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Configure Eb/No for AWGN Channels with Coding

This example shows how to set the bit energy to noise density ratio (Eb/No) for communication links employing channel coding.

Construct a (15,9) Reed-Solomon encoder and a 16-PSK modulator. Set the System objects™ so that they accept bit inputs.

N = 15;
K = 9;
hEnc = comm.RSEncoder('CodewordLength', N, 'MessageLength', K, ...
    'BitInput',true);
hMod = comm.PSKModulator('ModulationOrder', 16, 'BitInput', true);

Create the corresponding Reed-Solomon decoder and 16-PSK demodulator objects.

hDec = comm.RSDecoder('CodewordLength', N,'MessageLength', K, ...
    'BitInput',true);
hDemod = comm.PSKDemodulator('ModulationOrder', 16, 'BitOutput', true);

Calculate the Reed-Solomon code rate based on the ratio of message symbols to the codeword length.

codeRate = hEnc.MessageLength/hEnc.CodewordLength;

Determine the bits per symbol for the PSK modulator.

bitsPerSymbol = log2(hMod.ModulationOrder);

Set the uncoded Eb/No in dB.

UncodedEbNo = 6;

Convert the uncoded Eb/No to the corresponding coded Eb/No using the code rate.

CodedEbNo = UncodedEbNo + 10*log10(codeRate);

Construct an AWGN channel taking into account the number of bits per symbol. Set the EbNo property of hCh to the coded Eb/No.

hCh = comm.AWGNChannel('BitsPerSymbol',bitsPerSymbol);
hCh.EbNo = CodedEbNo;

Set the random number generator seed so that results are repeatable.

prevState = rng;
rng(577)

Set the total number of errors and bits for the simulation. For accuracy, the simulation should run until a sufficient number of bit errors are encountered. The number of total bits is used to ensure that the simulation does not run too long.

totalErrors = 100;
totalBits = 1e6;

Construct an error rate calculator System object™ and initialize the error rate vector.

hErr = comm.ErrorRate;
errorVec = zeros(1,3);

Run the simulation to determine the BER.

while errorVec(2) < totalErrors && errorVec(3) < totalBits
    % Generate random bits
    dataIn = randi([0,1],360,1);
    % Use the RS (15,9) encoder to add error correction capability
    dataEnc = step(hEnc, dataIn);
    % Apply 16-PSK modulation
    txSig = step(hMod, dataIn);
    % Pass the modulated data through the AWGN channel
    rxSig = step(hCh, txSig);
    % Demodulate the received signal
    demodData = step(hDemod, rxSig);
    % Decode the demodulated data with the RS (15,9) decoder
    dataOut = step(hDec, demodData);
    % Collect error statistics
    errorVec = step(hErr, dataIn, demodData);
end

Display the resultant bit error rate.

ber = errorVec(1)
ber =

    0.1065

Return the random number generator to its initial state.

rng(prevState)
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