comm.OFDMModulator

Modulate signal using OFDM method

Description

The OFDMModulator object modulates a signal using the orthogonal frequency division multiplexing method. The output is a baseband representation of the modulated signal.

To modulate a signal using OFDM:

1. Create the comm.OFDMModulator object and set its properties.

2. Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

Creation

Syntax

hMod = comm.OFDMModulator

hMod = comm.OFDMModulator(Name,Value)

hMod = comm.OFDMModulator(hDemod)

Description

hMod = comm.OFDMModulator creates an OFDM modulator System object™.

hMod = comm.OFDMModulator(Name,Value) specifies Properties using one of more name-value pair arguments. Enclose each property name in quotes. For example, comm.OFDMModulator('NumSymbols',8) specifies eight OFDM symbols in the time-frequency grid.

hMod = comm.OFDMModulator(hDemod) sets the OFDM modulator system object properties based on the specified OFDM demodulator system object comm.OFDMDemodulator.

Properties

Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the release function unlocks them.

If a property is tunable, you can change its value at any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

FFTLength — Number of FFT points

64 (default) | positive integer

Number of Fast Fourier Transform (FFT) points, specified as a positive integer. The length of the FFT, N_FFT, must be greater than or equal to 8 and is equivalent to the number of subcarriers.

Data Types: double

NumGuardBandCarriers — Number of subcarriers to the left and right guard bands

[6;5] (default) | two-element column vector of integers

Number of subcarriers allocated to the left and right guard bands, specified as a two-element column vector of integers. The number of subcarriers must fall within [0, ⌊N_FFT/2⌋ − 1]. This vector has the form [N_leftG, N_rightG], where N_leftG and N_rightG specify the left and right guard bands, respectively.

Data Types: double

InsertDCNull — Option to insert DC null

false or 0 (default) | true or 1

Option to insert DC null, specified as a numeric or logical 0 (false) or 1 (true). The DC subcarrier is the center of the frequency band and has the index value:

• (FFTLength / 2) + 1 when FFTLength is even

• (FFTLength + 1) / 2 when FFTLength is odd

PilotInputPort — Option to specify pilot input

false or 0 (default) | true or 1

Option to specify pilot input, specified as a numeric or logical 0 (false) or 1 (true). If this property is 1 (true), you can assign individual subcarriers for pilot transmission. If this property is 0 (false), pilot information is assumed to be embedded in the input data.

PilotCarrierIndices — Pilot subcarrier indices

[12; 26; 40; 54] (default) | column vector

Pilot subcarrier indices, specified as a column vector. If the PilotCarrierIndices property is set to 1 (true), you can specify the indices of the pilot subcarriers. You can assign the indices to the same or different subcarriers for each symbol. Similarly, the pilot carrier indices can differ across multiple transmit antennas. Depending on the desired level of control for index assignments, the dimensions of the property vary. Valid pilot indices fall in the range

$$\left[N_{\text{leftG}}+1,N_{\text{FFT}}/2\right]\cup \left[N_{\text{FFT}}/2+2,N_{\text{FFT}}-N_{\text{rightG}}\right],$$

where the index value cannot exceed the number of subcarriers. When the pilot indices are the same for every symbol and transmit antenna, the property has dimensions N_pilot-by-1. When the pilot indices vary across symbols, the property has dimensions N_pilot-by-N_sym. If you transmit only one symbol but multiple transmit antennas, the property has dimensions N_pilot-by-1-by-N_t., where N_t. is the number of transmit antennas. If the indices vary across the number of symbols and transmit antennas, the property has dimensions N_pilot-by-N_sym-by-N_t. If the number of transmit antennas is greater than one, ensure that the indices per symbol must be mutually distinct across antennas to minimize interference.

To enable this property, set the PilotInputPort property to 1 (true).

CyclicPrefixLength — Length of cyclic prefix

16 (default) | positive integer | row vector

Length of cyclic prefix, specified as a positive integer. If you specify a scalar, the prefix length is the same for all symbols through all antennas. If you specify a row vector of length N_sym, the prefix length can vary across symbols but remains the same through all antennas.

Data Types: double

Windowing — Option to apply raised cosine window between OFDM symbols

false or 0 (default) | true or 1

Option to apply raised cosine window between OFDM symbols, specified as true or false. Windowing is the process in which the OFDM symbol is multiplied by a raised cosine window before transmission to more quickly reduce the power of out-of-band subcarriers. Windowing reduces spectral regrowth.

WindowLength — Length of raised cosine window

1 (default) | positive scalar

Length of raised cosine window, specified as a positive scalar. This value must be less than or equal to the minimum cyclic prefix length. For example, in a configuration of four symbols with cyclic prefix lengths 12, 14, 16, and 18, the window length must be less than or equal to 12.

