Physical Layer Sensing Using Long Pseudo Noise Codes

Andrew Goodney, Young H. ChoInformation Sciences Institute

University of Southern CaliforniaMarina Del Rey, CA 90292

{goodney, younghch}@usc.edu

ABSTRACTAs research into building underwater sensor networks pro-ceeds, researchers are focusing on using these networks tosolve applicable problems. In particular we have found thatunderwater sensor networks are capable of performing acous-tic tomography, even at very small scales. As sensor net-works consist of a network of power constrained devices,researchers must also look for efficient ways to perform therequired tasks.

In our work we are developing an acoustic tomographysystem implemented in an underwater sensor network. Tra-ditionally, acoustic signals used for tomography would befollowed by acoustic signals carrying data about the previ-ous operations. In this paper we present an acoustic networkphysical layer that provides for simultaneous data transmis-sion and sensing using the same acoustic signal. By combin-ing data and sensing transmissions we conserve energy. Wedescribe the physical layer followed by experimental datathat shows our system can perform as desired.

1. INTRODUCTIONUnderwater sensor networks are an attractive solution to

the underwater sensing problem because they use low cost,networked nodes with on board sensors allowing researchersto deploy a multitude of nodes throughout bodies of waterunder study. Due to favorable propagation properties, mostunderwater sensor networks will use acoustic communica-tions to create the network. Since the speed of sound foran acoustic signal in water is dependent on several physi-cal properties (most significantly temperature and currentflow), the time-of-flight for acoustic signal can be used forsensing. Thus the physical layer of an underwater sensornetwork can be used for sensing.

Deploying spatially distributed sensor nodes across an areaincreases the spatial resolution of the data collected, howeverthere is almost always a limit (either financial or technical)to the number of nodes that can be deployed. Therefore, tofurther increase the spatial resolution of data collected for

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certain water properties (e.g. temperature), we are develop-ing a small scale acoustic tomography system that can sensethe properties of the water between nodes by leveraging thephysical layer of the sensor network itself.

In general, water temperature is a critical piece of datathat is collected by virtually every marine experiment. Highresolution water temperature sensing in small to mediumsized bodies of water has both ecological and national se-curity applications. For example, harmful algal blooms areoften triggered by the up welling of colder, nutrient richwater. However, the up welling is often only monitored inone location in a given coastal area, typically at a pier orbuoy [13]. Since the spatial resolution of this data is verysparse, detailed analysis of the coastal dynamics that leadto the up welling is difficult to study. By deploying severallow-cost buoys (perhaps at different depths) and then per-forming acoustic tomography between the nodes, a greatlyincreased 2D or 3D image of the water temperature dynam-ics can be obtained.

As a national security application, sensor network acous-tic tomography can be used to detect smaller submarines.Such submarines are quiet and with the development of ma-terials that render boats acoustically transparent, they canbe difficult to impossible to detect with active SONAR [17].However, all submarines, diesel or nuclear, must dissipateheat into the water. A sensor network that performs acous-tic tomography between the nodes can be used as a virtualsubmarine net across waterways of critical importance bydetecting the thermal signature of a submarine.

Acoustic tomography is typically deployed at the scale of100’s to 1000’s of kilometers. By using the calculated times-of-flight for acoustic signals through the water, tomographicinversion techniques create a water temperature map thatincludes reconstructed data points that are located betweenthe transmitter/receiver pairs. While working with acousticcommunications for underwater sensor networks, we conjec-tured that the acoustic communications channel could alsoperform this function, however at a much smaller scale (50m to 1 km).

Therefore, we set out to develop a small scale acoustictopography system capable of providing increased spatialresolution and accurate temperature resolution. A key com-ponent of any acoustic tomography system is the acousticsignal (chirp) sent and received by the nodes to measurethe time-of-flight. Chirps must provide for robust detectionin the noisy underwater environment, while also providingsufficient time resolution, as the time resolution determinesthe limit of temperature resolution. We are targeting our

system to low power sensor network nodes, and thus cannotexpect high-power transmissions. Hence we must develop achirp signal that can be detected at our targeted distancewith a minimum of transmit power.

We also observed that typical signals used for transmittingdata underwater, do not necessarily provide the required at-tributes to be suitable as a tomography signal. This is beforethe cost of commercial underwater modems is considered.On the other hand, the signals used for chirps in SONARand other underwater ranging techniques are not generallyappropriate for use in a sensor network.

