IR-UWB Detection and Fusion Strategies using Multiple Detector Types

0.17 MB·English

by  Vijaya Yajnanarayana

IR-UWB Detection and Fusion Strategies using
Multiple Detector Types
Vijaya Yajnanarayana, Satyam Dwivedi, Peter Ha¨ndel
ACCESS Linnaeus Center,
Department of Signal Processing,
KTH Royal Institute of Technology, Stockholm, Sweden.
email:{vpy,dwivedi,ph}@kth.se
6
1
Abstract—Optimal detection of ultra wideband (UWB) pulses using a wideband LNA. The signal is then converted into the
0
2 in a UWB transceiver employing multiple detector types is digital domain by a high sampling rate ADC and digitally
proposed and analyzed in this paper. To enable the transceiver
processed.IR-UWBpulsesareextremelynarrow(orderoffew
r tobeusedformultipleapplications,thedesignershave different
a nano-seconds)andoccupyveryhighbandwidth,thereforehigh
types of detectors such as energy detector, amplitude detector,
M
etc., built in to a single transceiver architecture. We propose speed ADCs are needed for faithful digital representation of
severalfusiontechniquesforfusingdecisionsmadebyindividual the IR-UWB pulses. The recentprogressin the ADC technol-
1 IR-UWB detectors. In order to get early insight into theoretical ogy, as suggested by [4], indicates that such high speed ADC
achievable performance of these fusion techniques, we assess having good resolution with signal to noise and distortion
] the performance of these fusion techniques for commonly used
T ratio (SNDR) of higher than 30 dB can be achieved for a
detectortypeslikematchedfilter,energydetectorandamplitude
.I detector under Gaussian assumption. These are valid for ultra bandwidth of 10 GHz. This has enabled the digital designs
s short distance communication and in UWB systems operating for IR-UWB technology. In order to exploit the regulatory
c
in millimeter wave (mmwave) band with high directivity gain. bodyspecificationsoptimally,the transceiversmustoperateat
[
In this paper, we utilize the performance equations of different a 3.1−10GHz range or in the unlicensed millimeter wave
4 detectors, to device distinct fusion algorithms. We show that the
(mmwave) frequency [2].
v performancecanbeimprovedapproximatelyby4dBintermsof
9 signal to noise ratio (SNR) for high probabilityof detection of a The digital samples from the ADC will be processed by
0 UWBsignal(>95%), byfusingdecisionsfrommultipledetector a digital baseband processing block for detection. In many
4 types compared to a standalone energy detector, in a practical hardware platforms, a single UWB transceiver mounted on
0 scenario. sensors is used for multiple applications like ranging, local-
0 Index terms: Ultra Wideband (UWB), UWB ranging, Sensor
ization,communication,etc.,eachusingparticularstatisticsof
. Networks, Time of Arrival (TOA), Neyman-Pearson test.
1 the received samples for UWB pulse detection. For example,
0 I. INTRODUCTION largedistancecommunicationusingUWBmayemployenergy
5
An ultra wideband (UWB) communicationsystem is based detectoroveralargenumberofpulses;whereasshortdistance
1
: on spreading a low power signal into wideband. Impulse tracking application may use amplitude detector on a few
v
radio based UWB (IR-UWB) schemes are most popular as pulses. To enable the transceiver to be used for multiple
i
X they provide better performance and complexity trade-offs applications, the designers have different types of detectors
r compared to other UWB schemes [1]. likeamplitudedetector,energydetector,etc.,builtintoasingle
a IR-UWB schemes employ narrow impulse signals, which transceiver.Eachdetector1usesitsowndetectionalgorithmon
can yield high time resolution, and hence can be used for the received samples to infer a hypothesis from the received
accurate position localization and ranging. Narrow pulse du- samples and report it to the higher layers for further process-
ration coupled with low amplitude due to the restriction from ing. These algorithms are typically implemented in FPGA
regulatoryagencieslikeFederalCommunicationsCommission for faster processing, and hence, only the computed hard
(FCC) makes the detection of these pulses challenging [2], or soft-value decisions are available. In some applications,
[3]. Generally, transmit signaling employs multiple pulses there are no stringent constraints to bind the usage of a
and the receiver aggregates certain characteristics from these particular detector type; for example, demodulation of short
pulseslikeenergy,amplitude,position,etc.,tomakestatistical rangelowratecommunicationdata.Inthesesituations,instead
inferencesonthe transmittedinformationlike range(localiza- ofresortingtoasingledetectortypetoarriveatthehypothesis,
tion) or transmitted symbol value (communication) etc. The decisioninformationfromallofthedifferenttypesofdetectors
performanceofthereceiverdependsonhowwellthereceived can be concurrently utilized to make more informed decision
pulse statistics are utilized for a chosen application. on the hypothesis. This will utilize transceiver infrastructure
In this paper, we will consider the structure of a digital
sampling receiver shown in Fig 1. The received signal is
1Detectors and detector types are interchangeably used. In Fig. 1, each
filtered by an RF band-pass filter (BPF) and is amplified detector intheset,(Detector-1,...,Detector-L)areofdifferent type.
