MIMO Systems 所有程序.docx

MIMO Systems 所有程序.docx

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MIMOSystems所有程序

IntroductiontoMIMOSystems

ThisdemointroducesMultiple-Input-Multiple-Output（MIMO）systems,whichusemultipleantennasatthetransmitterandreceiverendsofawirelesscommunicationsystem.MIMOsystemsareincreasinglybeingadoptedincommunicationsystemsforthepotentialgainsincapacitytheyrealizewhenusingmultipleantennas.Multipleantennasusethespatialdimensioninadditiontothetimeandfrequencyones,withoutchangingthebandwidthrequirementsofthesystem.

Foragenericcommunicationslink,thisdemofocusesontransmitdiversityinlieuoftraditionalreceivediversity.Usingtheflat-fadingRayleighchannel,itillustratestheconceptofOrthogonalSpace-TimeBlockCoding,whichisemployablewhenmultipletransmitterantennasareused.Itisassumedherethatthechannelundergoesindependentfadingbetweenthemultipletransmit-receiveantennapairs.

Forachosensystem,italsoprovidesameasureoftheperformancedegradationwhenthechannelisimperfectlyestimatedatthereceiver,comparedtothecaseofperfectchannelknowledgeatthereceiver.

Contents

∙PART1:

TransmitDiversityvs.ReceiveDiversity

∙PART2:

Space-TimeBlockCodingwithChannelEstimation

∙PART3:

OrthogonalSpace-TimeBlockCodingandFurtherExplorations

PART1:

TransmitDiversityvs.ReceiveDiversity

Usingdiversityreceptionisawell-knowntechniquetomitigatetheeffectsoffadingoveracommunicationslink.However,ithasmostlybeenrelegatedtothereceiverend.In[1],Alamoutiproposesatransmitdiversityschemethatofferssimilardiversitygains,usingmultipleantennasatthetransmitter.Thiswasconceivedtobemorepracticalas,forexample,itwouldonlyrequiremultipleantennasatthebasestationincomparisontomultipleantennasforeverymobileinacellularcommunicationssystem.

Thissectionhighlightsthiscomparisonoftransmitvs.receivediversitybysimulatingcoherentbinaryphase-shiftkeying（BPSK）modulationoverflat-fadingRayleighchannels.Fortransmitdiversity,weusetwotransmitantennasandonereceiveantenna（2x1notationally）,whileforreceivediversityweemployonetransmitantennaandtworeceiveantennas（1x2notationally）.

Thesimulationcoversanend-to-endsystemshowingtheencodedand/ortransmittedsignal,channelmodel,andreceptionanddemodulationofthereceivedsignal.Italsoprovidestheno-diversitylink（singletransmit-receiveantennacase）andtheoreticalperformanceofsecond-orderdiversitylinkforcomparison.Itisassumedherethatthechannelisknownperfectlyatthereceiverforallsystems.WerunthesimulationoverarangeofEb/NopointstogenerateBERresultsthatallowustocomparethedifferentsystems.

Westartbydefiningsomecommonsimulationparameters

frmLen=100;%framelength

numPackets=1000;%numberofpackets

EbNo=0:

2:

20;%Eb/Novaryingto20dB

N=2;%maximumnumberofTxantennas

M=2;%maximumnumberofRxantennas

andsetupthesimulation.

%Seedstatesforrepeatability

seed=[9876512345];randn（'state',seed

（1））;rand（'state',seed

（2））;

%CreateBPSKmod-demodobjects

P=2;%modulationorder

bpskmod=modem.pskmod（'M',P,'SymbolOrder','Gray'）;

bpskdemod=modem.pskdemod（bpskmod）;

%Pre-allocatevariablesforspeed

tx2=zeros（frmLen,N）;H=zeros（frmLen,N,M）;

r21=zeros（frmLen,1）;r12=zeros（frmLen,2）;

z21=zeros（frmLen,1）;z21_1=zeros（frmLen/N,1）;z21_2=z21_1;

z12=zeros（frmLen,M）;

error11=zeros（1,numPackets）;BER11=zeros（1,length（EbNo））;

error21=error11;BER21=BER11;error12=error11;BER12=BER11;BERthy2=BER11;