To enable this property, set the Windowing property to 1 (true).

NumSymbols — Number of OFDM symbols

1 (default) | positive integer

Number of OFDM symbols in the time-frequency grid, specified as a positive integer.

NumTransmitAntennnas — Number of transmit antennas

1 (default) | positive integer

Number of transmit antennas, used to transmit the OFDM modulated signal, specified as a positive integer.

Usage

Syntax

waveform = hMod(insignal)

waveform = hMod(data,pilot)

Description

waveform = hMod(insignal) applies OFDM modulation the specified baseband signal and returns the modulated OFDM baseband signal.

waveform = hMod(data,pilot) assigns the pilot signal, pilot, into the frequency subcarriers specified by the PilotCarrierIndices property value of the hMod system object. To enable this syntax set the PilotCarrierIndices property to true.

Input Arguments

insignal — Input baseband signal

matrix | 3-D array

Input baseband signal, specified as a matrix or 3-D array of numeric values. The input baseband signal must be of size N_f-by-N_sym-by-N_t. where N_f is the number of frequency subcarriers excluding guard bands and DC null.

Data Types: double
Complex Number Support: Yes

data — Input data

matrix | 3-D array

Input data, specified as a matrix or 3-D array. The input must be a numeric of size N_d-by-N_sym-by-N_t. where N_d is the number of data subcarriers in each symbol. For more information on how N_d is calculated, see the PilotCarrierIndices property.

Data Types: double
Complex Number Support: Yes

pilot — Pilot signal

3-D array

Pilot signal, specified as a 3-D array of numeric values. The pilot signal must be of size N_pilot-by-N_sym-by-N_t.

Data Types: double
Complex Number Support: Yes

Output Arguments

waveform — OFDM Modulated baseband signal

2-D array

OFDM Modulated baseband signal, returned as a 2-D array. If the CyclicPrefixLength property is a scalar, the output waveform is of size ((N_FFT+CP_len)⁎N_sym)-by-N_t. Otherwise, the size is (N_FFT⁎N_sym+∑(CP_len))-by-N_t.

Data Types: double
Complex Number Support: Yes

Object Functions

To use an object function, specify the System object as the first input argument. For example, to release system resources of a System object named obj, use this syntax:

release(obj)

Specific to comm.OFDMModulator

info	Provide dimensioning information for OFDM modulator
showResourceMapping	Show the subcarrier mapping of the OFDM symbols created by the OFDM modulator System object

Common to All System Objects

step	Run System object algorithm
release	Release resources and allow changes to System object property values and input characteristics
reset	Reset internal states of System object

Examples

Create and Modify OFDM Modulator

Create and display an OFDM modulator System object™ with default property values.

hMod = comm.OFDMModulator

hMod = 
  comm.OFDMModulator with properties:

               FFTLength: 64
    NumGuardBandCarriers: [2x1 double]
            InsertDCNull: false
          PilotInputPort: false
      CyclicPrefixLength: 16
               Windowing: false
              NumSymbols: 1
     NumTransmitAntennas: 1

Modify the number of subcarriers and symbols.

hMod.FFTLength = 128;
hMod.NumSymbols = 2;

Verify that the number of subcarriers and the number of symbols changed.

disp(hMod)

  comm.OFDMModulator with properties:

               FFTLength: 128
    NumGuardBandCarriers: [2x1 double]
            InsertDCNull: false
          PilotInputPort: false
      CyclicPrefixLength: 16
               Windowing: false
              NumSymbols: 2
     NumTransmitAntennas: 1

Use the showResourceMapping object function to show the mapping of data, pilot, and null subcarriers in the time-frequency space.

showResourceMapping(hMod)

Create OFDM Modulator from OFDM Demodulator

Create an OFDM demodulator System object™ with default property values. Then, specify pilot indices for a single symbol and two transmit antennas.

