experimental results of novel doa estimation algorithms...

Research ArticleExperimental Results of Novel DoA Estimation Algorithms forCompact Reconfigurable Antennas

Henna Paaso1 Aki Hakkarainen2 Nikhil Gulati3 Damiano Patron3 Kapil R Dandekar3

Mikko Valkama2 and Aarne Maumlmmelauml1

1VTT Technical Research Centre of Finland Kaitovayla 1 PO Box 1100 90571 Oulu Finland2Department of Electronics andCommunications Engineering TampereUniversity of Technology PO Box 553 33101 Tampere Finland3Department of Electrical and Computer Engineering Drexel University 3141 Chestnut Street Philadelphia PA 19104 USA

Correspondence should be addressed to Henna Paaso hennapaasovttfi

Received 9 September 2016 Revised 18 December 2016 Accepted 13 April 2017 Published 24 July 2017

Academic Editor Sergiy A Vorobyov

Copyright copy 2017 Henna Paaso et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Reconfigurable antenna systems have gained much attention for potential use in the next generation wireless systems Howeverconventional direction-of-arrival (DoA) estimation algorithms for antenna arrays cannot be used directly in reconfigurableantennas due to different design of the antennas In this paper we present an adjacent pattern power ratio (APPR) algorithm for two-port composite rightleft-handed (CRLH) reconfigurable leaky-wave antennas (LWAs) Additionally we compare the performancesof the APPR algorithm and LWA-based MUSIC algorithms We study how the computational complexity and the performance ofthe algorithms depend on number of selected radiation patterns In addition we evaluate the performance of the APPR andMUSICalgorithms with numerical simulations as well as with real world indoor measurements having both line-of-sight and non-line-of-sight components Our performance evaluations show that the DoA estimates are in a considerably good agreement with the realDoAs especially with the APPR algorithm In summary the APPR and MUSIC algorithms for DoA estimation along with theplanar and compact LWA layout can be a valuable solution to enhance the performance of the wireless communication in the nextgeneration systems

1 Introduction

Direction-of-arrival (DoA) estimation algorithms usingcompact antenna sizes are of significant importance to nextgeneration wireless systems Directive adaptive antennas canestimate the DoA steer the beam to the desired directionand suppress the power in undesired directions to avoidinterference Thus they can greatly improve the spectrumreuse interference avoidance and device localization

Adaptive antennas can be divided into two categoriesphased arrays and reconfigurable antennas Convention-ally phased arrays use many antenna array elements toadapt the radiation pattern shape and beam direction [12] Antenna arrays usually require one receiver chain perantenna branch The cost usually increases with the numberof antenna elements because the array needs the samenumber of radio frequency (RF) high-power or low-noiseamplifiers as the elements in traditional antenna arrays [3]

Particularly for digital beamforming antennas the samenumber of frequency converters RF amplifiers and digital-to-analog (DA) or analog-to-digital (AD) converters areneeded This leads to high-power consumption and highfabrication cost In contrast to multielement antenna arraysreconfigurable antennas do not need the multiple antennaelements or feeding networks [4] In this paper we presenta certain type of compact reconfigurable antennas namelythe composite rightleft-handed (CRLH) leaky-wave antenna(LWA) [5] The reconfigurable LWAs have many advantageslow manufacturing cost low DC power consumption full-space beam scanning using significantly less printed circuitboard space and absence of extra RF circuitry By consideringthese advantages especially compactness and beamsteeringCRLH-LWAs have a significant potential to be used in DoAsystems

In the context of conventional antenna arrays DoAestimation algorithms have been extensively researched in

HindawiInternational Journal of Antennas and PropagationVolume 2017 Article ID 1613638 13 pageshttpsdoiorg10115520171613638

2 International Journal of Antennas and Propagation

1 2

0∘

RF port 1 RF port 2

Stored M receivedsignals

DoA estimationalgorithms

Figure 1 System model

the literature [6ndash10] However these algorithms cannotbe used directly in CRLH-LWAs because of the inherentdesign and operation of the LWAs versus multielementantenna arrays An LWA has only one port and thus ithas a single observation available at each sampling incidentunlike in multielement antenna arrays where signals canbe detected from different elements of the antenna array[11] For this reason DoA estimation algorithms for LWAsrequire that the LWA receives the transmitted signal 119872times through119872 different radiation patterns as illustrated inFigure 1

There are only a limited number of papers where DoAestimation algorithms are introduced for LWAs In [12 13]we preliminarily introduced a modified multiple signal clas-sification (MUSIC) algorithm for LWAsTheCRLH-LWAhasthe inherent difference in the design Our modified MUSICalgorithm uses 119872 received signals each obtained with adifferent radiation pattern and measured from two antennaportsThen a correlationmatrix can be formed by using these119872 received signals We presented experimental results of aLWA-based MUSIC algorithms in [14] where we introducedthe performance of the MUSIC and power pattern cross-correlation (PPCC) algorithms in real wireless multipathenvironment However the paper presents only results forone radiation pattern configuration and does not study howdifferent configurations affect the performance of the algo-rithms Additionally an adjacent pattern power ratio (APPR)algorithm and the complexity analysis of the algorithms arenot presented in [14] Similar work for DoA estimation hasalso been presented independently in [15 16] that use theMUSIC algorithm forCRLH-LWA In [15] only experimentalresults are introduced and the authors do not present how theMUSIC algorithm can be built up using LWAs Additionally[15 16] present only experimental results of the MUSICalgorithm in an anechoic chamber In addition [17 18] intro-duce reactance domain MUSIC [17] and unitary MUSIC [18]algorithms for electronically steerable parasitic array radiator(ESPAR) antennas In [19] APPR algorithm is introduced

for the ESPAR antenna The APPR algorithm is a simpleDoA estimation algorithm which measures signal powersfrom119872 different directions and chooses the radiation patternwith the maximum signal power Then the adjacent patternpower ratios with respect to the maximum signal powerpattern are calculated and theDoA is estimated by comparingthese ratios with the predefined ratios from a look-up table(LUT) The performance of the algorithm is presented byusing computer simulations and experiments in an anechoicchamber

In this paper we apply the APPR DoA estimationalgorithm for CRLH-LWA Additionally we compare theperformance of the APPR algorithm with the performanceof the LWA-based MUSIC algorithm The computationalcomplexity of the APPR algorithm is much smaller thanthat of the MUSIC algorithm without much degradation inestimation accuracy Unlike in our previous studies [12ndash14]and other DoA estimation techniques in the literature [19]we now study how the computational complexity and theperformance of the algorithms depend on the number ofselected radiation patterns in different kinds of environmentstheoretical additive white Gaussian noise (AWGN) channeland a real world indoor multipath wireless environmentwith both line-of-sight (LoS) and non-line-of-sight (NLoS)components

This paper is organized as follows Section 2 introducesa detailed description of the DoA estimation algorithmsfor a compact CRLH-LWA Section 3 presents shortly theCRLH-LWA design Numerical and complexity analysis andexperimental results of the DoA estimation algorithms arepresented in Section 4 Finally conclusions are drawn inSection 5

2 CRLH-LWA-Based DoAEstimation Algorithms

In this section we introduce an APPR DoA estimation algo-rithm for LWAs Additionally we present briefly a modifiedsingletwo-port MUSIC algorithms [12] whose performancewe compare with the APPR algorithm The first algorithm isbased on evaluating the received powers for different voltagesets and the second algorithm is variant of the popularMUSIC algorithm [6] that we have modified to work withLWA In the following sections 120579 denotes the DoA and 120579 anestimate thereof

21 SingleTwo-Port MUSIC Algorithm Traditionally theMUSIC algorithm [6] defines the spatial correlation matrixusing the signals received by multiple antenna elements Inthis subsection we present how the spatial capabilities of thetraditional antenna array can be virtually formulated with theCRLH-LWA and how the correlation matrix can be definedwhen using the two-port LWA

Firstly we have to collect the same transmitted signal119906(119896) 119872 times while the LWA switches between 119872 differentradiation patterns Thus we can recreate spatial diversitydue to 119872 observations of the same signal but with different

International Journal of Antennas and Propagation 3

beams With the LWA the 119872 times 1 received signal vector y(119896)can be expressed as

y (119896) = a (120579) 119906 (119896) + z (119896) (1)

where 119896 denotes the received symbol index z(119896) is an119872 times 1AWGN vector where the elements have variance equal to 1205902and a(120579) is the119872times 1 steering vector The119898th element of thesteering vector can be defined as