better, and since every detector decision is new information TABLEI
aboutthe signaled hypothesis,it shouldyield better reliability PARAMETERSONWHICHDETECTORSPERFORMANCEDEPENDS.
and improved performance.
Parameter Description
The proposed transceiver structure shown in Fig. 1, is ap- PFA Probability offalsealarm
plicable to the future evolution of our in-house flexible UWB SNR Signaltonoiseratio
Np NumberofUWBpulsesusedindetection
hardwareplatform[3],[5].Thisplatformcanbeusedforjoint
Ep EnergyoftheUWBpulses
ranging and communication applications. The platform has a s(t) ShapeoftheUWBpulses
digital processing section comprising of an FPGA, where the
proposed techniques of this paper can be implemented. Even
thoughthe applicabilityof the techniquesare demonstratedin The transmitted signal under hypothesis H1 consists of NT
frames, such that
simulation,theresultsprovideanearlyinsightintoachievable
performance. The variant of the proposed structure in Fig. 1 N ≥Ni ∀i∈[1,2,...,L],
T p
forhypothesestestingarealsoemployedin[6]and[7].In[6],
the authorsdiscuss the UWB hypothesistesting for a bank of where,Ni,denotesthenumberofframesusedbyDetector-iin
p
similar analog detectors, where as in [7], authors proposes a thehypothesistest.EachframeconsistsofoneIR-UWBpulse,
distributed fusion of results from multiple UWB sensors, by and during hypothesis H0 nothing is transmitted (NT empty
allocatingthedifferentnumberofpulsestoeachsensor,under frames).Each UWB pulse is of fixedduration,T,represented
the constraint of maximum number of allocated pulses, such by s(t), sampled at the rate, 1/Ts, and has Ns =T/Ts, sam-
that the error is minimized. Thus, both are different from the ples. Thus, both hypotheses can be mathematically expressed
proposed application of this paper. as
In this paper, we formulate a binary hypothesis problem NT−1Ns−1
s(t−nT)δ(t−nT −iT ) under H
of IR-UWB pulse detection, where decisions from different s 1 , (1)
types of detectors are fused using different fusion methods 0nP=0 iP=0 under H
0
before deciding on the hypothesis as shown in Fig. 1. We
where, δ(t), denotes the Dirac delta function and the model
demonstrate the methods using three commonly employed
usesN identicalframesin each hypothesistest cycle.This is
UWBdetector-types(L=3inFig.1),havingenergydetector T
similar to time hopped impulse radio (TH-IR) UWB models
(ED), matched filter (MF), and amplitude detector (AD) for
proposed in [1], [8], except that we are not considering time
Detector-1,Detector-2andDetector-3respectively.Thebinary
hopping, as it has no effect on the statistics collected by the
decisions signaling the hypothesis from these three detectors
d=[d ,d ,d ] arefedtothefusionalgorithmtoarriveatthe detectoracrossmultiple frames.The function,s(t−nT)δ(t−
1 2 3
nT −iT ), represents i-th discrete sample of the n-th frame
binary decision regarding the hypothesis, d . s
fused
under hypothesis H and is denoted by s(n,i). The received
The rest of the paper is organized as follows. In Section 1
signaliscorruptedbyGaussiannoise.Thus,thereceivedsignal
II, we will discuss the system model. Here, we will define
used in the hypothesistest under both hypotheses is given by
the signal model which will be used in the rest of the paper.
Section III, discusses different fusion strategies. In Section NT−1Ns−1
x(t−nT)δ(t−nT −iT ) under H
IV, we will discuss the analytical expression for P as a s 1
D
function of PFA, and SNR for matched filter, energy detector NnPT=−01NiPs=−01 , (2)
and amplitude detector for multi-pulse IR-UWB signal. In w(t−nT)δ(t−nT −iTs) under H0
Section V, we will evaluate the performance of the different nP=0 iP=0
fusion strategies. Finally in Section VI, we will discuss the where, x(t), is the received pulse shape. The function, x(t−
conclusions. nT)δ(t−nT −iTs), represents the i-th sample of the n-th
receivedframeunderhypothesisH andisdenotedbyx(n,i).
