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BPSK bpsk in awgn not matching theoretical results

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Russell Geschrey
Russell Geschrey el 19 de En. de 2021
Editada: Russell Geschrey el 19 de En. de 2021
I am doing a monte carlo simulation for BPSK signals and I am getting a result of (roughly):
I know the result is supposed to be:
Can someone please look at my code provide some pointers as to what I'm doing wrong?
Fs = 10; %Sample Frequency
Ts= 1/Fs;
t= 0:Ts:1;
degree=1; %Degree of the space ie. BPSK= 1
sim_length= 40000; %Number of symbols sent in the simulation
error_count=0;
%Define the two symbols to transmit
p{1,1}= sqrt(2)*sin(2*pi*t);
p{1,2}= sqrt(2)*sin(2*pi*t+pi);
x=0;
for Eb_No= 0:10
%Begin Monte Carlo for the desired SNR
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i=1:sim_length
%ceil rounds up always
symbol= ceil(2*degree*rand); %Pick rand Symbol index
symbol_to_tx= cell2mat(p(symbol)); %Create that symbol to transmit
%%%%%%%%% https://www.mathworks.com/help/comm/ug/awgn-channel.html
Eb_No_SAMPLE = Eb_No+10*log10(1/Fs) ;
noisy_sig= awgn(symbol_to_tx, Eb_No_SAMPLE, 'measured' ); %Signal is injected with noise
for j=1:2*degree
%%Multiply against each symbol in the dicationary, and then
%%integrate over one period
symbol_dictinory= cell2mat(p(j));
test_funct= noisy_sig .* symbol_dictinory;
ML_vector(j)=trapz(test_funct)* (1/Fs);
% (1/Fs) is required to normalize because of sampling
% note that trapz is an approximation
%Highest output in ML vector is the "most likely" symbol that was tx'ed.
end
[~,ML_symbol] = max(ML_vector);
%If the ML decoder was wrong, incrment the error count
if ML_symbol ~= symbol
error_count=error_count+1;
end
P_error= error_count/sim_length;
end
%End Monte Carlo for the desired SNR
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
x=x+1;
ber(x)=P_error;
%https://www.mathworks.com/help/comm/ug/bit-error-rate-ber.html
%%%This is just the theoretical error of the AWGN QPSK to compare
Eb_No_db(x)=Eb_No;
Eb_No_lin=10.^(Eb_No_db./10);
% theory_ber=0.5.*erfc(sqrt(Eb_No_lin));
theory_ber= qfunc( sqrt(2*Eb_No_lin) );
%%%Reset counters for next dB iteration
error_count=0;
P_error=0;
end
semilogy(Eb_No_db,ber,'-bo',Eb_No_db,theory_ber,'-mh')
grid on
title('BPSK with AWGN');
xlabel('E_b/N_o');
ylabel('P_b = BER');
legend('Simulated BPSK','bpsk theory')

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