly summa-

rizes and addresses the problems faced during

acoustic communication in snapping shrimp

noise. We discuss how the noise process can be

characterized by a certain statistical model based

on the symmetric

a

-stable (S

a

S) family of distri-

butions. Within the framework of this model,

we highlight problems and the corresponding

solutions faced in

various stages

of digital com-

munication system design. Both single and multi-

carrier systems are commented on. The resulting

schemes are robust to outliers and offer excel-

lent error performance in comparison to conven-

tional methods in impulsive noise.

I

ntroduction

The snapping shrimp inhabits warm shallow

underwater regions around the world. These

small critters live in large populations and are

immediately distinguishable due to their asym-

metrical front claws [1]. This physical attribute

allows them to generate snaps (sudden surges

in acoustic pressure) which are used for hunting

prey and communicating. A typical snap, inclu-

sive of the reverberations that follow, tends to

last over a few milliseconds with peak-to-peak

source levels recorded to be as high as 190 dB

re 1

m

Pa at 1 m [1, 2]. The collective snaps of

a snapping shrimp colony prove to be a chal-

lenge for underwater acoustic system designers

[3]. In fact, for frequencies over 2 kHz, snapping

shrimp noise is known to dominate the acoustic

spectrum [4]. A noise process that depicts sud-

den snaps (or impulses) is rightly termed impul-

sive noise.

In this article, we highlight the quandary a

communication system designer faces in the pres-

ence of snapping shrimp noise. We cover recent

advances in the understanding of the noise pro-

cess and summarize new techniques for robust

digital communication in such scenarios.

A

mplitude

S

tatistics of

S

napping

S

hrimp

N

oise

In Fig. 1, recorded samples of dynamic pressure for

a snapping shrimp colony are presented. This data

set was recorded by the Acoustic Research Lab-

oratory (ARL) in Singapore. The snaps are clearly

visible, and therefore the noise process is indeed

impulsive. A first step for any communications

engineer is to find a suitable model that depicts the

statistics of the ambient noise process in question.

In the literature, impulsive noise models are typical-

ly based on heavy-tailed distributions as they assign

large probability to outliers (or extreme values). To

highlight this, we present the empirical

amplitude

distribution

of the noise realization in Fig. 1. We

also show the fits offered by the Gaussian and sym-

metric

a

-stable (S

a

S) probability density functions

(PDFs) under maximum-likelihood (ML) parame-

ter estimation [5]. The well-known Gaussian PDF

has light (exponential) tails and is clearly

unable

to track the empirical PDF efficiently. As observed

in Fig. 1, the tails of the Gaussian curve fall rather

quickly. On the other hand, the heavy-tailed S

a

S

PDF tracks the empirical distribution fairly well. This

observation is substantiated further in the literature

via formal statistical tests [2, 3].

PDFs belonging to the S

a

S family are unimodal

and symmetric (around zero). They also exhib-

it interesting limiting and stability properties [6].

In fact, the zero-mean Gaussian distribution is a

member of the S

a

S family. It is well known that

for a Gaussian input, the output distribution is also

Gaussian under any linear transformation [7]. This

result extends to S

a

S inputs as well and is essen-

tially the

stability property

that is uniquely associ-

ated with this class of distributions. An S

a

S PDF

depends on two parameters: the

characteristic

exponent

a

(0, 2], which controls the heaviness

of the tails, and the

scale

d

R

+

[6]. Consequent-

ly, the distribution can be denoted by the abridged

notation

S

(

a

,

d

) [8]. The lower the value of

a

, the

heavier the tails of the distribution. Moreover, for

a

= 2, the S

a

S distribution is zero-mean Gauss-

ian with variance 2

d

2

, that is,

S

(2,

d

)

d

=

N

(0, 2

d

2

),

where

d

= implies equality in distribution. With the

exception of the Gaussian case, all members of

the S

a

S family are heavy-tailed (algebraic-tailed)

distributions [6]. Going back to Fig. 1, the zero-

mean Gaussian and S

a

S fits correspond to

N

(0,

2(24.76)

2

)and

S

(1.51, 12.09), respectively. Note

that the Gaussian distribution tries to compensate

for heavier tails by increasing the scale.

Ambient Noise in Warm Shallow Waters:

A Communications Perspective

Ahmed Mahmood and Mandar Chitre

A

ccepted

from

O

pen

C

all

The authors summarize

and address the problems

faced during acoustic

communication in snap-

ping shrimp noise. They

discuss how the noise

process can be character-

ized by a certain statistical

model based on the

symmetric

a

-stable (S

a

S)

family of distributions.

Within the framework of

this model, they highlight

problems and the corre-

sponding solutions faced

in various stages of digital

communication system

design.

Digital Object Identifier:

10.1109/MCOM.2017.1500617

SEO Version