ofdmmod

Modulate frequency-domain signal using orthogonal frequency division multiplexing (OFDM)

Syntax

ofdmSig = ofdmmod(inSym,nfft,cplen)

ofdmSig = ofdmmod(inSym,nfft,cplen,nullidx)

ofdmSig = ofdmmod(inSym,nfft,cplen,nullidx,pilotidx,pilots)

ofdmSig = ofdmmod(inSym,nfft,cplen,___,OvesamplingFactor=Value)

Description

ofdmSig = ofdmmod(inSym,nfft,cplen) performs OFDM modulation on the frequency-domain input data subcarriers, inSym, using an FFT size specified by nfft and cyclic prefix length specified by cplen. For information, see OFDM Modulation.

ofdmSig = ofdmmod(inSym,nfft,cplen,nullidx) inserts null subcarriers into the frequency domain input data signal prior to performing OFDM modulation. The null subcarriers are inserted at index locations from 1 to nfft, as specified by nullidx. For this syntax, the number of rows in the input inSym must be nfft – length(nullidx). Use null carriers to account for guard bands and DC subcarriers. For information, see Subcarrier Allocation, Guard Bands and Guard Intervals.

ofdmSig = ofdmmod(inSym,nfft,cplen,nullidx,pilotidx,pilots) inserts null and pilot subcarriers into the frequency domain input data symbols prior to performing OFDM modulation. The null subcarriers are inserted at the index locations specified by nullidx. The pilot subcarriers, pilots, are inserted at the index locations specified by pilotidx. For this syntax, the number of rows in the input inSym must be nfft – length(nullidx) – length(pilotidx). The function assumes pilot subcarrier locations are the same across each OFDM symbol and transmit antenna.

ofdmSig = ofdmmod(inSym,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 output 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, ofdmmod(inSym,nfft,cplen,OversamplingFactor=2) upsamples the output signal by a factor of two.

Examples

OFDM Modulation over Two Antennas

OFDM-modulate a fully packed input over two transmit antennas.

Initialize input parameters, generate random data, and perform OFDM modulation.

M = 16;      % Modulation order for 16QAM
nfft  = 128; % Number of data carriers
cplen = 16;  % Cyclic prefix length
nSym  = 5;   % Number of symbols per RE
nt    = 2;   % Number of transmit antennas
dataIn = randi([0 M-1],nfft,nSym,nt);
qamSig = qammod(dataIn,M,'UnitAveragePower',true);
y1 = ofdmmod(qamSig,nfft,cplen);

Apply OFDM Assigning Null Subcarriers

Apply OFDM modulation assigning null subcarriers.

Initialize input parameters and generate random data.

M = 16;     % Modulation order for 16QAM
nfft  = 64; % FFT length
cplen = 16; % Cyclic prefix length
nSym  = 10; % Number of symbols per RE

nullIdx  = [1:6 33 64-4:64]';
numDataCarrs = nfft-length(nullIdx);
inSym = randi([0 M-1],numDataCarrs,nSym);

QAM modulate data. Perform OFDM modulation.

qamSig = qammod(inSym,M,'UnitAveragePower',true);
outSig = ofdmmod(qamSig,nfft,cplen,nullIdx);

Perform OFDM Modulation Varying Cyclic Prefix per Symbol

Perform OFDM modulation to input frequency domain data signal varying cyclic prefix length applied to each symbol.

Initialize input parameters and generate random data.

M = 16; % Modulation order for 16QAM
nfft  = 64;
cplen = [4 8 10 7 2 2 4 11 16 3];
nSym  = 10;
nullIdx  = [1:6 33 64-4:64]';
numDataCarrs = nfft-length(nullIdx);
inSym = randi([0 M-1],numDataCarrs,nSym);

QAM modulate the data symbols and perform OFDM modulation to the QAM signal.

qamSig = qammod(inSym,M,UnitAveragePower=true);
outSig = ofdmmod(qamSig,nfft,cplen,nullIdx);

Apply OFDM to QPSK Signal Spatially Multiplexed over Two Antennas

Apply OFDM modulation to a QPSK signal that is spatially multiplexed over two transmit antennas.

Initialize input parameters and generate random data for each antenna.

M = 4;      % Modulation order for QPSK
nfft  = 64;
cplen = 16;
nSym  = 5;
nt    = 2;
nullIdx  = [1:6 33 64-4:64]';
pilotIdx = [12 26 40 54]';
numDataCarrs = nfft-length(nullIdx)-length(pilotIdx);
pilots = repmat(pskmod((0:M-1).',M),1,nSym,2);

ant1 = randi([0 M-1],numDataCarrs,nSym);
ant2 = randi([0 M-1],numDataCarrs,nSym);

QPSK modulate data individually for each antenna. Perform OFDM modulation.

qpskSig(:,:,1) = pskmod(ant1,M);
qpskSig(:,:,2) = pskmod(ant2,M);
y1 = ofdmmod(qpskSig,nfft,cplen,nullIdx,pilotIdx,pilots);

OFDM Modulation with Null and Pilot Packing

OFDM-modulate data input, specifying null and pilot packing.

Initialize input parameters, defining locations for null and pilot subcarriers. Generate random data, apply 16-QAM to data, QSPK to pilots, and perform OFDM modulation.

