DC subcarrier insertion, inverse fast Fourier transform (IFFT) calculation,
cyclic prefix insertion, and optional raised cosine windowing and
overlapping of adjacent OFDM symbols of the complex symbols in the
a 3-D array containing the resource elements (REs) for a number of
subframes across all configured antenna ports, as described in Represent Resource Grids. It could
also be multiple concatenated matrices to give multiple subframes,
using concatenation across the columns or second dimension. The antenna
grid are each OFDM modulated to yield
the columns of the output
grid can span multiple subframes. Windowing
and overlapping are applied between all adjacent OFDM symbols, including
the last of one subframe and the first of the next. Therefore, a different
result is obtained than if
called on individual subframes and then those time-domain waveforms
are concatenated. In that case, the resulting waveform has discontinuities
at the start or end of each subframe. It is recommended that all subframes
for OFDM modulation first be concatenated before calling
the resulting multi-subframe array. However, individual subframes
can be OFDM modulated and the resulting multi-subframe time-domain
waveform created by manual overlapping.
Perform OFDM Modulation
Perform OFDM modulation of one subframe of random uniformly distributed noise using a 10 MHz two-antenna configuration.
enb = struct('NDLRB',50,'CyclicPrefix','Normal','CellRefP',2); dims = lteDLResourceGridSize(enb); regrid = reshape(lteSymbolModulate(randi([0,1],prod(dims)*2,1), ... 'QPSK'),dims); waveform = lteOFDMModulate(enb,regrid);
enb — Cell-wide settings
Cell-wide settings, specified as a structure.
contain the following fields.
|Parameter Field||Required or Optional||Values||Description|
Cyclic prefix length
Number of time-domain samples over which the function applies windowing and overlapping of OFDM symbols
is absent, a default value for the number of windowed and overlapped
samples is used. The default value is chosen as a function of
NRB to compromise between the effective duration
of cyclic prefix, and thus the channel delay spread tolerance, and the
spectral characteristics of the transmitted signal, not considering any
additional FIR filtering. The value used is returned in
The issues concerning concatenation of subframes before OFDM modulation
do not apply when
grid — Resource elements
3-D numeric array
Resource elements, specified as a 3-D numeric array.
the resource elements for a number of subframes across all configured
grid is an M-by-N-by-P array,
where M is the number of subcarriers, N is
the number of OFDM symbols, and P is the number
M must be a multiple of 12 REs per Resource Block, since number of resource blocks is NRB =M / 12. N must be a multiple of the number of symbols in a subframe, L, where L is 14 for normal cyclic prefix and 12 for extended cyclic prefix.
Complex Number Support: Yes
windowing — OFDM sample span
Number of time-domain samples over which the function applies windowing and overlapping of
OFDM symbols, specified as a nonnegative integer. This value overwrites the
value of the parameter field
Nfft — Number of IFFT points
The number of IFFT points to use in the OFDM modulation, specified as a positive integer.
waveform — OFDM modulated waveform
OFDM modulated waveform, returned as a numeric matrix of size
T-by-P, where P
is the number of antennas and T is the number of
T = K × 30720 / 2048 × Nfft
where Nfft is the IFFT size and
K is the number of subframes in the input
Nfft is a function of the
number of resource blocks (NRB), as shown in the
In general, Nfft is the smallest power of 2 greater than or equal to 12×NRB/0.85. It is the smallest FFT that spans all subcarriers and results in a bandwidth occupancy, 12×NRB/0.85, of no more than 85%.
Complex Number Support: Yes
info — OFDM modulated waveform information
OFDM modulated waveform information, returned as a structure.
the following fields.
SamplingRate — Time-domain waveform sampling rate
Time-domain waveform sampling rate, returned as a scalar.
SamplingRate = 30.72 MHz / 2048 × Nfft.
Nfft — Number of FFT points
scalar power of 2
Number of FFT points, returned as a scalar power of 2.
Nfft is the smallest
power of 2 greater than or equal to
NRB / 0.85.
It is the smallest FFT that spans all subcarriers and results in
a bandwidth occupancy
NRB / Nfft)
of no more than 85%.
Windowing — OFDM sample span
Number of time-domain samples over which the function applies windowing and overlapping of OFDM symbols, returned as a nonnegative integer.
CyclicPrefixLengths — Cyclic prefix length
Cyclic prefix length (in samples) of each OFDM symbol in a subframe.
|for ||for |
|2048||[160 144 144 144 144 144 144 160 144 144 144 144 144 144]||[512 512 512 512 512 512 512 512 512 512 512 512]|
|1024||[80 72 72 72 72 72 72 80 72 72 72 72 72 72]||[256 256 256 256 256 256 256 256 256 256 256 256]|
|512||[40 36 36 36 36 36 36 40 36 36 36 36 36 36]||[128 128 128 128 128 128 128 128 128 128 128 128]|
|256||[20 18 18 18 18 18 18 20 18 18 18 18 18 18]||[64 64 64 64 64 64 64 64 64 64 64 64]|
|128||[10 9 9 9 9 9 9 10 9 9 9 9 9 9]||[32 32 32 32 32 32 32 32 32 32 32 32]|
.Nfft < 2048,
2048 scaled by
The use of the IFFT within the OFDM modulator constitutes the use of a rectangular pulse shape. This use of the IFFT means that discontinuities occur from one OFDM symbol to the next, resulting in out of band emissions. (Alternatively, considering the frequency domain, the frequency response of this rectangular pulse shape is a sinc pulse.) The discontinuities between OFDM symbols can be reduced by using windowing, which smooths the transitions between OFDM symbols. LTE Toolbox™ performs windowing by following this procedure.
For Windowing = N samples, the cyclic prefix added to the nominal OFDM symbol extends by N additional samples.
This extended waveform is windowed by pointwise multiplication in the time domain with a raised cosine window, which applies a taper to the first N and last N samples, with all other values being 1. The y values in the first N samples are:
The values in the last N samples are the same values in reverse order.
The windowed OFDM symbols are then overlapped by commencing transmission of each windowed OFDM symbol N samples before the end of the previous OFDM symbol. This overlapping ensures that the time between OFDM symbols is maintained as required by the standard. The taper at the start of the first OFDM symbol for transmission is removed and is overlapped with the taper at the end of the last OFDM symbol.
The processing performed by this function is illustrated in this diagram.
The number of samples used for windowing depends on the number of resource blocks (NRB) and whether the cyclic prefix length is normal or extended. The number of samples is chosen in accordance with the maximum values implied by TS 36.101 , Tables F.5.3-1 and F.5.4-1.
|NRB||Windowing Samples for Normal Cyclic Prefix||Windowing Samples for Extended Cyclic Prefix|
The number of windowing samples is a compromise between the effective duration of cyclic prefix, and therefore the channel delay spread tolerance, and the spectral characteristics of the transmitted signal, not considering any additional FIR filtering. For a larger amount of windowing, the effective duration of the cyclic prefix is reduced but the transmitted signal spectrum has smaller out-of-band emissions.
 3GPP TS 36.101. “Evolved Universal Terrestrial Radio Access (E-UTRA); User Equipment (UE) Radio Transmission and Reception.” 3rd Generation Partnership Project; Technical Specification Group Radio Access Network. URL: https://www.3gpp.org.
Version HistoryIntroduced in R2014a
R2022b: Specify IFFT size
You can specify the IFFT size by using the