%SetupafigureforvisualizingBERresults

h=gcf;gridon;holdon;

set（gca,'yscale','log','xlim',[EbNo

（1）,EbNo（end）],'ylim',[1e-51]）;

xlabel（'Eb/No（dB）'）;ylabel（'BER'）;set（h,'NumberTitle','off'）;

set（h,'renderer','zbuffer'）;set（h,'Name','Transmitvs.ReceiveDiversity'）;

title（'Transmitvs.ReceiveDiversity'）;

%LoopoverseveralEbNopoints

foridx=1:

length（EbNo）

%Loopoverthenumberofpackets

forpacketIdx=1:

numPackets

data=randint（frmLen,1,P）;%datavectorperuserperchannel

tx=modulate（bpskmod,data）;%BPSKmodulation

%AlamoutiSpace-TimeBlockEncoder,G2,fullrate

%G2=[s1s2;-s2*s1*]

s1=tx（1:

N:

end）;s2=tx（2:

N:

end）;

tx2（1:

N:

end,:

）=[s1s2];

tx2（2:

N:

end,:

）=[-conj（s2）conj（s1）];

%CreatetheRayleighdistributedchannelresponsematrix

%fortwotransmitandtworeceiveantennas

H（1:

N:

end,:

:

）=（randn（frmLen/2,N,M）+...

j*randn（frmLen/2,N,M））/sqrt

（2）;

%assumeheldconstantfor2symbolperiods

H（2:

N:

end,:

:

）=H（1:

N:

end,:

:

）;

%Receivedsignals

%foruncoded1x1system

r11=awgn（H（:

1,1）.*tx,EbNo（idx））;

%forG2-coded2x1system-withnormalizedTxpower,i.e.,the

%totaltransmittedpowerisassumedconstant

r21=awgn（sum（H（:

:

1）.*tx2,2）/sqrt（N）,EbNo（idx））;

%forMaximal-ratiocombined1x2system

fori=1:

M

r12（:

i）=awgn（H（:

1,i）.*tx,EbNo（idx））;

end

%Front-endCombiners-assumechannelresponseknownatRx

%forG2-coded2x1system

hidx=1:

N:

length（H）;

z21_1=r21（1:

N:

end）.*conj（H（hidx,1,1））+...

conj（r21（2:

N:

end））.*H（hidx,2,1）;

z21_2=r21（1:

N:

end）.*conj（H（hidx,2,1））-...

conj（r21（2:

N:

end））.*H（hidx,1,1）;

z21（1:

N:

end）=z21_1;z21（2:

N:

end）=z21_2;

%forMaximal-ratiocombined1x2system

fori=1:

M

z12（:

i）=r12（:

i）.*conj（H（:

1,i））;

end

%MLDetector（minimumEuclideandistance）

demod11=demodulate（bpskdemod,r11.*conj（H（:

1,1）））;

demod21=demodulate（bpskdemod,z21）;

demod12=demodulate（bpskdemod,sum（z12,2））;

%Determineerrors

error11（packetIdx）=biterr（demod11,data）;

error21（packetIdx）=biterr（demod21,data）;

error12（packetIdx）=biterr（demod12,data）;

end%endofFORloopfornumPackets

%CalculateBERforcurrentidx

%foruncoded1x1system

BER11（idx）=sum（error11）/（numPackets*frmLen）;

%forG2coded2x1system

BER21（idx）=sum（error21）/（numPackets*frmLen）;

%forMaximal-ratiocombined1x2system

BER12（idx）=sum（error12）/（numPackets*frmLen）;

%fortheoreticalperformanceofsecond-orderdiversity

BERthy2（idx）=berfading（EbNo（idx）,'psk',2,2）;

%Plotresults

semilogy（EbNo（1:

idx）,BER11（1:

idx）,'r*',...

EbNo（1:

idx）,BER21（1:

idx）,'go',...

EbNo（1:

idx）,BER12（1:

idx）,'bs',...

