Phase-shift keying (PSK) Input Decision Output …

1 Phase-shiftkeying (PSK) BothOOKandFSKweres howntoresultina probabilityoferrorofp DerfcsEb ;whereEbis s discussionofwhy OOKandFSKdon t binaryphase-shiftkeyed(BPSK) !ct/;where!cis thecarrierfrequency, a polarbinarybasebandsignaltakingonthevalu e1 fora markand 1 fora differentsignals,andthey differonlybya changeofsign,thissignallingschemeis alsocalledphase-reversalkeying(PRK). !1t/;0<t T; Acos.!1t/;0<t T:Whenthebasebandsignalconsistsofsquarep ulseswithamplitudetakingonvaluesofC1 and 1 withequalprobability, it fc/ fc/ 2C14 2:HerethedatarateisRD1= essentiallythesameasthePSDobtainedbyassu minga deterministicalternatingsquarewave takingonvaluesofC1 and 1 insequence,whichcanbeconsidereda ,thereis noneedtohave two presentat theinput,and theoutputofthefilterisE =2,sotheoverallprobabilityoferroratthere ceiverisP Derfc 2 EpE =2 Derfcs2E :Sincethesignalshave thesameenergywhena zeroanda onearetransmitted,thiscanbewrittenasP Derfcs2Eb.

2 Forthesamecommunicationchannel, , thereis a coherentreferenceforsynchronousdetection cannotbeobtainedbytheuseofanordinaryphas e-lockedtrackingloop,sincetherearenospec trallinecomponentsat fc. However, sincethesignalhasa spectrumthatissymmetricwithrespecttothe( suppressed)carrierfrequency, squaringloopina coherentdetectoris shownbelow:2 BPFL imiterSquare ! !ct/A0cos.! ! [ !ct/] , a Costasphase-lockedloopcanalsoperformthet ask:VCOLPF phase shift 90 !ct/A0cos.!ctC e/A0sin.!ctC 12A0 Acsin e 12A0 Accos e lockedtotheinputsuppressedcarrierfrequen cyfc, witha constantphaseerrorof e. eis small, Furthermore, , soit filteredwitha LPFthathascutoff frequency ewhereKD1= theDClevel ThisDCcontrolvoltageis sufficienttokeeptheVCOlockedtofcwitha smallphaseerror onedisadvantage a 180degreephaseambiguity.

3 It canbeshownthatthenoiseperformanceofthesq uaringloopandtheCostasPLLareequivalent,s othechoiceofwhichtoimplementdependsonthe relative costoftheloopcomponentsandtheaccuracy thatcanberealisedwheneachcomponentis However, a partiallycoherenttechniquecanbeusedwhere bythephasereferenceforthepresentsignalli nginterval is providedbya :ThresholdDelayTLPFS ampleand holdIf a zero-noiseBPSK signalis appliedtothereceiverinput,theoutputofthe sample-and-holdcircuitwillbepositive (binary1)if thepresentdatabitandthepreviousdatabitar ethesame;theoutputis negative (binaryzero)if thedataintheBPSKis differentiallyencoded,thenthedecodedsequ encewillberecoveredat moregeneralrepresentationfora !

4 Ctcos[ 1m]CAcos!ctsin[ 1m];wheremDcos1 is definedtobethemodulationindex. , Asin! m2 Acos!ct:Thefirsttermcontainsthepilotcarr ier, , m2/A2= fractionm2ofthetotalpowerinthemodulatedw aveformis allocatedtothecarrier. It followsthatthecarriercomponentis zeroina PRKwaveform,forwhich1 D = m2/= :Thustheeffectofallocatinga fractionm2ofthetotalpowertothecarrieris todegradeP m2 , theresultingwaveformhasa spectrallineat thecarrier, whichcanbefoundusinga coherentlydetectedOOKsystemisP DerfcsE2 ;whereEis thebitenergyontransmissionofa thepeakpoweris theimportantdesignparameter. If marksandspacesoccurwithequalprobability, thenthiscanbewrittenasP DerfcsEb ;withEbtheaveragebitenergy.

5 Becauseofthepresenceofa largecarriercomponent,noncoherentdetecti onofOOKis alsopossible,sosimpleenvelopedetectionca nbeusedinthereceiver. Synchronousdetectionoffersonlyabouta centeredat!c, andhasanidenticalshapetothecorresponding on-off ,thetheoreticalmaximumbandwidthefficienc y is1 , Thedecisionthresholdinthereceiverdoeshow everhave tobeadjustedwithchangesinreceivedsignall evels, DerfcsE :Sincethesignalis active allthetime,thiscanbeexpressedintermsofth eaveragebitenergyEbasP DerfcsEb :Intermsofaveragepowerrequired,theperfor manceofFSKis , intermsofpeakpower, FSKhasa zerodecision-thresholdregardlessofthecar riersignalstrength, , thereis , however, accordingtowhethercoherentornoncoherentd etectionis quitesimpletoperform,andis , thefrequenciesusedmustthensatisfythecond ition21f T 1, 21fC2B, ,butcasesfor21f T<12resultina S/Npenalty.

6 Derfcs2E ;orP Derfcs2Eb :ThusPSKsystemsrequirelesstransmittedpow erfora required,duetotheabsenseofa thereforemorecomplex goodcompromise,offeringsimplercircuitrya t PSKwaveformis centeredaround!c, < =2,thereis a carriercomponentandthePSDhasanimpulseat thecarrierfrequency. ofPSKsystemsis 1 Theorderofperformance,fromworsttobest,is NoncoherentASK CoherentASK8 NoncoherentFSK CoherentFSK DPSK ,DPSK.