最相邻边界·.pptx

5 ObtainsimulatedBERresultsforGray codedQPSKand8 PSKbycreatingaMATLABTMprogram RunsimulationsforEb N0intherangefrom0to15dB InwhichregiondoesthenearestneighborunionboundonBER seeProblem3 appeartobetight snrstart dB 0 StartEb N0 dB snrstop dB 15 StopEb N0 dB snrdelta dB 0 5 Stepsize dB samples 1e6 NumberofsamplesperEb N0point Results estimatedbiterrorprobabilities result antip result QPSK result 8PSK StartaloopoverthespecifiedEb N0values forsnr dB snrstart dB snrdelta dB snrstop dB PrintoutcurrentSNR snr dB Non dBEb N0snr 10 snr dB 10 Assumethatthesamesymbolistransmittedallthetime Notethatthisisnotalwaysavalidassumption First binaryantipodalsignalling CreatezeromeanGaussiannoisevariableswithunitvariance noise randn 1 samples snr Eb N0 var N0 2 1 N0 2 Eb snr 2 Detectionthreshold sqrt Eb Ifa zeromean noisesampleislargerthansqrt Eb awrongdecisionismade Howmanyerrors error vector noise sqrt snr 2 error antip sum error vector Storeresults result antip result antiperror antip samples CoherentGraycodedQPSKsignalling Note twobitspersymbol snr Eb N0 var N0 2 1 onbothIandQchannels N0 2 Eb snr 2 Es 2 Eb Es 4 snr Acorrectdecisionismadeiftheconstellationpointangle iswithinpi 4and pi 4 Createthetransmittedsignal atsqrt Es t sqrt 4 snr CreatetheIandQnoisesamples zeromean unitvariance noiseI randn 1 samples noiseQ randn 1 samples Thereceivedsignals r t noiseI noiseQ i Anglesforallsamples phi angle r Howmanyerrors Onebiterror error vector phi pi 4 Squareddistancestoallsignalalternatives Howmanyerrors Differencevectortosignalalternativei r s i diff diff diff abs r s 1 diff diff abs r s 2 diff diff abs r s 3 diff diff abs r s 4 diff diff abs r s 5 diff diff abs r s 6 diff diff abs r s 7 diff diff abs r s 8 Gettheindicesofthesignalalternativeswiththeminimum squared distanceforeachsample MinVal Index min diff Onebiterrors error vector Index 2 s 2 error 8PSK sum error vector error vector Index 6 s 6 error 8PSK error 8PSK sum error vector error vector Index 8 s 8 error 8PSK error 8PSK sum error vector Twobiterrors error vector Index 3 s 3 error 8PSK error 8PSK 2 sum error vector error vector Index 5 s 5 error 8PSK error 8PSK 2 sum error vector error vector Index 7 s 7 error 8PSK error 8PSK 2 sum error vector Threebiterrors error vector Index 4 s 4 error 8PSK error 8PSK 3 sum error vector Storeresults threebitspersample result 8PSK result 8PSKerror 8PSK samples 3 end TheEb N0values snr dB snrstart dB snrdelta dB snrstop dB Plottheresults figure semilogy snr dB Q sqrt 2 10 snr dB 10 holdon semilogy snr dB result antip semilogy snr dB result QPSK o semilogy snr dB 2 3 Q sqrt 6 10 snr dB 10 sin pi 8 semilogy snr dB result 8PSK d ylabel BER xlabel E b N 0 dB legend ExactBPSKandQPSK SimBPSK SimQPSK NNUB8 PSK Sim8 PSK FigureExactandsimulatedBERforBPSKandQPSK Nearestneighborunionbound NNUB BERandsimulatedBERfor8 PSK ItcanbeseeninFigurethatthes