To design and evaluate an Orthogonal Frequency Division Multiplexing (OFDM) system in MATLAB

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To design and evaluate an Orthogonal Frequency Division Multiplexing (OFDM) system in MATLAB, follow these steps:

1. OFDM System Design

Key Parameters

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N = 64;           % Number of subcarriers
CP = 16;          % Cyclic prefix length
M = 4;            % Modulation order (4 = QPSK)
numSymbols = 100; % Number of OFDM symbols
snrdB = 0:2:20;   % SNR range (dB)

Transmitter

  1. Bit Generation: Generate random bits.
  2. Modulation: Map bits to symbols (e.g., QPSK).
  3. IFFT: Convert frequency-domain symbols to time domain.
  4. Add Cyclic Prefix (CP): Append the end of the symbol to the start.
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% Generate bits
bitsPerSymbol = N * log2(M);
totalBits = bitsPerSymbol * numSymbols;
bits = randi([0 1], totalBits, 1);

% Modulate using QPSK
modulatedSymbols = qammod(bits, M, 'InputType', 'bit', 'UnitAveragePower', true);

% Reshape into OFDM symbols and perform IFFT
ofdmSymbols = reshape(modulatedSymbols, N, numSymbols);
timeDomainSymbols = ifft(ofdmSymbols, N);

% Add cyclic prefix
cp = timeDomainSymbols(end-CP+1:end, :);
txSignal = [cp; timeDomainSymbols];
txSignalSerial = txSignal(:); % Serialize for transmission

Channel Model

Add AWGN (Additive White Gaussian Noise):

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rxSignalSerial = awgn(txSignalSerial, snrdB(idx), 'measured');

Receiver

  1. Remove CP: Discard the cyclic prefix.
  2. FFT: Convert time-domain signal back to frequency domain.
  3. Demodulation: Recover bits from symbols.
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% Remove CP and perform FFT
rxSignal = reshape(rxSignalSerial, size(txSignal));
rxSymbols = rxSignal(CP+1:end, :);
frequencyDomainSymbols = fft(rxSymbols, N);

% Demodulate
rxBits = qamdemod(frequencyDomainSymbols(:), M, 'OutputType', 'bit', 'UnitAveragePower', true);

2. Performance Evaluation

Bit Error Rate (BER) vs SNR

Compare simulated BER with theoretical QPSK performance:

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ber = zeros(size(snrdB));
for idx = 1:length(snrdB)
    % ... (transmit and receive steps)
    ber(idx) = sum(bits ~= rxBits) / totalBits;
end

% Theoretical BER (adjust for CP overhead)
EsN0_linear = 10.^(snrdB/10);
EbN0_linear = EsN0_linear * (N / (N + CP)) / log2(M);
theoryBER = 0.5*erfc(sqrt(EbN0_linear));

% Plot results
semilogy(snrdB, ber, 'b-o', snrdB, theoryBER, 'r--');
xlabel('SNR (dB)'); ylabel('BER'); grid on;
legend('Simulated', 'Theoretical');

PAPR (Peak-to-Average Power Ratio)

Calculate the CCDF (Complementary Cumulative Distribution Function) of PAPR:

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% Generate time-domain symbols
ofdmSymbolsPAPR = ifft(ofdmSymbols(:,1:numSymbols), N);

% Compute PAPR
signalPower = mean(abs(ofdmSymbolsPAPR).^2, 1);
peakPower = max(abs(ofdmSymbolsPAPR).^2, [], 1);
papr_dB = 10*log10(peakPower ./ signalPower);

% Plot CCDF
[Nccdf, Xccdf] = ecdf(papr_dB);
semilogy(Xccdf, 1-Nccdf);
xlabel('PAPR (dB)'); ylabel('Probability (PAPR > X)'); grid on;

3. Simulation Output

  • BER Curve: Simulated BER should align with the theoretical curve after correcting for CP overhead.
  • PAPR CCDF: Shows the probability of PAPR exceeding a threshold (e.g., 10 dB for QPSK).

Extensions for Advanced Evaluation

  1. Multipath Fading Channels:
    • Model using rayleighchan or comm.RayleighChannel.
    • Include channel estimation and equalization (e.g., using pilots).
  2. Channel Coding:
    • Add convolutional or LDPC coding using comm.ConvolutionalEncoder/comm.LDPCEncoder.
  3. Throughput Analysis:
    • Measure data rate after accounting for coding overhead and retransmissions.

Example Code

[Refer to the detailed code in the Answer section for implementation.]

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