119886푚 (120579)

= radic119866耠푚푁

sum푛=1

119868푛 exp [119895 (119899 minus 1) 1198960119889 (sin (120579) minus sin (120579푚))] (2)

where119898 = 1 119872119873 is the number of cascaded unit cellsand

119866耠푚 = 119866푚(sum푁푛=1 119868푛)

2 (3)

where 120579 is the angular direction of the received signal 120579푚is the main beam direction of the LWA with control voltageset 119898 119868푛 = 1198680exp[minus120572(119899 minus 1)119889] is an exponential functionwith a leakage factor 120572 and 119866푚 is the measured antenna gain(in linear scale) of set 119898 The initial value of the exponentialfunction 1198680 = 1 with structure period 119889 [5]

The MUSIC algorithm makes eigenvalue decompositionof the signal covariancematrix and uses a subspace algorithmto estimate DoA Firstly we have to estimate the covariancematrix from the received signals The estimated covariancematrix can be expressed as

R푦푦 = 1119873s

푁s

sum푘=1

y (119896) ydagger (119896) (4)

where 119873s denotes the number of samples and the Hermitiantranspose of y is denoted as ydagger Then the eigenvalue decom-position (EVD) of R푦푦 can be represented as

R푦푦 = E푠Λ 푠Edagger푠 + E푛Λ 푛Edagger푛 (5)

where E푠 = [e1 e2 e퐿] includes the estimated eigen-vectors for the signal subspace Λ 푠 = diag[1 2 퐿]denotes a diagonal matrix of the largest estimated eigenval-ues and 119871 is the number of incident sources AdditionallyE푛 = [e퐿+1 e퐿+2 e푀] is the noise subspace matrixand Λ 푛 = diag[퐿+1 퐿+2 푀] denotes the diagonalmatrix of 119872 minus 119871 noise eigenvalues Finally the MUSICpseudospectrum can be generated as

119875MUSIC (120579) = adagger (120579) a (120579)adagger (120579) E푛Edagger푛a (120579)

(6)

The estimated direction-of-arrival (DoA) is the angle wherethe pseudospectrum 119875MUSIC(120579) attains its maximum that is

120579MUSIC = argmax휃

119875MUSIC (120579) (7)

The MUSIC algorithm is limited to uncorrelated signalsThe estimated covariance matrix R푦푦 is nonsingular as longas the incident signals are not highly correlated [20] Whenthe incident signals are highly correlated signals or signalswith a low SNR the performance of the MUSIC algorithmsreduces or the algorithm fails even completely [21] Thusthe MUSIC algorithm has problems when determining thenumber of impinging source that is it cannot divide thesignal subspace and noise subspace correctly and thus itis not able to estimate the spatial spectrum correctly Thisproblem can be solved by using spatial smoothing techniquessignal feature vector technique and frequency smoothingtechniques among others However these techniques are outof the scope of this paper

22 Adjacent Pattern Power Ratio Adjacent pattern powerratio is introduced for ESPAR antennas in [19] The APPRalgorithmcalculates the adjacent power pattern ratio betweenthe maximum received power pattern and the adjacentpatterns In this paper we show how to apply the APPRalgorithm to LWAs and show how configuring the antennaradiation patterns for signal observations can impact theperformance of the algorithm which has not been furtherevaluated in [19] We first calculate the received power119875푚 from 119872 different directions and normalize each poweryielding the gain-normalized powers 119875norm

푚 = 119875푚119866푚Then the radiation pattern that gives the maximum receivedpower is selected Thereafter the adjacent pattern powerratio between the adjacent pattern to the selected patternis calculated Firstly the APPR ratio is calculated from themeasured radiation patterns in an anechoic chamber TheAPPR can be presented as

Γ푚+ (120579) =119875norm푚 (120579)

119875norm푚+1 (120579) (8)

Γ푚minus (120579) =119875norm푚 (120579)

119875norm푚minus1 (120579) (9)

Equation (8) tells that when the DoA falls into the right sideof the 119898th pattern 119875norm

푚+1 (120579) gt 119875norm푚minus1 (120579) as illustrated in

Figure 2 Additionally (9) tells that when the DoA falls intothe left side of the 119898th pattern 119875norm

푚minus1 (120579) gt 119875norm푚+1 (120579) These

ratios for the selected 120579 range are calculated and stored intoan LUTbeforehand to reduce run-time computationsHencethe DoA is to be estimated over the 120579 range The length of 120579range 119869 depends on how radiation pattern configuration isselected These searching areas are illustrated as a dotted linein Figure 2 Secondly the APPR is measured for the receivedpower and it can be presented as

Γ푚+ (120579) =norm푚 (120579)

norm푚+1 (120579)

Γ푚minus (120579) =norm푚 (120579)

norm푚minus1 (120579)

(10)

Finally we compare these adjacent pattern power ratiosThe selection of Γ푚+푚minus is defined in the following way if


0 5005

055

06

065

07

075

08

085

09

095

1

Angle (degrees)

Nor

mal

ized

pow

er

minus50

Pm

Pm+1

Pmminus1

Figure 2 Theoretical radiation patterns

norm푚+1 (120579) gt norm

푚minus1 (120579) we compare Γ푚+(120579) and Γ푚+(120579) Ifnorm푚+1 (120579) lt norm

푚minus1 (120579) we compare Γ푚minus(120579) and Γ푚minus(120579) Hencethe estimated DoA can be defined as

120579

=

argmin 10038161003816100381610038161003816Γ푚minus (120579) minus Γ푚minus (120579)10038161003816100381610038161003816 if norm푚+1 (120579) lt norm

푚minus1 (120579) argmin 10038161003816100381610038161003816Γ푚+ (120579) minus Γ푚+ (120579)10038161003816100381610038161003816 if norm

푚+1 (120579) gt norm푚minus1 (120579)

(11)

The computational complexity and the performance ofthe algorithm depend on the number of received directionsThese options are researched in Section 4

3 Antenna Design

TheAPPR and MUSIC algorithms were designed to performthe DoA estimation using reconfigurable CRLH-LWA Theleaky-wave antenna is a traveling-wave antenna [5] Asopposed to conventional resonating-wave antennas LWAsleak out energy progressively as the wave travels along thewaveguide structure The main radiation beam of the LWAis normal to the plane of the antenna and can be in generaldirected by changing the electrical properties of the radiatingelements

The introduced LWAconsists of 12 cascadedmetamaterialCRLH unit cells which are populated with two varactordiodes in series and one in shunt configuration The physicalsize of the antenna is 156mmndash38mm By changing the twoDC bias voltages across the varactors the antenna is ableto steer the main beam from broadside to backward andforward directions Due to the practically symmetric antennastructure the ports of the antenna have symmetric radiationproperties with respect to the broadside direction The beamsymmetry is illustrated in Figure 1 where 1205791 = minus1205792 Theused LWAs are able to steer their main beam orientationapproximately from minus50∘ to +50∘ The CRLH-LWAs wereadjusted to operate within the entire 24GHzWiFi bandThemeasurements of the radiation patterns were measured at the

Table 1 Measured LWAmain beam directions and gains

Sector 1 2 3 4 5 6Main beam direction 120579푚 (∘) plusmn0 plusmn8 plusmn18 plusmn28 plusmn39 plusmn47Gain 119866푚 (dB) 50 51 56 58 49 35

Table 2 Selection of radiation patterns in DoA estimation cases

Case Main beam directions (∘)minus47 minus39 minus28 minus18 minus8 0 8 18 28 39 47

Case 1 x x x x x x x x x x xCase 2 x x x x x xCase 3 x x x x xCase 4 x x x xCase 5 x x x

frequency of 246GHz in the anechoic chamber facility Themeasuredmain beam directions and the corresponding gainsare presented in Table 1

4 Numerical and ComplexityAnalysis and Experimental Results ofDoA Estimation Algorithms

To verify and validate the performance of the proposedDoA estimation algorithms for the LWA we perform severalsimulations to numerically evaluate the performances andconduct experimental measurements which are performedin an indoor multipath environment We research the effectof the number of radiation patterns on the accuracy of theestimatedDoAsWe particularly consider different choices ofthe radiation patterns for estimating the DoA In Table 2 dif-ferent radiation pattern choices are shown The first columnin this table shows cases 1 to 5 that correspond to differentchoices for the number of radiation patterns and their mainbeam directions For each case we estimate the DoA usingonly the radiation patterns which are identified by cross-marks