M = 16;     % Modulation order
nfft = 64;  % FFT length
cplen = 16; % Cyclic prefix length
nSym  = 10; % Number of symbols per RE

nullIdx  = [1:6 33 64-4:64]';
pilotIdx = [12 26 40 54]';

numDataCarrs = nfft-length(nullIdx)-length(pilotIdx);
dataSym = randi([0 M-1],numDataCarrs,nSym);
qamSig = qammod(dataSym,M,UnitAveragePower=true);
pilots = repmat(pskmod((0:3).',4),1,nSym);

y2 = ofdmmod(qamSig,nfft,cplen,nullIdx,pilotIdx,pilots);

OFDM Modulate with Upsampling and Nulls

Apply OFDM modulation to symbols. Insert nulls in the OFDM grid and oversample the output signal.

Initialize variables for the modulation order, oversampling factor, FFT size, cyclic prefix length, and null indices.

M = 64;      % Modulation order
osf = 3;     % Oversampling factor
nfft = 256;  % FFT length
cplen = 16;  % Cyclic prefix length

nullidx  = [1:6 nfft/2+1 nfft-5:nfft]';
numDataCarrs = nfft-length(nullidx);

Generate data symbols, apply QAM, and OFDM-modulate the data.

x = randi([0 M-1],numDataCarrs,1);
qamSig = qammod(x,M,UnitAveragePower=true);
y = ofdmmod(qamSig,nfft,cplen,nullidx,OversamplingFactor=osf); 

Input Arguments

inSym — Input data subcarriers

3-D array

Input data subcarriers, specified as an N_D-by-N_Sym-by-N_T array of symbols. The number of data subcarriers, N_D, must equal nfft – length(nullidx) – length(pilotidx). N_Sym is the number of OFDM symbols per transmit antenna, N_T is the number of transmit antennas.

Input data symbols to an OFDM modulator are typically created with a baseband digital modulator, such as qammod.

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 modulation 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.

For more information, see Subcarrier Allocation, Guard Bands and Guard Intervals.

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.

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.

Data Types: double

pilots — Pilot subcarriers

3-D array

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

Data Types: double | single

Output Arguments

ofdmSig — Modulated OFDM symbols

2-D array of complex symbols

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

• If cplen is a scalar, the array size is ((nfft + cplen) × N_Sym)-by-N_T.

• If cplen is a row vector, the array size is ((nfft × N_Sym) + sum(cplen))-by-N_T.

  N_Sym is the number of symbols per transmit antenna and N_T is the number of transmit antennas.

Data Types: double | single
Complex Number Support: Yes

More About

OFDM Modulation

OFDM belongs to the class of multicarrier modulation schemes. Since the multiple data streams can be transmitted simultaneously with multiple carriers, OFDM is not influenced by noise to the same degree as single-carrier modulation.

OFDM operation divides a high-rate data stream into lower data rate substreams by decomposing the transmission frequency band into N contiguous individually modulated subcarriers. Multiple parallel and orthogonal subcarriers carry the samples with almost the same bandwidth as a wideband channel. By using narrow orthogonal subcarriers, the OFDM signal gains robustness over a frequency-selective fading channel and eliminates adjacent subcarrier interference. Intersymbol interference (ISI) is reduced because the lower data rate substreams have symbol durations larger than the channel delay spread.

This image shows a frequency domain representation of orthogonal subcarriers in an OFDM waveform.

The transmitter applies inverse fast Fourier transform (IFFT) to N symbols at a time. Typically, the output of the IFFT is the sum of the N orthogonal sinusoids:

$$x(t)={\displaystyle \sum _{k=0}^{N-1}{X}_k{e}^{j2\pi k\Delta ft}},0\le t\le T,$$

where {X_k} are data symbols, and T is the OFDM symbol time. The data symbols X_k are typically complex and can be from any digital modulation alphabet (for example, QPSK, 16-QAM, 64-QAM, ...).

Note

The MATLAB^® implementation of the discrete Fourier transform normalizes the output of the IFFT by 1/N. For more information, see Discrete Fourier Transform of Vector on the ifft reference page.

The subcarrier spacing is Δf = 1/T, ensuring that the subcarriers are orthogonal over each symbol period, as shown below:

$$\frac{1}{T}{\displaystyle {\int }_0^T{\left(e^{j2\pi m\Delta ft}\right)}^{*}\left(e^{j2\pi n\Delta ft}\right)}dt=\frac{1}{T}{\displaystyle {\int }_0^T{e}^{j2\pi (m-n)\Delta ft}}dt=0\text{for}m\ne n.$$

An OFDM modulator consists of a serial-to-parallel conversion followed by a bank of N complex modulators, individually corresponding to each OFDM subcarrier.

Subcarrier Allocation, Guard Bands and Guard Intervals

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 used for channel estimation.

• Null subcarriers transmit no data. Subcarriers with no data are used to 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 are used in OFDM to protect the integrity of transmitted signals 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. Guard intervals are created by using cyclic prefixes. Cyclic prefix insertion copies the last part of an OFDM symbol as the first part of the OFDM symbol.

As long as the span of the time dispersion does not exceed the duration of the cyclic prefix, the benefit of cyclic prefix insertion is maintained.

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.

Extended Capabilities

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

Version History

Introduced in R2018a