Experimental Analysis of Detection andLocalization of Multiple Emitters in

Multipath Environments

UJ4ur SaraV1'3 . F. Kerem Harmanc?, and Tayfun AkguiiP4

'Department of Electronics and Communications EngineeringIstanbul Technical University, Istanbul, Turkey

E-mail: sarac~uekae.tubitak.gov.tr, tayfun.akguI~itu.edu.tr2 Department of Electric and Electronic Engineering

Bo~azii~i University, Istanbul, TurkeyE-mail: harmanci@boun.edu.tr

3TUBITAK-UEKAEKocaeli, Turkey

4 TOBITAK MRC Earth and Marine Sciences InstituteKocaeli, Turkey

Abstract

An effective way for the joint detection and localization of multiple RF transmitters in a multipath environment is to enumeratethe number of paths using the minimum-description-length information-theoretic algorithm, and to then measure the angle ofarrival of each path, using an antenna array with a high-resolution direction-finding algorithm, such as MUSIC. The possiblepropagation paths are the angles corresponding to the peaks of the MUSIC pseudo-spectrum. Since more than one path maycorrespond to a single emitter source, further processing is required. The time-domain signals incident from these paths arethen extracted with beamnforming techniques, such as minimum variance, in order to estimate their coefficients of correlationwith each other. These correlation coefficients are used to decide whether or not these paths correspond to the same emitter.Among the paths that appear to originate from the same source, the path with the time signal that contains the highest poweris selected as the original path of the source. Hence, the number of emitters and their angles of arrival are jointly estimated. Aperformance analysis of the method is presented via real-time laboratory experimentation and discussed in this paper. Todemonstrate the effectiveness of the proposed technique, experimental results with two uncorrelated sources were comparedto experimental results with a single source and a reflector. All of the experiments were conducted in an anechoic testchamber.

Keywords: Direction of arrival estimation; multipath channels; navigation; array signal processing; information theory

1. Introduction

Direction finding (DF), or, in other words, estimation of theLangle of arrival (AQA), has been an active area of research

since the beginning of the 20th century. Direction finding has sev-eral applications, such as military applications, GSM withimproved channel capacity, localization of illegal transmitters (TVand radio stations), location of a mountaineer losing his/her path,in addition to spectrum monitoring.

When multiple sources are simultaneously incident on anantenna array, classical direction-finding methods, such as interfer-ometry and Doppler, cannot resolve these sources [1, 2]. An effec-tive solution to the problem is to use high-resolution subspace-

IEEE Antennas and Propagation Magazine, Vol. 50, No. 5, October 2008

based algorithms. Multiple signal identification and classification(MUSIC) is the most powerful and widely used subspace-basedmethod. This method was applied by Schmidt [3] to direction-finding problems in 1986. MUSIC is known to successfully resolvetwo or more sources if they are incoherent. However, in practice,signals often propagate in multipath environments. A source signalis thus incident on the array from many paths, which implies thatcoherent signals at different angles will be received by an array.

For source localization with MUSIC in a multipath environ-ment, it is critical to initially detect the number of incident paths.The simplest algorithms that enumerate these paths are based oncounting the nonzero eigenvalues of the array's covariance matrix[4]. Information-theoretic criteria (ITC), such as the Akaike infor-mation criteria (AIC) [5] and the minimum description length

ISSN 1045-9243/2008/$25 ©2008 IEEE 61

(MDL) [6]1, are widely used advanced algorithms for path enu-meration. Minimum description length was proposed by Max andKailath [7] for source enumeration in the presence of multipath andsignal coherence. It was further improved by Wax and Ziskind [8]in 1989, and by Wax [9] in 1991. Some of the later improvementson information-theoretic criteria can be found in [10-12]. As inMUSIC, these information-theoretic-criteria algorithms are alsoaffected in a multipath environment. This is due to the fact thatsignal coherence in a multipath environment alters the eigen-structure of the sensor array's correlation matrix. This, in turn,affects the performance of both the MUSIC and information-theo-retic criteria algorithms.

