Fixed passband, should now be correct

[4yp.git] / passband.m

function passband(rolloff, M, numSymbs)
  %% Set defaults for inputs
  if nargin < 3
    numSymbs = 1000;
  end
  if nargin < 2
    M = 2;
  end
  if nargin < 1
    rolloff = 0.5;
  end


  %% https://www.mathworks.com/help/comm/examples/passband-modulation-with-adjacent-channel-interference.html
  Rsym = 1e6; % symbol rate (sym/sec)

  span = 6; % filter span
  sps = 4; % samples per symbol

  txFilter = comm.RaisedCosineTransmitFilter...
                 ('Shape', 'Square root', ...
                  'RolloffFactor', rolloff, ...
                  'FilterSpanInSymbols', span, ...
                  'OutputSamplesPerSymbol', sps);
  rxFilter = comm.RaisedCosineReceiveFilter...
                 ('Shape', 'Square root', ...
                  'RolloffFactor', rolloff, ...
                  'FilterSpanInSymbols', span, ...
                  'InputSamplesPerSymbol', sps, ...
                  'DecimationFactor', 1);

  fs = Rsym * sps; % sampling freq (Hz)

  t = (0 : 1 / fs : numSymbs / Rsym + (1.5 * span * sps - 1) / fs)';


  EbN0_db = 0:0.2:10;
  EbN0 = 10 .^ (EbN0_db ./ 10);

  Es = 1;
  Eb = Es / log2(M);
  N0 = Eb ./ EbN0;

  EsN0 = EbN0 .* log2(M);
  EsN0_db = 10 .* log10(EsN0);

  plotlen = length(EbN0);

  ber = zeros(1, plotlen);




  data = randi([0 M - 1], numSymbs, 1);
  modData = pskmod(data, M, 0, 'gray');

  xBaseband = txFilter([modData; zeros(span, 1)]);


  %fc = 2.5e6; % Carrier freq (Hz)
  %carrier = sqrt(2) * exp(j * 2 * pi * fc * t);

  %xPassbandIdeal = normalizeEnergy...
  %                   (real(xBaseband .* carrier(1:length(xBaseband))), numSymbs, 1);

  %txLOFreq = [2.49e6, 2.5e6, 2.51e6];
  %%txLOEnergy = [0.05, 0.9, 0.05];
  %txLOEnergy = [0 1 0];
  txLOFreq = [1e8];
  txLOEnergy = [1];

  carrier = zeros(length(t), 1);
  for i = 1 : length(txLOFreq)
    carrier = carrier + ...
              sqrt(2 * txLOEnergy(i)) * exp(j * 2 * pi * txLOFreq(i) * t);
  end

  xPassband = normalizeEnergy...
                (xBaseband .* carrier(1:length(xBaseband)), numSymbs, 1);

  for i = 1:plotlen
    snr = EbN0_db(i) + 10 * log10(log2(M)) - 10 * log10(sps); % why sps?
    noiseEnergy = 10 ^ (-snr / 10);

    yPassband = awgn(xPassband, snr, 'measured');

    rBaseband = rxFilter([yPassband .* conj(carrier(1:length(yPassband))); zeros(span * sps, 1)]);
    %% truncate filter transients
    rBaseband = rBaseband(span * sps / 2 + 1 : end);
    %% normalize energy
    rBaseband = normalizeEnergy(rBaseband, numSymbs, 1 + noiseEnergy);

    rSampled = rBaseband(sps*span/2+1:sps:(numSymbs + span/2) * sps);

    demodData = pskdemod(rSampled, M, 0, 'gray');
    [bitErrors, ber(i)] = biterr(data, demodData);

  end

  fig1 = figure(1);
  clf;

  %% Plot simulated results
  semilogy(EbN0_db, ber, 'r', 'LineWidth', 2);
  hold on;

  %% Plot theoretical curve
  %% BPSK: bit error when noise Nr > sqrt(Eb)
  %%   Pr(Nr > sqrt(Eb))
  %% = Pr(Z > sqrt(Eb) / sqrt(N0/2))
  %%
  %% QPSK = 2 BPSKs, one real and one imaginary, each with one bit
  %% so BER is the same as BPSK (assuming Gray code)
  if M == 2 || M == 4
    ber_th = qfunc(sqrt(2 * EbN0));
    semilogy(EbN0_db, ber_th, 'b', 'LineWidth', 1);
    legend('Simulated RRC', 'Discrete');
  else
    %% Approximation: J.G. Proakis and M. Salehi, 2000, Contemporary
    %%                Communication Systems using MATLAB (Equations
    %%                7.3.18 and 7.3.19), Brooks/Cole.
    ber_ap = 2 * qfunc(sqrt(EbN0 * log2(M) * 2) * sin(pi / M)) / log2(M);
    semilogy(EbN0_db, ber_ap, 'b', 'LineWidth', 1);
    legend('Simulated RRC', 'Discrete');
  end

  title(strcat(num2str(M), '-PSK RRC with Gray code'));
  grid on;
  xlabel('$E_b/N_0$ (dB)');
  ylabel('BER');

  formatFigure;
  %saveas(gcf, strcat('BER_SNR_', num2str(M), 'PSK_', num2str(numSymbs), ...
  %                   '.svg'));

  %scatterplot(rxFilt);
  %eyediagram(rxFilt, sps);

end


function y = normalizeEnergy(x, numSymbs, e)
  energy = sum(abs(x) .^ 2) / numSymbs;
  y = x * sqrt(e / energy);
end