Report on adaptive beamforming algorithms for advanced antenna types for aerial platform and ...

175 Pages·2006·9.35 MB·English

FP6-IST-2003-506745 CAPANINA
Deliverable Number D17
Report on adaptive beamforming algorithms for advanced
antenna types for aerial platform and ground terminals

Document Number CAP-D17-WP3.3-UOY-PUB-01
Contractual Date of Delivery to the CEC 1st Feb 06
Actual Date of Delivery to the CEC 31st Jan 06
Author(s): G. White (UOY), E. Falletti (POLITO), Z. Xu (UOY), D.
Borio (POLITO), F. Sellone (POLITO), Y. Zakharov (UOY),
L. Lo Presti (EUCON), F. Daneshgaran (EUCON)
Participant(s) (partner short names): UOY, POLITO, EUCON
Editor (Internal reviewer) Marina Mondin
Workpackage: WP3.3
Estimated person months
30
Security (PUBlic, CONfidential, PUB
REStricted)
Nature Report
CEC Version 1.1
Total number of pages (including cover): 175

Abstract:
This document presents technical descriptions of signal processing and cross-layer algorithm design for
beamforming from high altitude platforms (HAPs) to ground terminals, and vice versa, using advanced antenna
types - so-called 'smart antennas'. The research covers topics including vertical antenna arrays for
communications from HAPs, optimised antenna array beampatterns for cellular coverage from HAPs, array
topologies and SINR balancing in adaptive beamforming from HAPs, data communications to trains from HAPs
incorporating DOA estimation and tracking methods, LMS-based beamforming with Doppler recovery and RLS-
based beamforming for single carrier IEEE 802.16, both focussed towards HAP applications, and the
development of a DSP simulator for smart antenna terminals.

Keyword list: Smart antennas, HAPs, beamforming, array signal processing, DOA estimation
antenna types for aerial platform and ground terminals CAP-D17-WP3.3-UOY-PUB-01
DOCUMENT HISTORY

Date Revision Comment Author / Editor Affiliation
31st Jan 06 01 First issue George White UOY

Document Approval (CEC Deliverables only)

Date of Revision Role of approver Approver Affiliation
approval
31st Jan 06 01 Editor (Internal reviewer) Marina Mondin POLITO
31st Jan 06 01 On behalf of Scientific David Grace UOY
Board

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TABLE OF CONTENTS
ExecutiveSummary 16
1 Introduction 17
1.1 Overviewofreport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.2 BackgroundtoHAP-relatedbeamforming . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.3 Complexityconsiderations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.4 Disseminationofresults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2 OptimisedantennaarraybeampatternsforHAPcoverage 21
2.1 Backgroundtoconventionalbeamformingmethods . . . . . . . . . . . . . . . . . . . . . . 21
2.2 Projectmotivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3 Communicationsscenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4 Descriptionofmethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.5 Simulationresults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3 Verticalantennaarraysandring-shapedcellularconfigurations 31
3.1 Introductiontoring-shapedcellsandverticalantennaarrays. . . . . . . . . . . . . . . . . 31
3.2 Systemmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3 Determinationofnumberandsizeofcells . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.4 Numericalresults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4 ArraytopologiesfortheHAP-basedsmartantenna 38
4.1 HAPcommunicationsscenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.2 EffectofHAPpitch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.3 Caponbeamforming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.4 Methodologyforperformanceevaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.4.1 Powercontrol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.4.2 Linkbudget . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.5 Arraytopologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.7 Anexplanationoftheresults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