A recent solution proposed for solving the problem of signalcoherence is the spatial smoothing (SS) preprocessing algorithm,proposed by Shan, Wax, and Kailath [13]. Spatial smoothingessentially removes the effect of coherency between incoming sig-nals in the eigen-structure of the correlation matrix. The source-localization process [13] therefore involves the following steps.First, the array antenna's output is processed to form a samplecovariance matrix. Spatial smoothing is then applied to this matrix,after which the number of signals is estimated. Based on the previ-ous step, MUSIC is used to generate an angle spectrum. Pillai andKwon [14] used forward-backward spatial smoothing (FBSS),which provided an advantage in terms of the number of antennasrequired in the array.

High-resolution direction-finding methods like MUSIC arevery sensitive to antenna gain, antenna phase, and mutual-couplingerrors. To reduce the effects of these irregularities, eight identicaldipole antennas were manufactured and tested to identify, theircharacteristics. In practice, these methods require a calibrationalgorithm to measure the errors and to correct them. Many suchcalibration methods have been proposed in the literature [ 15-19]. Inthis paper, the calibration technique proposed in [18] is applied.

It is important to note that in a multipath environment, theuse of information-theoretic criteria with spatial smoothing merelydetects the number of paths, i.e., the signals originating fromsources directly or coming from the reflectors. The MUSIC algo-rithm then localizes all the signals in the angle/angle-of-arrivalpseudo-spectrum. In other words, information-theoretic criteriaand/or the MUSIC-angle-of-arrival pseudo-spectrum indicate thenumnber of paths and not the mnuber of independent sources pre-sent in a multipath environment. This is a significant problem if theobjective is to localize actual independent sources in a multipathenvironment. Yong, Ci, and Zhong [20] have investigated thisproblem, and proposed a method that measures the correlationbetween the time series from each path to pinpoint the sources.However, they presented simulation results without any perform-ance analysis. In 2006, Sarar, Harmanci, and Akgtil [21] experi-mented with methods similar to that of Yong et al., and presented aperformance analysis through simulations. This study shows theresults and performance of the analysis of these methods based onreal experimental data. The paper is organized as follows. In Sec-tion 2, the signal model is discussed. The method used in this studyis described in Section 3. Section 3 also includes a subsection,Section 3.5, which explains the application of the above techniqueto estimate the position of a source using two antenna arrays.

2. Signal Model

The signal model is based on a multiple-emitter, multipathscenario. Here, signals originating from point sources generate

wavefronts that are propagating in a nondispersive medium, andthese wavefronts are measured by an antenna array. Signals emittedfrom the distinct sources are assumed to be uncorrelated, whilesignals on distinct paths but originating from the same sourcethrough reflections are considered fully or partially correlated. Thiscorrelation relation is the basic assumption of this study.

To understand the characteristics of the multipath environ-ment, it will be useful to examine, in particular, the scenario inFigure 1. Suppose that there are two point sources ( K = 2 ), andthree reflectors causing three extra wavefront paths. As a result, byignoring any additional multiple reflections, the direction-findingsystem will have at least five different wavefront paths (D = 5 ).

In general, let signals emitted from K sources arrive at thearray antenna from D different paths, where K < D. Consider anarray system composed of M identical antennas. For simplicity, letthe sources and antennas be in the same plane, and let the sourcesbe in the far field of the array system.

If the M x 1 vector y represents a narrowband signalreceived by the array, then it can be expressed as

Dy =As +g ~a (01)s, + g, (1)

where A is the M x D matrix of steering/wavefront vectors a (0,)

of the signal from the path in direction 01 s is the D xlI incomingsignal vector, and g is an M x 1 noise vector. Here,[A].m, -=am (01) is the response of antenna m to the lth signal.

