Ultrasound modulation and codification for

localization systems

Fernando Seco Granja and Antonio Ramon Jimenez

Instituto de Automatica Industrial (CSIC)Ctra. de Campo Real km 0,200 (La Poveda) 28500 Arganda del Rey, Madrid

Tfno. 91 871 19 00 Fax. 91 871 70 50Corresponding e-mail: fseco@iai.csic.es

Published in New Acoustics: selected topics II, pp. 167-186CSIC, Biblioteca de Ciencias (2006)

Abstract

This paper aims to serve as a short introduction tothe advantages that can be obtained by applyingmodulation and codification techniques in many pro-cesses involving ultrasonic signals, and specifically, inthe localization systems designed and built at the In-stitute for Industrial Automation. We will considerdigital modulation of the ultrasonic signals, use-ful pseudo-random sequences for codification, trans-ducer technologies and the expected theoretical ben-efits from the process. Some of these features will bedemonstrated with experimental tests.

1. INTRODUCTION

Ultrasonic sonar has long been one of the key tech-nologies used in Robotics for localization and en-vironment exploration. Its key features are wellknown: good range resolution, ruggedness, simplicityand small processing demands; among its disadvan-tages we can list the slow update rate, the difficultyto interpret the information provided by complex en-vironments, and the interference or crosstalk whenseveral transducers operate simultaneously.

A typical ultrasound-based system for localizationof an autonomous vehicle is illustrated in figure 1.A set of ultrasonic transmitters or beacons placedat known locations are periodically sending pulseswhich are picked by two receivers (A and B) on boardof a mobile vehicle. A processing platform on the ve-hicle computes the times-of-flight (TOFs) of the ul-trasonic signals (synchronization is achieved througha radio link), and by triangulation finds its own posi-tion and orientation. Determination of three coordi-nates (x, y, θ) requires the measurement of the TOFsfrom at least two beacons, although a robust systemwill commonly redundant beacons to provide somedegree of outlier rejection, and verify the positionmeasurement integrity.

In the simplest scheme, the beacons are fired sequen-tially (at times ti, ti+1, etc), allowing enough time

A

B

A B

A

B

ti

ti+1

ti+2

BEACON 3

BEACON 2BEACON 1

TOFA

i

TOFB

i

Figure 1: Tracking of a mobile vehicle with an ultra-sonic positioning system.

for travelling and proper attenuation of the ultra-sonic signal between consecutive emissions. How-ever, at the relatively slow propagation speed of ul-trasound in air, the vehicle’s coordinates will havechanged during the completion of an emission cy-cle. As a result, it is not clear which vehicle’sposition we are computing through measurements{TOFi

A,TOFiB,TOFi+1

A ,TOFi+1B , . . .}. There are

ways to incorporate this difficulty into the positionestimation algorithm (using, for example, a Kalmanfilter), but it would be much more convenient if wecould collect all the ranges from the beacons at thesame time.

Concluding, it is clear that in this particular localiza-tion system, the simultaneous operation of all trans-mitters would increase the measurement update rate,in principle by a factor equal to the number of bea-cons, if we neglect the processing time. An addedbenefit is that the radio link used for synchroniza-tion with the mobile vehicle could be suppressed andthe pseudoranges (time differences instead of abso-lute times) to the beacons could be used for triangu-

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lation, in the same fashion as the GPS does [1].

2. CDMA BASIC THEORY

If a communications engineer was to consider theproblem stated in the introduction, she would speakof a situation of multiple access (MA) to a channel(the ultrasonic signals propagating through the air)by several users (the beacons). A well known exam-ple of MA is a mobile telephony cell, with severalusers speaking to and communicating with the basestation simultaneously.

There are three basic schemes for multiple access:

• Time division multiple access (TDMA), in whichthe users take turns to emit and receive theirsignals; this is essentially the scheme describedin the introduction.

• Frequency division multiple access (FDMA), inwhich the users are allocated different frequencybands which they use simultaneously, as in con-ventional radio. This is very difficult to im-plement with ultrasonic signals because currentair transducer technology does not offer enoughbandwidth to accommodate more than perhapsone or two users (see section 5). In principleone could use a set of physically different trans-ducers, each tuned to a given frequency, and as-signed to a given user. Although this approachwould probably work, it is inelegant and diffi-cult to set up, considering the different physi-cal parameters (impedance, sensibility, emittingpattern, attenuation, etc) of each transducer.