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5 ChannelallocationmethodforadaptivebeamformingfromHAPs 51
5.1 Backgroundtochannelallocationmethodsforsmartantennas . . . . . . . . . . . . . . . 51
5.2 Descriptionofchannelallocationmethod . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.3 ApplicationofchannelallocationmethodtoHAPcommunicationsscenario . . . . . . . . 53
5.3.1 Effectofchannelallocationmethodondistancesbetweenco-channelusers . . . . 53
5.3.2 Methodologyforbeamformingperformanceevaluation . . . . . . . . . . . . . . . . 53
5.3.3 EffectofchannelallocationmethodonSIRofusers . . . . . . . . . . . . . . . . . 54
5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
6 SINRbalancingfortheHAP-userdownlink 57
6.1 DescriptionofSchubertandBochemethod . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6.1.1 OptimisationofpowerassignmentforSINRbalancing . . . . . . . . . . . . . . . . 58
6.1.2 JointoptimisationofpowerassignmentandweightvectorforSINRbalancing . . . 58
6.2 Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.3 ApplicationofSINRbalancingtotheHAPscenario . . . . . . . . . . . . . . . . . . . . . . 60
6.4 Importanceofeffectivechannelallocation . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.5 MonteCarloperformancestudy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
7 DatacommunicationstorailwaytrainsfromHAPs 66
7.1 Chapteroverview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
7.2 Systemmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
7.3 DOAestimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
7.3.1 Spectral-basedDOAestimation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
7.3.2 Polynomial-basedDOAestimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
7.3.3 Powerestimationofsignalsfromtrains. . . . . . . . . . . . . . . . . . . . . . . . . 76
7.3.4 Estimatingthenumberoftrains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
7.3.5 Dataattribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
7.4 TrackingtrainsusingextendedKalmanfiltering . . . . . . . . . . . . . . . . . . . . . . . . 77
7.4.1 ExtendedKalmanfiltering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
7.4.2 InitialisationofKalmanfilter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
7.5 Beamformingontheuplink . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
7.6 Performancestudy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
7.6.1 Scenario1: Maximumnumberoftrains . . . . . . . . . . . . . . . . . . . . . . . . 79
7.6.2 Scenario2: Trainscrossing-DOAandBFconsiderations . . . . . . . . . . . . . . 82
7.6.3 Scenario3: Trainscrossing-theDOAattributionproblem . . . . . . . . . . . . . . 85
7.6.4 Scenario4: Trainenterstunnel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
7.6.5 Scenario5: Trainentersstation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
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7.6.6 Scenario6: RobustnesstoHAPmotion . . . . . . . . . . . . . . . . . . . . . . . . 90
7.7 Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
8 An adaptive LMS-based beamforming algorithm with Doppler shift recovery scheme for
OFDMtransmissiontotheHAP 93
8.1 DopplereffectanditsperturbationsonanOFDMsystem . . . . . . . . . . . . . . . . . . 94
8.2 TheLMSalgorithmforbeamformingpurposes . . . . . . . . . . . . . . . . . . . . . . . . 95
8.3 Some adaptive beamforming schemes to suppress both delayed and Doppler-shifted
signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
8.3.1 PilotLMSbeamformer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
8.3.2 Pilot-ZeroesLMSbeamformer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
8.3.3 Pilot-ExponLMSbeamformer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