In this paper we describe our effort at building an un-derwater sensor network that can use the acoustic physicallayer to sense and communicate. We present the details ofour technique that provides for a large set of chirps thatmeets the requirements described above: robust detectionin a noisy environment, sufficient time resolution and theability to carry data transmissions. The technique uses longpseudo noise sequences modulated with binary phase-shiftkeying to generate large sets of orthogonal codes. A keycontribution of this paper is the identification of an algo-rithm using Legendre sequences that can generate arbitrarylength codes that are especially suited to this application.These long codes can be used to obtain large amounts of de-tection gain as required when transmitting in a very noisyenvironment. We describe and show results from real-worldexperiments carried out in our underwater testbed. Theseresults show that our system performs as desired in a ex-tremely noisy environment.

2. RELATED WORK

2.1 Ocean Acoustic TomographyOcean acoustic tomography is a technique to measure

ocean temperatures by exploiting the relationship betweenwater temperature and speed of sound in water. The tech-nique was first proposed in 1978, and since then several ex-periments have been carried out[9, 16, 2]. These experimentshave been conducted in open ocean locations such as theNorway Sea, Mediterranean Sea and Mid-Atlantic Ocean.Distances between nodes are on the order of 100’s to 1000’sof kilometers. Sound propagating over such distances in theocean is bent along predictable paths (’rays’) and thus oceanacoustic tomography can yield temperature data about theocean at different depths, while time-of-flight for the acous-tic signal is measured in minutes.

We have drawn inspiration from ocean acoustic topog-raphy, however we must take into account two importantdifferences. First we are able to simplify the tomographicinversions because at distances of less than 5 km we canassume that sound is taking a direct path between trans-mitter and receiver[12]. On the other hand we must developa highly precise time-of-flight measurement system becausethe travel time for an acoustic signal at short distances ismeasured on the order of 10’s of milliseconds with changesdue to temperature on the order of 10’s to 100’s of microsec-onds.

2.2 Underwater Acoustics: Sensing, Ranging,and Communications

Performing specialized acoustic tomography, an invertedecho sounder (IES) is a device that measures the average

temperature of a water column at a point location in theocean. The device is placed on the sea floor and transmitsa ping to the surface. This ping is reflected off the surfaceof the water and when received back, the round-trip-timeis calculated. Given the depth of the water at the IES, theaverage temperature of the water column can be calculated.This technique operates at the same distances as our system,however we envision a sensor network of active transmittersand receivers at different depths which can provide 2D or3D temperature maps.

Underwater positioning systems such as long or short base-line navigation systems use a set of fixed location transpon-ders that reply with fixed delay to interrogation signals.Given the round-trip time and fixed delay, the acoustic prop-agation time and thus distance to the transponder can becalculated. With adaptation, such a system could be usedto perform tomography. However, existing systems are de-signed for a specific positional accuracy which dictates therequired time-of-flight accuracy. Thus, the time-of-flight ac-curacy required to obtain the positional accuracy specifiedby current underwater ranging systems is typically insuffi-cient for use as a tomography system.

Underwater acoustic communications is a well studied fieldwith a plethora of academic papers published on modems,modulation techniques and media access control schemes[14,1, 3, 15]. These academic researchers offer details on howto construct specific components from the transducers toDSP or FPGA based modems. There are also several com-mercial underwater modems systems that offer varying bitrates and modulation schemes. Two modulation methodsare worth discussing here, frequency shift keying (FSK) anddirect sequence spread spectrum (DSSS).

Frequency-shift keying has been shown to have good prop-erties under a wide range of conditions in underwater com-munications and is therefore offered as a modulation tech-nique on most underwater modems. FSK offers reliablecommunication and simple modulator/demodulator design,however it does not perform well in the presence of multi-path interference, and is thus most suited to open or deepwaters. We are specifically targeting (but not limited to)shallow coastal waters, or even lakes, and thus need a systemthat performs well in the presence of multi-path interferenceand low signal to noise ratio.

Direct sequence spread spectrum communications systemsdraw on the advantageous mathematical properties of longpseudo-noise codes to improve noise immunity (spreadinggain) and resistance to multi-path interference. DSSS sys-tems include a synchronization method that can be usedfor precise time-of-flight mechanisms, however the spread-ing gain may not be enough to overcome a noisy channelwith very low transmit powers.

A well cited example modem is the WHOI MicroModem.The feature most similar to our system is the wide-bandREMUS compatible navigation system. This system use acoded PSK signal to interrogate transponders. Using theknown locations of the transponders and the round-trip-times, the modems can perform ranging. If the locationsof the nodes in a sensor network is known and fixed, rang-ing is equivalent to performing tomography, however dueto system design the WHOI MicroModem allows for 125µsin temporal resolution. Our system is capable of deliveringapproximately 10 times the temporal resolution.