• Code division multiple access (CDMA) in whichthe users emit simultaneously and share thesame frequency band, but are assigned differ-ent codes which can be processed to uniquelyidentify them. This involves the use of digitalmodulation technologies to imprint an identifi-cation code onto the signal transmitted by eachtransducer.

Details of the modulation and codification processesare offered next.

2.1. Digital modulation schemes

Digital modulation serves to translate a bit messagefrom the baseband into the passband of the trans-ducer, and is usually achieved by manipulating theamplitude, the frequency or the phase of a carriersignal at a proper frequency [2].

Phase modulation (PSK) is the most common way ofdigitally modulating an ultrasonic air signal 1. PSK

1Amplitude modulation (ASK) is found in the ultrasonicranger reported in [3]. A simple two-bit FSK signal usedfor time delay estimation is described in [4]. Full FSK ul-trasonic coding is used in the Hexamite positioning system(http://www.hexamite.com).

consists in encoding the transmitted message (a se-quence of bits g[n]) into the phase φ(t) of the carriersignal:

s(t) = sin(2πf0t + φ(t)), (1)

where a single bit takes ncyc cycles of the carrier. Inthe case of binary PSK (or BPSK), the phase shiftsbetween φ(t) = 0 if g[n] = −1 and φ(t) = π if g[n] =1. We will adopt the convention of taking -1 and +1as possible bit values, instead of 0 and 1.

2.2. Codification schemes. Pseudo-random

sequences

In CDMA communications, each user i is assigned aNb bits long binary code gi[n], which is modulatedas described above and transmitted into the medium.As all users can emit simultaneously and share thebandwidth, the ability to isolate a given user dependson two principles: (a) that there is a way to processa signal and detect a given code (the correlation op-erator); and (b) that codes can be built that haveminimum mutual interference (code orthogonality).Mathematically we can write these desirable proper-ties of a set of digital codes {gi[n]} as:

Rii[m] =∑

n

gi[n]gi[n + m] = δ[m]

Rij [m] =∑

n

gi[n]gj [n + m] = 0,(2)

where Rij [m] is the correlation of codes i and j andδ[m] is Kronecker’s delta. The first condition statesthat correlating a code with itself will give a peakplaced at the true lag (corresponding to the echo’sarrival time) and a zero value elsewhere; the secondthat the codes are perfectly orthogonal and the in-fluence of any number of them can be exactly elim-inated. Mathematically, white noise signals uncor-related to each other would verify the set of equa-tions 2; as this is not a practical approach, digi-tal codes which resemble white noise (but are oth-erwise completely deterministic) are used instead—that’s the reason why these signals are called pseudo-random codes.

Unfortunately, no set of codes can be built that sat-isfy exactly the conditions above, a fact which hasspanned several code families with different charac-teristics. We will enumerate only the most popularin the literature2. Maximum length sequences haveoptimum autocorrelation but far from optimal cross-correlation properties. Hadamard-Walsh codes fulfillexactly the conditions given in equation 2, but onlyin the case of synchronicity (m = 0), which makesthem useful in mobile telephony but not in ultrasonicapplications where the time of flight is a priori un-known. Golay codes have long been favored by theultrasonic community; they fulfill exactly the condi-

2The study and construction of orthogonal codes is an areaof active research, linked to the field of commutative algebra.

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−60 −40 −20 0 20 40 60−20

0

20

40

60

80

100

120

lag

autocorrelation

crosscorrelation

Figure 2: Autocorrelation (blue) and cross-correlation(green) of two 127 bits long Gold codes.

tions in equation 2 if used in pairs, requiring quad-riphase (QPSK) modulation to encode the two-bitsymbol. A limitation of Golay codes is that there isonly one pair of sequences which is perfectly orthog-onal to a given Golay pair, so only two users could beaccommodated with them; the workaround consistsin employing complementary (sets of more than twosequences modulated at the same time) or polyphasesequences. An advantage of Golay sequences is thatefficient (in the sense of required number of opera-tions) correlators exist for them, a fact which hasbeen considered by the group of Urena and cowork-ers [5] to design sensor units and dedicated hardwarethat exploit these complexity reduction properties.