41 Simulation Setup andNumerical Analysis Firstly we havestudied how the selection of the radiation pattern impactson the performance of the DoA estimation algorithms Inthe simulations we formulate the received signal accordingto the signal model (1) We generate orthogonal frequency-division multiplexing (OFDM) with 48 active subcarriers asthe physical signal waveform We use the same radiationpatterns as in our experimental measurements The LWAis chosen to have 6 radiation patterns with the 12 mainbeam directions as shown in Table 1 In all estimation cases100 complex in-phasequadrature (IQ) samples are used toestimate the DoA The estimations are done prior to fastFourier transform (FFT) processing The direction of theincoming signal is steered from minus54∘ to 54∘ with a resolutionof 1∘ The estimation results are averaged over 1000 signalrealizations for each estimated DoA

In Figure 3 the root-mean-squared error (RMSE) of theMUSIC and APPR algorithms as a function of the SNR is


0 2 4 6 8 10 12 14 16 18 20SNR (dB)

0123456789

1011

RMSE

(deg

rees

)

APPR case 1APPR case 2APPR case 3APPR case 4APPR case 5

MUSIC case 1MUSIC case 2MUSIC case 3MUSIC case 4MUSIC case 5

Figure 3 RMSE of the APPR and MUSIC algorithms as a functionof the SNR

presentedThe plot shows results for cases 1ndash5 FromFigure 3it can be noted that the MUSIC algorithm works better thanthe APPR algorithm However if the SNR is higher than10 dB the RMSE difference between the algorithms in case 3is lower than 05∘ It can be observed that case 1 gives clearlythe best result for the MUSIC algorithm Furthermore theMUSIC algorithm has less performance difference betweendifferent cases than the APPR algorithm For example ifthe SNR is higher than 10 dB the differences between thedifferent cases are less than 03∘ for the MUSIC algorithm Itcan be also seen that the APPR algorithm works reasonablywell in all cases except in case 5 Cases 2-3 in turn givethe best performances in all SNR values and their RMSEsare almost the same Moreover we can see that the RMSEis significantly large for case 5 Additionally case 1 worksworse than cases 2ndash4 The reason for these observations isthat the radiation patterns cover very well the estimationarea in cases 2ndash4 especially in case 3 as seen in Figure 4The radiation patterns are not too near to or too far fromeach other However in case 1 the radiation patterns are toonear whereas they are too far in case 5 (as also visible inFigure 5) causing higherDoA estimation errors for theAPPRalgorithm

Figures 6 and 7 depict the simulated performance of theAPPR and MUSIC algorithm as a function of the DoA whenthe SNR is fixed to 10 dB It is visible in Figure 6 that theRMSE is the smoothest in cases 2-3 We can also notice thatthe configuration of the radiation pattern should be selectedcarefully for the APPR algorithm If we selected five radiationpatterns as in case 3 instead of the 11 radiation patterns asin case 1 the overall signal storing time would be halvedHowever the estimation DoA range increases when usingfewer radiation patterns because of the increased gap betweenthe adjacent radiation patterns However we do not needto calculate the power of the signal so many times if fewerradiation patterns are selected Furthermore the amount of

0 5002

03

04

05

06

07

08

09

1

Angle (degrees)

Nor

mal

ized

pow

er

Pm

Pm+1

Pmminus1

minus50

Figure 4 Measured radiation patterns for case 3

0 500

01

02

03

04

05

06

07

08

09

1

Angle (degrees)

Nor

mal

ized

pow

er

minus50

Pm

Pm+1

Pmminus1


data to be processed offline and online will be decreased iffewer radiation patterns are selected Based on the results inFigure 7 for the MUSIC algorithm we notice that the RMSEbehaves similarly in all cases and only the absolute level ofthe RMSE is varying in different cases The highest numberof radiation patterns provides again the best performanceas expected From the results we can say that the selectionof the number of radiation patterns is a trade-off betweenthe desired performance and computational complexity InSection 42 computational complexity is analyzed in moredetail

42 Computational Complexity Analysis In this section weanalyze the computational complexity of the singletwo-portMUSIC and APPR algorithms We define the complexity ofthese DoA estimation algorithms in terms of basic operations[22] that is additions and subtractions multiplications and


0 500

05

1

15

2

25

3

35

4

45

RMSE

(deg

rees

)

DoA (degrees)

Case 1Case 2

Case 3Case 4

minus50

Figure 6 RMSE of the APPR algorithm as a function of the DoA

0 500

02

04

06

08

1

RMSE

(deg

rees

)

DoA (degrees)

Case 1Case 2

Case 3Case 4

minus50

Figure 7 RMSE of the MUSIC algorithm as a function of the DoA

divisions and refer to them as ADD MUL and DIV respec-tively In theAPPRalgorithmcase part of the calculations canbe calculated offline and stored into the LUT in which casethey do not need to be calculated in real time The analysisis presented in Table 3 There 1198690 is the number of the DoAestimation points and is here equal to 109∘ (minus54∘ to 54∘ with1∘ resolution) In addition 119869 is the length of the specificrange of 120579 for the APPR algorithm which depends on howthe radiation pattern configuration is selected as explainedin Section 22 Selecting 119872 = 11 results in 119869 = 15∘ whereasfor 119872 = 5 we get 119869 = 31∘ Regarding the computationalcomplexities the covariance matrix of the MUSIC algorithmhas 119873푠1198722 multiplications and (119873푠 minus 1)1198722 additions andsubtractions Additionally the EVD has the complexity of

RX5

TX2

RX6

TX1

RX3 TX3RX4 RX2

RX1

2398

m

1670m

1875m

Stairs

1560

m

1m

ReceiverTransmitter

Figure 8 Layout of the measurement lobby area and the locationsof the TXs and RXs

Table 3 The computational complexity analysis

Algorithm MUSIC APPRMUL 1198723 +1198722(119873푠 + 21198690) 2119872119873푠DIV 1198690 2ADD 1198722(119873푠 minus 1 + 21198690) minus 21198690119872 119869 +119872(119873푠 minus 1)LUT mdash (1198721198690)MUL

(2119872119869 +1198721198690)DIV

1198723 and the calculations of the MUSIC spectra need 119869021198722multiplications 1198690 divisions and 1198690(21198722 minus 2119872) additionsand subtractions The APPR algorithm in turn needs 2119872119873푠multiplications 2 divisions and 119869 +119872(119873푠 minus 1) additions andsubtractions In addition we need 1198721198690 multiplications and2119872119869+1198721198690 divisions that are calculated offline and stored intoa LUT It is clear that the APPR algorithm has much lowercomputational complexity than the MUSIC algorithm

43 Measurement Setup The performance of the LWA-basedAPPR and MUSIC DoA estimation algorithms is evaluatedusing experimental measurements performed in a multi-path indoor environment The experiments are done in thepremises of theDrexelUniversityThe indoor setup is a closedlarge lobbywith stairs and glasswalls In this lobby setting themeasured signals experience both LoS andNLoS componentsdue to severe multipath between the transmitters (TXs) andthe receivers (RXs) The layout illustrated in Figure 8 showsthe arrangement of TXs and RXs in the described indoorenvironment In our measurements we used three TX nodesand six RX nodes


In the RX nodes the reconfigurable two-port CRLH-LWAs were used and the three TX nodes were equippedwith two standard omnidirectional antennas The lobbydimensions and the locations of the transceiver antennas arecarefully measured with a measuring tape In Figure 8 theorange arrows show the broadside direction 120579 = 0∘ of the RXLWAs We made measurements in such a way that only oneTX-RX pair was active at a timeThus we needed to ensure ajustness between different transmission links by transmittingthe same data over all linksWemeasured all the TX-RX pairsbut the data with TX3 were studied only for RX1ndashRX3 andRX5-RX6 because the TX3-RX4 pair was out of the spatialscanning directions

In our measurement campaign each transceiver usesa field-programmable gate array (FPGA) based softwaredefined radio platform which is called wireless open-accessresearch platform (WARP) v3 [23] Each WARP board wasconnected to its own antenna and to a centralized controllingsystem which centrally synchronize all the nodes controlantenna beam directions and collect all the measurementdata We used OFDM signals with the total of 64 sub-carriers where 48 subcarriers were used for loading datasymbols 4 for carrier frequency offset (CFO) correctionand 12 empty subcarriers After each transmission all theRXs stored 300 packets each containing 5420 binary phaseshift keying (BPSK) complex symbols and then the antennabeam direction was steered for the next reception The TXpower of the TX nodes was set to 15 dBm Additionally weused 119889 = 13 cm and 120572 = 1 in the measurement processingfor the MUSIC algorithm Furthermore we assume thatonly one signal is received in the RX and thus we set119871 = 1

