constant false alarm rate (cfar)

104 Pages·2006·0.7 MB·English

CONSTANT FALSE ALARM RATE (CFAR)
DETECTION BASED ESTIMATORS WITH
APPLICATIONS TO SPARSE WIRELESS CHANNELS
A Thesis Submitted to
the Graduate School of Engineering and Sciences of
˙
Izmir Institute of Technology
in Partial Fulfillment of the Requirements for the Degree of
MASTER OF SCIENCE
in Electrical and Electronics Engineering
by
¨
Umit KARACA
October 2006
˙ ˙
IZMIR
Weapprovethethesisof U¨mitKARACA
DateofSignature
..................................... 12October2006
Assist. Prof. Serdar O¨ZEN
Supervisor
DepartmentofElectricalandElectronicsEngineering
˙IzmirInstituteofTechnology
..................................... 12October2006
Assist. Prof. MustafaAzizALTINKAYA
DepartmentofElectricalandElectronicsEngineering
˙IzmirInstituteofTechnology
..................................... 12October2006
Assoc. Prof. OlcayAKAY
DepartmentofElectricalandElectronicsEngineering
DokuzEylu¨lUniversity
..................................... 12October2006
Prof. F.AcarSAVACI
HeadofDepartment
DepartmentofElectricalandElectronicsEngineering
˙IzmirInstituteofTechnology
........................................
Assoc. Prof. Dr. Semahat O¨ZDEMI˙R
HeadoftheGraduateSchool
ABSTRACT
CONSTANT FALSE ALARM RATE (CFAR) DETECTION BASED
ESTIMATORS WITH APPLICATIONS TO SPARSE WIRELESS
CHANNELS
We provide Constant False Alarm Rate (CFAR) based thresholding methods for
training based channel impulse response (CIR) estimation algorithms for communica-
tion systems which utilize a periodically transmitted training sequence within a continu-
ous stream of information symbols. After obtaining the CIR estimation by using known
methods in the literature, there are estimation errors which causes performance loss at
equalizers. The channel estimation error can be seen as noise on CIR estimations and
CFAR based thresholding methods, which are used in radar systems to decide the pres-
ence of a target, can effectively overcome this problem. CFAR based methods are based
on determining threshold values which are computed by distribution of channel noise.
We provide exact and approximate distribution of channel noise appear at CIR estimate
schemes. WeappliedCellAveraging-CFAR(CA-CFAR)andOrderStatistic-CFAR(OS-
CFAR) methods on the CIR estimations. The performance of the CFAR estimators are
then compared by their Least Square error in the channel estimates. The Signal to Inter-
ferenceplusNoiseRatio(SINR)performanceofthedecisionfeedbackequalizers(DFE),
ofwhichthetapvaluesarecalculatedbasedontheCFARestimators,arealsoprovided.
iii
¨
OZET
˙ ˙
SABIT YANLIS¸ ALARM ORANI SEZIMLEME TABANLI KANAL
˙ ˙ ˙ ˜ ˙
KESTIRIMI VE YOGUN OLMAYAN TEKIL KANALLARA
UYGULAMALARI
Bu c¸alıs¸mada, haberles¸me sistemlerinde kullanılan Kanal Du¨rtu¨ Yanıtı (CIR) ke-
stirimlerinin es¸iklemesinde kullanılmak u¨zere, Sabit Yanlıs¸ Alarm Oranı (CFAR) sez-
imleme tabanlı metotlar ele alınmıs¸tır. Haberles¸me literatu¨ru¨nde bilinen yo¨ntemlerle
elde edilen kanal du¨rtu¨ yanıtları, kestirim hatası tas¸ımakta, bu durum denkles¸tiricilerde
performans kaybına neden olmaktadır. Bu kestirim hatası, kanal du¨rtu¨ yanıtındaki
gu¨ru¨ltu¨ olarakdeg˜erlendirilebilir. Radarsistemlerindehedeftespitedilmesindekullanılan
Sabit Yanlıs¸ Alarm Oranı (CFAR) sezimleme tabanlı es¸ikleme metotları, bahsedilen bu
gu¨ru¨ltu¨nu¨n temizlenmesinde kullanılabilir. Sabit Yanlıs¸ Alarm Oranı (CFAR) sezim-
leme tabanlı metotlar, kanal gu¨ru¨ltu¨su¨nu¨n istatistiksel dag˜ılımı yardımıyla hesaplanan
es¸ikdeg˜erlerinedayanmaktadır.