Finally, Gold codes are a good approximation toequations 2, providing a high auto-correlation peakand bounded cross-correlation properties; these arethe codes of choice for the GPS positioning system.Their properties approach the ideal results when thenumber of bits (Nb) grows. In figure 2 we show thecorrelation properties of the length 127 codes thatwill be used later in this paper. The small peaksaround the maximum are sometimes called sidelobesin the literature (not to be mistaken with the angularsidelobes of ultrasonic transducers).

2.3. Processing of the received signal

The advantages of CDMA schemes are achievedthrough signal processing. A schematic vision of aCDMA receiver is shown in figure 3.

Part (a) of figure 3 shows the demodulator stage. It isa common practice in carrier modulation schemes toshift the signal down to an intermediate frequency orto the baseband (near 0 Hz) before further process-ing. Due to the relatively low carrier frequencies usedin ultrasonic air applications, most processing sys-tems can handle signals in the passband right away,so this step would not be strictly required. However,

it will be followed in this paper, and we will use thestandard inphase-quadrature (IQ) demodulator toconstruct the complex envelope r(t) = rI(t)+ jrQ(t)from the incoming signal s(t). The continuous signalr(t) is sampled at the bit intervals3 to produce thediscrete signal: r[n] = r(nTb).

Detection of each individual user is achieved with thecorrelator bank of part (b) of figure 3. It consists in aset of filters matched to the codes {gi[n]}, producingthe following outputs:

yi[m] =∑

n

r[n]gi[n + m]. (3)

A peak detector finds the time of arrival TOFi andamplitude Ai of the signal from the ith transducer.

2.4. Alternatives to digital modulation

To conclude this section, we would like to commentthat CDMA schemes, which are based in digital mod-ulation of the ultrasonic signals, are not the only wayto achieve good resolution, low crosstalk and extractrich information of the environment. Other alterna-tives exist, whose common feature seems to be thefull exploitation of the bandwidth that is available.One example is the sonar system described in [6],that uses pseudo random noise signals created tomatch the transducer’s bandwidth.

The chirp (a linearly modulated frequency sweep)has long been used for pulse compression in sonarand medical ultrasound [7]. Bats, which use ultra-sound for navigating and hunting, produce signalswhich are a combination of modulated frequency andconstant frequency (in order to use the informationfrom the Doppler shift of the returned echo), and alsoemploy the higher harmonics of the base signal, span-ning a typical range from 20 to 120 kHz. Evolutionhas fine-tuned the ultrasonic echolocalization systemof bats to an amazing degree of complexity, enablingthem to build a three dimensional map of the sur-rounding environment, with potential resolution ofmillimeters, and use it for navigation and huntingin cluttered environments [8]. This is beyond thecapacity of any man made ultrasound system builtyet.

3. ADVANTAGES OF SIGNAL

MODULATION AND

CODIFICATION

In this section we will describe the benefits that canbe obtained from the processes of modulation andcodification of ultrasonic signals.

3Signal synchronization is a tricky issue which we do nothave space to deal with properly here. We will consider itagain in the experiment of section 6.3.

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s(t)

In-phase

Quadrature

LowpassFilter-2sin 2 f tp 0

2cos f tp 02

r (t)I

r (t)Q

(a) IQ demodulator

r(t)=rI(t)+jrQ(t)

r[n]

Tb

Peakdetector

r[n]

åg1[n]

Peakdetector

Nb

g2[n]

Peakdetector

gK[n]

A1,TOF1y1[n]

y2[n]

yK[n]

(b) Matched filter bank

A2,TOF2

AK,TOFK

åNb

åNb

Figure 3: Processing stages of a CDMA system: (a) Inphase-quadrature (IQ) demodulator used to compute the complexenvelope or baseband representation of the ultrasonic signal; (b) Correlator bank to detect the different users.

3.1. Simultaneous operation of several

transducers

Notably, the capacity of CDMA to accommodateseveral users simultaneously makes it a very usefultechnique in communication systems. Ultimately thecapacity of a CDMA system is limited by the multi-ple access interference (MAI) between users, a prob-lem which is documented in the literature from mo-bile telephony [9]. Algorithms for MAI mitigationexist, with significant improvement at the expenseof more intense signal processing.

