% Theoritical and Practical BER COMPARISON of different M-ary QAM
% ========================================%
% User Defined Functions used in this File are
% s2p --> Serial to Parallel Conversion
% p2s --> Parallel to Serial Conversion
% QAM_T ---> Theoritical M-QAM BER Calculation
% ========================================%
clc;
clear all;
close all;
bits = 1.e6;
msg = round(rand(1,bits)); % Generating Random Bit Stream
M = [4 16 64 256]; % M-ary
for j=1:4
% ============================= Tx ===========================%
%% 16-QAM Modulation
bits_sym = log2(M(j)); % Bits per Symbol for M-ary
sym_tx = s2p(msg,bits_sym); % Serial to Parallel Conversion for QAM
H_Tx = modem.qammod('M', M(j), 'PHASEOFFSET', 0, 'SYMBOLORDER', 'BINARY', ...
'INPUTTYPE', 'BIT'); % Generate Handle for Modulation
qam_tx = modulate(H_Tx,sym_tx); % Modulation
%======================== CHANNEL========================%
Eb_No = -11:1:11; % Eb/No in DB
SNR = Eb_No + 10*log10(log2(M(j))); % Finding out SNR from Eb/No
for i=1:length(Eb_No)
qam_n = awgn(qam_tx,SNR(i),'measured'); % Adding AWGN
% ======================== Rx ============================%
%% QAM De-Modulation
qam_rx = p2s(qam_n);
H_Rx = modem.qamdemod('M', M(j), 'PHASEOFFSET', 0, 'SYMBOLORDER', 'BINARY', ...
'OUTPUTTYPE', 'BIT'); % Generate Handle for Modulation
sym_rx = demodulate(H_Rx,qam_rx); % Modulating data to QAM
%% Symbols to Msg Conversion
msg_rx = p2s(sym_rx);
msg_rx = msg_rx(1,1:length(msg));
[ErrBits BER(i,j)] = symerr(msg_rx,msg); % Calculating BER by comparisson of Rx and Tx msg
BER_T (i,j) = QAM_T(Eb_No(i),M(j)); % Theoritical BER calculation using formula
end
end
%% Plot of BER vs Eb/No
BER
BER_T
semilogy(Eb_No,BER(:,1),'r-*',Eb_No,BER_T(:,1),'g-o',Eb_No,BER(:,2),'b-v',Eb_No,BER_T(:,2),'k-x',Eb_No,BER(:,3),'c-*',Eb_No,BER_T(:,3),'m-o',Eb_No,BER(:,4),'y-x',Eb_No,BER_T(:,4),'k-*');
legend('M=4','M_T=4','M=16','M_T=16','M=64','M_T=64','M=256','M_T=256');
title('Theoritical and Practical BER COMPARISON of different M-ary QAM');
ylabel('BER');
xlabel('Eb/No (dB)');
grid;
-------------------------------------------------------------------------------------------------------------------------
%% Function Serial to Parallel I/P msg and No. of Parallel Channels
function p_data = s2p(s_data,N)
l = length(s_data);
mode = mod(l,N);
if mode ~= 0
z_add = zeros(1,N-mode);
data = [s_data z_add];
else
data = s_data;
end
M = length(data)/N;
p_data = reshape(data,N,M);
end
--------------------------------------------------------------------------------------------------------------------------
%% Function Parallel to Serial
function s_data = p2s(data)
data1 = data(:);
s_data = data1.';
end
--------------------------------------------------------------------------------------------------------------------------
%% Function Serial to Parallel I/P msg and No. of Parallel Channels
function BER = QAM_T(Eb_No,M)
EbNo=10.^(Eb_No/10);
k=log2(M);
x=sqrt(3*k*EbNo/(M-1));
Pb=(4/k)*(1-1/sqrt(M))*(1/2)*erfc(x/sqrt(2));
BER = 1-(1-Pb)^2;
end
---------------------------------------------------------------------------------------------------------------------------
Result