All the measured data were saved for offline postpro-cessing with the DoA estimation algorithms introduced inSection 2 The DoA estimation was done before the FFTFurthermore the measurements were carried out in theWiFifrequency range of 2452GHzndash2472GHz as the leaky-waveantennas (LWAs) were calibrated for this range Since themeasurements were carried out at open WiFi frequencieswith various WiFi access points in the close vicinity all WiFitraffic acts directly as cochannel interference making themeasurement environment very challenging Additionallythis WiFi traffic and passersby are not stationary during themeasurements

44 Experimental Results Based on Measurements The aimof our experiment measurement is to demonstrate the DoAestimation capabilities for LWAs using the algorithms whichwere introduced in Section 2 Based on the simulation resultswith the AWGN channel cases 2-3 give the best RMSE resultsfor the APPR algorithm and case 1 gives the best resultsfor the MUSIC algorithm and thus we analyzed these threecases also in a real multipath environment Here we presentalso the results of the power detector (PD) algorithm as areference because the APPR algorithm is based on these PDresults The summary of the results for the APPR MUSICalgorithms and PD is presented in Tables 4ndash12 DoA estima-tion results for TX1-RX6 TX3-RX6 and TX2-RX6 pairs are

Table 4 DoA estimation results for TX1 with PD APPR andMUSIC algorithms in case 1

120579real (∘) PD APPR MUSIC120579 (∘) 120598 (∘) 120579 (∘) 120598 (∘) 120579 (∘) 120598 (∘)

RX1 minus3 8 11 12 15 25 28RX2 12 minus18 minus30 minus21 minus33 minus16 minus28RX3 3 8 5 8 5 0 minus3RX4 2 minus8 10 minus13 minus15 0 minus4RX5 minus9 minus28 minus19 minus33 minus24 1 10RX6 22 28 6 22 0 28 6RMSE 160 189 168



RX1 minus39 minus47 minus8 minus41 minus2 minus54 minus15RX2 minus5 minus28 minus23 minus24 minus19 minus1 minus4RX3 22 0 minus22 4 minus18 18 minus4RX4 3 8 5 6 3 0 minus3RX5 14 8 minus6 8 minus6 1 minus13RX6 49 39 minus10 39 minus10 54 5RMSE 144 118 87



RX1 35 47 12 42 7 48 13RX2 62 47 minus15 41 minus21 54 minus8RX3 minus57 minus47 10 minus47 10 minus54 3RX5 minus34 minus47 minus13 minus44 minus10 minus54 minus20RX6 minus1 minus28 minus27 minus32 minus31 minus17 minus16RMSE 165 181 134

also illustrated in Figures 9ndash11 for three considered cases Inthe figures the first column (a) illustrates ameasurement casewhen all methods estimate very well the DoA of the receivedsignalThe second column (b) presents a measurement whenthe APPR algorithm and PD fail to estimate the DoAThe lastcolumn (c) illustrates the measurement case when the APPRalgorithm estimates very well the DoA while the MUSICalgorithm fails the DoA estimation

441 Case 1 Based on the results of Tables 4ndash6 the totalRMSE calculated over all TX cases is 139∘ for the PD 98∘for the APPR algorithm and 136∘ for the MUSIC algorithmin case 1 If the DoA estimation error is large in the PD casethe APPR algorithm cannot estimate the DoA accurately asillustrated in Figure 9(b) It can be noticed that the APPRhas the best performance if we compare overall results Aswe explained earlier in Section 21 the MUSIC algorithmworks well only for uncorrelated signals In our experimental




RX1 minus3 8 11 1 4 19 22RX2 12 minus28 minus40 minus18 minus30 minus4 minus16RX3 3 8 5 1 minus2 0 minus3RX4 2 minus8 10 minus17 minus19 minus1 minus3RX5 minus9 minus28 minus19 minus19 10 1 10RX6 22 28 6 22 0 38 16RMSE 193 152 136



RX1 minus39 minus47 minus8 minus39 0 minus54 minus15RX2 minus5 minus28 minus23 minus21 minus16 13 18RX3 22 28 6 35 13 36 14RX4 3 8 5 3 0 0 minus3RX5 14 8 minus6 17 3 1 minus13RX6 49 47 minus2 37 minus12 37 minus12RMSE 108 98 133






RX1 minus3 minus18 minus15 minus8 minus5 minus4 1RX2 12 minus18 minus30 minus26 38 minus13 minus25RX3 3 0 minus3 8 5 32 29RX4 2 minus18 10 minus9 minus11 minus2 minus4RX5 minus9 minus39 minus30 minus28 minus19 minus19 minus10RX6 22 18 minus4 26 4 17 minus5RMSE 202 182 164

measurements the measured signals experience both LoSand NLoS components due to severe multipath betweenthe TX and the RX in the indoor environment Multipathsignals are mutually correlated and the signal covariancebecomes rank-deficient [21] Consequently the eigenvalue



RX1 minus39 minus39 0 minus32 7 minus54 minus15RX2 minus5 minus18 minus13 minus26 minus21 minus3 2RX3 22 0 minus22 6 16 minus15 minus37RX4 3 minus18 21 minus11 minus14 minus1 minus4RX5 14 0 minus14 9 minus5 6 minus8RX6 49 39 minus10 32 minus17 54 5RMSE 152 145 168



RX1 35 39 4 35 0 54 19RX2 62 39 minus23 29 33 54 minus8RX3 minus57 minus39 18 minus42 15 54 111RX5 minus34 minus39 minus5 minus34 minus34 minus54 minus20RX6 minus1 minus39 minus38 minus29 minus28 minus6 minus5RMSE 216 205 513

decomposition of the signal covariance fails to split the signaland noise subspaces That is the reason why the resultsof the MUSIC algorithms are so much poorer in indoorenvironments than in the AWGN channel environmentWhat is also interesting is that we can notice multiple peaksin the PD plots in Figures 9(b) and 9(c) and the power of thesignal is noticeably lower than in Figure 9(a) The peaks aremost likely affected by the multipath effects like reflectionsfrom the walls and stairs passersby or WiFi traffic actingdirectly as cochannel interference in these measurementsFor the PD it is clear that multipath or other signals resultin additional peaks in the figures In cases where the PDestimator has no high peaks in the results or there are two ormore low peaks or the received signal power level is low theMUSIC algorithm has difficulties in estimating the DoAThissomewhat flat response is again most probably affected by aweak LoS component as well as rich scattering environmentcausing multiple impinging NLoS signal paths

There are large differences in the DoA estimation accu-racy in different receiver locations The estimated DoAs arein good agreement with the real DoAs in the several APPRalgorithm cases particularly in TX1-RX3 TX1-RX6 TX2-RX1 and TX2-RX4 cases The MUSIC algorithm has alsogood accuracy in these TX-RX pairs except the TX2-RX1caseThis is clearly the worst result for theMUSIC algorithmas seen in Figure 9(c) and is most probably affected byharmful reflections from the stairs which are made of metalconcrete and glass

442 Case 2 Based on the results of Tables 7ndash9 the totalRMSE calculated over all TX cases is 150∘ for the PD 102∘for the APPR algorithm and 148∘ for the MUSIC algorithm


25 30 350

1

2

0

0

2

4

minus40 minus20 0 20 40

Angle (degrees)

Angle (degrees)

Angle (degrees)

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

minus50 0 50

(a)

0

1

2

minus20 0 20

Angle (degrees)

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

0

1

2

APP

R

minus35 minus30 minus25

Pseu

dosp

ectr

um (d

B)

Angle (degrees)minus50 0 50

(b)

minus20 0 20

Angle (degrees)

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

0

1

2

APP

R


0

2

4

Pseu

dosp

ectr

um (d

B)


(c)

Figure 9 DoA estimation results with PD APPR and MUSIC algorithms in case 2 with different TX-RX pairs (a) TX1-RX6 120579real = 22∘ (b)TX3-RX6 120579real = minus1∘ and (c) TX2-RX1 120579real = minus39∘

in case 2 It can be seen that there is not a significantperformance difference between case 1 and case 2 From thetables we can notice again that the estimation error is rathersmall smaller than 11∘ in many TX-RX pairs in severalcases However there are also many larger DoA estimationerrors which are most likely caused by severe reflections andother multipath effects as explained earlier and illustrated inFigure 10(b)