As a by-product, CDMA also provides system re-sistance to multipath propagation, which is ubiq-uitous in indoor ultrasonic applications, since mostobjects reflect sound waves specularly. Multipathpropagation can be viewed as a multiuser problem(in this case, self-interference) and partially rejectedwith CDMA techniques.

3.2. Enhanced precision in estimation

processes

In robot navigation an ultrasonic signal is emittedinto the air to detect the presence and position ofobstacles in its way. In medical elastography an ul-trasonic signal is sent into the human body to deter-mine the thickness of a muscular tissue. These twoapplications are examples of estimation processes.The accuracy of the obtained results (range to a tar-get, tissue thickness) depends on the characteristicsof the signal and the environment, and is quantifiedmathematically by the so-called lower bounds [10].One well studied example is the determination of theTOF (or range) to a target (see figure 1); it can beproven that for a coherent process (i.e., one whichincludes the information of the phase) and with asufficiently high SNR, the variance of the measure-ment is given by the Cramer-Rao criterion, which

numerically amounts to [11]:

σ2TOF ≥

1

16π2BTf20 SNR

. (4)

From this equation we see that several factors con-tribute to obtain higher precision. The first is thecentral frequency f0, which however is limited by theincreasing attenuation of ultrasonic propagation inair with high frequencies. Increasing the SNR is alsobeneficial to decrease the measurement error; how-ever the transducers used, the measurement range,etc, set a limit for the signal amplitude that canbe obtained (besides, in medical applications, healthregulations dictate the maximum peak power whichis allowed in an ultrasonic test). The last factorthat we can manipulate is the product of the signalbandwidth and duration (or BT product for short).For waveforms of the kind envelope times carrier thisproduct is limited (essentially equal to one), but itcan be increased without bounds if we use chirps orcoded waveforms, which are referred to as long BTsignals, or pulse compression waveforms. Therefore,use of coded waveforms leads to a more accurate de-termination of parameters in an estimation process.

3.3. Processing gain

Processing gain can be defined as the signal gainwhich is obtainable by taking advantage of the sig-nal’s structure—in essence it could be described as asmart averaging with the correlation operator. Nu-merically it can be shown that this gain is given by:

PG = 20 log10 Nb in dB,

where Nb is the number of bits of the encoded sig-nal. Processing gain is really another way of lookingat the precision enhancement mentioned above. Themain benefits of processing gain are the capacity todetect low amplitude signals (even below noise level)

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and the resistance to interference from noise sourcesand other users. Processing gain is obtained at theexpense of increased processing requirements (timeand storage capacity), and may pose a limit to sys-tems operating in real time.

3.4. Data transmission

The ultrasonic channel can also be used for digitaldata transmission among two points with line of vis-ibility, with a speed dictated by the available band-width and SNR. A possible application would be toreplace the radio links used for data transmission insome systems. We’ll show how ultrasonic communi-cation is feasible in section 6.3.

4. APPLICATIONS

In this section we list some of the applications ofmodulation and codification of ultrasound.

4.1. Localization systems

As stated in the introduction, our motivation forcoded excitation of ultrasound comes from the de-velopment of localization systems, and is inspired bythe very successful GPS system. Our group is cur-rently developing a positioning system to automatizethe job of archaeologists working in the findings inGran Dolina, in Atapuerca (Spain), where humanremainings from about 800000 years ago have beenfound, which could correspond to the first Europeaninhabitants (Homo antecessor).

The task of the archaeologist consists in recoveringall the different pieces (bones, glass, ceramics, etc)found in the place and noting down their positions;later all the data is used to recreate the original ar-rangement of the settlement. The process of local-ization of the pieces starts with a division of the areawith strings to form a reticule, and measuring man-ually (with a tape) and writing the coordinates ofthe found pieces with respect to this reticule (see fig-ure 4, left). This method is obviously slow and proneto human errors.