This, in turn, can be expressed as

am (01) = e-j2f(m-1)dsin(0,)/A (2)

Signal, s, and noise, g, are assumed to be uncorrelated. Each snap-shot of s and g is considered to have zero mean, and be independ-ently and identically distributed. When the antenna array isassumed to have no mutual coupling and is assumed to be perfectlycalibrated, the M x M autocorrelation matrix of y becomes

R), = APA H +Rgg, (3)

where H denotes the Hermitian conjugate, and

P=E [SSH] =Diag [PI,P2,..., PDJ is the D xD power matrix of

the signal. This power matrix is diagonal, since distinct pathsindexed with 1, with power P1 , are assumed to be uncorrelated.

The vector space spanning Ry, can be decomposed into a

signal space and a noise space. The first space consists of D eigen-vectors (Vl1 . -VD) for the largest D eigenvalues (A_.,AD); the

other consists of the M-D eigenvectors (VD±1I,'-,M)' respec-

tively. Since the signal and noise eigenvectors are orthogonal, thesignal and noise subspaces are also orthogonal. As a result, thea(Ok) mode vector, which is in the signal subspace, is orthogonal

to all vectors in the noise subspace. In vector notation, thisbecomes

aH (0k)vi =0, k-=l,...,D; i =D+l1,...,M,

which is the basic principle of the MUSIC algorithm.

(5)

62 IEEE Antennas and Propagation Magazine, Vol. 50, No. 5, October 200862

3. Methods Used in the Experiment

3.1 MUSIC

MUSIC is the prevailing subspace-based method for angle-of-arrival estimation. It is known for its high resolution and accu-racy. The noise-subspace eigenvectors and Equation (5) can bearranged in a way to obtain MUSIC for the source or path at direc-tion 9, i.e.,

(6)I a H (9) Vi=0.i--D+l

Equation (6) has D distinct 9 solutions, each corresponding to asource or path. From Equation (6), the pseudo-spectrum, P", (9),is obtained for the angle of arrival:

P. (0 = 1(7)a H (9)VVHa(9)'

Here, V is an M x D matrix the columns of which are theeigenvectors of the noise subspace. All angles between 00 and 3600are scanned for Equation (7) to obtain the MUSIC pseudo-spec-trum. An angle-search procedure over the pseudo-spectrum isrequired to estimate the angle-of-arrival, as stated in Equation (7).However, MUSIC has some drawbacks. First, MUSIC requires theprecise knowledge of the number of sources/paths in the medium.Second, MUSIC is sensitive to the signal coherency in the presenceof multipath. To address this last effect of coherency, spatialsmoothing is applied.

3.2 Spatial Smoothing

When several versions of a signal from the same sourcearrive at the antenna array simultaneously from different paths,they generate coherent signals over those paths. Such coherent sig-nals always occur in a multipath environment, and they can beobserved to be highly correlated. This correlation will in turn causethe matrix P to be ill-conditioned, or even singular, and will reducethe rank of the signal component of the correlation matrix, Rn,.This in turn markedly compromises the ability of MUSIC toresolve the angles-of-arrival of coherent signals.

In 1985, Wax [13] applied spatial smoothing to a uniformlinear array in order to address this problem. In the spatial-smoothing algorithm, M identical antennas are divided into over-lapping subarrays of size m, as seen in Figure 2. From these,

1 2 M-m-1y , y y are considered to be subarray outputs.

Let Rý be the sample correlation matrix of the ith subarray,

which can be defined as the sample average of the outer products,

yy ý , for each snapshot of the ith subarray. All R ' matrices arecombined to obtain a spatially smoothed sample covariance matrix

R as the sample means of the subarray covariance matrices

[13]:

IEEE Antennas and Propagation Magazine, Vol. 50, No. 5, October 2008

M-m-t-(8)

Now, each path received by the array can be arranged as if the sig-nals from distinct paths were uncorrelated. The minimum-descrip-tion length, MUSIC, and Minimum Variance Beamforming algo-rithms can all be applied to R in order to enumerate and localize

each path or to form beams in a specified direction. From now on,the spatially smoothed R will be used in all calculations, and

will be denoted simply as Rn,.*

3.3 Beamforming

Beamforming is a technique for controlling the directivity ofthe array. Its objective is to increase the gain in the direction ofreception of the desired signals, and to decrease the gain in allother directions. Beamforming is a form of spatial filtering.

