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)

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 and Guard Bands.

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.

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.

nfft  = 128;
cplen = 16;
nSym  = 5;
nt    = 2;
dataIn = complex(randn(nfft,nSym,nt),randn(nfft,nSym,nt));

y1 = ofdmmod(dataIn,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;
cplen = 16;
nSym  = 10;
nullIdx  = [1:6 33 64-4:64]';
numDataCarrs = nfft-length(nullIdx);
inSig = randi([0 M-1],numDataCarrs,nSym);

QAM modulate data. Perform OFDM modulation.

qamSym = qammod(inSig,M,'UnitAveragePower',true);
outSig = ofdmmod(qamSym,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);
inSig = randi([0 M-1],numDataCarrs,nSym);

QAM modulate data. Perform OFDM modulation.

qamSym = qammod(inSig,M,'UnitAveragePower',true);
outSig = ofdmmod(qamSym,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.

qpskSym(:,:,1) = pskmod(ant1,M);
qpskSym(:,:,2) = pskmod(ant2,M);
y1 = ofdmmod(qpskSym,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 and perform OFDM modulation.

nfft     = 64;
cplen    = 16;
nSym     = 10;

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

numDataCarrs = nfft-length(nullIdx)-length(pilotIdx);
dataIn = complex(randn(numDataCarrs,nSym),randn(numDataCarrs,nSym));
pilots = repmat(pskmod((0:3).',4),1,nSym);

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

Input Arguments

inSym — Input data subcarriers

numeric 3-D array

Input data subcarriers, specified as an N_D-by-N_Sym-by-N_T numeric 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 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

numeric 3-D array

Pilot subcarriers, specified as an N_Pilot-by-N_Sym-by-N_T numeric 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.

More About

OFDM Modulation

An OFDM modulator multiplexes a frequency-domain input signal over multiple subcarriers using orthogonal frequency division modulation.

The OFDM operation divides a high-rate transmit data stream into N lower data rate substreams. The individual substreams are sent over N parallel and orthogonal subchannels. Using an inverse fast Fourier transform (IFFT) to process the transmission data, OFDM can be transmitted with a single radio. Intersymbol interference (ISI) is reduced because the lower data rate substreams have symbol durations larger than the channel delay spread.

The output is a baseband representation of the modulated signal:

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

where {X_k} are data symbols, N is the number of subcarriers, and T is the OFDM symbol time. Using a subcarrier spacing of Δf = 1/T, the subcarriers are orthogonal over each symbol period, as expressed in this equation:

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

The data symbols, X_k, are typically complex and can be from any digital modulation alphabet (for example, QPSK, 16-QAM, 64-QAM).

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 and Guard Bands

Individual OFDM subcarriers are allocated as data, pilot, or null subcarriers.

As shown here, subcarriers are designated as data, DC, pilot, of 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 consecutive OFDM symbols to protect the integrity of transmitted signals by reducing intersymbol interference.

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.

Guard Intervals

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
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