The system developed at IAI [12] is shown in theright part of figure 4, and consists of two parts: anarray of ultrasonic transducers, placed at fixed posi-tions in a framework above the work area, and a setof sticks operated by the archaeologists. Each stickholds an ultrasonic transducer on its top and anotherin its middle point; when the user points the tip ofthe stick at the object to be positioned, and pressesa button in the stick, an ultrasonic transmission isinitiated from the stick to the static transducer net-work. Measurement of the times-of-flight and trian-gulation permits to find the position of the emittertransducers, and, from them, the coordinates of thetip. These coordinates are transmitted by a radiolink to a remote computer which keeps a log on thedifferent findings. CDMA codification of the ultra-sonic signals is required because: (a) several users

might be sharing the workspace; (b) we contemplatebidirectional transmission (i.e., also down from theframework transducers to the sticks) in order to mit-igate the effects of the wind on the propagation ofultrasound. The first trials with a prototype systemhave given accuracies in the millimeter range, whichare demanded in this kind of application.

4.2. SLAM

Simultaneous Location and Mapping (SLAM) is theuse of sonar ultrasonic signals by a robot to locateobstacles in its path and dynamically build a map ofits environment. To cover as wide an area as possi-ble, robots are equipped with many transducers (forexample, the venerable B-21 from RWI has a ring of24 capacitive sensors around its body), which causesthe aforementioned problems of crosstalk betweenemitters, and difficulty to identify the origin of thereceived echoes. Systems reported in the literatureemploy time scheduled sensor firings (i.e. TDMA)and use either the number of pulses in each emis-sion [13] or the time separation between consecutiveemissions [14] to uniquely identify the emitting trans-ducer. It is clear that CDMA schemes are potentiallymore efficient than these methods.

Another quite interesting research line concentratesin extracting more information from the environmentthan merely the range and bearing to the nearest ob-stacle provided by conventional sonars. In 1987 Kucpublished a classic paper [15] in which he demon-strated that the combination of the arrival timesof ultrasonic echoes at several transducers and thephysics of wave reflection, could be used to clas-sify the reflectors into three simple categories: flatwalls, edges and corners. Starting with these tem-plates as basic units permits to build more accu-rate environment maps, a very useful fact for SLAMapplications. Following this result, Peremans andAudenaert [16, 17] built a tri-aural (one transmit-ter and three receivers, or 1T/3R) structure whichused a BPSK modulated, 13 bit long Barker codesignal. The sensor was able to discriminate objectsas close as 2 cm, as well as correctly classify multiplereflectors into the three categories described abovein rather complex environments. This line of workwas further extended by Jorg [6], with a sensor withtwo emitters and two receivers (2T/2R), and pseudo-random signals, using a matched filter for process-ing the received echoes. More recently, the groupof Urena [18] at the Universidad de Alcala used atwo emitter and four receivers structure (2T/4R), asshown in figure 5 and Golay complementary pair se-quences for each transmitter, modulated with QPSK.His group has made use of the so called efficient Go-lay correlators (see section 2.2) to optimize the signalprocessing time. The use of custom designed FPGAhardware permits real time operation with long sig-nals (up to 128 bits), as was demonstrated in ex-perimental trials on board of a CyCab vehicle (see

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Remotesystem

Positioningtool

Referencesystem

B1

B2

B3

B4

B5

B6

B7

P1

P2

R1

Static beaconnetwork

Work area

Radiolink

Figure 4: Manual positioning of pieces in archaeological findings and the system developed at the IAI for assistanceand automatization of the task.

Figure 5: Four transducers (2T/4R) sensor structureemployed at the Universidad de Alcala, and its applica-tion for SLAM in a CyCab vehicle.

figure 5) [5].

4.3. Other applications

For the sake of completeness we mention other ar-eas where codification and modulation of ultrasonicsignals have found application.

Sonar (and radar) were the first fields to exploit theadvantages of coded signals, with all the basic con-cepts (long BT signals, matched filter, ambiguityfunctions, etc) being established during and after theSecond World War.

Medical ultrasound is a big field of application of

coded excitation today [19]. Activity on this topicbegan in the early 80s, with several researchers point-ing how improvements in penetration depth and ob-tainable resolution could be gained from signal codi-fication; around that time Lee [20] proposed the useof Golay sequences to permit multi-mode (several di-rections simultaneously) operation of phased arraysfor scanning. Progress in the area was slowed downby the difficulty in analyzing the propagation of ul-trasound in the human body (which adds complica-tions like frequency dependent tissue attenuation andthe presence of speckle) and the inexistence of trans-ducers with adequate bandwidth. However this fieldhas experimented phenomenal advances in the lastfive years; one needs only to see the spectacular qual-ity of today’s echographies, which can be attributed,among other factors, to the increased performanceobtained with coded signals [21].