8.3.4 Pilot-Zeroes-ExponLMSbeamformer . . . . . . . . . . . . . . . . . . . . . . . . . 101
8.3.5 Pilot-Zeroes-Expon-AlphaLMSbeamformer. . . . . . . . . . . . . . . . . . . . . . 102
8.4 Simulatedperformance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
8.4.1 Performancetestinflatfadingchannel . . . . . . . . . . . . . . . . . . . . . . . . . 104
8.4.2 Performancetestinmultipathchannel . . . . . . . . . . . . . . . . . . . . . . . . . 116
8.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
9 AnadaptiveRLS-basedbeamformingalgorithmforsinglecarriertransmissiontotheHAP119
9.1 OverviewoftheIEEE-802.16-SCPHYlayer . . . . . . . . . . . . . . . . . . . . . . . . . . 119
9.2 TheRLSbeamformingalgorithmforarraysignalprocessing . . . . . . . . . . . . . . . . . 120
9.2.1 RLSalgorithmfordirect-formFIRfilters . . . . . . . . . . . . . . . . . . . . . . . . 121
9.2.2 QRdecompositionforRLSestimation . . . . . . . . . . . . . . . . . . . . . . . . . 122
9.3 Simulatedperformance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
9.3.1 Performancetestinasimplifiedstaticmultipathchannel . . . . . . . . . . . . . . . 124
9.3.2 PerformancetestinfrequencyselectivechannelwithDopplereffect . . . . . . . . 125
9.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
10 Aself-calibrationalgorithmforsmartantennas 137
10.1 Motivationsandbackground . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
10.2 Signalmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
10.3 Problemformulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
10.4 Thecalibrationalgorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
10.4.1 Solutionoftheelementaryproblem. . . . . . . . . . . . . . . . . . . . . . . . . . . 142
10.4.2 Numericalimplementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
10.5 Simulatedperformance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
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10.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
11 ADSPsimulatorforsmartantennaterminals 153
11.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
11.2 Signalandchannelmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
11.2.1 TheOFDMsignal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
11.3 TheSIMOchannelmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
11.3.1 Thebeamformingalgorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
11.4 TheDSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
11.4.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
11.4.2 DescriptionoftheTMS320C6701module . . . . . . . . . . . . . . . . . . . . . . . 157
11.4.3 TheTMS320C6701evaluationmodule(EVM) . . . . . . . . . . . . . . . . . . . . 157
11.5 TheEmulator’sstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
11.6 Synchronizationaspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
11.7 System’slimitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
11.7.1 Frequencyselectivechannel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
11.7.2 “Angleselective”channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
11.8 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
11.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
12 Conclusions 168
12.1 Chapterconclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
12.2 Generalconclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
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LIST OF FIGURES
1 OutlineofDeliverable17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2 SteeringthepowertoadesiredpositionfromaHAPtotheground. . . . . . . . . . . . . . 22
3 Antennaarrayconfiguration.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4 121hexagonalcellsconfiguration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5 optimizedbeampatternofa424-elementantennaarray,steeredat(-5.46,+0)km. . . . . . 26