443 Case 3 Based on the results of Tables 10ndash12 the totalRMSE calculated over all TX cases is 141∘ for the PD112∘ for the APPR algorithm and 321∘ for the MUSIC

algorithm in case 3 It can be noticed that the differenceof the performance is not big between cases 1ndash3 for theAPPR algorithm In particular the difference of the RMSEis only 14∘ between case 1 and case 3 The results show thatwe can achieve almost the same performance using fewerradiation patterns thus the overall signal storing time will bedecreased However the adjacent radiation patterns cannotbe too far away from each other as seen in Section 41Regarding theMUSIC algorithm the RMSEs are significantlyhigher in case 3 when compared with cases 1-2 We canconclude that the MUSIC algorithm does not work verywell if the number of radiation patterns is only five in our


20 300

5

10

15

0

2

4

6


Angle (degrees)

minus50 0 50

Angle (degrees)

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

(a)

0

10

20

0

5

10

minus30 minus20

minus50 0 50

Angle (degrees)

minus20 0 20

Angle (degrees)

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

(b)

0

2

4

6

0

2

4

minus50 minus40

minus50 0 50

Angle (degrees)

Angle (degrees)

minus20 0 20

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

(c)

Figure 10 DoA estimation results with PD APPR andMUSIC algorithms in case 2 with different TX-RX pairs (a) TX1-RX6 120579real = 22∘ (b)TX3-RX6 120579real = minus1∘ and (c) TX2-RX1 120579real = minus39∘

real world measurements We can also notice that the totalRMSE difference between case 1 and case 2 is only 12∘ fortheMUSIC algorithm If fewer radiation patterns are selectedthe complexity of the MUSIC algorithm will be reducedsignificantly as explained in Section 42 To conclude theselection of the number of radiation patterns is a trade-off between the desired performance and computationalcomplexity

444 Discussion of the Experimental Results Based onour observations from the experimental results it seems

that the APPR algorithm works better in a real multipathenvironment than the MUSIC algorithm In our measure-ments the measured signals experience both LoS and NLoScomponents due to severe multipath between the TX andthe RX in the indoor environment Due to the correlatedmultipath signals the eigenvalue decomposition of the signalcovariance cannot split the signal and noise subspaces thusthe RMSE increases significantly when compared with theAWGN channel simulations In case 1 the total RMSE is38∘ less with the APPR algorithm than with the MUSICalgorithm It can be concluded that the performance gap


0 50

minus20 0 20

Angle (degrees)

10 20 30Angle (degrees)

Angle (degrees)minus50

0

01

005

Nor

mal

ized

pow

er o

f PD

0

400

200APP

R

0

2

4

6

8

Pseu

dosp

ectr

um (d

B)

(a)

0 50Angle (degrees)

minus50

Angle (degrees)minus50 minus40 minus30

minus20 0 20

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

0

10

20

APP

R

0

2

4

6

Pseu

dosp

ectr

um (d

B)

(b)

0

10

20

0 50Angle (degrees)

minus50


minus20 0 20

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

R

0

2

4

6Ps

eudo

spec

trum

(dB)

(c)


between these two algorithms increases when the number ofradiation patterns is decreased

The resolution of both the algorithms is the same thatis 1∘ However the computational complexity of the algo-rithms is significantly different as explained in Section 42The APPR algorithm has clearly lower computational com-plexity than MUSIC algorithm because the algorithm doesnot use eigenvalue decomposition We can conclude thatboth algorithms especially the APPR algorithm and theconsidered LWA structure enable reliable DoA estimationdespite very challenging demonstration and measurementenvironment

In ourmeasurement we have assumed particularly in theMUSIC algorithm case that only one signal is received ineach receiverWehave noticed that there aremultiple peaks inthe PDplots It is clear thatmultipath or other signals result inadditional peaks in the figures These interference signals areone reason why the performance of the MUSIC algorithm ismuch poorer than in AWGN simulations In general signalsare better resolvable if the bandwidth is increased (eg usingimpulse radio [24]) and if the beamwidth of the antenna isdecreased In literature Akaiake information criterion (AIC)[25] is presented and theminimumdescription length (MDL)[26] algorithms estimate the number of the incident signals


However it is shown that these algorithms can estimate awrong number of components for a small sample size anda low SNR [27] In future work we will study how wecould resolve the received signals that is multipath andinterference signals and estimate the number of the receivedsignals reliably so that the DoA estimation algorithms canwork in a more robust way

5 Conclusion

In this paper we considered DoA estimation with a certaintype of reconfigurable antennas namely CRLH-LWAs Westarted by presenting the APPR algorithm for two-portLWAsThereafter we evaluated the performance of the APPRsolution by numerical simulations in an AWGN channel andwith varying numbers of selected radiation patterns Theresults were also compared with those of the LWA-basedMUSIC algorithm We continued by evaluating the DoAestimation performance of both methods in an indoor envi-ronment based on real worldmeasurements involving typicalmultipath propagation with both line-of-sight and non-line-of-sight components Not only the results of numericalsimulations but also the measurement-based results showedthat the DoA estimates were in a good agreement with thereal DoAs especially with the APPR method indicatingthat CRLH-LWAs are capable of successful DoA estimationwhile having often a smaller form factor than conventionalantenna arrays with multiple antenna elements To concludethe combination of the proposed DoA estimation algorithmsand the CRLH-LWA implementation can provide a valu-able solution for future generation wireless communicationssystems where spectrum reuse interference avoidance anddevice localization are of special interest

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work has been performed in the framework of theReconfigurable Antenna Based Enhancement of DynamicSpectrum Access Algorithms (READS) and Future Small-Cell Networks using Reconfigurable Antennas (FUNERA)projects which were funded by VTT Technical ResearchCenter of Finland and the Finnish Funding Agency forTechnology and Innovation (Tekes) The authors wouldlike to thank Adant Srl for the antenna prototypes Themeasurements have been carried out at the Drexel UniversityThis work was also supported by CNS-1147838 from theUS National Science Foundation as part of the WirelessInnovation between Finland and United States (WiFiUS)partnership

References

[1] J D Kraus and R J Marhefka Antennas for All ApplicationsMcGraw-Hill Boston MA USA 3rd edition 2001

[2] C A Balanis AntennaTheory Analysis and Design JohnWileySons Hoboken NJ 3rd edition 2005

[3] T Ohira and K Gyoda ldquoElectronically steerable passive arrayradiator antennas for low-cost analog adaptive beamformingrdquoin Proceedings of the 2000 IEEE International Conference onPhased Array Systems and Technology pp 101ndash104 May 2011

[4] J R De Luis and F De Flaviis ldquoA reconfigurable dual frequencyswitched beam antenna array and phase shifter using PINdiodesrdquo in Proceedings of the 2009 IEEE International Sympo-sium on Antennas and Propagation and USNCURSI NationalRadio Science Meeting APSURSI 2009 June 2009

[5] C Caloz and T Itoh Electromagnetic Metamaterials Transmis-sion Line Theory and Microwave Applications John Wiley SonsHoboken NJ 2006

[6] R Schmidt ldquoMultiple emitter location and signal parameterestimationrdquo in Proceedings of the RADC Spectrum EstimationWorkshop pp 243ndash258 1979

[7] K-C Huarng and C-C Yeh ldquoA Unitary TransformationMethod for Angle-of-Arrival Estimationrdquo IEEE Transactions onSignal Processing vol 39 no 4 pp 975ndash977 1991

[8] M D Zoltowski GM Kautz and S D Silverstein ldquoBeamspaceroot-MUSICrdquo IEEE Transactions on Signal Processing vol 41no 1 pp 344ndash364 1993

[9] M Haardt and J A Nossek ldquoUnitary ESPRIT how to obtainincreased estimation accuracy with a reduced computationalburdenrdquo IEEE Transactions on Signal Processing vol 43 no 5pp 1232ndash1242 1995

[10] R Roy ESPRIT Estimation of Signal Parameters via RotationalInvariance Techniques [Phd Dissertation] Stanford UniversityStanford CA USA

[11] S Sugiura ldquoA review of recent patents on reactance-loadedreconfigurable antennasrdquo Recent Patents on Electrical Engineer-ing vol 2 no 3 pp 200ndash206 2009