1
Similarly, w(t−nT)δ(t−nT −iT ), representsthe Gaussian
II. SYSTEMMODEL s
noise corresponding to the i-th sample of the n-th received
We consider a binary hypothesis for detection, with H frameandisdenotedbyw(n,i).Weassumeasingle-pathline
0
representing signal is absent and H representing signal is of sight (LOS) channel, thus, the received samples, x(n,i)=
1
present. Each of the different types of detectors like MF, ED, βs(n,i)+w(n,i), where, β, indicates the path loss.
etc., in the UWB transceiver constructs a test statistic from Typically, the UWB channels are subject to multi-path
thereceivedsamples,basedonwhichinferenceismadeabout propagation, where a large number of paths can be observed
H orH bycomparingtheteststatistictosomethreshold,γ. at the receiver. However, if the transceivers are in close
0 1
Different detector types have different ways to construct the proximity with clear line of sight, the detectors here rely on
teststatistic,andthushavevaryingdegreesofperformancelike the first arriving path or LOS, this is in contrast to traditional
probabilityofdetection,P ,probabilityoferror,P ,etc.Apart channelmeasurementandmodeling.IftheUWBtransceiveris
D e
fromthechosenteststatistic,theperformanceoftheparticular operatingatmillimeterwavefrequencies,duetothecombined
detectoralso dependson allor few of the parameterslisted in effect of higher directivity gain due to the RF-beamforming
the Table I. and higher absorption characteristics of the channel results in
AnalogFrontend DigitalBasebandProcessingBlock
d
1
Detector-1
F
U
Detector-2 d2 SIO
N
RF BPF LNA ADC .. ALGOR dfused
... ITHM
.
Ts
d
L
Detector-L
d=[d1,d2···,dL]anddfused∈{H0,H1}
Fig.1. Depictionofdirectsamplingreceiverarchitecturewithmultidetectorfusion.The(Detector-1,...,Detector-L),arethedifferentdetectortypesavailable
inthetransceiver. Thedi,i∈[1,...,L],indicates thebinarydecisions madebythedifferent detectors[1] withregardtohypothesis. Thedfused,indicates the
fusedbinarydecision forthechosenhypothesis.
single-path LOS channels for distances less than 100 meters.
F1ch0oarrGathHcetze,trridastnuiscecsetooivfehtrihgoehpecerhraaretniflnneegcl,tiintohntehse,asrfserufermqaucpettinioocnnyssbaoanfnddsisnlcegaslteste-tprhianatngh d...dd21L ... dfused ddd...L21 ... dfused
LOS channel is valid only for extremely short distance of (a)ANDfusion (b)ORfusion
order less than 10 meters [3], [5], [9], [10]. These short
distance high speed UWB applicationsinclude transferjetand
d1
twmraiorcdetaleeblslpser.oUpWSoiBstehdo(wuhteUrlSeoBsws)ilol[f1m1ga]e,kne[e1rth2al]ei.tdyAi,slcwsuoes,suiaosdneopmβtian=thge1ma.asItiinmcatplhllyee ddd...21L P >≤LL//22 dfused dd...2L MAPFusion dfused
signal model proposed in (1) and (2), we assume perfect
(c)Fusionbasedonmajority (d)Maximum aposteriori (MAP)
synchronization, otherwise there will be degradation of the fusion
individual detectors (and fused) performance.
Fig.2. Depiction ofdifferent decision fusionmethods.
InthenextSection,we willdiscussthefusionstrategiesfor
fusing individual detector decisions (refer to Fig. 1).
for designinga fusion technique that is optimal in probability
III. FUSION RULESFOR IR-UWB SIGNALDETECTION
of error sense. For any prior probability for H and H , the
0 1
We consider a general counting rule, that is, deciding fusion rule that minimizes the probabilityof error is given by
for H1, if the sum of the decisions, Li=1di, exceeds the maximum a posteriori (MAP) formulation given below.