In this study, beamforming is used to extract the time-domainsignals coming from desired directions that are required to calcu-late the correlation coefficient with all directions of concern.Below, we compare different beamnforming methods, namelyminimum-variance, adaptive beamforming, and delay-and-sumnbeamforming, respectively.

3.3.1 Minimum-Variance Beamforming(MVB3F)

Minimum-variance beamnforming is the preferred adaptivearray-processing algorithm. It is based on constrained optimization[22]. Let a(9) represent an ideal wavefront incident on an array

from the 0 direction. The beamformer weight vector, w, isdesigned such that the signal coming from direction 0 is captured,while the power of signals coming from all other directions isminimized. This is achieved by calculating w with respect to theconstraint in Equation (9),

minfvw Ryyw), (9)

subject to Re IaH (9)w] = 1. This constrained minimization yields

[14]

(10)W HRa(9)waH(0) Ra(9)

IT .

Figure 2. The subarray configuration for spatial smoothing.

63

MIT mT-T-11 T -12T T T

hin practice, w relies on the sample covariance matrix of R Yand

the 9 direction. The time-domain signal propagating in this direc-tion is then denoted by

i=I(11)

Equation (11) is the time-series output of the Minimum VarianceDistortionless Response (MVDR) beamformer for the path indirection 9. Y(t) can be used to estimate the correlation coeffi-

cient. Note that in order to effectively extract Y(t) for a path at aparticular direction from coherent multipath signals, the correlationmatrix, Rn,, Iin Equation (10) is spatially smoothed.

3.3.2 Adaptive Beamforming

A matrix, Ak, of size M x (D - 1), that contains all wave-

fronts except a (9k), is formed by removing the mode vector

a(9k) due to the signal propagating from direction Ok from the

M x D matrix A. Assume Wk is the M x M orthogonal projec-tion matrix of Ak [20], i.e.,

Wk =I-L.Ak (Ak Ak)_ Ak (12)

where I is the M x M unit matrix. The time-domain signal propa-gating in the direction of Ok is then found from

y'k (t) =[Wk a (k)] HWk Y (). (13)

Clearly, Yk (t) is used to estimate the correlation coefficientsrelated to the path in direction Ok.

3.3.3 Delay-and-Sum Beamforming

Delay-and-sum beamforming is the oldest and simplest ofbeamnforming algorithms [22]. In this algorithm, each output of thearray antenna is shifted in time and added together. If the correcttime delay is chosen, a signal propagating in the desired directionwill be reinforced and noise will be suppressed.

If r. is the time delay to be added to the mth antenna to steerin a particular direction 9, the beam-formed signal Y(t) can bewritten as

M-'

Y~)=IWY.( .M=0

(14)

The time series YQt) thus obtained can be used to estimate thecorresponding correlation coefficient.

3.4 Correlation Coefficient

After the angle-of-arrival is estimated using MUSIC, beam-forming has to be applied to D angles that correspond to the peaksof the MUSIC pseudo-spectrum. The time series of the D paths,i.e., Y'1 (t), Y2 (Y.ID (t), can be obtained at the end of this proc-ess, and they can be utilized to calculate the correlation coefficient,

pyfor all the different signals propagating through D angles. The

correlation coefficient is an effective tool for deciding which signalbelongs to which source.

