: Hi am Mohit.d i would like to get details on matlab code for dpsk modulation and demodulation .

The following code is for simulating non-coherent DPSK for M=2,4,8,16,32 (bits per symbol).

This code is extended from the examples available in the ebook.


% Iman Bagheri / December 2013 / imaanibagheri[at]gmail.com
% Simple Matlab/Octave code for non-coherent demodulation of
% differentially encoded phase shift keying (DPSK)
clc;clear all;close all;

%———Input Fields————————
N = 1e6; % number of bits or symbols
EbN0dB = 6:2:16; % multiple Eb/N0 values
rangeofM = [2,4,8,16,32]; % DPSK constellation
colors=['b','r','g','k','m'];
%———————————————

colorIndex=1;
legendString=cell(1,10);

figure;
%— Reference Constellation for demodulation and Error rate computation–
for M =rangeofM,
display(M)
switch M
case 2
% Constellation 2-DPSK
refArray = [ 1.0000 + 0.0000i 0.0000 + 1.0000i -1.0000 + 0.0000i -0.0000 - 1.0000i];

case 4
% Constellation 4-DPSK
refArray = [ 1.0000 + 0.0000i 0.7071 + 0.7071i 0.0000 + 1.0000i -0.7071 + 0.7071i ...
-1.0000 + 0.0000i -0.7071 - 0.7071i -0.0000 - 1.0000i 0.7071 - 0.7071i];

case 8
% Constellation 8-DPSK
refArray = [ 1.0000 + 0.0000i 0.9239 + 0.3827i 0.7071 + 0.7071i 0.3827 + 0.9239i ...
0.0000 + 1.0000i -0.3827 + 0.9239i -0.7071 + 0.7071i -0.9239 + 0.3827i ...
-1.0000 + 0.0000i -0.9239 - 0.3827i -0.7071 - 0.7071i -0.3827 - 0.9239i ...
-0.0000 - 1.0000i 0.3827 - 0.9239i 0.7071 - 0.7071i 0.9239 - 0.3827i];

case 16
% Constellation 16-DPSK
refArray = [ 1.0000 + 0.0000i 0.9808 + 0.1951i 0.9239 + 0.3827i 0.8315 + 0.5556i ...
0.7071 + 0.7071i 0.5556 + 0.8315i 0.3827 + 0.9239i 0.1951 + 0.9808i ...
0.0000 + 1.0000i -0.1951 + 0.9808i -0.3827 + 0.9239i -0.5556 + 0.8315i ...
-0.7071 + 0.7071i -0.8315 + 0.5556i -0.9239 + 0.3827i -0.9808 + 0.1951i ...
-1.0000 + 0.0000i -0.9808 - 0.1951i -0.9239 - 0.3827i -0.8315 - 0.5556i ...
-0.7071 - 0.7071i -0.5556 - 0.8315i -0.3827 - 0.9239i -0.1951 - 0.9808i ...
-0.0000 - 1.0000i 0.1951 - 0.9808i 0.3827 - 0.9239i 0.5556 - 0.8315i ...
0.7071 - 0.7071i 0.8315 - 0.5556i 0.9239 - 0.3827i 0.9808 - 0.1951i];
case 32
% Constellation 32-DPSK
refArray = [ 1.0000 + 0.0000i 0.9952 + 0.0980i 0.9808 + 0.1951i 0.9569 + 0.2903i ...
0.9239 + 0.3827i 0.8819 + 0.4714i 0.8315 + 0.5556i 0.7730 + 0.6344i ...
0.7071 + 0.7071i 0.6344 + 0.7730i 0.5556 + 0.8315i 0.4714 + 0.8819i ...
0.3827 + 0.9239i 0.2903 + 0.9569i 0.1951 + 0.9808i 0.0980 + 0.9952i ...
0.0000 + 1.0000i -0.0980 + 0.9952i -0.1951 + 0.9808i -0.2903 + 0.9569i ...
-0.3827 + 0.9239i -0.4714 + 0.8819i -0.5556 + 0.8315i -0.6344 + 0.7730i ...
-0.7071 + 0.7071i -0.7730 + 0.6344i -0.8315 + 0.5556i -0.8819 + 0.4714i ...
-0.9239 + 0.3827i -0.9569 + 0.2903i -0.9808 + 0.1951i -0.9952 + 0.0980i ...
-1.0000 + 0.0000i -0.9952 - 0.0980i -0.9808 - 0.1951i -0.9569 - 0.2903i ...
-0.9239 - 0.3827i -0.8819 - 0.4714i -0.8315 - 0.5556i -0.7730 - 0.6344i ...
-0.7071 - 0.7071i -0.6344 - 0.7730i -0.5556 - 0.8315i -0.4714 - 0.8819i ...
-0.3827 - 0.9239i -0.2903 - 0.9569i -0.1951 - 0.9808i -0.0980 - 0.9952i ...
-0.0000 - 1.0000i 0.0980 - 0.9952i 0.1951 - 0.9808i 0.2903 - 0.9569i ...
0.3827 - 0.9239i 0.4714 - 0.8819i 0.5556 - 0.8315i 0.6344 - 0.7730i ...
0.7071 - 0.7071i 0.7730 - 0.6344i 0.8315 - 0.5556i 0.8819 - 0.4714i ...
0.9239 - 0.3827i 0.9569 - 0.2903i 0.9808 - 0.1951i 0.9952 - 0.0980i];

end

symErrSimulated = zeros(1,length(EbN0dB));
k = log2(M); % number of bits per symbol
EsN0dB = EbN0dB + 10*log10(k);

