16-QAM modulation and demodulation - missing one line in the graph - matlab

Question

I am trying to do modulation and demodulation for 16-QAM and then trying to compare theoretical and simulated BER.
I am not getting simulation-line in the graph.
I can not understand what is wrong with my code. Can anybody help me?
here is the code:
M=16;
SNR_db = [0 2 4 6 8 10 12];
x = randi([0,M-1],1000,1);
hmod = modem.qammod(16);
hdemod = modem.qamdemod(hmod,'SymbolOrder', 'Gray');
tx = zeros(1,1000);
for n=1:1000
tx(n) = modulate(hmod, x(n));
end
rx = zeros(1,1000);
rx_demod = zeros(1,1000);
for j = 1:7
err = zeros(1,7);
err_t = zeros(1,7);
for n = 1:1000
rx(n) = awgn(tx(n), SNR_db(j));
rx_demod(n) = demodulate(hdemod, rx(n));
if(rx_demod(n)~=x(n))
err(j) = err(j)+1;
end
end
% err_t = err_t + err;
end
theoryBer = 3/2*erfc(sqrt(0.1*(10.^(SNR_db/10))));
figure
semilogy(SNR_db,theoryBer,'-',SNR_db, err, '^-');
grid on
legend('theory', 'simulation');
xlabel('Es/No, dB')
ylabel('Symbol Error Rate')
title('Symbol error probability curve for 16-QAM modulation')

Answer 1

http://www.dsplog.com/db-install/wp-content/uploads/2008/06/script_16qam_gray_mapping_bit_error_rate.m
That does what you want manually, without assuming any toolbox functionality (i.e. the fancy modulator and demodulators).
Also you can try
edit commdoc_mod
Make a copy of that file and you should be able to get it to do what you want with one simple loop.
Edit
Here are the modifications to that file that give you the simulated EbNo curves instead of the symbol error rate ones. Should be good enough for any practical purpose.
M = 16; % Size of signal constellation
k = log2(M); % Number of bits per symbol
n = 3e4; % Number of bits to process
nSyms = n/k; % Number of symbols
hMod = modem.qammod(M); % Create a 16-QAM modulator
hMod.InputType = 'Bit'; % Accept bits as inputs
hMod.SymbolOrder = 'Gray'; % Accept bits as inputs
hDemod = modem.qamdemod(hMod); % Create a 16-QAM based on the modulator
x = randi([0 1],n,1); % Random binary data stream
tx = modulate(hMod,x);
EbNo = 0:10; % In dB
SNR = EbNo + 10*log10(k);
rx = zeros(nSyms,length(SNR));
bit_error_rate = zeros(length(SNR),1);
for i=1:length(SNR)
rx(:,i) = awgn(tx,SNR(i),'measured');
end
rx_demod = demodulate(hDemod,rx);
for i=1:length(SNR)
[~,bit_error_rate(i)] = biterr(x,rx_demod(:,i));
end
theoryBer = 3/(2*k)*erfc(sqrt(0.1*k*(10.^(EbNo/10))));
figure;
semilogy(EbNo,theoryBer,'-',EbNo, bit_error_rate, '^-');
grid on;
legend('theory', 'simulation');
xlabel('Eb/No, dB');
ylabel('Bit Error Rate');
title('Bit error probability curve for 16-QAM modulation');

Answer 2

In your code, you confuse Symbol Error Probability and Bit Error Probability. Moreover err = zeros(1,7); is misplaced.
After the corrections:
M=16;
SNR_db = 0:2:12;
N=1000;
x = randi([0,M-1],N,1);
k = log2(M); % bits per symbol
tx = qammod(x, M,'Gray');
err = zeros(1,7);
for j = 1:numel(SNR_db)
rx = awgn(tx, SNR_db(j),'measured');
rx_demod = qamdemod( rx, M, 'Gray' );
[~,err(j)] = biterr(x,rx_demod);
end
theorySER = 3/2*erfc(sqrt(0.1*(10.^(SNR_db/10))));
figure
semilogy(SNR_db,theorySER,'-',SNR_db, err*k, '^-');
grid on
legend('theory', 'simulation');
xlabel('Es/No, dB')
ylabel('Symbol Error Rate')
title('Symbol Error Probability curve for 16-QAM modulation')
And the resulting graph is: