ofdmdemod
Demodulate using OFDM method
Syntax
Description
Y = ofdmdemod(X,nfft,cplen)X using
the orthogonal frequency division multiplexing (OFDM) method with an FFT size
specified by nfft and cyclic prefix length specified by
cplen. For information, see OFDM Demodulation.
Y = ofdmdemod(X,nfft,cplen,symOffset,nullidx)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(, 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.nullidx)
[
returns pilot subcarriers for the pilot indices specified in
Y,pilots] = ofdmdemod(X,nfft,cplen,symOffset,nullidx,pilotidx)pilotidx. For this syntax, the symbol sampling offset is
applied to each OFDM symbol and number of rows in the output Y
is nfft –
length( –
nullidx)length(, 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
stream.pilotidx)
Y = ofdmdemod(X,nfft,cplen,___,OversamplingFactor=Value)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.
Tip
If you set the oversampling factor to a noninteger rational number, specify a fractional value
rather than a decimal value. For example, with an FFT length of 12 and an
oversampling factor of 4/3, their product is the integer
16. However, rounding 4/3 to
1.333 when setting the oversampling factor results in a noninteger
product of 15.9960, which results in a code error.
Examples
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
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-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 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
Output Arguments
More About
Algorithms
The orthogonal frequency division multiplexing (OFDM) method demodulates an OFDM input signal by using an FFT operation that results in N parallel data streams.
The figure shows an OFDM demodulator consisting of a bank of N correlators with one correlator assigned to each OFDM subcarrier. A parallel-to-serial conversion follows the correlator bank.
Individual OFDM subcarriers are allocated as data, pilot, or null subcarriers.
As shown here, subcarriers are designated as data, DC, pilot, or guard-band subcarriers.
Data subcarriers transmit user data.
Pilot subcarriers are for channel estimation.
Null subcarriers transmit no data. Subcarriers with no data provide a DC null and serve as buffers between OFDM resource blocks.
The null DC subcarrier is the center of the frequency band with an index value of (
nfft/2 + 1) ifnfftis even, or ((nfft+ 1) / 2) ifnfftis odd.The guard bands provide buffers between adjacent signals in neighboring bands to reduce interference caused by spectral leakage.
Null subcarriers enable you to model guard bands and DC subcarrier locations for specific standards, such as the various 802.11 formats, LTE, WiMAX, or for custom allocations. You can allocate the location of nulls by assigning a vector of null subcarrier indices.
Similar to guard bands, guard intervals protect the integrity of transmitted signals in OFDM by reducing intersymbol interference.
Assignment of guard intervals is analogous to the assignment of guard bands. You can model guard intervals to provide temporal separation between OFDM symbols. The guard intervals help preserve intersymbol orthogonality after the signal passes through time-dispersive channels. You create guard intervals by using cyclic prefixes. Cyclic prefix insertion copies the last part of an OFDM symbol as the first part of the OFDM symbol.
OFDM benefits from the use of cyclic prefix insertion as long as the span of the time dispersion does not exceed the duration of the cyclic prefix.
Inserting a cyclic prefix results in a fractional reduction of user data throughput because the cyclic prefix occupies bandwidth that could be used for data transmission.
To reduce intersymbol interference (ISI) introduced by signal windowing applied at the transmitter, a fractional symbol offset is applied before demodulation of each OFDM symbol. Signal windowing is often applied to transmitted OFDM symbols to smooth the discontinuity between consecutive OFDM symbols. Windowing reduces intersymbol out-of-band emissions but increases ISI.
The windowed OFDM symbol consists of the cyclic prefix (CP), ODFM symbol data, plus windowing regions at the beginning and end of the symbol. The discussion and figures in this section assume an oversampling factor of 1. The leading and trailing windowing shoulders have tails as shown in this figure.
To reduce ISI, you can align signal sample timing by specifying a symbol sampling offset that gets applied before OFDM symbol demodulation.
Specify the symbol sampling offset as a value in the range [0, LCP], where LCP is the cyclic prefix length.
When the symbol sampling offset is a scalar, the FFT window begins at the X+1 sample of the cyclic prefix.
When the symbol sampling offset is zero, no offset is applied and the FFT window starts at the first sample of the symbol.
When the symbol sampling offset is LCP, the FFT window begins after the last CP sample. If symbol sampling offset is not specified, LCP is the default setting.
