num_bits = 1e6;
num_symb = num_bits / 2;
symb_energy = 1;
A_qpsk = sqrt(symb_energy);
A_zero = sqrt(4/3*symb_energy);

qpsk_alphabet = zeros(4, 1);
qpsk_alphabet(1) = A_qpsk * exp(1i*pi/4);
qpsk_alphabet(2) = A_qpsk * exp(1i*3*pi/4);
qpsk_alphabet(3) = A_qpsk * exp(1i*5*pi/4);
qpsk_alphabet(4) = A_qpsk * exp(1i*7*pi/4);

zero_alphabet = zeros(4, 1);
zero_alphabet(1) = 0;
zero_alphabet(2) = A_zero;
zero_alphabet(3) = A_zero * exp(1i*2*pi/3);
zero_alphabet(4) = A_zero * exp(1i*4*pi/3);

symbols = randi(4, num_symb, 1);
qpsk_sig = zeros(num_symb, 1);
zero_sig = zeros(num_symb, 1);

snr_vec = 0:30; % in dB;
serr_vec_qpsk = zeros(size(snr_vec));
serr_vec_zero = zeros(size(snr_vec));

% Map
for k=1:num_symb
    qpsk_sig(k) = qpsk_alphabet(symbols(k));
    zero_sig(k) = zero_alphabet(symbols(k));
end

% plot(real(qpsk_sig), imag(qpsk_sig), '.');
% hold on;
% plot(real(zero_sig), imag(zero_sig), '.');
% grid on;
% xlim([-1.5 1.5]);
% ylim([-1.5 1.5]);

for six = 1:numel(snr_vec)
    % Add noise
    snr = snr_vec(six);
    noise_energy = symb_energy * 10^(-snr/10);
    noise = sqrt(noise_energy/2) .* (randn(num_symb, 1) + 1i*randn(num_symb, 1));
    qpsk_sig_rx = qpsk_sig + noise;
    zero_sig_rx = zero_sig + noise;

    % figure;
    % plot(real(qpsk_sig_rx), imag(qpsk_sig_rx), '.');
    % hold on;
    % plot(real(zero_sig_rx), imag(zero_sig_rx), '.');
    % grid on;
    % xlim([-1.5 1.5]);
    % ylim([-1.5 1.5]);

    % Demap
    symbols_qpsk_rx = zeros(size(symbols));
    symbols_zero_rx = zeros(size(symbols));
    for k=1:num_symb
        qdist = abs(qpsk_sig_rx(k).*ones(4, 1) - qpsk_alphabet).^2;
        [~, ix] = min(qdist);
        symbols_qpsk_rx(k) = ix;

        zdist = abs(zero_sig_rx(k).*ones(4, 1) - zero_alphabet).^2;
        [~, ix] = min(zdist);
        symbols_zero_rx(k) = ix;
    end
    num_serr_qpsk = sum( symbols ~= symbols_qpsk_rx );
    num_serr_zero = sum( symbols ~= symbols_zero_rx );
    serr_rate_qpsk = num_serr_qpsk / num_symb;
    serr_rate_zero = num_serr_zero / num_symb;
    serr_vec_qpsk(six) = serr_rate_qpsk;
    serr_vec_zero(six) = serr_rate_zero;
    fprintf('%d dB: QPSK/ZERO: %f / %f\n', snr, serr_rate_qpsk, serr_rate_zero);
end

figure;
semilogy(snr_vec, serr_vec_qpsk);
hold on;
semilogy(snr_vec, serr_vec_zero);
legend('QPSK', 'Proposed');
grid on;
ylabel('symbol error rate');
xlabel('SNR in dB');