In the signal model, we assumed that signals emitted fromdifferent sources are uncorrelated, and signals emitted from thesame source are fully or partially correlated. Our solution to thelocalization problem is to use these properties of the sources. If thecorrelation coefficient is smaller than a threshold, then these sig-nals are assumed to be emitted from different sources. If the corre-lations coefficient is bigger, then these signals are assumed to beemitted from the same source. Clearly, the selection of the thresh-old is a crucial process. One can select it either as a constant [20],or define a method to adaptively estimate it [2 1]

3.5 Localization

In order to locate sources in the environment, at least twodirection-finding stations at distinct locations are required. Assumethe K and D represent the number of sources and number of pathsin two different direction-finding stations [20]. In. the first step, theangles of arrival of signals, {9A1,9A2,--0,AD} and

{9sI I 9B2, ... I9BD}IIthat are incident on direction-finding station Aand B, respectively, are estimated. Signals from each of thesedirections are obtained through beamnforming as{ YA1 (),yA2 (),...,yAD (t)} and {YBI (t),YB2 (),...,YBD (0)}.Correlation coefficients are calculated using these sets of signalsfor each signal pair of base-station A, as PALl]' and of base-sta-

tion B, as P&BiB] For station A, if the correlation coefficient,

PAiM]' is higher than a threshold value, paths from angles OAi or9 Aj correspond to multipath from the same source. To distinguishthe direct-path angle from the multipath angles, the power of thetime signals from 9 Ai and from 01Aj are calculated, and the path

angle with the highest power is hypothesized as the direct pathfrom that source. The same process is repeated for station B.

In the second step, angles of direct paths and signals fromthese angles are considered in a command station. In this case,{YAI (t),YA42(t),...YAK (t)} are compared with

{ Yai(t),YB2 (t).-YBK (t)} by calculating the cross correlationcoefficients of A with B. If the cross correlation coefficients arehigher than a threshold, then signals YAi (t) and Y~f (t) areconsidered to have originated from the same source. With these,the location of the ith source is found to be at the intersection pointof the path of 9 Aj from station A and the path of 9~i from sta-tion B.

64 IEEE Antennas and Propagation Magazine, Vol. 50, No. 5, October 200864

EWWtor2

20h' u43W

31h i8WSk hW 1

4U~ ,jpo

EmittwlJ

Fiue .Aneam l o rfecin .cnri.f. ae.ots0... W 10 2 1..0 1 hWW183 2

with signl rgntn fo 2sucs n nieto

~-100

-1 W -

Figre . n eam le f reletio senaioof avfrots0 20 40 arn 83 10 12 140 11 1D83S 200

Figue 8.Thcreeco-fuin yted anlesecru wi 5pths c(ignrtiong when Figure 10. The phase graph in the icoherent case for tonmuthepclirtosorewsath20psiinsoc/ne reflector.s)

IEEE Antennas and Propagation Magazine, Vol. 50, No. 5, October 2008 665

As seen above, correlation coefficients and power values areenough to determine the positions of the sources.

3.6 Calibration

Gain, phase, and mutual-coupling errors can be expressed asa weighted linear combination of antenna outputs without errors[17]. To formulate these errors, an M xM error matrix, C, isinserted into Equation (I), and an uncalibrated antenna outputM x 1 vector x is obtained as

x-CAs+n. (5

To compensate for the error caused by C, the antenna array is firstcalibrated using sources at known locations. To this end, eigen-decomposition is applied to the correlation matrix of a measuredarray output. If there is a single source incident on the array, theeigenvector with the highest eigenvalue gives the uncalibratedarray response wavefront, A,~ to a source with known location. A

calibration matrix, G, is then calculated by minimizing the dis-tance to A-GAe through least squares [17]. The calibration

matrix G is therefore chosen as acting as the inverse of C. Theleast-squares estimate of G is

G HA (AýAýH)_. (16)

The calibrated antenna output vector is then

y=Gx. (17)

This antenna output is then used in all of the algorithms describedabove.

4. Experiments

Experiments were carried out in an anechoic test chamber(ATC) at the National Research Institute of Electronics and Cryp-tology (UEKAE) of the Scientific and Technological ResearchCouncil of Turkey (TIJBITAK). The anechoic test chamber wasespecially designed to eliminate any reflection from the walls, sothat no undesired multipath effect was observed. This enabled thecontrol of the number of paths inside the anechoic test chamber.The transmitter and receiver antenna array inside the anechoic testchamber are shown in Figures 3 and 4. In Figure 3, three Schwarz-back log-periodic antennas were used to generate two distinctsource signals, in addition to one interference source. To realize thecoherent-path scenario, one source antenna and one 1.5 m x 2 mmetal reflector were used, as seen in Figure 4. The antenna arraywas on a turntable that could be rotated from 0' to 3600 degrees.