Proje kapsamında, Hu¨cre Ortalamalı (CA-CFAR) ve ˙Istatistiksel Sıralamalı (OS-
CFAR) Sabit Yanlıs¸ Alarm Oranı sezimleme tabanlı metotlar kullanılarak elde edilen
es¸ik deg˜erleri, c¸es¸itli kanal kestirimlerine uygulanmıs¸tır. Bahsedilen metotların perfor-
mansları, es¸ikleme is¸leminden sonra elde edilen kanal kestirim sinyallerinin En Ku¨c¸u¨k
Kareler Hataları (NLSE) kars¸ılas¸tırılarak go¨sterilmis¸tir. Ayrıca, Sinyallerin Giris¸im ve
Gu¨ru¨ltu¨ye Oranları (SINR), Karar Gerido¨nu¨s¸u¨mlu¨ Denkles¸tiriciler (DFE) kullanılarak
go¨sterilmis¸tir.
iv
TABLE OF CONTENTS
LISTOFFIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
LISTOFTABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
LISTOFABBREVIATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . x
CHAPTER1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2. OrganizationandContributionsoftheThesis . . . . . . . . . 2
CHAPTER2. SIGNALANDCHANNELMODEL . . . . . . . . . . . . . . . 4
2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2. OverviewoftheDataTransmissionModel . . . . . . . . . . . 4
CHAPTER3. GENERALIZEDLEASTSQUARESBASEDCHANNELESTIMA-
TION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.1. MethodofLeastSquares . . . . . . . . . . . . . . . . . . . . 13
3.2. ExistingChannelEstimationMethods . . . . . . . . . . . . . 15
3.2.1. Least-SquaresChannelEstimation . . . . . . . . . . . . . 15
3.2.2. CorrelationBasedChannelEstimation . . . . . . . . . . . 17
3.3. CovarianceMatrixUpdateBasedIterativeChannelEstimation 21
3.3.1. FurtherImprovementstotheInitialChannelEstimate . . . 22
3.3.2. StatisticalAnalysisofBaselineNoise . . . . . . . . . . . 24
3.3.3. ApproximationsofDistribution . . . . . . . . . . . . . . 30
3.3.4. IterativeAlgorithmtoCalculatetheChannelEstimate . . 31
3.3.5. OtherApproachesBackground(MatchingPursuit) . . . . 34
CHAPTER 4. CONSTANT FALSE ALARM RATE (CFAR) BASED THRESH-
OLDING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.2. UsingCFARTechniquesforChannelEstimation . . . . . . . 37
v
4.2.1. ApproximationsandFurtherSimplifications . . . . . . . 41
4.3. CellAveraging(CA)CFARBasedDetection . . . . . . . . . 41
4.4. OrderStatistic(OS)CFARBasedDetection . . . . . . . . . . 44
4.5. Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
CHAPTER5. CHANNELESTIMATE-BASEDDECISIONFEEDBACKEQUAL-
IZERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.1. Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
APPENDIXA. 8-VSBPULSESHAPE . . . . . . . . . . . . . . . . . . . . . . 90
1.1. ComplexRoot-RaisedCosinePulse . . . . . . . . . . . . . . 90
1.2. ComplexRaisedCosinePulse . . . . . . . . . . . . . . . . . 91
APPENDIXB. TESTCHANNELS . . . . . . . . . . . . . . . . . . . . . . . . 93
vi
LIST OF FIGURES
Figure Page
Figure2.1 Systemblockdiagram . . . . . . . . . . . . . . . . . . . . . . . . 5
Figure2.2 Dataframe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Figure3.1 CorrelationpropertiesoffinitePNsequences . . . . . . . . . . . . 18
Figure3.2 Thehistogramoftherealandimaginarypartsofthe418thtapvalue
(cid:179) (cid:180)
(cid:161) (cid:162)
oftheterm AHA −1AH Hd+Qη . . . 27
[−Na−Lq:N+Nc−1+Lq]
Figure3.3 The normality plot of the real and imaginary parts of the 418th tap
(cid:179) (cid:180)
(cid:161) (cid:162)
valueoftheterm AHA −1AH Hd+Qη 28