(a) Aerial Photo with Node Locations

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Figure 1: Underwater Testbed, Marina Del Rey.

2.3 Acoustic Ranging for Sensor NetworksIn the context of sensor networks, work has been done on

using acoustic signals for ranging and localization. Directlyof interest to this work is the work by Girod while at UCLACENS[4]. In order to locate multiple sensor nodes, Girodconstructed orthogonal chirps using BPSK. Like our system,in order to get robust detection in a noisy environment, longPN codes with good ACF and CCF properties are required.However, Girod’s method for finding such codes is ad-hocand the difficulty of finding a large set of codes grows ex-ponentially with code length. In section 6 we describe howLegendre sequences can be transformed into PN codes withthe required properties with no restriction on length or in-creasing difficulty.

3. SYSTEM DESIGNFor our underwater sensor network we assume the network

is made up of small, low cost, and energy constrained nodes.We desire that our nodes transmit an acoustic signal peri-odically so that acoustic tomography between the nodes canbe performed. Our system must operate in small, shallowbodies of water (for example our experiments are performedin a marina). Due to energy constraints, transmit power willbe low and since we are operating in shallow water, we ex-pect multi-path effects. Additionally, we would like for anyone node to be able to send without considering other nodes,i.e. we do not want to implement a MAC layer. Consider-ing these factors, a modulated signal based on orthogonalpseudo-noise sequences is the approach we choose. Certain

families of pseudo-noise codes have been used in spread spec-trum techniques because they provide signal-to-noise ratiogain by spreading the signal out in time. These code familiesare also constructed such that the cross correlation function(CCF) of any two codes has a maximum of some small mag-nitude, while the auto correlation function (ACF) for anyone code is large (near or at the Welch bound). The lengthof a code determines the spreading gain, if P is the lengththen spreading gain G is 10 log10(P ). Thus in our underwa-ter sensor network adjusting the spreading gain is the pri-mary ‘knob’ by which we can tune the system to overcomea noisy channel.

Gold, Bent or No [5, 11, 10] codes are common familiesused in DSSS (and therefore CDMA) systems for RF or un-derwater communications. However, by their constructionP = 2n−1 with n increasing by a minimum of two when in-creasing the code length. This results in a minimum increasein code length of a factor of 4. For example, if we were usinga code length P = 511 and required more spreading gain,the next two code lengths are of P = 2047 and P = 8191.

Therefore we select a code family constructed by Guohuaand Quan [7] based on Legendre sequences where the lengthP = 3 mod 4, i.e. the length is a prime number where P + 1is a multiple of 4. These sequences have several desirableproperties: good CCF and ACF properties, good balanceproperties and flexible code length. See section 6 for a sum-mary of the construction method.

To build our set of orthogonal chirps we choose the lengthP = 3 mod 4, and some decimation d. When then choose anumber of k’s to give us the desired number of codes. Theseparameters are used as shown in section 6 and will generatea set of orthogonal binary sequences from set M or N thathave the desired ACF and CCF properties.

Finally, we use binary phase shift keying to modulate acarrier of appropriate frequency (we use 12 kHz or 18 kHz)with the orthogonal codes. This gives us a (potentially large)set of codes that can be used for sensing and communicationsat low signal to noise ratios in the underwater environment.

4. UNDERWATER EXPERIMENTS

4.1 Marina Del Rey TestbedAs sensor network research at its core is about sensing the

environment, we endeavor to focus our research on solutionsthat perform in the real world. To provide a real-world envi-ronment for underwater acoustic sensor network research, wehave constructed a five node underwater testbed at a smallboat marina located in Marina Del Rey, California. Eachnode consists of a standard small-form-factor PC, GPS re-ceiver, receive hydrophone and transmit hydrophone with apower amplifier. The computers are networked to our officesacross the street using inexpensive 5GHz Wi-Fi equipment.The nodes are placed in various locations around the ma-rina, with internode distances varying from 60 m to 200m. As discussed in [6] our novel use of the GPS pulse-per-second signal allows for acoustic time-of-flight measurementsaccurate to approximately 10µs. For deep underwater ap-plications we show similar accuracy, but without the needfor GPS.

Figure 1(a) shows the locations of the nodes in the MDRtestbed. Figure 1(b) is a schematic diagram indicating thenode names used for the experiments discussed in this paper.The remainder of this section describes several experiments

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Figure 2: Orthogonal Data Transmission and Reception

carried out in the MDR testbed that serve to illustrate thereal-world performance of our physical layer sensing.