[12] H Paaso A Mammela D Patron and K R Dandekar ldquoModi-fied MUSIC algorithm for doa estimation using CRLH leaky-wave antennasrdquo in Proceedings of the 2013 8th InternationalConference on Cognitive Radio Oriented Wireless Networks andCommunications CROWNCOM 2013 pp 166ndash171 usa July2013

[13] D Patron H Paaso A Mammela D Piazza and K R Dan-dekar ldquoImproved design of a CRLH leaky-wave antenna andits application for DoA estimationrdquo in Proceedings of the 20133rd IEEE-APS Topical Conference on Antennas and Propagationin Wireless Communications IEEE APWC 2013 pp 1343ndash1346September 2013

[14] H Paaso N Gulati D Patron et al ldquoDoA estimation usingcompact CRLH leaky-wave antennas novel algorithms andmeasured performancerdquo IEEE Transactions on Antennas Inpress

[15] V Vakilian J-F Frigon and S Roy ldquoDirection-of-arrival esti-mation in a clustered channel modelrdquo in Proceedings of the 2012IEEE 10th International New Circuits and Systems ConferenceNEWCAS 2012 pp 313ndash316 can June 2012

[16] V Vakilian H VNguyen S Abielmona S Roy and J-F FrigonldquoExperimental study of direction-of-arrival estimation usingreconfigurable antennasrdquo in Proceedings of the 2014 IEEE 27thCanadian Conference on Electrical and Computer EngineeringCCECE 2014 can May 2014

[17] C Plapous J Cheng E Taillefer A Hirata and T OhiraldquoReactance domain MUSIC algorithm for ESPAR antennasrdquo inProceedings of the 33rd European Microwave Conference EuMC2003 pp 793ndash796 deu October 2003


[18] S Akkar and A Gharsallah ldquoReactance domains unitaryMUSIC algorithms based on real-valued orthogonal decom-position for electronically steerable parasitic array radiatorantennasrdquo IET Microwaves Antennas and Propagation vol 6no 2 pp 223ndash230 2012

[19] Y Ozaki J Ozawa E Taillefer J Cheng and Y Watanabe ldquoAsimple DoA estimator using adjacent pattern power ratio withswitched beam antennardquo Progress In Electromagnetics ResearchC vol 22 pp 55ndash71 2011

[20] M Wax Detection and estimation superimposed signals [PhDthesis] Stanford University Stanford 1985

[21] Z Chen Introduction to Direction-of-Arrival Estimation ArtechHouse Books Norwood MA USA 2010

[22] P Pirsch Architectures for Digital Signal Processing ArtechHouse Books John Wiley amp Sons Chichester UK 1996

[23] ldquoMango communications WARP v3 kitrdquo httpmangocommcomproductskitswarp-v3-kit

[24] S Gezici Z Tian G B Giannakis et al ldquoLocalization via ultra-wideband radios a look at positioning aspects of future sensornetworksrdquo IEEE Signal Processing Magazine vol 22 no 4 pp70ndash84 2005

[25] H Akaike ldquoA new look at the statistical model identificationrdquoIEEE Transactions on Automatic Control vol 19 no 6 pp 716ndash723 1974

[26] M Wax and T Kailath ldquoDetection of signals by informationtheoretic criteriardquo Institute of Electrical and Electronics Engi-neers Transactions on Acoustics Speech and Signal Processingvol 33 no 2 pp 387ndash392 1985

[27] P M Djuric ldquoA model selection rule for sinusoids in whitegaussian noiserdquo IEEE Transactions on Signal Processing vol 44no 7 pp 1744ndash1751 1996

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of


International Journal of

RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



1 2

0∘

RF port 1 RF port 2

Stored M receivedsignals

DoA estimationalgorithms

Figure 1 System model

the literature [6ndash10] However these algorithms cannotbe used directly in CRLH-LWAs because of the inherentdesign and operation of the LWAs versus multielementantenna arrays An LWA has only one port and thus ithas a single observation available at each sampling incidentunlike in multielement antenna arrays where signals canbe detected from different elements of the antenna array[11] For this reason DoA estimation algorithms for LWAsrequire that the LWA receives the transmitted signal 119872times through119872 different radiation patterns as illustrated inFigure 1

There are only a limited number of papers where DoAestimation algorithms are introduced for LWAs In [12 13]we preliminarily introduced a modified multiple signal clas-sification (MUSIC) algorithm for LWAsTheCRLH-LWAhasthe inherent difference in the design Our modified MUSICalgorithm uses 119872 received signals each obtained with adifferent radiation pattern and measured from two antennaportsThen a correlationmatrix can be formed by using these119872 received signals We presented experimental results of aLWA-based MUSIC algorithms in [14] where we introducedthe performance of the MUSIC and power pattern cross-correlation (PPCC) algorithms in real wireless multipathenvironment However the paper presents only results forone radiation pattern configuration and does not study howdifferent configurations affect the performance of the algo-rithms Additionally an adjacent pattern power ratio (APPR)algorithm and the complexity analysis of the algorithms arenot presented in [14] Similar work for DoA estimation hasalso been presented independently in [15 16] that use theMUSIC algorithm forCRLH-LWA In [15] only experimentalresults are introduced and the authors do not present how theMUSIC algorithm can be built up using LWAs Additionally[15 16] present only experimental results of the MUSICalgorithm in an anechoic chamber In addition [17 18] intro-duce reactance domain MUSIC [17] and unitary MUSIC [18]algorithms for electronically steerable parasitic array radiator(ESPAR) antennas In [19] APPR algorithm is introduced

for the ESPAR antenna The APPR algorithm is a simpleDoA estimation algorithm which measures signal powersfrom119872 different directions and chooses the radiation patternwith the maximum signal power Then the adjacent patternpower ratios with respect to the maximum signal powerpattern are calculated and theDoA is estimated by comparingthese ratios with the predefined ratios from a look-up table(LUT) The performance of the algorithm is presented byusing computer simulations and experiments in an anechoicchamber

In this paper we apply the APPR DoA estimationalgorithm for CRLH-LWA Additionally we compare theperformance of the APPR algorithm with the performanceof the LWA-based MUSIC algorithm The computationalcomplexity of the APPR algorithm is much smaller thanthat of the MUSIC algorithm without much degradation inestimation accuracy Unlike in our previous studies [12ndash14]and other DoA estimation techniques in the literature [19]we now study how the computational complexity and theperformance of the algorithms depend on the number ofselected radiation patterns in different kinds of environmentstheoretical additive white Gaussian noise (AWGN) channeland a real world indoor multipath wireless environmentwith both line-of-sight (LoS) and non-line-of-sight (NLoS)components

This paper is organized as follows Section 2 introducesa detailed description of the DoA estimation algorithmsfor a compact CRLH-LWA Section 3 presents shortly theCRLH-LWA design Numerical and complexity analysis andexperimental results of the DoA estimation algorithms arepresented in Section 4 Finally conclusions are drawn inSection 5

2 CRLH-LWA-Based DoAEstimation Algorithms

In this section we introduce an APPR DoA estimation algo-rithm for LWAs Additionally we present briefly a modifiedsingletwo-port MUSIC algorithms [12] whose performancewe compare with the APPR algorithm The first algorithm isbased on evaluating the received powers for different voltagesets and the second algorithm is variant of the popularMUSIC algorithm [6] that we have modified to work withLWA In the following sections 120579 denotes the DoA and 120579 anestimate thereof

21 SingleTwo-Port MUSIC Algorithm Traditionally theMUSIC algorithm [6] defines the spatial correlation matrixusing the signals received by multiple antenna elements Inthis subsection we present how the spatial capabilities of thetraditional antenna array can be virtually formulated with theCRLH-LWA and how the correlation matrix can be definedwhen using the two-port LWA

Firstly we have to collect the same transmitted signal119906(119896) 119872 times while the LWA switches between 119872 differentradiation patterns Thus we can recreate spatial diversitydue to 119872 observations of the same signal but with different



y (119896) = a (120579) 119906 (119896) + z (119896) (1)


119886푚 (120579)


sum푛=1



119866耠푚 = 119866푚(sum푁푛=1 119868푛)

2 (3)



R푦푦 = 1119873s

푁s

sum푘=1

y (119896) ydagger (119896) (4)





(6)



119875MUSIC (120579) (7)




Γ푚+ (120579) =119875norm푚 (120579)

119875norm푚+1 (120579) (8)

Γ푚minus (120579) =119875norm푚 (120579)

119875norm푚minus1 (120579) (9)






Γ푚+ (120579) =norm푚 (120579)

norm푚+1 (120579)

