16_QAM.m

clc;
clear;
clear all;
samplesPerSymbol=8;
p_pulseEnergy = 6;
numSymbols = 50000;
numSimulations = 1;
noiseMean = 0;
numPlotSym=500;
f_oversamp=8;
group_delay=4;
p_of_t=rcosflt([1], 1, f_oversamp, 'sqrt', 0.5, group_delay)';
p_of_t=p_of_t(1:end-8);
p_of_t = p_of_t*(sqrt(p_pulseEnergy/(p_of_t*p_of_t')));
transmittedSymbols=rand(1,4*numSymbols);
transmittedSymbols(transmittedSymbols>0.5)=1;
transmittedSymbols(transmittedSymbols<=0.5)=0;
idx7 = 1;
idx8 = 1;
for ii = -5:1:10
    
idx = 1;
for i = 1:2:length(transmittedSymbols)-1
if ((transmittedSymbols(i) == 0) && (transmittedSymbols(i+1) == 0))
    tx_sig(idx) = -3;
end
if ((transmittedSymbols(i) == 0) && (transmittedSymbols(i+1) == 1))
    tx_sig(idx) = -1;
end
if ((transmittedSymbols(i) == 1) && (transmittedSymbols(i+1) == 0))
    tx_sig(idx) = 3;
end
if ((transmittedSymbols(i) == 1) && (transmittedSymbols(i+1) == 1))
    tx_sig(idx) = 1;
end
idx = idx + 1;
end
idx1 = 1;
for k =1:2:length(tx_sig)-1
 tx_sym(idx1)= tx_sig(k) + j*tx_sig(k+1);
 idx1 = idx1 +1;
end
up_sampled = upsample(tx_sym,f_oversamp);
delay_fun = 2* group_delay * f_oversamp;
pulseshaped_signalling = conv(p_of_t,up_sampled);
signal_length = length(pulseshaped_signalling);
eb2n(idx7) = ((ii)*2)+10*log10(1/(sqrt(10)));
eb_num(idx7) = 10.^(eb2n(idx7)/10);
noiseVariance(idx7) = 26/(2*eb_num(idx7));
noise = noiseMean + sqrt(noiseVariance(idx7)/2)*((randn(1,signal_length)) + (j*randn(1,signal_length)));
transmitted_signal = pulseshaped_signalling + noise;
idx2 =  1;
idx9 = 1;
for l = 1:8:((length(transmitted_signal)- 71)+1)
    op = conv(transmitted_signal(l:l+70),fliplr(p_of_t));
    rx_op1(idx9:idx9+133) = op;
    sam_op(idx2) = op(64);
    idx2 = idx2 + 1;
    idx9 = idx9 + 134;
end
threshold_1 = 2*p_pulseEnergy;
threshold_2 = -2*p_pulseEnergy;
idx3 = 1;
idx5 = 1;
idx6 = 1;
for v = 1:1:length(sam_op)
    if (real(sam_op(v)) > threshold_1)
        rx_sym(idx3) = 3;
        rx_bit(idx6:idx6+1)= [1,0];
    end
    if (real(sam_op(v)) <= threshold_1 && real(sam_op(v))> 0)
        rx_sym(idx3) = 1;
        rx_bit(idx6:idx6+1)= [1,1];
    end
     if (real(sam_op(v)) >= threshold_2 && real(sam_op(v))< 0)
        rx_sym(idx3) = -1;
        rx_bit(idx6:idx6+1)= [0,1];
     end
    if (real(sam_op(v))< threshold_2 )
        rx_sym(idx3) = -3;
        rx_bit(idx6:idx6+1)= [0,0];
    end
    if (imag(sam_op(v)) > threshold_1)
        rx_sym_imag(idx5) = 3;
        rx_bit(idx6+2:idx6+3)= [1,0];
    end
    if (imag(sam_op(v)) <= threshold_1 && imag(sam_op(v))> 0)
        rx_sym_imag(idx5) = 1;
        rx_bit(idx6+2:idx6+3)= [1,1];
    end
     if (imag(sam_op(v)) >= threshold_2 && imag(sam_op(v))< 0)
        rx_sym_imag(idx5) = -1;
        rx_bit(idx6+2:idx6+3)= [0,1];
     end
    if (imag(sam_op(v)) < threshold_2 )
        rx_sym_imag(idx5) = -3;
        rx_bit(idx6+2:idx6+3)= [0,0];
    end
    idx3 = idx3+1;
    idx5 = idx5 +1;
    idx6 = idx6 + 4;
end
    y = bitxor(transmittedSymbols,rx_bit);
    bit_err(idx7) = (numel(find(y)))/(4*numSymbols);
    theoryBer(idx7) = (1/4)*(3/2)*erfc(sqrt(4*0.1*eb_num(idx7)));
    
idx4 = 1;
idx8 = idx8+1;
for b = 1:1:length(rx_sym)
    rx_op(idx4) = rx_sym(b) + j*(rx_sym_imag(b));
    idx4 = idx4 +1;
end

idx7 = idx7 +1;
end
figure(1),semilogy(eb2n,theoryBer,'bs-','LineWidth',1);
hold on;
figure(1),semilogy(eb2n,bit_err,'mx-','LineWidth',1);
axis([-10 20 10^-5 1])
grid on
xlabel('Eb/No, dB')
ylabel('Bit Error Rate')
title('Bit error probability curve for 16-QAM modulation')
legend('theoritical','observed');
figure(2),plot(real(sam_op(1:500)),imag(sam_op(1:500)),'o');
grid on
xlabel('Real part of matched filter output samples')
ylabel('Imaginary part of matched filter output samples')
title('Scatter plot for 16-QAM modulation at 20 dB')
figure(3),plot(real(sam_op(1:500)),imag(sam_op(1:500)));
grid on
xlabel('Real part of matched filter output samples')
ylabel('Imaginary part of matched filter output samples')
title('constellation trajectory plot for 16-QAM modulation at 20 dB')
eyediagram(sam_op(1:numPlotSym),2);