Finally, other fields which benefit from ultrasoniccodification are non-destructive testing and non-contact ultrasonic imaging, as the system for studyof wood samples described in [22].

5. TRANSDUCTION

TECHNOLOGIES

Unlike the case of electromagnetic signals, wherehuge bandwidths are readily available for codifica-tion and modulation, ultrasonic systems in air aremuch more restricted by the transducer technologyavailable and physical constraints, like the high dif-ference of acoustic impedances between transducermaterials and air and the attenuation of the signalat high frequencies. The net result is relatively lowtransducer bandwidth and sensibility [23].

Piezoelectric transducers are resonant devices with ahigh quality factor and correspondly low bandwidth

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(typically 2 kHz for a 40 kHz central frequency); theyare commonly used in pulse-echo air applications,without codification. Several methods have been de-veloped for damping the resonance and increasingthe bandwidth, like the careful use of backing lay-ers. Piezopolymer (PVDF) transducers show higherbandwidth (in the order of 8–10 kHz), due to their re-duced acoustic impedance (closer to that of air). Ofthe commonly available transducers, the capacitiveones have the highest bandwidth (about 30 kHz forsome Polaroid models), and they are the ones usuallyemployed for modulation and codification [17, 6, 18].

More recently arrived technologies show the promiseof combining high SNR and bandwidth, althoughfor the moment they are not available as off-the-shelf components. Multifrequency piezocompositesare piezoelectric ceramic rods of different thicknessesembedded in an inert polymer matrix, which have abandwidth controllable by design [24]. The capaci-tive micromachined ultrasonic transducers (CMUTs)are small capacitors fabricated with CMOS tech-nology, with a remarkable capability for array fab-rication and relative large bandwidths (for exam-ple, in [25], a bandwidth of 600 kHz and a cen-tral frequency of 1.2 MHz are reported). Recentlyintroduced, the electromechanical film (EMFi) is apolypropylene film which holds a permanent chargeand therefore acts like an electret [26]. These trans-ducers have found their first application in the ultra-sonic field as general broadband transducers in theCirce project4, where a usable frequency range of20–200 kHz has been reported.

6. EXPERIMENTAL TESTS

We will clarify some of the features of the signal codi-fication and modulation with the experimental setupshown in figure 6. The system consists in a PC con-nected through the GPIB bus to an Agilent’s 33120Aarbitrary waveform generator which is used to createthe coded waveforms. The signals are emitted andreceived with a couple of Prowave’s 400WB16 ‘wide-band’ piezoelectric transducers, placed 1 m apart.They have a quoted bandwidth of 15 kHz, whichis achieved by damping the piezo disk with sili-cone (this design also causes a drop of amplitude ofabout 23 dB with respect to the resonant version ofthe same transducers). The received echo is ampli-fied with a Bruel&Kjaer 5935 amplifier (adjustablegain from 0 to 50 dB) and captured with an AdlinkPCI-9812 acquisition card (the sampling frequencyis taken as 1 MHz). Waveform generation and signalprocessing takes place in a PC running the Matlabenvironment with the Instrument Control toolbox.

The first step of our experimental procedure con-

4Circe is a research project funded by the EuropeanUnion, whose goal is producing a functional replica of a bat’sbiosonar system. More information in the project webpagehttp://www.circe-project.org.

20 25 30 35 40 45 50 55 600

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Frequency (kHz)

Gai

n

Prowave 400WB16 E/R − gain

Figure 7: Frequency response gain of the transducersof figure 6.

sisted in finding a system model for the completetransmission-reception process. For that purpose weexcited the emitter with sequences of pseudo-randompulses designed so that their frequency content isin the band 0–100 kHz, and recorded the receivedsignals. Next we applied the techniques of systemidentification [27] to the input-output sequences, andfound an output-error (OE) model which was capa-ble of reproducing the behavior of the system withhigh accuracy. The frequency response of the modelis shown in figure 7, with a measured bandwidth of16 kHz (-3 dB) centered at 40 kHz. Both amplitudeand phase responses are quite nonlinear within thepassing band. It seems likely that enhanced perfor-mance of the transducer system could be obtainedby equalization of the ultrasonic channel [2]; how-ever, we will not deal with this topic in this paper.