threshold, k. If we define the decision Pof the i-th detector in
the Fig. 1, as di = 0 and di = 1 for hypothesis H0 and Pr(H |d)H≷1Pr(H |d). (3)
1 0
H1 respectively,thenthespecialcasesoftheseincludesimple H0
fusion rules such as “AND” (k = L), “OR” (k = 1), and
Where, d, is a L-size vector of binary values signaling the
“Majority-Voting”(k =L/2). These fusion rules are depicted
hypothesis of the decisions made by different detectors (refer
in Fig. 2a, Fig. 2b and Fig. 2c. These rules are simple to
to Fig. 1). We can write (3) as
implement and has been proved to posses robustness features
with respect to performance as shown in [13], [14]. log Pr(H1|d) H≷10. (4)
The counting rule based fusion is biased either toward (cid:18)Pr(H |d)(cid:19)
0 H0
hypothesisH (UWBpulsedetectioninourmodel),ortoward
1 If we define sets I, S and S as
H . For example, fusing using the “OR” rule will have supe- H1 H0
0
rior detection performance, but will also have a larger false I := {1,2,...,L}, (5)
alarm rate. Similarly, the “AND” fusion rule is conservative
S := {i:d =1}, (6)
in the UWB pulse detection, but has superior false alarm H1 i
S := I\S :={i:d =0}, (7)
rate performance. These aspects are further illustrated with H0 H1 i
numericalexamplesinthelatersections.Ifwedefinethemis-
where,d ,isthebinarydecisionofthedetector-i(i∈I),then,
i
classification of the hypothesis as an error and the objective
P
irsulteodmisicnuimssiezdeatbhoevperoabreabsiulibty-oopftimerarol.r,TPhies, tihsetnhethmeodteivcaistiioonn Pr(H1|d) = p(d1)i∈YSH1PDii∈YSH0(1−PDi) (8)
Here, we assumed that the decisions of each of the detectors
paroethiensdisepHen1daenndt opf(·e)adchenoottheetrh.ePp1roisbatbhielitpyrodbenabsiitlyityfuonfcthioyn- r(n,i) NnPpk=−01NiPs=−01fk(r(n,i)) Tk ≤>γγkk dk
(PDF). Pi is the probability of detection of the detector-i in
D
Fig.1. Similarly, we can write
Detector
P
Pr(H |d) = 0 Pi (1−Pi ) (9) Fig.3. Generic detector structure. Thedifferent detector types usedifferent
0 p(d)i∈YSH1 FAi∈YSH0 FA functionfk(·),toconstructtheteststatistic, Tk.
P is the probability of hypothesis H . Pi is the false alarm
0 0 FA 1
ofthei-thdetector.Inmanyapplicationssuchasincommuni-
0.9
cation, hypothesistesting is used for symboldecoding,where
0.8
boththehypothesesareequallylikely.Substituting(8)and(9)
0.7
in(4)andassumingbothhypothesesareequallylikely,weget
0.6
the decision rule as PD0.5
Pr(H |d) Pi 0.4
log(cid:18)Pr(H10|d)(cid:19)=i∈XSH1log(cid:18)PFDiA(cid:19) (10) 00..23 MMEEADDDFFstssthiihimmmeeououurrllleaaeatttttiiiiicocooaannnll
(1−Pi) H1 0.1 ADtheoretical
+ log D ≷ 0. 0
(cid:18)(1−Pi )(cid:19) -30 -28 -26 -24 -22 -20 -18 -16 -14 -12
i∈XSH0 FA H0 SNR[dB]
Unlikethe countingrulebased fusion,the MAPfusionrule Fig. 4. Theperformance ofdifferent detectors intheory and simulation are
employed in (10), requires Pis and Pi s at the fusion center. shown. A normalized second order Gaussian pulse of width 10 ns sampled
D FA at5GHz,isusedinthesimulation.
Inpracticethisisnotalwaysavailable.Also,thefusionrulein
(10),canbeviewedasaweightedcountingrule,alsoknownas
“Chair-Varshney”rule[15].InthenextSection,wewillderive and compare it with a threshold to decide on a hypothesis.
the detection performance of these detectors, which will be Depending on the test statistic generation function, f (·), we
k
used in the later Sections to evaluate the fusion performance. have different types of detectors like matched filter, energy
detector, amplitude detector, etc,. In this paper, we use MF,
IV. DETECTORPERFORMANCE
ED, and AD detectors, thus we have, k ∈ {MF, ED, AD}.
As discussed in Section II, each transmit frame constitutes Nk denote number of frames used by the detector-k, in the
p
a UWB pulse,s(t), sampledat1/Ts. We defineframeenergy, hypothesis testing. The r(n,i), denotes the received samples
Ep as and is equal to x(n,i) and w(n,i) during hypothesesH1 and
Ns−1 H respectively.