Setting the PilotCarrierIndices property of the demodulator affects the number of transmit antennas in the OFDM modulator when you use the demodulator in the creation of the modulator. The number of receive antennas in the demodulator is uncorrelated with the number of transmit antennas.

ofdmDemod = comm.OFDMDemodulator;
ofdmDemod.PilotOutputPort = true;
ofdmDemod.PilotCarrierIndices = ...
    cat(3,[12; 26; 40; 54],[13; 27; 41; 55]);

Use the OFDM demodulator to construct the OFDM modulator.

ofdmMod = comm.OFDMModulator(ofdmDemod);

Display the properties of the OFDM modulator and demodulator, verifying that the applicable properties match.

disp(ofdmMod)

  comm.OFDMModulator with properties:

               FFTLength: 64
    NumGuardBandCarriers: [2x1 double]
            InsertDCNull: false
          PilotInputPort: true
     PilotCarrierIndices: [4x1x2 double]
      CyclicPrefixLength: 16
               Windowing: false
              NumSymbols: 1
     NumTransmitAntennas: 2

disp(ofdmDemod)

  comm.OFDMDemodulator with properties:

               FFTLength: 64
    NumGuardBandCarriers: [2x1 double]
         RemoveDCCarrier: false
         PilotOutputPort: true
     PilotCarrierIndices: [4x1x2 double]
      CyclicPrefixLength: 16
              NumSymbols: 1
      NumReceiveAntennas: 1

Visualize Time-Frequency Resource Assignments for OFDM Modulator

The showResourceMapping method displays the time-frequency resource mapping for each transmit antenna.

Construct an OFDM modulator.

mod = comm.OFDMModulator;

Apply the showResourceMapping method.

showResourceMapping(mod)

Insert a DC null.

mod.InsertDCNull = true;

Show the resource mapping after adding the DC null.

showResourceMapping(mod)

Create OFDM Modulator and Specify Pilots

Create an OFDM modulator and specify the subcarrier indices for the pilot signals. Specify the indices for each symbol and transmit antenna. When the number of transmit antennas is greater than one, set different pilot indices for each symbol between antennas.

Create an OFDM modulator System object, specifying two symbols and inserting a DC null.

mod = comm.OFDMModulator('FFTLength',128,'NumSymbols',2,...
    'InsertDCNull',true);

Enable the pilot input port so you can specify the pilot indices.

mod.PilotInputPort = true;

Specify the same pilot indices for both symbols.

mod.PilotCarrierIndices = [12; 56; 89; 100];

Visualize the placement of the pilot signals and nulls in the OFDM time-frequency grid by using the showResourceMapping object function.

showResourceMapping(mod)

Specify different indices for the second symbol by concatenating a second column of pilot indices to the PilotCarrierIndices property.

mod.PilotCarrierIndices = cat(2,mod.PilotCarrierIndices, ...
    [17; 61; 94; 105]);

Verify that the pilot subcarrier indices differ between the two symbols.

showResourceMapping(mod)

Increase the number of transmit antennas to two.

mod.NumTransmitAntennas = 2;

Specify the pilot indices for each of the two transmit antennas. To provide indices for multiple antennas while minimizing interference among the antennas, set the PilotCarrierIndices property as a 3-D array such that the indices for each symbol differ among antennas.

mod.PilotCarrierIndices = cat(3,[20; 50; 70; 110], [15; 60; 75; 105]);

Display the resource mapping for the two transmit antennas. The gray lines denote the insertion of custom nulls. The nulls are created by the object to minimize interference among the pilot symbols from different antennas.

showResourceMapping(mod)

Create OFDM Modulator with Varying Cyclic Prefix Lengths

Specify the length of the cyclic prefix for each OFDM symbol.

Create an OFDM modulator, specifying five symbols, four left and three right guard-band subcarriers, and the cyclic prefix length for each OFDM symbol.

mod = comm.OFDMModulator('NumGuardBandCarriers',[4;3],...
    'NumSymbols',5,...
    'CyclicPrefixLength',[12 10 14 11 13]);

Display the properties of the OFDM modulator, verifying that the cyclic prefix length changes across symbols.

disp(mod)

  comm.OFDMModulator with properties:

               FFTLength: 64
    NumGuardBandCarriers: [2x1 double]
            InsertDCNull: false
          PilotInputPort: false
      CyclicPrefixLength: [12 10 14 11 13]
               Windowing: false
              NumSymbols: 5
     NumTransmitAntennas: 1

Determine OFDM Modulator Data Dimensions

Get the OFDM modulator data dimensions by using the info object function.

Construct an OFDM modulator System object™ with user-specified pilot indices, an inserted DC null, and specify two transmit antennas.

hMod = comm.OFDMModulator('NumGuardBandCarriers',[4;3], ...
    'PilotInputPort',true, ...
    'PilotCarrierIndices',cat(3,[12; 26; 40; 54], ...
    [11; 25; 39; 53]), ...
    'InsertDCNull',true, ...
    'NumTransmitAntennas',2);

Use the info object function to get the modulator input data, pilot input data, and output data sizes.

info(hMod)

ans = struct with fields:
     DataInputSize: [48 1 2]
    PilotInputSize: [4 1 2]
        OutputSize: [80 2]

Create OFDM Modulated Data

Generate OFDM modulated symbols for use in link-level simulations.

