Simulate 16-QAM on MATLAB

Question

I want to write a program which simulates the modulation and demodulation of 16-QAM. First, this program creates an array of 1000000 randomly generated bits, it groups them as 4-bit values and converts into numerical values. Then it enters 16-QAM modulation, AWGN noise is added for SNRs 0 to 20dB. Then it is demodulated and each result is converted to binary. When I compare the BER for theoritical and experimental result, I see that my results are much worse than theoritical values. This program worked well for 4-QAM but it got not-so-well results for 16-QAM. Can you help please?

clear all
clc

a = randi([0 1], 1, 1000000);%random binary array
b = zeros(1,250000);
for i=1:250000%4-bits grouped into one
    b(i) = 8*a(4*i-3) + 4*a(4*i-2) + 2*a(4*i-1) + a(4*i);
end
c = qammod(b,16,'UnitAveragePower',true);%16-QAM modulation

k = 0:20;%SNR

d = zeros(length(k),250000);
for i=1:length(k)
    d(i,1:250000) = awgn(c,k(i),'measured');%noise is added for different SNR values
end
e = qamdemod(d,16);%demodulation of 16-QAM
f = zeros(length(k),1000000);
for j=1:length(k)%results of numerical values are converted to 4-bit binary
    for i=1:250000
        temp = e(j,i);
        f(j,4*i-3) = floor(temp/8);
        temp = temp - 8;
        f(j,4*i-2) = floor(temp/4);
        temp = temp - 4;
        f(j,4*i-1) = floor(temp/2);
        temp = temp - 2;
        f(j,4*i) = rem(e(j,i),2);
    end
end

r = zeros(1,length(k));%BER is calculated
for i=1:length(k)
    for j=1:1000000
        if(a(1,j) ~= f(i,j))
            r(i) = r(i) + 1/1000000;
        end
    end
end

t = zeros(1,length(k));%Theoritical result for BER is calculated
M = 16;
for i=1:length(k)
    t(1,i) = 1-(1-2*sqrt(M-1)/sqrt(M)*qfunc(sqrt(3*k(1,i)/(M-1)))).^2;
end

plot(k,t)%results are plotted
hold on
plot(k,r)

score 0 · Answer 1 · answered Jun 09 '20 at 20:21

0

If you are having problem with qammod and qamdemod functions you can simulate QAM, without using them. Look for 16-QAM mapping in the internet, you can give them necessary values and demodulate them by using decision boundaries.

answered Jun 09 '20 at 20:21

harold_finch

80
3
11

This may be an alternate solution for QAM simulation but I would prefer if I can do it by using qammod() and qamdemod() functions. Doing by hand is more complex and I want to use this program for 64-QAM too. It would be very hard to do that if I use your method. – user6210457 Jun 09 '20 at 20:31

Simulate 16-QAM on MATLAB

1 Answers1