Compensate for Frequency Offset Using Coarse and Fine Compensation

Correct for a phase and frequency offset in a noisy QAM signal by using a carrier synchronizer. Then correct for the offsets using both a carrier synchronizer and a coarse frequency compensator.

Set the example parameters.

fs = 10000;   % Symbol rate (Hz)
sps = 4;      % Samples per symbol
M = 16;       % Modulation order
k = log2(M);  % Bits per symbol
EbNo = 20;    % Eb/No (dB)
SNR = convertSNR(EbNo,"ebno",BitsPerSymbol=k,SamplesPerSymbol=sps);

Create a constellation diagram object to visualize the effects of the offset compensation techniques. Specify the constellation diagram to display only the last 4000 samples.

constdiagram = comm.ConstellationDiagram( ...
    ReferenceConstellation=qammod(0:M-1,M), ...
    SamplesPerSymbol=sps, ...
    SymbolsToDisplaySource='Property', ...
    SymbolsToDisplay=4000, ...
    XLimits=[-5 5], ...
    YLimits=[-5 5]);

Introduce a frequency offset of 400 Hz and a phase offset of 30 degrees.

phaseFreqOffset = comm.PhaseFrequencyOffset( ...
    FrequencyOffset=400, ...
    PhaseOffset=30, ...
    SampleRate=fs);

Generate random data symbols and apply 16-QAM modulation.

data = randi([0 M-1],10000,1);
modSig = qammod(data,M);

Create a raised cosine filter object and filter the modulated signal.

txfilter = comm.RaisedCosineTransmitFilter( ...
    OutputSamplesPerSymbol=sps, ...
    Gain=sqrt(sps));
txSig = txfilter(modSig);

Apply the phase and frequency offset, and then pass the signal through the AWGN channel.

freqOffsetSig = phaseFreqOffset(txSig);
rxSig = awgn(freqOffsetSig,SNR);

Apply fine frequency correction to the signal by using the carrier synchronizer.

fineSync = comm.CarrierSynchronizer( ...
    DampingFactor=0.7, ...
    NormalizedLoopBandwidth=0.005, ...
    SamplesPerSymbol=sps, ...
    Modulation='QAM');
rxData = fineSync(rxSig);

Display the constellation diagram of the last 4000 symbols.

constdiagram(rxData)

Even with time to converge, the spiral nature of the plot shows that the carrier synchronizer has not yet compensated for the large frequency offset. The 400 Hz offset is 1% of the sample rate.

Repeat the process with a coarse frequency compensator inserted before the carrier synchronizer.

Create a coarse frequency compensator to reduce the frequency offset to a manageable level.

coarseSync = comm.CoarseFrequencyCompensator( ...
    Modulation='QAM', ...
    FrequencyResolution=1, ...
    SampleRate=fs*sps);

Pass the received signal to the coarse frequency compensator and then to the carrier synchronizer.

syncCoarse = coarseSync(rxSig);
rxData = fineSync(syncCoarse);

Plot the constellation diagram of the signal after coarse and fine frequency compensation. The received data now aligns with the reference constellation.

constdiagram(rxData)