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ofdmdemod

Demodulate using OFDM method

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Syntax

Y = ofdmdemod(X,nfft,cplen)
Y = ofdmdemod(X,nfft,cplen,symOffset)
Y = ofdmdemod(X,nfft,cplen,symOffset,nullidx)
[Y,pilots] = ofdmdemod(X,nfft,cplen,symOffset,nullidx,pilotidx)
Y = ofdmdemod(X,nfft,cplen,___,OversamplingFactor=Value)

Description

example

Y = ofdmdemod(X,nfft,cplen) demodulates the input time domain signal specified in 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) applies the symbol sampling offset, symOffset, for each OFDM symbol before demodulation of the input.

example

Y = ofdmdemod(X,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.

example

[Y,pilots] = ofdmdemod(X,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 Y 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.

example

Y = ofdmdemod(X,nfft,cplen,___,OversamplingFactor=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, and 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.

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

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Open Live Script

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
Open Live Script

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.
Open Live Script

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
Open Live Script

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

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OFDM-modulated baseband signal, specified as an (osf × NIn)-by-NR numeric array or a dlarray (Deep Learning Toolbox) object. For more information, see Array Support.

  • osf is the oversampling factor, as determined by OversamplingFactor.

  • NIn = NCPTotal + (NFFT × NSym)

  • NCPTotal represents the cyclic prefix length over all the symbols.

    • NCP represents the cyclic prefix length as determined by cplen.

    • When cplen is a scalar, NCPTotal = NCP × NSym.

    • When cplen is a row vector, NCPTotal = ∑ NCP.

  • NFFT represents the number of subcarriers, determined by nfft.

  • NSym is the number of symbols per antenna.

  • NR is the number of receive antennas.

Data Types: double | single
Complex Number Support: Yes

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

Cyclic prefix length, specified as a scalar or row vector of length NSym. Cyclic prefix length must be nonnegative.

  • When you specify cplen as a scalar, the value must be in the range [0, NFFT]. In this case, all symbols through all antennas have the same cyclic prefix length.

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

NSym is the number of symbols per antenna.

Data Types: double

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

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 Y is (nfft-length(nullidx)). For information, see Subcarrier Allocation and Guard Bands.

Data Types: double

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 Y is (nfft – length(nullidx) – length(pilotidx)).For information, see Subcarrier Allocation and Guard Bands.

Data Types: double

Output Arguments

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Output baseband signal, returned as an NOut-by-NSym-by-NR numeric array or a dlarray (Deep Learning Toolbox). The output data format matches the input signal, X. For more information, see Array Support.

  • The number of data subcarriers, NOut = nfft – length(nullidx) – length(pilotidx).

  • NSym is the number of OFDM symbols per antenna.

  • NR is the number of receive antennas.

For information, see OFDM Demodulation.

Pilot subcarriers, returned as an NPilot-by-NSym-by-NR numeric array, dlarray (Deep Learning Toolbox), or gpuArray (Parallel Computing Toolbox). For more information, see Array Support. The output data format matches the input signal, X.

  • NPilot equals the length of pilotidx.

  • NSym is the number of OFDM symbols per antenna.

  • NR is the number of receive antennas.

The function assumes that the pilot subcarrier locations are the same across each OFDM symbol and transmit antenna. To vary pilot subcarrier locations across OFDM symbols or antennas, use the comm.OFDMDemodulator System object™.

More About

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Array Support

The ofdmdemod function supports input signals represented in a numeric array, dlarray (Deep Learning Toolbox), or gpuArray (Parallel Computing Toolbox).

The number of batch observations (NB) is an optional dimension that can be added to this input for all supported data types.

  • X — The modulated OFDM symbols can be an array of up to three dimensions, specified as NS-by-NR-by-NB array.

NS is the number of samples and NR is the number of receive antennas.

For a list of Communications Toolbox™ features that support dlarray objects, see AI for Wireless.

Algorithms

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OFDM Demodulation

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.

OFDM demodulator block diagram.

Subcarrier Allocation and Guard Bands

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.

Individual data, DC, pilot, and 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) if nfft is even, or ((nfft + 1) / 2) if nfft is 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 symbol period

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.

Windowing and Symbol Offset

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.

OFDM symbol windowing

To reduce ISI, you can align signal sample timing by specifying a symbol sampling offset that gets applied before OFDM symbol demodulation.

OFDM symbol sampling offset

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.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2018a

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See Also

Functions

Objects

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