[−Na−Lq:N+Nc−1+Lq]
Figure4.1 Cell-AveragingCFAR . . . . . . . . . . . . . . . . . . . . . . . . 42
Figure4.2 NLSEofCA-CFARandCAGO-CFARfordifferentwindowsize . 45
Figure4.3 Kversusalpha . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Figure4.4 CIRestimationsforChannel1 . . . . . . . . . . . . . . . . . . . 52
Figure4.5 CIRestimationsforChannel2 . . . . . . . . . . . . . . . . . . . 53
Figure4.6 CIRestimationsforChannel3 . . . . . . . . . . . . . . . . . . . 54
Figure4.7 CIRestimationsforChannel3-plus . . . . . . . . . . . . . . . . . 55
Figure4.8 CIRestimationsforChannel4 . . . . . . . . . . . . . . . . . . . 56
Figure4.9 CIRestimationsforChannel5 . . . . . . . . . . . . . . . . . . . 57
Figure4.10 CIRestimationsforChannel6 . . . . . . . . . . . . . . . . . . . 58
Figure4.11 CIRestimationsforChannel7 . . . . . . . . . . . . . . . . . . . 59
Figure4.12 CIRestimationsforChannel8 . . . . . . . . . . . . . . . . . . . 60
Figure4.13 NLSEvaluesofCIRestimatesversusSNR(dB)forChannel1 . . . 61
Figure4.14 NLSEvaluesofCIRestimatesversusSNR(dB)forChannel2 . . . 62
Figure4.15 NLSEvaluesofCIRestimatesversusSNR(dB)forChannel3 . . . 63
Figure4.16 NLSEvaluesofCIRestimatesversusSNR(dB)forChannel3-plus 64
Figure4.17 NLSEvaluesofCIRestimatesversusSNR(dB)forChannel4 . . . 65
Figure4.18 NLSEvaluesofCIRestimatesversusSNR(dB)forChannel5 . . . 66
Figure4.19 NLSEvaluesofCIRestimatesversusSNR(dB)forChannel6 . . . 67
vii
Figure4.20 NLSEvaluesofCIRestimatesversusSNR(dB)forChannel7 . . . 68
Figure4.21 NLSEvaluesofCIRestimatesversusSNR(dB)forChannel8 . . . 69
Figure5.1 DFEEqualizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Figure5.2 ResidualChannelafterFeed-ForwardFilter . . . . . . . . . . . . 76
Figure5.3 ResidualChannelafterFeed-BackFilter . . . . . . . . . . . . . . 77
Figure5.4 SINR versusSNRforChannel1forvariouschannelestimates. 78
DFE
Figure5.5 SINR versusSNRforChannel2forvariouschannelestimates. 79
DFE
Figure5.6 SINR versusSNRforChannel3forvariouschannelestimates. 80
DFE
Figure5.7 SINR versus SNR for Channel 3-plus for various channel esti-
DFE
mates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Figure5.8 SINR versusSNRforChannel4forvariouschannelestimates. 82
DFE
Figure5.9 SINR versusSNRforChannel5forvariouschannelestimates. 83
DFE
Figure5.10 SINR versusSNRforChannel6forvariouschannelestimates. 84
DFE
Figure5.11 SINR versusSNRforChannel7forvariouschannelestimates. 85
DFE
Figure5.12 SINR versusSNRforChannel8forvariouschannelestimates. 86
DFE
viii
LIST OF TABLES
Table Page
Table4.1 K valuescomputedfromEquation(4.49) . . . . . . . . . . . . . . 49
TableB.1 Simulated9ChannelImpulseResponses . . . . . . . . . . . . . . 94
ix
LIST OF ABBREVIATIONS
AR Auto-regressive
CFAR ConstantFalseAlarmRate
CA-CFAR CellAveragingConstantFalseAlarmRate
CAGO-CFAR CellAveragingGreatest-OfConstantFalseAlarmRate
CIR ChannelImpulseResponse
DFE DecisionFeedbackEqualizer
DTV DigitalTelevision
ISI Inter-SymbolInterference
LE LinearEqualizer
LMS LeastMeanSquare
LS LeastSquares
ML MaximumLikelihood
MLSE MaximumLikelihoodSequenceEstimation(Estimator)
MMSE MinimumMean-squaredError
MP MatchingPursuit
MSE Mean-squaredError
OS-CFAR OrderStatisticConstantFalseAlarmRate
RLS RecursiveLeastSquare
SINR Signal-to-Interference-Plus-NoiseRatio
SNR Signal-to-NoiseRatio
VSB VestigialSide-band
x