The setup of the transmitting antennas and processing units atthe receiving side are shown in Figure 5.

The uniform linear antenna array used in this experiment con-sisted of eight identical patch antennas with an inter-elementspacing of 15 cm. Receiving-mode dipole-antennas in the receiverarray played a vital role for determining emitter location. A set ofmeasurements was performed in order to obtain the characteristics

66

Figure 3. The inside appearance of the anechoic: test chamber(ATC) with two sources and one interference source.

Figure 4. The inside appearance of the anechoic test chamber(ATC) with one source and one reflector.

Figure 5. The general scheme of the experimental setup.

IEEE Antennas and Propagation Magazine, Vol. 50, No. 5, October 2008

Table 1. The antenna factors of the receiving-mode dipoleantenna.

Frequency

480 M1Hz500 MHz520 MHz

Antenna Factord(/r)30.9731.4435.25

Radiation Pattern (Azimruthi)

0 Structure: tt=91;

240 300

Figure 6. The radiation pattern of the receiving-mode dipoleantenna (azimuth).

120

180

Figure 7. The radiation pattern of the receivingantenna (elevation).

of these dipole-antenna arrays. These included areturn loss (dB), and the radiation pattern.

The antenna factors (the conversion factor frotfield to voltage) and the receiving capabilities of eatested in the GTEM cell (Gigahertz Transverse Eletcell), using the method proposed in [23]. The anteigiven in Table 1. The return loss of the antenna wausing an Agilent Network Analyzer in the anechoictwas -22 dB at the resonant frequency of 480 MHvariations in the frequency band from 480 MHz tomeasured to be about 0.5 dB. The phase angle of th1770 at the resonant frequency. To minimize all ph

It is relevant to mention here that setting up the controllablemultipath environment was not an easy task. It can be created onlyin a wide anechoic chamber, and this is expensive. Since we had asmaller-size anechoic test chamber, we conducted our experimentswith only two transmitter antennas, corresponding to two inde-pendent sources. In our experiments, two cases were analyzed: (1)Single source/two paths, and (2) two sources/two paths, with apoint-source interference in both cases. In the first case, one source

structure: . and one reflector were used. In Case 1, The signal source was con-nected to an antenna, which was assumed to generate the directpath. The other signal incident from the reflector was assumed tobe the indirect path. In Case 2, distinct source outputs were con-nected to two antennas, and both antennas were assumned to gener-ate direct paths.

The phase graphs of the experimental data for the two casesare given in Figures 9 and 10. The graph of the phase receivedfrom coherent sources seemed to follow a regular-linear pattern,which was not present in the phase graph for incoherent sources.

F-mode dipole These phenomena of the coherent responses can be interpreted asthe effect of constructive interference for coherent sources, whichwas not observed in the incoherent case. Any relationship related tothe incident angle of the paths cannot be extracted from the abovefigures. Only the coherency effect might be seen.

itenna factors, A performance analysis offers valuable information for the

choice of detection and estimation parameters, such as thresholds,

mn the received as well as for the choice of the algorithms. We repeated the:h antenna was experiments with the different beamnforming methods listed above.:troMagnetics-ma factors are 4.1 Determination of the Characteristics ofsmeasured by Correlation Coefficients for

est chamber. It Different Incoming Angles[. Retum-loss

500MNHz werete antenna was In the first experiment, data were acquired at four positions ofase and ampli- a turntable. At each position of the rotating turntable, signal wave-

IEEE Antennas and Propagation Magazine, Vol. 50, No. 5, October 2008 6

tude errors originating from receiver-system components, i.e.,antennas, cables, etc., the lengths of the cables and the feed loca-tions of the dipoles were adjusted according to the measurementsresults. The measured radiation patterns are given in Figures 6 and7.