E = s2(n,i). (11) 0
p
Xi=0 A. Matched Filter
We assume all the frames in the transmission are of same For matched filter, the test statistic in (14) will have
pulse shape, s(t), and energy, E . As discussed in (2), the
p
f (r(n,i))=r(n,i)s(n,i). (15)
receivedsignalunderbothhypotheses,H1andH0iscorrupted MF
by AWGN noise samples, w(n,i). We assume that these The performance in terms of probability of detection for
noisesamplesareindependentandidenticallydistributed(IID) matchedfilter,PMF,asafunctionofprobabilityoffalsealarm,
with w(n,i) ∼ N 0,σ2/Ns , where N, denotes the normal PMF, and SNR isDshown in Appendix-1 of [16] to be
distribution, such t(cid:0)hat the to(cid:1)tal noise energy in the frame is FA
given by Ns−1 PDMF =Q(cid:16)Q−1(PFMAF)−qNsNpMFSNR(cid:17), (16)
E w2(n,i) =σ2. (12) where Q is the tail probability of the standard normal distri-
Xi=0 (cid:2) (cid:3) bution.
Here, E, denotes the expectation operator. We define signal-
B. Energy Detector
to-noise ratio, SNR, as
In energy detector, the test statistic in (14) will have
E
p
SNR= . (13)
σ2 f (r(n,i))=r2(n,i). (17)
ED
TypicaldetectorstructureusedinFig1isasshowninFig.3.
The performance in terms of probability of detection for
Each detector will construct a test statistic, T , such that
k energy detector, PED, as a function of probability of false
D
Npk Ns−1 alarm, PFEAD, and SNR is shown in Appendix-2 of [16] to be
Tk =nX=0 Xi=0 fk(r(n,i)), (14) PDED =Q−Xν12(λ)(cid:16)q2NpEDNsQ−1(PFEAD)+NpEDNs(cid:17). (18)
Where QX2(λ) is the tail probability of the non-central chi- TABLEII
square distrνibution with ν =NEDN , degrees of freedom, and CONFIGURATIONOFPARAMETERSFORDIFFERENTDETECTORSUSEDIN
p s THEFUSION.
centrality parameter, λ=NEDN SNR.
p s
Detector Type PFA Np
C. Amplitude Detector Matched Filter 10−7 100
EnergyDetector 10−1 1000
In the amplitudedetector, the test statistic in (14) will have Amplitude Detector 10−4 100
f (r(n,i))=|r(n,i)|. (19)
AD
D. Simulation Study
The performance in terms of probability of detection for
The performance equation for energy detector, (18), as-
amplitude detector, PAD, as a function of probability of false
D sumes large number of pulses are used in the detection. Sim-
alarm, PAD, is shown in Appendix-3 of [16] to be
FA ilarly, for the amplitude detector, the performance equation,
PAD (23), assumes a UWB pulse shape given in (22). In this
PDAD =Q(cid:18)Q−1(cid:18) 2FA (cid:19)−α NpADEpSNR(cid:19) section, we will simulate the detectors and demonstrate the
q
(20) validity of the approximations, for a practical UWB signal
PAD
+Q(cid:18)Q−1(cid:18) 2FA (cid:19)+αqNpADEpSNR(cid:19) sfreatumpesihsoowfn10innsTdabulreatIiIo.nW,heavuisnegaosniegnnaolrmmaoldizeeldinsewchoincdhoeradcehr
where α is defined as Gaussianpulseasdefinedin(22)withτ =3.33ns,sampledat
5GHz. The received samples are corrupted by AWGN noise
Ns−1 with variance 1/SNR (since pulses are normalized, that is
s(i)=αEp. (21) Ep =1). Monte-Carlo simulations are done using 1000 inde-
Xi=0 pendentrealizations. The detector performancein simulations
are shown in red, matches the analytical expressions in (16),
As shown by (21) and (20), the performance of the ampli-
(18), and (23), shown in blue in Fig. 4. Notice that in Fig. 4,
tude detector depends on the shape of the UWB pulse used.