EbNo（1:

idx）,BERthy2（1:

idx）,'m'）;

legend（'NoDiversity（1Tx,1Rx）','Alamouti（2Tx,1Rx）',...

'Maximal-RatioCombining（1Tx,2Rx）',...

'Theoretical2nd-OrderDiversity'）;

drawnow;

end%endofforloopforEbNo

%Performcurvefittingandreplottheresults

fitBER11=berfit（EbNo,BER11）;

fitBER21=berfit（EbNo,BER21）;

fitBER12=berfit（EbNo,BER12）;

semilogy（EbNo,fitBER11,'r',EbNo,fitBER21,'g',EbNo,fitBER12,'b'）;

holdoff;

Thetransmitdiversitysystemhasacomputationcomplexityverysimilartothatofthereceivediversitysystem.

Theresultingsimulationresultsshowthatusingtwotransmitantennasandonereceiveantennaprovidesthesamediversityorderasthemaximal-ratiocombined（MRC）systemofonetransmitantennaandtworeceiveantennas.

Alsoobservethattransmitdiversityhasa3dBdisadvantagewhencomparedtoMRCreceivediversity.Thisisbecausewemodelledthetotaltransmittedpowertobethesameinbothcases.Ifwecalibratethetransmittedpowersuchthatthereceivedpowerforthesetwocasesisthesame,thentheperformancewouldbeidentical.Thetheoreticalperformanceofsecond-orderdiversitylinkmatchesthetransmitdiversitysystemasitnormalizesthetotalpoweracrossallthediversitybranches.

Theaccompanyingfunctionalscripts,MRC1M.mandOSTBC2M.maidfurtherexplorationfortheinterestedusers.

PART2:

Space-TimeBlockCodingwithChannelEstimation

Buildingonthetheoryoforthogonaldesigns,Tarokhetal.[2]generalizedAlamouti'stransmitdiversityschemetoanarbitrarynumberoftransmitterantennas,leadingtotheconceptofSpace-TimeBlockCodes.Forcomplexsignalconstellations,theyshowedthatAlamouti'sschemeistheonlyfull-rateschemefortwotransmitantennas.

Inthissection,westudytheperformanceofsuchaschemewithtworeceiveantennas（i.e.,a2x2system）withandwithoutchannelestimation.Intherealisticscenariowherethechannelstateinformationisnotknownatthereceiver,thishastobeextractedfromthereceivedsignal.Weassumethatthechannelestimatorperformsthisusingorthogonalpilotsignalsthatareprependedtoeverypacket[3].Itisassumedthatthechannelremainsunchangedforthelengthofthepacket（i.e.,itundergoesslowfading）.

Asimulationsimilartotheonedescribedintheprevioussectionisemployedhere,whichleadsustoestimatetheBERperformanceforaspace-timeblockcodedsystemusingtwotransmitandtworeceiveantennas.

Againwestartbydefiningthecommonsimulationparameters

frmLen=100;%framelength

maxNumErrs=300;%maximumnumberoferrors

maxNumPackets=3000;%maximumnumberofpackets

EbNo=0:

2:

12;%Eb/Novaryingto12dB

N=2;%numberofTxantennas

M=2;%numberofRxantennas

pLen=8;%numberofpilotsymbolsperframe

W=hadamard（pLen）;

pilots=W（:

1:

N）;%orthogonalsetpertransmitantenna

andsetupthesimulation.

%Seedstatesforrepeatability

seed=[9876512345];randn（'state',seed

（1））;rand（'state',seed

（2））;

%Pre-allocatevariablesforspeed

tx2=zeros（frmLen,N）;r=zeros（pLen+frmLen,M）;

H=zeros（pLen+frmLen,N,M）;H_e=zeros（frmLen,N,M）;

z_e=zeros（frmLen,M）;z1_e=zeros（frmLen/N,M）;z2_e=z1_e;

z=z_e;z1=z1_e;z2=z2_e;

BER22_e=zeros（1,length（EbNo））;BER22=BER22_e;

%SetupafigureforvisualizingBERresults

clf（h）;gridon;holdon;

set（gca,'yscale','log','xlim',[EbNo

（1）,EbNo（end