%—Generating a uniformly distributed random numbers in the set [0,1,2,..,2M-1]
data = 2*ceil(M.*rand(N,1))-1;

%—generating differential modulated symbols
% phi[k] = phi[k-1] + Dphi[k]
data_diff = filter(1,[1 -1],data); % start with 0 phase
s = refArray(mod(data_diff,2*M)+1);

%—Place holder for Symbol Error values for each Es/N0 for particular M value–
index =1;

for x = EsN0dB,
%——————————————-
%Channel Noise for various Es/N0
%——————————————-
%Adding noise with variance according to the required Es/N0
noiseVariance = 1/(10.^(x/10));%Standard deviation for AWGN Noise
noiseSigma = sqrt(noiseVariance/2);
%Creating a complex noise for adding with M-PSK modulated signal
%Noise is complex since M-PSK is in complex representation
noise = noiseSigma*(randn(1,N)+1i*randn(1,N));
received = s + noise; % additive white gaussian noise

%————-I-Q Branching—————
% non-coherent demodulation
estPhase = angle(received);
% Dphi[k] = phi[k] – phi[k-1]
est_diffPhase = filter([1 -1],1,estPhase)*M/pi;

%—Decision Maker-Compute—————
y = mod(2*floor(est_diffPhase/2)+1,2*M); % quantizing

%————–Symbol Error Rate Calculation——————————-
symErrSimulated(1,index) = sum(y~=data')/(N*k);
index=index+1;
end

%—– Compute Theoretical Symbol Error Rates ———————
%EsN0lin = 10.^(EsN0dB/10);
EbN0lin = 10.^(EbN0dB/10);
switch M
case 2
% Binary DPSK
%symErrTheory = 0.5*exp(-EbN0lin);
symErrTheory = [0.183939720585721 0.141979500801581 0.102484842127614 ...
0.067988990214236 0.040557538392161 0.021164609811602 ...
0.009332812280759 0.003329212408816 0.000909404448079 ...
0.000177519600853 0.000022699964881 0.000001704222951 ...
0.000000065443471 0.000000001080577 0.000000000006166 ...
0.000000000000009 0.000000000000000 0.000000000000000 ];
case 4
% Differential QPSK
%a=sqrt(2*EbN0lin*(1-sqrt(1/2)));
%b=sqrt(2*EbN0lin*(1+sqrt(1/2)));
%symErrTheory = marcumq(a,b,1)-1/2.*besseli(0,a.*b).*exp(-1/2*(a.^2+b.^2));
symErrTheory = [0.163915782266879 0.130340353948448 0.099340421148833 ...
0.071869728598461 0.048749014238557 0.030494396050703 ...
0.017235903419554 0.008580057996167 0.003642946260782 ...
0.001267104127630 0.000343192915859 0.000067892932192 ...
0.000009052660025 0.000000735017339 0.000000031977237 ...
0.000000000635827 0.000000000003089 0.000000000000007 ];
case 8
symErrTheory = [0.196675320594916 0.168799069367571 0.143259404905542 ...
0.119998893639366 0.098698763280930 0.079010610808322 ...
0.060880009244594 0.044595058027306 0.030628544606260 ...
0.019407939124153 0.011123484946738 0.005625145220373 ...
0.002432717332426 0.000865008450586 0.000240644104472 ...
0.000049204284217 0.000006834131510 0.000000583844516 ];
case 16
symErrTheory = [0.243074286641906 0.218961084181130 0.195636576083976 ...
0.173346218117303 0.152347699061127 0.132844412178026 ...
0.114865468034590 0.098250190259514 0.082723802722015 ...
0.068052705520753 0.054189237989625 0.041325099979299 ...
0.029825850007615 0.020093727460903 0.012425714485646 ...
0.006906628353420 0.003360747495832 0.001384823107176 ];
case 32
symErrTheory = [0.282159201893397 0.262866216107126 0.244005575175439 ...
0.225547469806512 0.207369762783772 0.189326601312768 ...
0.171408441450489 0.153784137864677 0.136740490766681 ...
0.120568432564742 0.105461710785496 0.091458039575941 ...
0.078439736690143 0.066204165894016 0.054584201989410 ...
0.043560046102459 0.033298163658265 0.024098747991940 ];
end

%—————Plotting commands———————–

semilogy(EbN0dB,symErrTheory(EbN0dB+1),colors(colorIndex),'LineWidth',1.5);hold on;
semilogy(EbN0dB,symErrSimulated,[colors(colorIndex),'*'],'LineWidth',1.5);hold on;
legendString{2*colorIndex-1} = [num2str(M),' DPSK Theory'];
legendString{2*colorIndex}=[num2str(M), ' DPSK Simulated'];
colorIndex=colorIndex+1;
end
legend(legendString)

xlabel('Eb/N0(dB)');
ylabel('Bit Error Rate (Pb)');
title('Simulation BER vs. Theoretical BER for Digital Modulation');
grid on;