Modulate using OFDM method
The OFDMModulator
object modulates
using the orthogonal frequency division modulation method. The output
is a baseband representation of the modulated signal.
To modulate an OFDM signal:
Define and set up the OFDM modulator object. See Construction.
Call step
to modulate a signal
according to the properties of comm.OFDMModulator
.
The behavior of step
is specific to each object in
the toolbox.
Starting in R2016b, instead of using the step
method
to perform the operation defined by the System
object™, you can
call the object with arguments, as if it were a function. For example, y
= step(obj,x)
and y = obj(x)
perform
equivalent operations.
H = comm.OFDMModulator
creates a modulator System
object, H
,
that modulates the input signal using the orthogonal frequency division
modulation (OFDM) method.
H = comm.OFDMModulator(
creates
a OFDM modulator object, Name
,Value
)H
, with each specified
property set to the specified value. You can specify additional namevalue
pair arguments in any order as (Name1
,Value1
,...,NameN
,ValueN
).
H = comm.OFDMModulator(hDemod)
creates
an OFDM modulator object, H
, whose properties are
determined by the corresponding OFDM demodulator object, hDemod
.

The length of the FFT, N_{FFT},
is equivalent to the number of subcarriers used in the modulation
process. Specify the number of subcarriers. The default is 

The number of guard band subcarriers allocated to the left and right guard bands. Specify the number of left and right subcarriers as nonnegative integers from 0 to
( 

This is a The DC subcarrier is the center of the frequency band and has the index value:


This is a 

If the $$\left[{\text{N}}_{\text{leftG}}+1,\text{\hspace{0.17em}}{\text{N}}_{\text{FFT}}/2\right]\cup \left[{\text{N}}_{\text{FFT}}/2+2,\text{\hspace{0.17em}}{\text{N}}_{\text{FFT}}{\text{N}}_{\text{rightG}}\right],$$ 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}by1,
where N_{pilot} is the number of pilot subcarriers.
When the pilot indices vary across symbols, the property has dimensions
of N_{pilot}byN_{sym},
where N_{sym} is the number
of symbols. If there is only one symbol but multiple transmit antennas,
the property has dimensions of N_{pilot}by1byN_{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 of N_{pilot}byN_{sym}byN_{T}.
It is desirable that when the number of transmit antennas is greater
than one, the indices per symbol should be mutually distinct across
antennas to avoid interference. The default value is 

The 

This is a 

This property specifies the length of the raised cosine window
when 

This property specifies the number of symbols, N_{sym}. 

This property determines the number of antennas, N_{T},
used to transmit the OFDM modulated signal. The property is a positive
integer. The default value is 
info  Provide dimensioning information for the OFDM method 
reset  Reset states of the OFDMModulator System
object 
showResourceMapping  Show the subcarrier mapping of the OFDM symbols created by the OFDM modulator System object. 
step  Modulate using OFDM method 
Common to All System Objects  

release  Allow System object property value changes 
Orthogonal frequency division modulation (OFDM) divides a highrate transmit data stream into N lowerrate streams, each of which has a symbol duration larger than the channel delay spread. This serves to mitigate intersymbol interference (ISI). The individual substreams are sent over N parallel subchannels which are orthogonal to each other. Through the use of an inverse fast Fourier transform (IFFT), OFDM can be transmitted using a single radio. Specifically, the OFDM Modulator System object modulates an input signal using orthogonal frequency division modulation. The output is a baseband representation of the modulated signal:
$$v(t)={\displaystyle \sum _{k=0}^{N1}{X}_{k}{e}^{j2\pi k\Delta ft}},\text{\hspace{1em}}0\le t\le T,$$
where {X_{k}} are data symbols, N is the number of subcarriers, and T is the OFDM symbol time. The subcarrier spacing of Δf = 1/T makes them orthogonal over each symbol period. This is expressed as:
$$\frac{1}{T}{\displaystyle {\int}_{0}^{T}{\left({e}^{j2\pi m\Delta ft}\right)}^{*}\left({e}^{j2\pi n\Delta ft}\right)}\text{\hspace{0.17em}}dt=\frac{1}{T}{\displaystyle {\int}_{0}^{T}{e}^{j2\pi (mn)\Delta ft}}\text{\hspace{0.17em}}dt=0\text{\hspace{1em}}\text{for}\text{\hspace{0.17em}}m\ne n.$$
The data symbols, X_{k}, are usually complex and can be from any modulation alphabet, e.g., QPSK, 16QAM, or 64QAM.
The figure shows an OFDM modulator. It consists of a bank of N complex modulators, where each corresponds to one OFDM subcarrier.
There are three types of OFDM subcarriers: data, pilot, and null. Data subcarriers are used for transmitting data while pilot subcarriers are used for channel estimation. There is no transmission on null subcarriers, which provide a DC null and provide buffers between OFDM resource blocks. These buffers are referred to as guard bands whose purpose is to prevent intersymbol interference. The allocation of nulls and guard bands vary depending upon the applicable standard, e.g., 802.11n differs from LTE. Consequently, the OFDM modulator object allows the user to assign subcarrier indices.
Analogous to the concept of guard bands, the OFDM modulator object supports guard intervals which are used to provide temporal separation between OFDM symbols so that the signal does not lose orthogonality due to timedispersive channels. As long as the guard interval is longer than the delay spread, each symbol does not interfere with other symbols. Guard intervals are created by using cyclic prefixes in which the last part of an OFDM symbol is copied and inserted as the first part of the OFDM symbol. The benefit of cyclic prefix insertion is maintained as long as the span of the time dispersion does not exceed the duration of the cyclic prefix. The OFDM modulator object enables the setting of the cyclic prefix length. The drawback in using a cyclic prefix is the penalty from increased overhead.
While the cyclic prefix creates 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. This causes spectral regrowth, which is the 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 provides a smooth transition from one symbol to the next.
The raised cosine window, w(t), in the time domain can be expressed as:
$$w(t)=\{\begin{array}{l}1,\text{\hspace{0.17em}}\text{}0\le \leftt\right<\frac{T{T}_{W}}{2}\\ \frac{1}{2}\left\{1+\mathrm{cos}\left[\frac{\pi}{{T}_{W}}\left(\leftt\right\frac{T{T}_{W}}{2}\right)\right]\right\},\text{}\frac{T{T}_{W}}{2}\le \leftt\right\le \frac{T+{T}_{W}}{2}\\ 0,\text{}\text{otherwise}\end{array}$$
,
where
T represents the OFDM symbol duration including the guard interval.
T_{W} represents 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.
[1] Dahlman, E., S. Parkvall, and J. Skold. 4G LTE/LTEAdvanced for Mobile Broadband. London: Elsevier Ltd., 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”, http://wireless.agilent.com/rfcomms/n4010a/n4010aWLAN/onlineguide/ofdm_raised_cosine_windowing.htm.
[4] Montreuil, L., R. Prodan, and T. Kolze. “OFDM TX Symbol Shaping 802.3bn”, http://www.ieee802.org/3/bn/public/jan13/montreuil_01a_0113.pdf. Broadcom, 2013.
[5] “IEEE Standard 802.16^{TM}2009,” New York: IEEE, 2009.