The distance between the antenna array and the sources was5.5 m, which was enough to ensure the far-field effect [22]. Thesubarray size for spatial smoothing was five. The carrier frequencywas 500 MI~z, the signal power at the input of the log-periodicantenna was 10 dBm, the signal bandwidth was 20 kHz, and thesignal had FM modulation. "White" interference was temporallyproduced by a commercial noise generator. Array antenna outputswere down-converted to the baseband frequency, sampled at a rateof 100 kHz, and transferred to a computer for processing.

Array calibration against gain and phase errors and mutualcoupling was implemented throughout the experiment. Figure 8shows the improvement in angular spectrum due to array calibra-tion.

The localization of a point source requires at least two differ-ent direction-finding stations, i.e., two separate antenna arrays.Unfortunately, the anechoic test chamber used in our experimentsdid not provide enough space for a second receiver antenna arrayfor localization purposes. The localization algorithm given in Sec-tion 3.5 could only be applied outdoors.

67

Table 2. The estimated values of the correlation coefficients and propagation angles for thecoherent-signals case (no interference signal here).

Estimated IRealValues IValues

Estimated IRealValues IValues

EstimatedValues

RealValues

EstimatedValues

-W450 -42.50 -400 -39.10 -350 -34.3 300 -28.50

02ŽL 50 6.50 100 10.40 150 35.0 -30 20.20P -1 0.86 -1 0.92 -1 0.88 --1 0.84

Table 3. The estimated values of correlation coefficients and propagation angles for theincoherent-signals case (no interference signal here).

*I. p ~ P 7 P

EstimatedValues

RealValues

EstimatedValues

RealValues

EstimatedValues

RealValues

EstimatedValues

6 -450 I -43.20 -400 -f39.70 -350 -f34.50 -300 -29.2002 50 5.80 100 10.30 150 15.60 200 21.30

P 0 0.52 -0 0.47 -0 0.65 -0 0.75

fronts from two distinct angles were incident on the receiver array.Using MIUSIC, these two angles were estimated for each position.This procedure was carried out both for the single source/two pathsand double source/two paths scenarios. An average of the correla-tion coefficients was also estimated, using minimum-variancebeamforming. These correlation-coefficient estimates are presentedin Table 2 for coherent signals, and in Table 3 for non-coherentsignals. The most important result here was that the correlationcoefficient was approximately one in the case of multipath (seeTable 2), and stayed below a maximum of 0.75 when there was nomultipath (see Table 3). Therefore, the correlation coefficient canbe considered to be a suitable parameter for classify'ing signalsoriginating from the same source and signals originating from adifferent source. Note that the variances of the correlation coeffi-cients were observed to be relatively small in both cases.

These results demonstrated that the correlation-coefficientestimation technique presented in this work can be used in realapplications to decide whether or not the signals incident from twodistinct angles originated from the same source.

In a simpler experiment, we estimated the incident angles andcorrelation coefficients for two cases. In the first case, two sourceswere located at angles of -10' and 200 with respect to the antennaarray's normal. In the second case, one source and one reflectorwere located at angles of -l5* and 260, respectively. A 10 dBmnRE signal was applied to Schwarzback log-periodic source anten-nas. A 1.5 m x 2 m metal surface was used as a reflector. The dis-tance between the source antenna and the array antenna was 5.5 m.All measurements were done in an anechoic test chamber. Experi-mental data corresponding to these two cases can be found at thefollowing Web address: http://www.su6.itu.edu.tr/doa/ data.rar.

4.2 Performance Comparison ofBeamforming Methods

In order to estimate the correlation coefficient between sig-nals incident from distinct angles, the time-domain signal of eachpath should be accurately extracted via beamforming. We testedthree different beamforming algorithms: minirmum-variance beam-forming, adaptive beamforming, and delay-and-sum beamforming.