6 One section in Fig.5 along the X-axis at Y=Y =0 km; solid line: optimized beampattern
0
using3-stagemethod;dashline: equalamplitudeweightingmethod. . . . . . . . . . . . . 27
7 Beampatternofa424-elementantennaarray,steeredat(-16.38,+18.914)km,usinguni-
formweighting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
8 Beampatternofa424-elementantennaarray,steeredat(-16.38,+18.914)km, usingop-
timizedmethod.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
9 OnesectionofthefunctionF (X,Y)inFig.8alongtheX-axisatY=Y =18.914km. . . . . 29
1 0
10 Multi-beamsteeringtoallcellsofchannel3. . . . . . . . . . . . . . . . . . . . . . . . . . . 29
11 Coverage performance: (1) best cell performance of the 424-element antenna array
(dashedline);(2)worstcellperformanceofthe424-elementantennaarray(dottedline);
(3)averagecellperformanceofthe424-elementantennaarray(dot-dashedline)(4)set
oflensapertureantennas[1](solidline). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
12 Verticalantennaarrayandring-shapedcellsforHAPcommunications. . . . . . . . . . . . 32
13 An algorithm of connecting beampatterns in order to determine number and size of the
cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
14 Comparisonofthefrequencyresponseofseveralwindowfunctions. . . . . . . . . . . . . 35
15 Comparison of the beampatterns of a vertical antenna with subarray and non-subarray
structures: redline: non-subarray,121elems,Hammingwindow;blueline: subarray,190
elems,Hamming/Chebyshevwindow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
16 Comparison of coverage performance with directive aperture antennas and vertical an-
tenna array using different window functions. A.121.30: Aperture antenna, 121 elems.,
30 cells; H.121.42: Vertical antenna, Hamming, 121 elems., 42 cells; C.121.32: Verti-
cal antenna, Chebyshev, 121 elems., 32 cells; B.121.32: Vertical antenna, Blackman,
121 elems., 32 cells; K.121.32: Vertical antenna, Kaiser, 121 elems., 32 cells; S.121.42:
Subarrayverticalantenna,Hamming/Chebyshev,121elems.,42cells. . . . . . . . . . . . 36
17 HAPcommunicationsscenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
18 TheeffectofHAPpitchonCartesianco-ordinatesystemrelativetonormaltoarray. . . . 40
19 Arraytopologies: a)smallsquare,d=0.5λ,b)circular,d=0.5λ,c)largesquare,d=1.6λ. 43
20 Beampatternsofthreetopologiesthroughazimuthφ=0o . . . . . . . . . . . . . . . . . . 43
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21 CoverageforCaponbeamfromsmallsquarearray.. . . . . . . . . . . . . . . . . . . . . . 44
22 CoverageforCaponbeamfromcirculararray. . . . . . . . . . . . . . . . . . . . . . . . . . 45
23 CoverageforCaponbeamfromlargesquarearray. . . . . . . . . . . . . . . . . . . . . . . 46
24 CDFofa)SNR,b)SIRandc)SINR,withpitchvariation,σ =0.5o . . . . . . . . . . . . . 47
p
25 Testscenario: ReferenceuserUmovesinstepsfromSPPtoECP. . . . . . . . . . . . . . 48
26 DirectivityindirectionofuserUinstepsfromSPPtoECP. . . . . . . . . . . . . . . . . . . 48
27 CaponbeampatternforsmallsquarearraywithUandBclosely-spaced. . . . . . . . . . . 49
28 CaponbeampatternforcirculararraywithUandBclosely-spaced. . . . . . . . . . . . . . 49
29 CaponbeampatternforlargesquarearraywithUandBclosely-spaced. . . . . . . . . . . 50
30 HAPcommunicationsscenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
31 Allocationofusersacrosschannelsina)firstrowandb)secondrowofA . . . . . . . . . 54
32 CDFofpairwiseseparationD (km)ofco-channelusers . . . . . . . . . . . . . . . . . . . 54
s
33 CDFofSIRforreferenceuserwithrandomandproposedchannelallocations. . . . . . . 55
34 a) Favourable user distribution, b) less-favourable user distribution of 8 users, c) User
SINRsforCapon’smethodwithpowercontrolwithfavourabledistribution,d)UserSINRs
forCapon’smethodwithpowercontrolwithless-favourabledistribution . . . . . . . . . . . 62
35 a)UserSINRsforSINR-balancing withfavourabledistribution, d)UserSINRsforSINR-