The next logical step is designing a modulated wave-form whose spectrum will fit into the bandwidth ofthe transducer system. As a standard waveform forthe experiments, we settled for a 127 bits long Goldcode, encoded with BPSK modulation and ncyc=4cycles/bit (total length of 12.7 ms). In figure 8 (a)we show the original spectral density of the signal,and in part (b), how it is changed by the processesof transmission and reception. Although they mod-ify considerably the frequency content of the signals,the transducers chosen allow for a 15 kHz bandwidth,instead of merely 2 kHz as would be the case withresonant piezo-transducers.

In the following sections we will illustrate some of thecharacteristics of the modulation and codification ofultrasonic signals empirically.

6.1. Multi-user capacity

As was shown in section 2, the orthogonality of thedigital codes permits simultaneous emission by sev-eral users. In this experiment, we have used two

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FUNCTIONGENERATOR

PCACQUISITIONCARD

AMPLIFIER

EMITTER RECEIVER

GPIBBUS

Figure 6: Experimental setup for the modulation and codification of ultrasonic signals.

30 35 40 45 500

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Spe

ctra

l den

sity

Emitted

(a)

30 35 40 45 500

0.5

1

1.5

2

2.5x 10

−4

Frecuency (kHz)

Spe

ctra

l den

sity

Received

(b)

Figure 8: Spectral density of a modulated Gold code:(a) as emitted; (b) after reception.

closely placed ultrasonic transmitters, which emitsynchronously two different Gold sequences. Thereceived waveform is processed as indicated in sec-tion 2.3 and then correlated with each code to lo-cate the individual echoes. The results are shownin figure 9 for two different separations of the emit-ters: (a) 53 mm, and (b) 3 mm (for comparison, thespatial length of the code is 4.3 m). Notice, in thesecond case, the considerable signal fading caused by

the destructive interference between the two trans-ducers. Even in these circumstances, the individualechoes are easily resolvable.

6.2. Processing gain and resistance to

interference

We saw before that the processing gain provides acapability for working in low SNR environments orin the presence of interference from other sources; afeature which will be demonstrated now through aset of three different experiments.

In the first experiment the signal amplitude at theemitting transducer was lowered until a SNR of-6.4 dB is obtained. The signal, as shown in fig-ure 10 (a), is hardly distinguishable from the noise.Actually, in part (c) of the same figure we can seethat the spectral density is below the noise level formost frequencies. However, when the signal is corre-lated with the emitted code, a clear detection peakappears (figure 10 (b)).

In the second experiment the emitting transducer istransmitting the coded signal while another trans-ducer placed very close emits a pure tone at 40 kHzwith a relative amplitude 11.6 dB above the signalto be detected (see figure 11 (a)). This is a situationof narrowband noise interference right at the car-rier frequency (see part (c) of the figure), in whichmost conventional detectors would be rendered use-less. However, through processing gain we are ableto detect the emitted signal, and obtain a clear cor-relation peak (figure 11 (b)).

Finally, the third experiment illustrates the resis-tance to wideband, impulsive noise. The acousticenergy produced by many mechanical phenomenacontains both audible and ultrasonic noise whichmay cause malfunction of ultrasonic based systems.In this case we created wideband noise by shakinga set of metal keys right in front of the receivingtransducer. The received waveform, shown in fig-ure 12 (a), had an estimated SNR of about -15 dB,

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tion

(d)

Figure 9: Echo separation capability of two orthogonal codes. In (a) the emitting transducers are separated 53 mm(156 µs); the correlations with each code are shown in (b). In (c) and (d) the transducer separation is 3 mm (8.7 µs).

0 2 4 6 8 10 12 14 16 18−0.06

−0.04

−0.02

0

0.02

0.04

0.06

Time (ms)

Sig

nal

(a)

15 20 250

1

2

3

4

5

6

7x 10

5

Time (ms)

Cor

rela

tion

(b)

and a noise spectra as shown in part (c). Again thecorrelation operator was able to produce a peak anddetect the presence of the signal (figure 12 (b)).

