%Run from editor Debug(F)%This m file(ASK.m) analyzes a coherent amplitute shift keyed(ASK) and a binary%phase shift keyed(BPSK) communication system. The receiver uses a correlator%(mixer-integrator [lpf]) configuration with BER measurements comparing measured%and theoretical results. The band pass and low pass filters used in the receiver are%constructed using z transforms. M files on BPF and LPF design using z%transforms can be found in the author index (CJ) mathworks file exchange. A fundemental %question to ask is: "Why does BPSK show a 3dB improvement(as you will see using the %program)in BER over ASK?". A simple answer is that the signal for ASK is being%transmitted only half the time. A reference is provided at the end of the program that%was used in writing the program. Always remember a journey of a thousand%miles requires a first one small step.%========================================% Set universal parameters% =======================================clearfs=8e5;%sampling frequencyfm=20e3;%square wave modulating frequency(NRZ)= 40KHz bit raten=2*(6*fs/fm);final=(1/fs)*(n-1);fc=2e5; % carrier frequencyt=0:1/fs:(final);Fn=fs/2;%nyquist frequency%=========================================%Generate square wave by using cosine wave%==========================================% cosine wave% 2 pi fc t is written as belowtwopi_fc_t=2*pi*fm*t; A=1;phi=0;x = A * cos(twopi_fc_t + phi);% square waveam=1;x(x>0)=am;%x(x<0)=0;%use for ASK-comment out BPSKx(x<0)=-1;%use for BPSK-remember ASK variables become BPSKsubplot(321);plot(t,x);axis([1e-4 3e-4 -2 2]);title('Square Wave Modulating Input To Transmitter');grid oncar=sin(2*pi*fc*t);%Sinewave carrier waveformask=x.*car;%modulate carrier(ASK or BPSK)subplot(322);plot(t,ask);axis([0 100e-6 -2 2]);title('Modulated Sinewave Carrier Waveform');grid on;%=====================================================%Noise generator SNR=Eb/No=20log(Signalrms/Noiserms)%======================================================%vn=0;vn=.1;%set noise level 0.1~=6db=SNR=Eb/Nonoise=vn*(randn(size(t)));%noise generatorsubplot(323);plot(t,noise);grid on;title('Noise Level');axis([0 .6e-3 -1 1]);askn=(ask+noise);%modulated carrier plus noisesubplot(324);plot(t,askn);axis([0 100e-6 -2 2]);title('Modulated Carrier Waveform Plus Noise');grid on;%======================================================================%Receiver bandpass filter(two poles two zeros) %======================================================================fBW=40e3;f=[0:3e3:4e5];w=2*pi*f/fs;z=exp(w*j);BW=2*pi*fBW/fs;a=.8547;%BW=2(1-a)/sqrt(a)p=(j^2*a^2);gain=.135;Hz=gain*(z+1).*(z-1)./(z.^2-(p));subplot(325);plot(f,abs(Hz));title('Receiver Bandpass Filter Response');grid on;Hz(Hz==0)=10^(8);%avoid log(0)subplot(326);plot(f,20*log10(abs(Hz)));grid on;title('Receiver -3dB Filter Response');axis([1e5 3e5 -3 1]);%filter coefficientsa=[1 0 .7305];%[1 0 p]b=[.135 0 -.135];%gain*[1 0 -1]faskn=filter(b,a,askn);figure;subplot(321);plot(t,faskn);axis([0 100e-6 -2 2]);title('Receiver BPF Output');grid on;cm=faskn.*car;%multiply modulated carrier with unmodulated carriersubplot(322);plot(t,cm);axis([0 100e-6 -2 2]);grid on;title('Receiver Multiplier Output');%===================================================================%Low pass filter(one pole one zero)%==================================================================p=.72;gain1=.14;%gain=(1-p)/2Hz1=gain1*(z+1)./(z-(p));%0.65=53KHz%0.7=45KHz%0.72=40KHZ=best for lowest BER-Theory says set equal to the bit rate%0.75=37KHz%0.8=28KHz%subplot(323);%plot(f,abs(Hz1));%title('Receiver LPF Response');%grid on;subplot(323);Hz1(Hz1==0)=10^(-8);%avoid log(0)plot(f,20*log10(abs(Hz1)));grid on;title('LPF -3dB response');axis([0 