different detectors are optimal at different SNR regions. For
WehaveconsideredanormalizedsecondorderGaussianpulse
applications, where there are no stringent constraints to bind
as described in [3]. This is given by
the usage to a particular detector type, instead of resorting
−2πt2 −τ2+4πt2 to a single arbitrary detector to arrive at the hypothesis,
s(t)=−4πe τ2 (cid:18) τ4 (cid:19). (22) decision information from all the detectors can be fused to
make more informed decision on the hypothesis. This will
Here τ can be used to control the impulse spread. Energy utilize transceiver infrastructure better to provide improved
normalized pulse, Ep = 1, with τ = 3.33 ns, sampled at performance. We will evaluate the performance of proposed
5 GHz, will result in α=4.49. Thus, for this pulse shape the fusion methods in the next Section.
performance of the amplitude detector is given by
V. PERFORMANCE EVALUATION OFFUSION METHODS
PAD For counting rule based fusion discussed in Section III,
PDAD =Q(cid:18)Q−1(cid:18) 2FA (cid:19)−4.49qNpADEpSNR(cid:19) with L = 3, having MF, ED and AD as detectors for
(23)
“AND”, “OR” and “Majority-Voting” fusion, we should have
PAD
+Q(cid:18)Q−1(cid:18) 2FA (cid:19)+4.49qNpADEpSNR(cid:19) k = 3, k = 1 and k > 2 respectively. We performed
Monte-Carlo simulations with similar signal configurations
From (16), (18), and (23) the performance of matched describedinSectionIV-D.Wegenerated1000randomsignals
filter, energy detector and amplitude detector depends on corresponding to hypotheses, H and H as defined in (1).
1 0
environment(SNR) andonthesystem configurationortuning The probability of correct detection of hypothesis, H , when
1
variables like number of frames considered in the hypothesis H was indeed signaled, P , and the probability of mis-
1 D
testing,N ,andprobabilityoffalsealarm,P .Inthematched classificationofhypotheses,P ,wasevaluatedusingthefusion
p FA e
filter and energy detector, the performance is agnostic to the rules discussed in Section III. The false alarm, P , and
FA
system specifications like pulse shape, which are fixed for a number of frames employed, N , for each detector type are
p
givenhardware.However,in the amplitudedetector,detection takenfromTableII.Resultsforfusedprobabilityofdetection,
performance depends on the shape of the pulse as shown in P , and probability of error, P , are as shown in Fig. 5a
D e
(20) and (21). As discussed in Section I, each detector is and Fig. 5b respectively. Notice that for a fixed SNR, the
pre-configured with detection parameters like N , P , etc., probabilityof detection is high for the “OR” fusion, however,
p FA
considering a particular application in mind. For an example the probability of error is also high due to the higher false
configuration shown in Table II, the probability of detection, alarm rate.
P ,versesSNRusingtheanalyticalexpression(16),(18),and The performance is also evaluated using the MAP fusion
D
(23) is as shown in the blue color plots of Fig. 4. rule (10), for a detector set, (MF, ED, AD), yielding decision
(a)Probabilityofdetection (16), (18) and (20) for analyzing the fusion performance. We
1
analyzed the performance in terms of detection probability
0.8
and probability of error for different fusion methods like
0.6
D “AND”,“OR”and“Majority-Voting”.ThisisshowninFig.5a
P
0.4 ORfusion and Fig. 5b. Using the Bayes rule, we derived an optimal
ANDfusion
0.2 Majority-Votingfusion fusion rule (10) for UWB detection, which is optimal in the
0 probabilityoferrorsense and comparedits performance.This
-30 -28 -26 -24 -22 -20 -18 -16 -14 -12 -10
is shown in Fig. 6a and Fig. 6b.
(b)Probabilityoferror
Results indicate that by making a suitable choice of fusion
0.6
ORfusion rule, a trade-off between detection and false alarm can be
ANDfusion
0.4 Majority-Votingfusion achieved.Forexample,Fig. 5a, showsthat ORfusionis more
Pe biased toward detection, however, it also results in higher
0.2 errors (due to false alarms, refer to Fig. 5b). If the error
performance is critical for the UWB application, then MAP
0 fusion formulation gives superior performance in terms of
-30 -28 -26 -24 -22 -20 -18 -16 -14 -12 -10
SNR[dB] errors as shown in Fig. 6b. In general, if there are multiple
detectors available in the UWB transceiver platform, then
Fig. 5. Probability of detection and error performance for various fusion
decisioninformationfromthese detectorscan beconcurrently
techniques usingtheconfiguration definedinTableII.
utilizedandintelligentlyfusedbasedontheapplicationcriteria
(a)Probabilityofdetection to make a more informed decision on the hypothesis.
1
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0.8
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