function discretePSK_BER_SNR(M, numBits)
  %% Set defaults for inputs
  if nargin < 2
    numBits = 1000;
  end
  if nargin < 1
    M = 2;
  end

  if isOctave()
    pkg load communications
  end

  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], 1, numBits);
  txsig = pskmod(data, M, 0, 'gray');

  for i = 1:plotlen
    rxsig = awgn(txsig, EsN0_db(i));
    demodData = pskdemod(rxsig, 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', 'Theoretical');
  else
    %% Upper bound: R. Venkataramanan, Lent 2018, 3F4 Examples Paper 2
    %%              (Question 5), CUED.
    %% Approximation: J.G. Proakis and M. Salehi, 2000, Contemporary
    %%                Communication Systems using MATLAB (Equations
    %%                7.3.18 and 7.3.19), Brooks/Cole.
    ber_ub = 2 * qfunc(sqrt(EbN0 * log2(M)) * sin(pi / M));
    ber_ap = 2 * qfunc(sqrt(EbN0 * log2(M) * 2) * sin(pi / M)) / log2(M);
    semilogy(EbN0_db, ber_ub, 'b', 'LineWidth', 1);
    semilogy(EbN0_db, ber_ap, 'g', 'LineWidth', 1);
    legend('Simulated', 'Upper bound', 'Approximation');
  end

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

  formatFigure;
  saveas(gcf, strcat('BER_SNR_', num2str(M), 'PSK_', num2str(numBits), ...
                     '.svg'));
end