Γ푚minus (120579) =norm푚 (120579)


(10)



0 5005

055

06

065

07

075

08

085

09

095

1

Angle (degrees)

Nor

mal

ized

pow

er

minus50

Pm

Pm+1

Pmminus1





120579

=



푚+1 (120579) gt norm푚minus1 (120579)

(11)


3 Antenna Design














0 2 4 6 8 10 12 14 16 18 20SNR (dB)

0123456789

1011

RMSE

(deg

rees

)






0 5002

03

04

05

06

07

08

09

1

Angle (degrees)

Nor

mal

ized

pow

er

Pm

Pm+1

Pmminus1

minus50


0 500

01

02

03

04

05

06

07

08

09

1

Angle (degrees)

Nor

mal

ized

pow

er

minus50

Pm

Pm+1

Pmminus1





0 500

05

1

15

2

25

3

35

4

45

RMSE

(deg

rees

)

DoA (degrees)

Case 1Case 2

Case 3Case 4

minus50


0 500

02

04

06

08

1

RMSE

(deg

rees

)

DoA (degrees)

Case 1Case 2

Case 3Case 4

minus50



RX5

TX2

RX6

TX1

RX3 TX3RX4 RX2

RX1

2398

m

1670m

1875m

Stairs

1560

m

1m

ReceiverTransmitter




(2119872119869 +1198721198690)DIV











































25 30 350

1

2

0

0

2

4


Angle (degrees)

Angle (degrees)

Angle (degrees)

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

minus50 0 50

(a)

0

1

2

minus20 0 20

Angle (degrees)

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

0

1

2

APP

R


Pseu

dosp

ectr

um (d

B)


(b)

minus20 0 20

Angle (degrees)

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

0

1

2

APP

R


0

2

4

Pseu

dosp

ectr

um (d

B)


(c)






20 300

5

10

15

0

2

4

6


Angle (degrees)

minus50 0 50

Angle (degrees)

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

(a)

0

10

20

0

5

10

minus30 minus20

minus50 0 50

Angle (degrees)

minus20 0 20

Angle (degrees)

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

(b)

0

2

4

6

0

2

4

minus50 minus40

minus50 0 50

Angle (degrees)

Angle (degrees)

minus20 0 20

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

(c)






0 50

minus20 0 20

Angle (degrees)



0

01

005

Nor

mal

ized

pow

er o

f PD

0

400

200APP

R

0

2

4

6

8

Pseu

dosp

ectr

um (d

B)

(a)

0 50Angle (degrees)

minus50


minus20 0 20

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

0

10

20

APP

R

0

2

4

6

Pseu

dosp

ectr

um (d

B)

(b)

0

10

20

0 50Angle (degrees)

minus50


minus20 0 20

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

R

0

2

4

6Ps

eudo

spec

trum

(dB)

(c)







5 Conclusion




Acknowledgments


References





























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











y (119896) = a (120579) 119906 (119896) + z (119896) (1)


119886푚 (120579)


sum푛=1



119866耠푚 = 119866푚(sum푁푛=1 119868푛)

2 (3)



R푦푦 = 1119873s

푁s

sum푘=1

y (119896) ydagger (119896) (4)





(6)



119875MUSIC (120579) (7)




Γ푚+ (120579) =119875norm푚 (120579)

119875norm푚+1 (120579) (8)

Γ푚minus (120579) =119875norm푚 (120579)

119875norm푚minus1 (120579) (9)






Γ푚+ (120579) =norm푚 (120579)

norm푚+1 (120579)

Γ푚minus (120579) =norm푚 (120579)


(10)



0 5005

055

06

065

07

075

08

085

09

095

1

Angle (degrees)

Nor

mal

ized

pow

er

minus50

Pm

Pm+1

Pmminus1





120579

=



푚+1 (120579) gt norm푚minus1 (120579)

(11)


3 Antenna Design














0 2 4 6 8 10 12 14 16 18 20SNR (dB)

0123456789

1011

RMSE

(deg

rees

)






0 5002

03

04

05

06

07

08

09

1

Angle (degrees)

Nor

mal

ized

pow

er

Pm

Pm+1

Pmminus1

minus50


0 500

01

02

03

04

05

06

07

08

09

1

Angle (degrees)

Nor

mal

ized

pow

er

minus50

Pm

Pm+1

Pmminus1





0 500

05

1

15

2

25

3

35

4

45

RMSE

(deg

rees

)

DoA (degrees)

Case 1Case 2

Case 3Case 4

minus50


0 500

02

04

06

08

1

RMSE

(deg

rees

)

DoA (degrees)

Case 1Case 2

Case 3Case 4

minus50



RX5

TX2

RX6

TX1

RX3 TX3RX4 RX2

RX1

2398

m

1670m

1875m

Stairs

1560

m

1m

ReceiverTransmitter




(2119872119869 +1198721198690)DIV











































25 30 350

1

2

0

0

2

4


Angle (degrees)

Angle (degrees)

Angle (degrees)

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

minus50 0 50

(a)

0

1

2

minus20 0 20

Angle (degrees)

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

0

1

2

APP

R


Pseu

dosp

ectr

um (d

B)


(b)

minus20 0 20

Angle (degrees)

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

0

1

2

APP

R


0

2

4

Pseu

dosp

ectr

um (d

B)


(c)






20 300

5

10

15

0

2

4

6


Angle (degrees)

minus50 0 50

Angle (degrees)

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

(a)

0

10

20

0

5

10

minus30 minus20

minus50 0 50

Angle (degrees)

minus20 0 20

Angle (degrees)

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

(b)

0

2

4

6

0

2

4

minus50 minus40

minus50 0 50

Angle (degrees)

Angle (degrees)

minus20 0 20

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

(c)






0 50

minus20 0 20

Angle (degrees)



0

01

005

Nor

mal

ized

pow

er o

f PD

0

400

200APP

R

0

2

4

6

8

Pseu

dosp

ectr

um (d

B)

(a)

0 50Angle (degrees)

minus50


minus20 0 20

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

0

10

20

APP

R

0

2

4

6

Pseu

dosp

ectr

um (d

B)

(b)

0

10

20

0 50Angle (degrees)

minus50


minus20 0 20

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

R

0

2

4

6Ps

eudo

spec

trum

(dB)

(c)







5 Conclusion




Acknowledgments


References





























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 5005

055

06

065

07

075

08

085

09

095

1

Angle (degrees)

Nor

mal

ized

pow

er

minus50

Pm

Pm+1

Pmminus1





120579

=



푚+1 (120579) gt norm푚minus1 (120579)

(11)


3 Antenna Design














0 2 4 6 8 10 12 14 16 18 20SNR (dB)

0123456789

1011

RMSE

(deg

rees

)






0 5002

03

04

05

06

07

08

09

1

Angle (degrees)

Nor

mal

ized

pow

er

Pm

Pm+1

Pmminus1

minus50


0 500

01

02

03

04

05

06

07

08

09

1

Angle (degrees)

Nor

mal

ized

pow

er

minus50

Pm

Pm+1

Pmminus1





0 500

05

1

15

2

25

3

35

4

45

RMSE

(deg

rees

)

DoA (degrees)

Case 1Case 2

Case 3Case 4

minus50


0 500

02

04

06

08

1

RMSE

(deg

rees

)

DoA (degrees)

Case 1Case 2

Case 3Case 4

minus50



RX5

TX2

RX6

TX1

RX3 TX3RX4 RX2

RX1

2398

m

1670m

1875m

Stairs

1560

m

1m

ReceiverTransmitter




(2119872119869 +1198721198690)DIV











































25 30 350

1

2

0

0

2

4


Angle (degrees)

Angle (degrees)

Angle (degrees)

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

minus50 0 50

(a)

0

1

2

minus20 0 20

Angle (degrees)

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

0

1

2

APP

R


Pseu

dosp

ectr

um (d

B)


(b)

minus20 0 20

Angle (degrees)

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

0

1

2

APP

R


0

2

4

Pseu

dosp

ectr

um (d

B)


(c)






20 300

5

10

15

0

2

4

6


Angle (degrees)

minus50 0 50

Angle (degrees)

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

(a)

0

10

20

0

5

10

minus30 minus20

minus50 0 50

Angle (degrees)

minus20 0 20

Angle (degrees)

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

(b)

0

2

4

6

0

2

4

minus50 minus40

minus50 0 50

Angle (degrees)

Angle (degrees)

minus20 0 20

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

(c)