Construct an OFDM modulator with an inserted DC null, seven guard-band subcarriers, and two symbols having different pilot indices for each symbol.

mod = comm.OFDMModulator( ...
    'NumGuardBandCarriers',[4;3], ...
    'PilotInputPort',true, ...
    'PilotCarrierIndices',[12 11; 26 27; 40 39; 54 55], ...
    'NumSymbols',2, ...
    'InsertDCNull',true);

Determine input data, pilot, and output data dimensions.

modDim = info(mod);

Generate random data symbols for the OFDM modulator. The structure variable, modDim, determines the number of data symbols.

dataIn = complex( ...
    randn(modDim.DataInputSize),randn(modDim.DataInputSize));

Create a pilot signal that has the correct dimensions.

pilotIn = complex( ...
    rand(modDim.PilotInputSize),rand(modDim.PilotInputSize));

Apply OFDM modulation to the data and pilot signals.

modData = mod(dataIn,pilotIn);

Use the OFDM modulator object to create the corresponding OFDM demodulator.

demod = comm.OFDMDemodulator(mod);

Demodulate the OFDM signal and output the data and pilot signals.

[dataOut, pilotOut] = demod(modData);

Verify that, within a tight tolerance, the input data and pilot symbols match the output data and pilot symbols.

isSame = (max(abs([dataIn(:) - dataOut(:); ...
    pilotIn(:) - pilotOut(:)])) < 1e-10)

isSame = logical
   1

More About

Orthogonal Frequency Division Multiplexing

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.

Raised Cosine Windowing

While the cyclic prefix creates a guard period in time domain to preserve orthogonality, an OFDM symbol rarely begins with the same amplitude and phase exhibited at the end of the prior OFDM symbol causing spectral regrowth and therefore, spreading of signal bandwidth due to intermodulation distortion. To limit this spectral regrowth, it is desired to create a smooth transition between the last sample of a symbol and the first sample of the next symbol. This can be done by using a cyclic suffix and raised cosine windowing.

To create the cyclic suffix, the first N_WIN samples of a given symbol are appended to the end of that symbol. However, in order to comply with the 802.11g standard, for example, the length of a symbol cannot be arbitrarily lengthened. Instead, the cyclic suffix must overlap in time and is effectively summed with the cyclic prefix of the following symbol. This overlapped segment is where windowing is applied. Two windows are applied, one of which is the mathematical inverse of the other. The first raised cosine window is applied to the cyclic suffix of symbol k and decreases from 1 to 0 over its duration. The second raised cosine window is applied to the cyclic prefix of symbol k+1 and increases from 0 to 1 over its duration. This process provides a smooth transition from one symbol to the next.

The raised cosine window, w(t), in the time domain can be expressed as:

$$w(t)=\{\begin{array}{l}1,0\le \left|t\right|<\frac{T-T_W}{2}\\ \frac{1}{2}\left\{1+\cos \left[\frac{\pi }{T_W}\left(\left|t\right|-\frac{T-T_W}{2}\right)\right]\right\},\frac{T-T_W}{2}\le \left|t\right|\le \frac{T+T_W}{2}\\ 0,\text{otherwise}\end{array}$$

where:

• T is the OFDM symbol duration including the guard interval.

• T_W is the duration of the window.

Adjust the length of the cyclic suffix via the window length setting property, with suffix lengths set between 1 and the minimum cyclic prefix length. While windowing improves spectral regrowth, it does so at the expense of multipath fading immunity. This occurs because redundancy in the guard band is reduced because the guard band sample values are compromised by the smoothing.

The following figures display the application of raised cosine windowing.

References

[1] Dahlman, Erik, Stefan Parkvall, and Johan Sköld. 4G LTE/LTE-Advanced for Mobile Broadband. Amsterdam: Elsevier, Acad. Press, 2011.

[2] Andrews, J. G., A. Ghosh, and R. Muhamed. Fundamentals of WiMAX. Upper Saddle River, NJ: Prentice Hall, 2007.

[3] Agilent Technologies, Inc., "OFDM Raised Cosine Windowing", https://rfmw.em.keysight.com/wireless/helpfiles/n7617a/ofdm_raised_cosine_windowing.htm.

[4] Montreuil, L., R. Prodan, and T. Kolze. "OFDM TX Symbol Shaping 802.3bn", https://www.ieee802.org/3/bn/public/jan13/montreuil_01a_0113.pdf. Broadcom, 2013.

[5] "IEEE Standard 802.16™-2009." New York: IEEE, 2009.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• See System Objects in MATLAB Code Generation (MATLAB Coder).

Version History

Introduced in R2014a