ofdmdemod

outSym = ofdmdemod(ofdmSig,nfft,cplen) performs OFDM demodulation on the input time domain signal specified in ofdmSig, using an FFT size specified by nfft and cyclic prefix length specified by cplen. For information, see OFDM Demodulation.

outSym = ofdmdemod(ofdmSig,nfft,cplen,symOffset) applies the symbol sampling offset, symOffset, for each OFDM symbol before demodulation of the input.

outSym = ofdmdemod(ofdmSig,nfft,cplen,symOffset,nullidx) removes null subcarriers from the locations specified in nullidx. For this syntax, the symbol sampling offset is applied to each OFDM symbol and the number of rows in the output is nfft – length(nullidx), which accounts for the removal of null subcarriers. Use null subcarriers to account for guard bands and DC subcarriers. For information, see Subcarrier Allocation and Guard Bands.

[outSym,pilots] = ofdmdemod(ofdmSig,nfft,cplen,symOffset,nullidx,pilotidx) returns pilot subcarriers for the pilot indices specified in pilotidx. For this syntax, the symbol sampling offset is applied to each OFDM symbol and number of rows in the output is nfft – length(nullidx) – length(pilotidx), which accounts for the removal of null and pilot subcarriers. The function assumes that pilot subcarrier locations are the same across each OFDM symbol and transmit antenna.

outSym = ofdmdemod(ofdmSig,nfft,cplen,___,OvesamplingFactor=Value) specifies the optional oversampling factor name-value argument in addition to input arguments in previous syntaxes. The oversampling factor for an upsampled input signal must be specified as a positive scalar. Additionally, the products (OversamplingFactor×nfft) and (OversamplingFactor×cplen) must both result in integers. The default value for OversamplingFactor is 1.

For example, ofdmdemod(inSym,nfft,cplen,OversamplingFactor=2) demodulates assuming the input signal was upsampled by a factor of two.

Examples

OFDM Demodulation with Different CP Lengths

OFDM-demodulate a signal with different CP lengths for different symbols.

Initialize input parameters defining locations for null and pilot subcarriers. Generate random data and perform OFDM modulation.

M = 16;
nfft = 64;
cplen = [16 32];
nSym = 2;
dataSym = randi([0 M-1],nfft,nSym);
qamSig = qammod(dataSym,M,UnitAveragePower=true);
y1 = ofdmmod(qamSig,nfft,cplen);

Demodulate the OFDM symbols. Compare the results to the original input data. The difference between the signals is negligible.

x1 = ofdmdemod(y1,nfft,cplen);
rxData = qamdemod(x1,M,UnitAveragePower=true);
isequal(rxData,dataSym)

ans = logical
   1

OFDM Mod-Demod SISO Link

Apply OFDM multiplexing to a 16-QAM signal filtered by a SISO link with Rayleigh fading.

Initialize simulation variables, and create Rayleigh fading channel and constellation diagram objects.

s1 = RandStream('mt19937ar',Seed=12345);
nFFT = 64;
cpLen = 16;
nullIdx = [1:6 33 64-4:64].';
numTones = nFFT-length(nullIdx);

k = 4; % bits per symbol
M = 2^k;
constSym = qammod((0:M-1),M, ...
    UnitAveragePower=true); % reference constellation symbols

maxDopp = 1;
pathDelays = [0 4e-3 8e-3];
pathGains = [0 -2 -3];
sRate = 1000;
sampIdx = round(pathDelays/(1/sRate)) + 1;

chan = comm.RayleighChannel(PathGainsOutputPort=true, ...
    MaximumDopplerShift=maxDopp, ...
    PathDelays=pathDelays, ...
    AveragePathGains=pathGains, ...
    SampleRate=sRate, ...
    RandomStream='mt19937ar with seed');

cdScope = comm.ConstellationDiagram( ...
    ShowReferenceConstellation=true, ...
    ReferenceConstellation=constSym);

Generate signal data and apply 16-QAM modulation.

data = randi(s1,[0 M-1],numTones,1);
modOut = qammod(data,M,UnitAveragePower=true);

Apply OFDM modulation and pass the signal through the channel.

y = ofdmmod(modOut,nFFT,cpLen,nullIdx);
[fadSig,pg] = chan(y);

Determine symbol sampling offset.

symOffset = min(max(sampIdx),cpLen)

symOffset = 9

OFDM demodulate the received signal with a time shift. Display the constellation diagram before equalization.

x = ofdmdemod(fadSig,nFFT,cpLen,symOffset,nullIdx);
cdScope(x);

Convert the vector of path gains, pg, to scalar tap gains that correspond to data subcarriers, h_datasubcarr. Use the h_datasubcarr tap gains for equalization during signal recovery.

hImp = complex(zeros(nFFT,1));
hImp(sampIdx) = mean(pg,1);
hall = fftshift(fft(hImp));
dataIdx = setdiff((1:nFFT)',nullIdx);
h_datasubcarr = hall(dataIdx);

Equalize the signal. Display the constellation diagram after equalization.

eqSig = x ./ h_datasubcarr;
cdScope(eqSig);

Demodulate the 16-QAM symbols to recover the signal. Compute the symbol error rate.

rxSym = qamdemod(eqSig,M,UnitAveragePower=true);
numErr = symerr(data,rxSym);
disp(['Number of symbol errors: ' num2str(numErr) ...
    ' out of ' num2str(length(data)) ' symbols.'])

