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Problem with OFDM transmit-receive code

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John-Davis
John-Davis on 30 Sep 2024
Commented: John-Davis on 1 Oct 2024
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;

Answers (1)

Suraj Kumar
Suraj Kumar on 1 Oct 2024
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 biterrfunction 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:
Happy Coding!
  1 Comment
John-Davis
John-Davis on 1 Oct 2024
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.

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