balancingwithless-favourabledistribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
36 HAPcommunicationsscenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
37 HAPcommunicationsscenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
38 DOAestimationfrompolynomialrootsa)two-trainscenario,b)complexz-planeforC (z),
x
c)complexz-planeforC (z). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
y
39 Scenario 1: Position estimates of trains for a) RM DOA, b) RM DOA/EKF, c) Magnitude
ofpositionalestimateerrorfortrainA,d)SINRfortrainA. . . . . . . . . . . . . . . . . . . 81
40 Scenario2: a)Positionalestimatesoftrains,b)Magnitudeofpositionalestimateerrorfor
trainA,c)SINRfortrainA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
41 Scenario2: BeampatternfortrainAa)Bartlettbeamforming,b)Caponbeamforming. . . 84
42 Scenario 3: a) Positional estimates of trains for RM DOA, b) Magnitude of positional
estimateerrorfortrainA,c)SINRfortrainA. . . . . . . . . . . . . . . . . . . . . . . . . . 86
43 Scenario4: a)PositionalestimatesoftrainsforRMDOA/EKF,b)SINRfortrainA. . . . . 87
44 Scenario 5: a) Positional estimates of trains for RM DOA/EKF, b) Speed of train A, c)
SINRfortrainAforRMDOA/EKF. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
45 Scenario6: a)PositionalestimatesoftrainsforRMDOA/EKF,b)Magnitudeofpositional
estimateerrorfortrainA,c)SINRfortrainA. . . . . . . . . . . . . . . . . . . . . . . . . . 91
46 M-elementsOFDMadaptiveantennaarray . . . . . . . . . . . . . . . . . . . . . . . . . . 96
47 OFDMmodelusedforsimulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
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48 Conventional Delay-and-Sum (DAS) beamformer output signal with higher (yellow) and
lower(red)Dopplershiftcomparedtothetransmittedsignal(black). . . . . . . . . . . . . 105
49 PilotLMS(a),(b)andPilot-ZeroesLMS(c),(d)algorithms. Receivedsignalscomparedto
thetransmittedones(black)for2084OFDMsymbolsand30dBofSignal-to-Noiseratio. . 106
50 Comparison between the Pilot LMS (red) and the Pilot-Zeroes LMS (green) adaptation
errors(a)andcostfunctions(b)for2084OFDMsymbolsand30dBofSignal-to-Noiseratio.106
51 Pilot-Expon LMS beamformer output signal compared to the transmitted one for 2084
OFDMsymbolsand30dBofSignal-to-Noiseratio(a)andthezoomedversion(b). . . . . 107
52 Pilot-Expon LMS beamformer adaptation error (a), cost function (b) and normalized fre-
quency estimate φ[n] = fd[n] (c) for 2084 OFDM symbols and 30 dB of Signal-to-Noise
2πTc
ratio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
53 Pilot-ExponLMS(magenta)andPilot-Zeroes-ExponLMS(yellow)beamformersreceived
signals compared to the transmitted one (black) for 2084 OFDM symbols and 30dB of
Signal-to-Noiseratio. Figure(b)isthezoomononesymbol. . . . . . . . . . . . . . . . . . 108
54 Pilot-ExponLMS(magenta)andPilot-Zeroes-ExponLMS(yellow)beamformersadapta-
tionerrors(a),costfunctions(b)andnormalizedfrequencyestimatesφ[n]= fd[n] (c)for
2πTc
2084OFDMsymbolsand30dBofSignal-to-Noiseratio. . . . . . . . . . . . . . . . . . . . 109
55 Pilot-Expon LMS and Pilot-Zeroes-Expon LMS beamformers array factors in the Theta-
Phi-Zspace(a),(c)andweighvectors(b),(d)for2084OFDMsymbolsans30dBofSignal-
to-Noiseratio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
56 Pilot-ExponLMS(magenta)andPilot-Zeroes-ExponLMS(yellow)beamformersnormal-
ized frequency estimates φ[n] = fd[n] for 2084 OFDM symbols and different Signal-to-
2πTc
Noiseratios: (a)20dB,(b)10dB,(c)0dB,(d) 5dB. . . . . . . . . . . . . . . . . . . . . 111
−
57 Pilot-Expon LMS and Pilot-Zeroes-Expon LMS beamformers array factors in the Theta-
Phi-Zspacefor2084OFDMsymbolsandtwodifferentSignal-to-Noiseratios: (a)and(c)
20dB,(b)and(d) 5dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
−
58 Pilot-ExponLMS(magenta)andPilot-Zeroes-ExponLMS(yellow)beamformersreceived