Number of symbol errors: 2 out of 52 symbols.

OFDM Demodulation with Null and Pilot Packing

OFDM-demodulate data input that includes null and pilot packing.

Initialize input parameters, defining locations for null and pilot subcarriers. Generate random data and perform OFDM modulation.

Mqam = 16;
Mpsk = 4;
nfft = 64;
cplen = 16;
nSym = 10;
nullIdx = [1:6 33 64-4:64]';
pilotIdx = [12 26 40 54]';
numDataCarrs = nfft-length(nullIdx)-length(pilotIdx);
dataSym = randi([0 Mqam-1],numDataCarrs,nSym);
qamSig = qammod(dataSym,Mqam,UnitAveragePower=true);
pilotSym = repmat((0:Mpsk-1).',1,nSym);
pilots = pskmod(pilotSym,Mpsk);
y2 = ofdmmod(qamSig,nfft,cplen,nullIdx,pilotIdx,pilots);

Demodulate the OFDM symbols. Compare the results to the original input data to show that the demodulated signal and the original data and pilot signals are equal.

symOffset = cplen;
[x2,rxPilots] = ofdmdemod(y2,nfft,cplen,symOffset,nullIdx,pilotIdx);
rxData = qamdemod(x2,Mqam,UnitAveragePower=true);
isequal(rxData,dataSym)

ans = logical
   1

rxPilotSym = pskdemod(rxPilots,Mpsk);
isequal(rxPilotSym,repmat((0:Mpsk-1).',1,nSym))

ans = logical
   1

Demodulate Oversampled OFDM Signal

Demodulate an oversampled OFDM modulation that has a sample offset. Insert nulls in the OFDM grid and oversample the output signal.

Initialize variables for the oversampling factor, FFT size, cyclic prefix length, and sample offset.

M = 64;
osf = 4/3;
nfft = 768;
cplen = 24;
sampOffset = 5;
symOffset = cplen - (sampOffset/osf);

Generate data symbols and OFDM-modulate the data.

dataSym = randi([0 M-1],nfft,1);
qamSig = qammod(dataSym,M,UnitAveragePower=true);
y3 = ofdmmod(qamSig,nfft,cplen,OversamplingFactor=osf);

Demodulate the signal and show the demodulated data symbols match the original input data symbols.

x3 = ofdmdemod(y3,nfft,cplen,symOffset,OversamplingFactor=osf);
rxSym = qamdemod(x3,M,UnitAveragePower=true);
isequal(rxSym,dataSym)

ans = logical
   1

Input Arguments

`ofdmSig` — Modulated OFDM symbols
2-D array of complex symbols

Modulated OFDM symbols, specified as a 2-D array of complex symbols.

If cplen is a scalar, the array size is ((nfft + cplen) × N_Sym)-by-N_R.
If cplen is a row vector, the array size is ((nfft × N_Sym) + sum(cplen))-by-N_R.
N_Sym is the number of symbols per antenna and N_R is the number of receive antennas.

Data Types: double | single
Complex Number Support: Yes

`nfft` — FFT length
integer greater than or equal to 8

FFT length, specified as an integer greater than or equal to 8. nfft is equivalent to the number of subcarriers used in the demodulation process.

Data Types: double

`cplen` — Cyclic prefix length
scalar | row vector of length N_Sym

Cyclic prefix length, specified as a scalar or as a row vector of length N_Sym.

When you specify cplen as a scalar, the cyclic prefix length is the same for all symbols through all antennas.
When you specify cplen as a row vector of length N_Sym, the cyclic prefix length can vary across symbols but remains the same length through all antennas.

Data Types: double

`symOffset` — Symbol sampling offset
`cplen` (default) | scalar | row vector

Symbol sampling offset, specified as values from 0 to cplen.

If you do not specify symOffset, the default value is an offset equal to cplen.
If you specify symOffset as a scalar, the same offset is used for all symbols.
If you specify symOffset as a row vector, the offset value can be different for each symbol.

For information, see Windowing and Symbol Offset.

Data Types: double

`nullidx` — Indices of null subcarrier locations
column vector

Indices of null subcarrier locations, specified as a column vector with element values from 1 to nfft. If you specify nullidx, the number of rows in outSym is (nfft-length(nullidx)). For information, see Subcarrier Allocation and Guard Bands.

Data Types: double

`pilotidx` — Indices of pilot subcarrier locations
column vector

Indices of pilot subcarrier locations, specified as a column vector with element values from 1 to nfft. If you specify pilotidx, the number of rows in outSym is (nfft-length(nullidx)-length(pilotidx)).For information, see Subcarrier Allocation and Guard Bands.

Data Types: double

Output Arguments

`outSym` — Output demodulated symbols
3-D array

Output demodulated symbols, returned as an N_D-by-N_Sym-by-N_R array of symbols. N_D must equal nfft – length(nullidx) – length(pilotidx). N_Sym is the number of OFDM symbols per antenna. N_R is the number of receive antennas. For information, see OFDM Demodulation.

`pilots` — Pilot subcarriers
3-D array

Pilot subcarriers, returned as an N_Pilot-by-N_Sym-by-N_R array of symbols. N_Pilot must equal the length of pilotidx. N_Sym is the number of OFDM symbols per antenna. N_R is the number of receive antennas. The function assumes that the pilot subcarrier locations are the same across each OFDM symbol and transmit antenna. Use the comm.OFDMDemodulator to vary pilot subcarrier locations across OFDM symbols or antennas.

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