68

Ideally, when two signals are "correlated," this means that thecorrelation coefficient is approximately one. When two signals are'uncorrelated," this means that the correlation coefficient isapproximately zero. However, in practice, mid-range values for theestimated correlation coefficient occur frequently, especially in thecase of uncorrelated sources. The probability of correctly decidingthat the two paths are indeed from distinct sources is plottedagainst the threshold values in Figures 11 and 12. Figure I11 corre-sponds to the case where the paths were incident from -40' and100. In Figure 12, the paths were incident from -300 and 20'.

For the cases of Figures 11 and 12, the performance of thebearnforming algorithms was measured according to how low athreshold was required in order to correctly decide whether or notthe two paths were from distinct sources. In both figures, P, repre-sents the detection probability of incoherent paths, and minimum-variance beamnforming gave the best performance, requiringthresholds between 0.5 and 0.75, respectively. Note that in thesecases, there was no interference source in the media.

According to the results in Tables 2 and 3 and Figures 11 and12, we determined the threshold value to be 0.8 in our experiment.

4.3 Performance Analysis Depending onSignal-to-Interference Ratio (SIR)

In this experiment, white noise was temporally applied to thedirected transmitter antenna in the anechoic test chamber to pro-duce the interference signal. The performance of the algorithm wasmeasured through the receiver operating characteristics (ROC).

The receiver operating characteristics graph in Figure 13showed that two distributions were successfully separated when theSIR level was higher than -5 dB. This means that a source can beclassified as being correlated or uncorrelated at these SIR levels.Any SIR level lower than -5 dB was observed to degrade the per-formance of this application.

IEEE Antennas and Propagation Magazine, Vol. 50, No. 5, October 2008

RealValues

RealValues

0 0.2 0.4 0.6 0.8 1

0.

~0.0.

§ 0.

0.

0..2

0 0.2 0.4 0.6 0.8 1Threshold Threshold

Figure 11. The detection probability of uncorrelated paths as a Figure 12. The detection probability of uncorrelated paths as afunction of threshold values for tý = -401, 02 = 100 (without function of threshold values for 01 = -300, 02 = 200 (withoutinterference), interference).

8:'B

10

I.0 0.2 0.41 0.6 0.8

Pt (Prmbablhfty of False Deolsbn)

Figure 13. The receiver operating characteristics

graph for dif-

ferent SIR values.

IEEE Antennas and Propagation Magazine, Vol. 50, No. 5, October 2008 6

9 .. .... ... . .. ..

7.........7~~6 . . . . . .. .. . . .. .. . .. .. .. . .

.4........3.... . . .. . . ... . . . .

41 .. . . .. . .. . . .. .. . . .. . .. . .. .. . ...

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5. Conclusion

Actual experiments for the joint detection and localization ofmultiple emitters in a multipath environment have been presented.The main principle of this novel method is based on exploiting thecorrelation among the propagating signals. Although the impact ofcorrelation-based methods has been pointed out in previous studies[20], we believe these are the first published experiments that util-ize a correlation-based approach.

Several algorithms are applied in cascade. hin the first stage,the number of paths is estimated using minimum-descriptionlength. In the second stage, MUSIC is applied to estimate theangle-of-arrival of each path, given the number of paths from theminimum-description length. Next, beamformers are applied toestimate time series incident from each path. Finally, correlationcoefficients are calculated for each time series. These correlationcoefficients are in tumn compared to a threshold to decide whetheror not the paths correspond to the same source. The performance ofthe proposed approach was tested on an experimental system in ananechoic test chamber. Two cases were considered in the experi-ment: One case with two uncorrelated sources, and the other with asingle source and a reflector. The results led to the conclusion thatthe proposed approach is promising and quite effective in thelocalization of emitters in a multipath environment. The results ofthe experimental tests showed that minimum-variance beamform-ing can be used effectively as a beamforming algorithm for suchscenarios.

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IEEE Antennas and Propagation Magazine, Vol. 50, No. 5, October 2008