4.2 Orthogonal Data TransmissionsFor this experiment a set of BPSK modulated codes of

length 3067 were created (referred to as ‘q1’, ‘q2’, ‘q3’). Themodulation frequency was set to 12 kHz, thus at a samplingrate of 96 kHz the signals are approximately 255 ms in dura-tion. The code ‘q1’ was transmitted from node C, while thecode ’q3‘ was transmitted from node D. The signals were re-ceived at node A. The transmissions were co-ordinated so asto arrive over-lapping. Figure 2(a) shows the audio from themarina at the time of transmission. Figures 2(b) and 2(c)show the overlapping, yet successful detection of the orthog-onal signals. With this simple experiment we show that outsystem has sufficient spreading gain to overcome the noisymarina environment, while also showing that the generatedcodes are orthogonal and do not interfere with each other.

4.3 Physical Layer SensingTo show that we can perform sensing with our system we

sent the tomography signal between nodes C and D. Eachnode transmitted their assigned signal at the start of eachminute over one week. Additionally, a USB temperaturesensor was used to record the water temperature at eachnode. Figure 3(a) shows time-of-flight recorded betweenthese nodes and figure 3(b) shows the USB temperaturedata. The strong correlation between these signals showsthat we can measure the arrival time of an acoustic signalaccurately enough to detect time-of-flight changes causedby changes in water temperature. Further, to show that oursystem can yield useful information about the water tem-perature between the nodes, we can test the following hy-pothesis. Since the heating of the marina is mostly due toexposure to the Sun, we expect the water along the pathswith fewer covering docks to heat up faster. We use threenodes (A, C and D) for this experiment. In our experimentalarrangement the two paths originating from node D (pathsAD and CD) are primarily through uncovered water. Ad-ditionally, the marina is shallower at the eastern end (nearnode A), so we also expect path AD to heat up faster thanpath CD. As it is mostly covered by docks, we expect thepath between nodes A and C (path AC) to heat up slowest.

With the time-of-flight measured between the nodes wecan use the MacKenzie Equation [8] to calculate the aver-age water temperature between the nodes. We use the datacollected at various times over one day, and calculate thetemperature change starting at 10am The data is shown infigure 4. The data nicely confirms our hypothesis, show-

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Figure 3: Measured Time-of-Flight vs. Temperature

ing that the shallow uncovered path AD heats up faster asthe Sun comes out, whereas the mostly covered path ACheats up slower and experiences less temperature rise over-all. Path CD is in the middle, it starts to heat up a littleafter path AD, but eventually heating approximately thesame amount.

5. CONCLUSION AND FUTURE WORKIn this paper we have presented an underwater acoustic

communications system that can also be used for acoustic to-mography. Based on a class of codes derived from Legendresequences, the flexible code length enables the system to betuned for low power transmissions as are required by under-water sensor networks. The system allows for simultaneousdata and sensing transmissions, a key contribution that con-serves energy. We present results from a set of experimentsthat show our system does indeed have the required proper-ties to perform correctly in a noisy, real-world environment.We believe the presentation of our microtomography results

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Figure 4: Marina Water Heating Analysis

represents the first 2D acoustic tomography performed atsuch a small scale. Going forward we are looking to de-sign embedded, real-time underwater sensor network nodesthat will implement the physical layer presented here to en-able the ecological, commercial and defense applications de-scribed in our introduction.

6. APPENDIX A: CONSTRUCTION OFGUOHUA AND QUAN SEQUENCES

This section is a summary of the construction methodfound in [7]. Arithmetic operations on the sequences beloware performed position-wise modulo 2. First we define anumber q ∈ Z to be a quadratic residue mod p of someprime p if the following holds:

∃x ∈ Z : x2 ≡ q mod p (1)

We call the set of all such q, QRP . q is called a quadricnon-residue if 1 does not hold, and we denote the set asQNRP .

A Legendre sequence L(t) of period P , P prime is definedas:

L(0) = 0, L(t) = 0, t ∈ QRP ;L(t) = 1, t ∈ QNRP

If Ld is the decimation by d of the sequence L(t) (i.e. takingevery dth element of L(t)), Guohua and Quan show that forLegendre sequences, Ld(t) takes only one of two forms:

Ld(t) = L(t), d ∈ QRP

or

Ld(t) = 1 + L(t), d ∈ QNRP

Finally we define the operator T k as a cyclic left shift byk positions. Given the above equations Guohua and Quanconstruct the following sets:

M = {T kLd(t)+L(t), t = 0, 1, . . . , P−1}, k = 1, 2, . . . , (P−1)/2

N ′ = {T kLd(t)+L(t), t = 0, 1, . . . , P−1}, k = (P+1)/2, . . . , P−1

N = N ′ ∪ L

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