signals compared to the transmitted one (black) for 2084 OFDM symbols and different
Signal-to-Noiseratios: (a)20dB,(b)10dB,(c)0dB,(d) 5dB. . . . . . . . . . . . . . . 113
−
59 Pilot-Zeroes-ExponLMS(yellow)andPilot-Zeroes-Expon-AlphaLMS(cyano)beamform-
ersreceivedsignalscomparedtothetransmittedone(black)for2084OFDMsymbolsand
differentSignal-to-Noiseratios: (a)20dB,(b)10dB,(c)0dB,(d) 5dB. . . . . . . . . . . 114
−
60 Pilot-Zeroes-ExponLMS(yellow)andPilot-Zeroes-Expon-AlphaLMS(cyano)beamform-
ersreceivedsignalscomparedtothetransmittedone(black)zoomedononesymbolfor
2084OFDMsymbolsanddifferentSignal-to-Noiseratios: (a)20dB,(b)10dB,(c)0dB,
(d) 5dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
−
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61 Pilot-Zeroes-Expon-Alpha LMS beamformer array factor in the Theta-Phi-Z space for
2084 OFDM symbols in the multipath environment with three reflected rays in DOAs
=[ 20 ,40 ,60 ]representedbythethreeredlines. Thegreenonerepresentstheuseful
◦ ◦ ◦
−
signalwithDOA=20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
◦
62 Pilot-Zeroes-Expon-Alpha LMS beamformer behavior for 30 dB ofSignal-to-Noise Ratio
and 2084 OFDM symbols in the multipath environment: (a) received vs. transmitted
signals,(b)adaptationerror,(c)costfunction,(d)normalizedfrequencyestimate,φ[n]. . . 117
63 BlockdiagramofanSCtransmitterthatusestrainingsequences. . . . . . . . . . . . . . . 119
64 Exampleofdatastreamthatalternatestrainingsymbolswithinformationsymbols. . . . . 119
65 ArchitectureoftheT/DD-RLSbeamformerforSCadaptivemodulations. . . . . . . . . . . 120
66 Semi-analyticSymbolErrorRateforCaseStudy1. E /N istheequivalentsignal-to-
b 0,eq
interference-and-noisepowerratiomeasuredattheantenna. . . . . . . . . . . . . . . . . 125
67 Radiation patterns obtained at SNR = 10 dB (left) and SNR = 3 dB (right), for Case
−
Study 1. w indicates the radiation pattern at the end of the first training interval; w
0 1
indicates the radiation pattern at the end of the last training interval; w indicates the
e
radiation pattern at the end of the last data interval. The red vertical line indicates the
usefulDOAθ ,whereasthegreenverticalonesindicatetheinterferingDOAs.. . . . . . . 126
0
68 ReceivedsymbolconstellationsobtainedatSNR=10dB(left)andSNR= 3dB(right),
−
for Case Study 1. Red marks indicate symbols sampled after beamforming; blue marks
indicatesymbolssampledafterasingle,non-directionalantenna. . . . . . . . . . . . . . . 127
69 Semi-analytic Symbol Error Rates for Case Study 2, compared with Case Study 2.
E /N istheequivalentsignal-to-interference-and-noiseratiomeasuredattheantenna.128
b 0,eq
70 Radiation patterns obtained at SNR = 3 dB using M = 8 sensors (left) and M = 20
−
sensors(right),forCaseStudy2. w indicatestheradiationpatternattheendofthefirst
0
traininginterval; w indicatestheradiationpatternattheendofthelasttraininginterval;
1
w indicatestheradiationpatternattheendofthelastdatainterval. Theredverticalline
e
indicatestheusefulDOAθ ,whereasthegreenverticalonesindicatetheinterferingDOAs.129
0
71 Received symbol constellations obtained at SNR = 3 dB using M = 8 sensors (left)
−
and M = 20 sensors (right), for Case Study 2. Red marks indicate symbols sampled
after beamforming; blue marks indicate symbols sampled after a single, non-directional
antenna. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
72 Radiation patterns obtained at SNR = 3 dB using M = 8 sensors (left) and M = 20
−
sensors(right),forCaseStudy3. w indicatestheradiationpatternattheendofthefirst
0
traininginterval; w indicatestheradiationpatternattheendofthelasttraininginterval;
1
w indicates the radiation pattern at the end of the last data interval.The red vertical
e
lines indicate the useful DOAs θ and θ , whereas the green vertical ones indicate the
0 0′
interferingDOAs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
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