5e4 -3 1]);%filter coefficientsa1=[1 -.72];%(z-(p))b1=[.14 .14];%gain*[1 1]so=filter(b1,a1,cm);so=so*10;%add gainso=so-mean(so);%removes DC componentsubplot(324);plot(t,so);axis([1e-4 3e-4 -2.5 2.5]);title('Receiver Output Signal-LPF');grid on;%======================================================%Comparator%======================================================High=2.5;Low=-2.5;vt=0;%sets comparator thresholderror=0;%calculate the number of elements in matrix so, the output of the filterlen1=length(so); %number of elements in sofor ii=1:len1  if so(ii) >= vt  Vs(ii)=High;  else  Vs(ii)=Low;  endendVo=Vs+2.5;subplot(325);plot (t,Vo), title('Receiver Regenerated signal'),axis([1e-4 3e-4 -8 8])grid on;xlabel('Time (s)'), ylabel('Magnitude(V)'),%========================================================%Generate delayed squarewave%=========================================================%cosine wave delayed to match receiver regenerated signal square waves.%filters have delay% 2 pi fc t is written as belowtwopi_fc_t1=2*pi*fm*(t-.59e-4);%adds delay %A=1;phi1=0;x1 = A * cos(twopi_fc_t1 + phi1);% square wavex1(x1>0)=am;x1(x1<0)=0;sr=x1;sf=5*sr;subplot(326);plot (t,sf), title('Input signal-delayed'),axis([1e-4 3e-4 -8 8]);grid on;xlabel('Time (s)'), ylabel('Magnitude(V)'),a=5*xor(sf,Vo); %show where errors occur against time.figure(3);plot (t,a), title('Error pulses'),axis([0 8e-4 -8 8]);grid on;xlabel('Time (s)'), ylabel('Magnitude(V)'),  %for ii=1:len1;  for ii=20:1:len1%during startup,errors are generated. The first 20 samples of len1                  %(480 samples) are bypassed and no noise gives zero errors. 480-20=460   if sf(ii) ~= Vo(ii) % if output and input are not the same then increment error  error=error+1;  endenderror %display number of errorsfigure(4);err=[0 0 0 0 0 0 error/460 0 0];%Measured at different values of SNR by setting vnsnr=10.^ ( [0:0.1:12]./10);Pb= 0.5*erfc(.707*sqrt(snr)); % BER (Theoretical-ASK)Pb1= 0.5*erfc(sqrt(snr)); % BER (Theoretical-BPSK)semilogy([0:8],err,'*',[0:0.1:12],Pb,'-',[0:0.1:12],Pb1,'--'); % plotgrid on; xlabel('SNR=Eb/No(dB)'); ylabel('BER');title('Simulation of BER for ASK and BPSK');legend('BER','ASK Theoretical','BPSK Theoretical');BER=error/460%display BER%Could have set up a for loop using vn to calculate all points(err) but would%complicate matters.Easier to run by hand and observe BER plot. Presently%set for SNR=6dB.%===================================================%Frequency domain plots%====================================================%Lets take a look at askn(unfiltered carrier + noise) and%faskn(band pass filtered carrier + noise) output on a spectrum analyzer.%This fft code is somewhat complex but comes from the mathworks. Works%great as it shows one what they would actually see using a spectrum analyzer.%y=askn;%unfiltered carrier + noise y=faskn;%band pass filtered carrier + noiseNFFY=2.^(ceil(log(length(y))/log(2)));FFTY=fft(y,NFFY);%pad with zerosNumUniquePts=ceil((NFFY+1)/2); FFTY=FFTY(1:NumUniquePts);MY=abs(FFTY);MY=MY*2;MY(1)=MY(1)/2;MY(length(MY))=MY(length(MY))/2;MY=MY/length(y);f1=(0:NumUniquePts-1)*2*Fn/NFFY;figure(5)subplot(2,2,1); plot(f1,MY);xlabel('FREQUENCY');ylabel('AMPLITUDE');axis([0 3e5 -.5 1]);%zoom in/outtitle('Modulated Tx carrier plus noise');grid on;subplot(2,2,2); plot(f1,20*log10(abs(MY).^2));xlabel('FREQUENCY');ylabel('DB');axis([0 3e5 -60 5]);grid on;title('Frequency domain plots')%Reference%http://soe.unn.ac.uk/ocr/people/ghassemlooy/%Prof. Z Ghassemlooy's website%Good site for theory and m files. I structured this m file from his work%and have added a few things. I constructed filters using z transforms%since I don't have the filter toolbox functions.