Notes

clc;
clear;
close all;

%% PARAMETERS
N = 8;
cp_len = 2;
numSymbols = 5000;
M = 16;
bits_per_sym = log2(M);

SNR_dB_range = 0:2:20;

BER_cp = zeros(size(SNR_dB_range));
BER_no_cp = zeros(size(SNR_dB_range));

%% LOOP OVER SNR
for snr_idx = 1:length(SNR_dB_range)

SNR_dB = SNR_dB_range(snr_idx);

%% BIT GENERATION
numBits = N * numSymbols * bits_per_sym;
bits = randi([0 1], 1, numBits);

%% 16-QAM MODULATION (MANUAL)
symbols = zeros(1, numBits/4);
k = 1;

for i = 1:4:numBits
b = bits(i:i+3);

% I mapping
if isequal(b(1:2), [0 0])
I = -3;
elseif isequal(b(1:2), [0 1])
I = -1;
elseif isequal(b(1:2), [1 1])
I = 1;
else
I = 3;
end

% Q mapping
if isequal(b(3:4), [0 0])
Q = -3;
elseif isequal(b(3:4), [0 1])
Q = -1;
elseif isequal(b(3:4), [1 1])
Q = 1;
else
Q = 3;
end

symbols(k) = I + 1j*Q;
k = k + 1;
end

symbols = symbols / sqrt(10);

%% SERIAL TO PARALLEL
symbols_parallel = reshape(symbols, N, numSymbols);

%% MANUAL IFFT
ofdm_time = zeros(N, numSymbols);

for sym = 1:numSymbols
for n = 1:N
sum_val = 0;
for k2 = 1:N
sum_val = sum_val + symbols_parallel(k2, sym) * ...
exp(1j*2*pi*(n-1)*(k2-1)/N);
end
ofdm_time(n, sym) = sum_val / N;
end
end

%% ADD CYCLIC PREFIX
ofdm_cp = [ofdm_time(end-cp_len+1:end, :); ofdm_time];

%% SERIALIZE
tx_cp = ofdm_cp(:).';
tx_no_cp = ofdm_time(:).';

%% ADD AWGN NOISE
snr_linear = 10^(SNR_dB/10);

noise_cp = (randn(size(tx_cp)) + 1j*randn(size(tx_cp))) / sqrt(2*snr_linear);
noise_no_cp = (randn(size(tx_no_cp)) + 1j*randn(size(tx_no_cp))) / sqrt(2*snr_linear);

rx_cp = tx_cp + noise_cp;
rx_no_cp = tx_no_cp + noise_no_cp;

%% RECEIVER (WITH CP)

% Reshape
rx_cp_matrix = reshape(rx_cp, N+cp_len, numSymbols);

% Remove CP
rx_cp_matrix = rx_cp_matrix(cp_len+1:end, :);

%% MANUAL FFT
rx_symbols_cp = zeros(N, numSymbols);

for sym = 1:numSymbols
for k2 = 1:N
sum_val = 0;
for n = 1:N
sum_val = sum_val + rx_cp_matrix(n, sym) * ...
exp(-1j*2*pi*(n-1)*(k2-1)/N);
end
rx_symbols_cp(k2, sym) = sum_val;
end
end

%% RECEIVER (WITHOUT CP)

rx_no_cp_matrix = reshape(rx_no_cp, N, numSymbols);

rx_symbols_no_cp = zeros(N, numSymbols);

for sym = 1:numSymbols
for k2 = 1:N
sum_val = 0;
for n = 1:N
sum_val = sum_val + rx_no_cp_matrix(n, sym) * ...
exp(-1j*2*pi*(n-1)*(k2-1)/N);
end
rx_symbols_no_cp(k2, sym) = sum_val;
end
end

%% PARALLEL TO SERIAL
rx_sym_cp = rx_symbols_cp(:).' * sqrt(10);
rx_sym_no_cp = rx_symbols_no_cp(:).' * sqrt(10);

%% 16-QAM DEMODULATION
bits_rx_cp = zeros(1, numBits);
bits_rx_no_cp = zeros(1, numBits);

k = 1;

for i = 1:length(rx_sym_cp)

% ----- WITH CP -----
I = real(rx_sym_cp(i));
Q = imag(rx_sym_cp(i));

% I decision
if I < -2
bI = [0 0];
elseif I < 0
bI = [0 1];
elseif I < 2
bI = [1 1];
else
bI = [1 0];
end

% Q decision
if Q < -2
bQ = [0 0];
elseif Q < 0
bQ = [0 1];
elseif Q < 2
bQ = [1 1];
else
bQ = [1 0];
end

bits_rx_cp(k:k+3) = [bI bQ];

% ----- WITHOUT CP -----
I = real(rx_sym_no_cp(i));
Q = imag(rx_sym_no_cp(i));

if I < -2
bI = [0 0];
elseif I < 0
bI = [0 1];
elseif I < 2
bI = [1 1];
else
bI = [1 0];
end

if Q < -2
bQ = [0 0];
elseif Q < 0
bQ = [0 1];
elseif Q < 2
bQ = [1 1];
else
bQ = [1 0];
end

bits_rx_no_cp(k:k+3) = [bI bQ];

k = k + 4;
end

%% BER CALCULATION
BER_cp(snr_idx) = sum(bits ~= bits_rx_cp) / numBits;
BER_no_cp(snr_idx) = sum(bits ~= bits_rx_no_cp) / numBits;

end

%% PLOT
figure;
semilogy(SNR_dB_range, BER_cp, '-o', 'LineWidth', 2); hold on;
semilogy(SNR_dB_range, BER_no_cp, '-s', 'LineWidth', 2);
grid on;

xlabel('SNR (dB)');
ylabel('BER');
legend('With CP', 'Without CP');
title('OFDM BER Performance (16-QAM)');