Notes

clc;
clear;
close all;

%% PARAMETERS
N = 8; % Subcarriers
cp_len = 2; % Cyclic Prefix length
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));

%% CHANNEL
h = [0.9 0.4 0.2];
H = fft(h, N);

%% 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) / sqrt(10);
k = k + 1;
end

%% 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 kk = 1:N
sum_val = sum_val + symbols_parallel(kk, sym) * ...
exp(1j*2*pi*(n-1)*(kk-1)/N);
end
ofdm_time(n, sym) = sum_val / N;
end
end

%% ================= WITH CP =================
ofdm_cp = [ofdm_time(end-cp_len+1:end, :); ofdm_time];
tx_cp = reshape(ofdm_cp, 1, []);

rx_cp = conv(tx_cp, h);

% AWGN
signal_power = mean(abs(rx_cp).^2);
noise_power = signal_power / (10^(SNR_dB/10));

noise = sqrt(noise_power/2)*(randn(size(rx_cp)) + 1j*randn(size(rx_cp)));
rx_cp = rx_cp + noise;

% Trim
rx_cp = rx_cp(1:(N+cp_len)*numSymbols);

% Remove CP
rx_parallel = reshape(rx_cp, N+cp_len, numSymbols);
rx_no_cp = rx_parallel(cp_len+1:end, :);

%% FFT
rx_freq = zeros(N, numSymbols);

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

%% EQUALIZATION
for sym = 1:numSymbols
rx_freq(:,sym) = rx_freq(:,sym) ./ H.';
end

%% SERIAL
rx_symbols = reshape(rx_freq, 1, []);

%% DEMODULATION
rx_bits = zeros(1, numBits);

for i = 1:length(rx_symbols)
I = real(rx_symbols(i)) * sqrt(10);
Q = imag(rx_symbols(i)) * sqrt(10);

idx = (i-1)*4 + 1;

% I bits
if I < -2
rx_bits(idx:idx+1) = [0 0];
elseif I < 0
rx_bits(idx:idx+1) = [0 1];
elseif I < 2
rx_bits(idx:idx+1) = [1 1];
else
rx_bits(idx:idx+1) = [1 0];
end

% Q bits
if Q < -2
rx_bits(idx+2:idx+3) = [0 0];
elseif Q < 0
rx_bits(idx+2:idx+3) = [0 1];
elseif Q < 2
rx_bits(idx+2:idx+3) = [1 1];
else
rx_bits(idx+2:idx+3) = [1 0];
end
end

%% BER WITH CP
BER_cp(snr_idx) = sum(bits ~= rx_bits) / numBits;

%% ================= WITHOUT CP =================
tx_no_cp = reshape(ofdm_time, 1, []);
rx_no_cp2 = conv(tx_no_cp, h);

% AWGN
signal_power = mean(abs(rx_no_cp2).^2);
noise_power = signal_power / (10^(SNR_dB/10));

noise = sqrt(noise_power/2)*(randn(size(rx_no_cp2)) + 1j*randn(size(rx_no_cp2)));
rx_no_cp2 = rx_no_cp2 + noise;

rx_no_cp2 = rx_no_cp2(1:N*numSymbols);

rx_parallel2 = reshape(rx_no_cp2, N, numSymbols);

%% FFT
rx_freq2 = zeros(N, numSymbols);

for sym = 1:numSymbols
for k = 1:N
sum_val = 0;
for n = 1:N
sum_val = sum_val + rx_parallel2(n, sym) * ...
exp(-1j*2*pi*(n-1)*(k-1)/N);
end
rx_freq2(k, sym) = sum_val;
end
end

%% Equalization (imperfect due to ISI)
for sym = 1:numSymbols
rx_freq2(:,sym) = rx_freq2(:,sym) ./ H.';
end

rx_symbols2 = reshape(rx_freq2, 1, []);

%% DEMODULATION
rx_bits2 = zeros(1, numBits);

for i = 1:length(rx_symbols2)
I = real(rx_symbols2(i)) * sqrt(10);
Q = imag(rx_symbols2(i)) * sqrt(10);

idx = (i-1)*4 + 1;

if I < -2
rx_bits2(idx:idx+1) = [0 0];
elseif I < 0
rx_bits2(idx:idx+1) = [0 1];
elseif I < 2
rx_bits2(idx:idx+1) = [1 1];
else
rx_bits2(idx:idx+1) = [1 0];
end

if Q < -2
rx_bits2(idx+2:idx+3) = [0 0];
elseif Q < 0
rx_bits2(idx+2:idx+3) = [0 1];
elseif Q < 2
rx_bits2(idx+2:idx+3) = [1 1];
else
rx_bits2(idx+2:idx+3) = [1 0];
end
end

%% BER WITHOUT CP
BER_no_cp(snr_idx) = sum(bits ~= rx_bits2) / 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');
title('OFDM BER Performance');

legend('With CP','Without CP');