0 50

minus20 0 20

Angle (degrees)



0

01

005

Nor

mal

ized

pow

er o

f PD

0

400

200APP

R

0

2

4

6

8

Pseu

dosp

ectr

um (d

B)

(a)

0 50Angle (degrees)

minus50


minus20 0 20

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

0

10

20

APP

R

0

2

4

6

Pseu

dosp

ectr

um (d

B)

(b)

0

10

20

0 50Angle (degrees)

minus50


minus20 0 20

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

R

0

2

4

6Ps

eudo

spec

trum

(dB)

(c)







5 Conclusion




Acknowledgments


References





























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 2 4 6 8 10 12 14 16 18 20SNR (dB)

0123456789

1011

RMSE

(deg

rees

)






0 5002

03

04

05

06

07

08

09

1

Angle (degrees)

Nor

mal

ized

pow

er

Pm

Pm+1

Pmminus1

minus50


0 500

01

02

03

04

05

06

07

08

09

1

Angle (degrees)

Nor

mal

ized

pow

er

minus50

Pm

Pm+1

Pmminus1





0 500

05

1

15

2

25

3

35

4

45

RMSE

(deg

rees

)

DoA (degrees)

Case 1Case 2

Case 3Case 4

minus50


0 500

02

04

06

08

1

RMSE

(deg

rees

)

DoA (degrees)

Case 1Case 2

Case 3Case 4

minus50



RX5

TX2

RX6

TX1

RX3 TX3RX4 RX2

RX1

2398

m

1670m

1875m

Stairs

1560

m

1m

ReceiverTransmitter




(2119872119869 +1198721198690)DIV











































25 30 350

1

2

0

0

2

4


Angle (degrees)

Angle (degrees)

Angle (degrees)

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

minus50 0 50

(a)

0

1

2

minus20 0 20

Angle (degrees)

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

0

1

2

APP

R


Pseu

dosp

ectr

um (d

B)


(b)

minus20 0 20

Angle (degrees)

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

0

1

2

APP

R


0

2

4

Pseu

dosp

ectr

um (d

B)


(c)






20 300

5

10

15

0

2

4

6


Angle (degrees)

minus50 0 50

Angle (degrees)

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

(a)

0

10

20

0

5

10

minus30 minus20

minus50 0 50

Angle (degrees)

minus20 0 20

Angle (degrees)

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

(b)

0

2

4

6

0

2

4

minus50 minus40

minus50 0 50

Angle (degrees)

Angle (degrees)

minus20 0 20

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

(c)






0 50

minus20 0 20

Angle (degrees)



0

01

005

Nor

mal

ized

pow

er o

f PD

0

400

200APP

R

0

2

4

6

8

Pseu

dosp

ectr

um (d

B)

(a)

0 50Angle (degrees)

minus50


minus20 0 20

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

0

10

20

APP

R

0

2

4

6

Pseu

dosp

ectr

um (d

B)

(b)

0

10

20

0 50Angle (degrees)

minus50


minus20 0 20

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

R

0

2

4

6Ps

eudo

spec

trum

(dB)

(c)







5 Conclusion




Acknowledgments


References





























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 500

05

1

15

2

25

3

35

4

45

RMSE

(deg

rees

)

DoA (degrees)

Case 1Case 2

Case 3Case 4

minus50


0 500

02

04

06

08

1

RMSE

(deg

rees

)

DoA (degrees)

Case 1Case 2

Case 3Case 4

minus50



RX5

TX2

RX6

TX1

RX3 TX3RX4 RX2

RX1

2398

m

1670m

1875m

Stairs

1560

m

1m

ReceiverTransmitter




(2119872119869 +1198721198690)DIV











































25 30 350

1

2

0

0

2

4


Angle (degrees)

Angle (degrees)

Angle (degrees)

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

minus50 0 50

(a)

0

1

2

minus20 0 20

Angle (degrees)

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

0

1

2

APP

R


Pseu

dosp

ectr

um (d

B)


(b)

minus20 0 20

Angle (degrees)

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

0

1

2

APP

R


0

2

4

Pseu

dosp

ectr

um (d

B)


(c)






20 300

5

10

15

0

2

4

6


Angle (degrees)

minus50 0 50

Angle (degrees)

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

(a)

0

10

20

0

5

10

minus30 minus20

minus50 0 50

Angle (degrees)

minus20 0 20

Angle (degrees)

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

(b)

0

2

4

6

0

2

4

minus50 minus40

minus50 0 50

Angle (degrees)

Angle (degrees)

minus20 0 20

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

(c)






0 50

minus20 0 20

Angle (degrees)



0

01

005

Nor

mal

ized

pow

er o

f PD

0

400

200APP

R

0

2

4

6

8

Pseu

dosp

ectr

um (d

B)

(a)

0 50Angle (degrees)

minus50


minus20 0 20

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

0

10

20

APP

R

0

2

4

6

Pseu

dosp

ectr

um (d

B)

(b)

0

10

20

0 50Angle (degrees)

minus50


minus20 0 20

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

R

0

2

4

6Ps

eudo

spec

trum

(dB)

(c)







5 Conclusion




Acknowledgments


References





























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















































25 30 350

1

2

0

0

2

4


Angle (degrees)

Angle (degrees)

Angle (degrees)

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

minus50 0 50

(a)

0

1

2

minus20 0 20

Angle (degrees)

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

0

1

2

APP

R


Pseu

dosp

ectr

um (d

B)


(b)

minus20 0 20

Angle (degrees)

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

0

1

2

APP

R


0

2

4

Pseu

dosp

ectr

um (d

B)


(c)






20 300

5

10

15

0

2

4

6


Angle (degrees)

minus50 0 50

Angle (degrees)

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

(a)

0

10

20

0

5

10

minus30 minus20

minus50 0 50

Angle (degrees)

minus20 0 20

Angle (degrees)

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

(b)

0

2

4

6

0

2

4

minus50 minus40

minus50 0 50

Angle (degrees)

Angle (degrees)

minus20 0 20

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

(c)






0 50

minus20 0 20

Angle (degrees)



0

01

005

Nor

mal

ized

pow

er o

f PD

0

400

200APP

R

0

2

4

6

8

Pseu

dosp

ectr

um (d

B)

(a)

0 50Angle (degrees)

minus50


minus20 0 20

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

0

10

20

APP

R

0

2

4

6

Pseu

dosp

ectr

um (d

B)

(b)

0

10

20

0 50Angle (degrees)

minus50


minus20 0 20

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

R

0

2

4

6Ps

eudo

spec

trum

(dB)

(c)







5 Conclusion




Acknowledgments


References





























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










20 300

5

10

15

0

2

4

6


Angle (degrees)

minus50 0 50

Angle (degrees)

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

(a)

0

10

20

0

5

10

minus30 minus20

minus50 0 50

Angle (degrees)

minus20 0 20

Angle (degrees)

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

(b)

0

2

4

6

0

2

4

minus50 minus40

minus50 0 50

Angle (degrees)

Angle (degrees)

minus20 0 20

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

RPs

eudo

spec

trum

(dB)

(c)






0 50

minus20 0 20

Angle (degrees)



0

01

005

Nor

mal

ized

pow

er o

f PD

0

400

200APP

R

0

2

4

6

8

Pseu

dosp

ectr

um (d

B)

(a)

0 50Angle (degrees)

minus50


minus20 0 20

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

0

10

20

APP

R

0

2

4

6

Pseu

dosp

ectr

um (d

B)

(b)

0

10

20

0 50Angle (degrees)

minus50


minus20 0 20

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

R

0

2

4

6Ps

eudo

spec

trum

(dB)

(c)







5 Conclusion




Acknowledgments


References





























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 50

minus20 0 20

Angle (degrees)



0

01

005

Nor

mal

ized

pow

er o

f PD

0

400

200APP

R

0

2

4

6

8

Pseu

dosp

ectr

um (d

B)

(a)

0 50Angle (degrees)

minus50


minus20 0 20

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

0

10

20

APP

R

0

2

4

6

Pseu

dosp

ectr

um (d

B)

(b)

0

10

20

0 50Angle (degrees)

minus50


minus20 0 20

Angle (degrees)

0

01

005

Nor

mal

ized

pow

er o

f PD

APP

R

0

2

4

6Ps

eudo

spec

trum

(dB)

(c)







5 Conclusion




Acknowledgments


References





























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











5 Conclusion




Acknowledgments


References





























RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation




















RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









experimental results of novel doa estimation algorithms...

Documents