Problem with OFDM transmit-receive code

Hello, I have a problem with my code. It's a basic ofdm transmitter and receiver implementation making use of BPSK. But when I increase the bps to 4 (i.e 16 QAM) and above, I don't get the desired BER curve. I need help with this Please.

% Parameters
bps = 1;  % Bits per symbol (1 for BPSK)
M = 2^bps;  % Modulation order
totalBandwidth = 20e6;  % Total bandwidth (Hz) 
subcarrierSpacing = 15e3;  % Subcarrier spacing (Hz)
nFFT = ceil(totalBandwidth / subcarrierSpacing);  % Number of FFT bins
EbNoVec = 1:1:10;  % Eb/No values (dB)

% Noise power values
noisePower_dBW = -120;  % AWGN noise power in dBW
noisePower_W = 10^(noisePower_dBW / 10);  % Convert noise power to watts

impulseNoisePower_dBW = -113;  % Impulse noise power in dBW
impulseNoisePower_W = 10^(impulseNoisePower_dBW / 10);  % Convert impulse noise power to watts

% Initialize BER vectors
berEstAWGN = zeros(size(EbNoVec));  % BER for AWGN only
berEstImp = zeros(size(EbNoVec));  % BER for AWGN + impulse noise

snr_dB = convertSNR(EbNoVec, "ebno", "snr", BitsPerSymbol=bps);  % Convert Eb/No to SNR

% Loop over SNR values
for n = 1:length(EbNoVec)
    %snr_dB = EbNoVec(n) + 10*log10(bps);  % Convert Eb/No to SNR
    
    % Initialize error and bit counters
    numErrsAWGN = 0;
    numErrsImp = 0;
    numBits = 0;
    
    while numErrsAWGN < 200 && numBits < 1e6
        % Generate random symbols and bits
        txSymbols = randi([0 M-1], nFFT, 1);
        txBits = int2bit(txSymbols, bps);

        % OFDM Modulation
        txGrid = qammod(txSymbols, M, 'UnitAveragePower', true);
        txOut = ifft(txGrid, nFFT);

        % Calculate signal power
        signalPower_dBW = snr_dB(n) + noisePower_dBW;
        signalPower_W = 10^(signalPower_dBW / 10);
        scalingFactor = sqrt(signalPower_W / mean(abs(txOut).^2));
        txOutScaled = txOut * scalingFactor;

        % AWGN
        noiseSignal_notscaled = randn(size(txOutScaled)) + 1j * randn(size(txOutScaled));
        noiseAWGN = sqrt(noisePower_W / 2) * noiseSignal_notscaled;

        % Impulse noise (bursty)
        impulseNoise = zeros(size(txOutScaled));  % Initialize as zeros
        burstPositions = rand(size(txOutScaled)) < 1;  % 5% of the time noise bursts occur
        impulseNoise(burstPositions) = sqrt(impulseNoisePower_W / 2) * ...
            (randn(sum(burstPositions), 1) + 1j * randn(sum(burstPositions), 1));

        % Received signal with AWGN only
        rxInAWGN = txOutScaled + noiseAWGN;

        % Received signal with AWGN + Impulse noise
        rxInImp = txOutScaled + noiseAWGN + impulseNoise;

        % OFDM Demodulation
        rxGridAWGN = fft(rxInAWGN, nFFT);
        rxGridImp = fft(rxInImp, nFFT);

        % Demodulate symbols
        rxSymbolsAWGN = qamdemod(rxGridAWGN, M, 'UnitAveragePower', true);
        rxSymbolsImp = qamdemod(rxGridImp, M, 'UnitAveragePower', true);

        % Convert symbols to bits
        rxBitsAWGN = int2bit(rxSymbolsAWGN, bps);
        rxBitsImp = int2bit(rxSymbolsImp, bps);

        % Count bit errors
        [bitErrorsAWGN, ~] = biterr(txBits, rxBitsAWGN);
        [bitErrorsImp, ~] = biterr(txBits, rxBitsImp);

        % Update error counters and transmitted bits
        numErrsAWGN = numErrsAWGN + bitErrorsAWGN;
        numErrsImp = numErrsImp + bitErrorsImp;
        numBits = numBits + nFFT * bps;
    end
    
    % Calculate BER
    berEstAWGN(n) = numErrsAWGN / numBits;
    berEstImp(n) = numErrsImp / numBits;
end

% Plot BER results
figure;
semilogy(EbNoVec, berEstAWGN, 'b-o', 'LineWidth', 2);  % AWGN only
hold on;
semilogy(EbNoVec, berEstImp, 'r--o', 'LineWidth', 2);  % AWGN + Impulse noise
grid on;
title('OFDM BER for BPSK with AWGN and Impulse Noise');
xlabel('Eb/No (dB)');
ylabel('Bit Error Rate (BER)');
legend('AWGN Only', 'AWGN + Impulse Noise');
hold off;

Answer 1

[Suraj Kumar]

Hi John,

Based on my understanding, you are working on transitioning your OFDM system from BPSK to 16-QAM modulation and are facing some challenges.

To resolve the issues, you can refer the following steps:

1. Ensure the modulation order M is calculated based on the bps, i.e. for 16-QAM, bps = 4 and hence M=16.

bps = 4; % Bits per symbol (4 for 16-QAM) 
M = 2^bps; % Modulation order

2. Model the noise accurately implementing AWGN and impulse noise, ensuring the noise is bursty.

noiseAWGN = sqrt(noisePower_W / 2) *  (randn(size(txOutScaled)) + 1j * randn(size(txOutScaled))); 
impulseNoise = zeros(size(txOutScaled)); 
burstPositions = rand(size(txOutScaled)) < 0.05; 
impulseNoise(burstPositions) = sqrt(impulseNoisePower_W / 2) * ... 
(randn(sum(burstPositions), 1) + 1j *       randn(sum(burstPositions), 1)); 
  
rxInAWGN = txOutScaled + noiseAWGN; 
rxInImp = txOutScaled + noiseAWGN + impulseNoise; 

3. Use the ‘biterr’ function in MATLAB to compute BER and plot the results.

[bitErrorsAWGN, ~] = biterr(txBits, rxBitsAWGN); 
[bitErrorsImp, ~] = biterr(txBits, rxBitsImp); 

numErrsAWGN = numErrsAWGN + bitErrorsAWGN; 
numErrsImp = numErrsImp + bitErrorsImp; 

You may refer to the output below for a clearer understanding:

To know more about the ‘convertSNR’ or ‘biterr’ function in MATLAB, kindly go through the following documentations:

• https://www.mathworks.com/help/comm/ref/convertsnr.html
• https://www.mathworks.com/help/comm/ref/biterr.html

Happy Coding!

[John-Davis]

I have checked all of these, everything seems to be in order. But I don't know why increasing the bps to 4 and above gives a result different from the result in theory. For instance on the theoretical 16 QAM BER curve, Eb/No value of 8 should correspond to 10^(-1) BER. This is quite different in this case.