As a conclusion, the processing gain takes advan-tage of the signal’s structure and is able to detectthe presence and time arrival of an ultrasonic echoin situations of low SNR or strong interference fromother sources. The three cases shown cover many

of the situations which degrade the performance ofultrasound based systems. Furthermore, the detec-tion capability of processing gain is controllable byincreasing the code’s length.

6.3. Data transmission

Like any other communication channel, the ultra-sonic transducers are able to transmit information

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0 10 20 30 40 50 60 70 80−150

−140

−130

−120

−110

−100

−90

−80

−70

−60

Frecuency (kHz)

Spe

ctra

l den

sity

(dB

)

(c)

Figure 10: Signal detection for low SNR: (a) received sig-nal, (b) correlation, and (c) spectrum of the signal (blue)and the noise (green).

0 2 4 6 8 10 12 14 16 18

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

Time (ms)

Sig

nal

(a)

18 20 22 24 26 280

0.5

1

1.5

2

2.5

3

3.5

4x 10

6

Time (ms)

Cor

rela

tion

(b)

0 10 20 30 40 50 60 70 80

−120

−100

−80

−60

−40

−20

Frecuency (kHz)

Spe

ctra

l den

sity

(dB

)

(c)

Figure 11: Signal detection with narrowband noise: (a)received signal, (b) correlation and (c) spectrum of the sig-nal (blue) and the noise (green).

in the form of digital messages. To illustrate thispoint, we designed a signal waveform, which consistsof a header, and a short digital message.

The header is needed because unless the position ofthe transducers is precisely determined (if, for exam-ple, they are mechanically fixed), the signal arrivaltime is unknown and the ultrasonic transmission isasynchronous. Then the header fulfills the purposesof detection and symbol synchronization.

The header is again a BPSK modulated Gold se-quence of length 127, with 4 cycles per bit. The

transmitted message is appended at the end of theheader and it is a random 256 bits sequence modu-lated with QPSK, with 16 cycles per symbol (or 8 cy-cles per bit). A Gray code is applied to reduce biterrors. The length of a complete transmission signalis 64 ms; and excluding the header (which does notcarry information), the transmission speed is about4 kbits/s (about 1/15th of the speed of a 56k mo-dem).

An experimental signal is shown in figure 13 (a), for atransducer separation of 1 m, and a resulting SNR of

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0 2 4 6 8 10 12 14 16 18−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

Time (ms)

Sig

nal

(a)

18 20 22 24 260

0.5

1

1.5

2

2.5

3

3.5

4x 10

6

Time (ms)

Cor

rela

tion

(b)

0 10 20 30 40 50 60 70 80−140

−120

−100

−80

−60

−40

−20

Frecuency (kHz)

Spe

ctra

l den

sity

(dB

)

(c)

Figure 12: Signal detection with impulsive noise: (a) re-ceived signal, (b) correlation, and (c) spectrum of the signal(blue) and the noise (green).

0 10 20 30 40 50 60 70 80 90−0.1

−0.05

0

0.05

0.1

0.15

Time (ms)

(a)Header Message

(b)

Figure 13: (a) Transmission signal, including the header and a 256 bits QPSK modulated message; (b) symbol con-stellation obtained after demodulation.

10 dB. As usual the signal is brought to the basebandand correlated with the header to obtain a ‘delta’-likespike, providing synchronization for the position ofthe message symbols. A matched filter is applied todemodulate the symbols. The results are shown inpart (b) of figure 13, which is the constellation of allpossible phases (0, π/2, π and 3π/2, correspondingrespectively to the two-bit symbols 00, 10, 11 and01), separated by the dashed lines.

For this relatively high signal amplitude (the SNR

per bit was found to be 29 dB), the bit error rate isvery low (in our case, the demodulator found all 256bits correctly in several trials).

7. CONCLUSIONS

This paper has shown some of the advantages obtain-able from the processing gain when signal codifica-tion and modulation are introduced in ultrasonic ap-plications. Namely, they consist of: enhanced SNRand resistance to interference, higher precision in

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estimation processes, support for several users andpossibility of data transmission through the ultra-sonic channel. These features can be very useful forultrasound-based positioning systems and the navi-gation of robots and autonomous vehicles.

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