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lteOFDMModulate

OFDM modulation

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Syntax

[waveform,info] = lteOFDMModulate(enb,grid)
[waveform,info] = lteOFDMModulate(enb,grid,windowing)

Description

example

[waveform,info] = lteOFDMModulate(enb,grid)performs 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 resource array,grid.gridis a 3-D array containing the resource elements (REs) for a number of subframes across all configured antenna ports, as described inRepresent Resource Grids. It could also be multiple concatenated matrices to give multiple subframes, using concatenation across the columns or second dimension. The antenna planes ingridare each OFDM modulated to yield the columns of the outputwaveform.

grid可以跨多个子帧。窗口和重叠ping 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 iflteOFDMModulateis 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 callinglteOFDMModulateon the resulting multi-subframe array. However, individual subframes can be OFDM modulated and the resulting multi-subframe time-domain waveform created by manual overlapping.

[waveform,info] = lteOFDMModulate(enb,grid,windowing)allows control of the number of windowed and overlapped samples used in the time-domain windowing, specified by thewindowingparameter. The value ofenb.Windowing, if present, is ignored, and the output,info.Windowingis set towindowing.

Examples

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Open Live Script

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);

Input Arguments

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Cell-wide settings, specified as a structure.enbcan contain the following fields.

Parameter Field Required or Optional Values Description
CyclicPrefix Optional

'Normal'(default),'Extended'

Cyclic prefix length
Windowing Optional Nonnegative integer

Number of time-domain samples over which the function applies windowing and overlapping of OFDM symbols

See note

Note

Ifenb.Windowingis absent, a default value for the number of windowed and overlapped samples is used. The default value is chosen as a function ofNRBto 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 ininfo.Windowing. The issues concerning concatenation of subframes before OFDM modulation do not apply whenenb.Windowingis zero.

Data Types:struct

Resource elements, specified as a 3-D numeric array.gridstores the resource elements for a number of subframes across all configured antenna ports.gridis anM-by-N-by-Parray, whereMis the number of subcarriers,Nis the number of OFDM symbols, andPis the number of antennas.

Mmust be a multiple of 12 REs per Resource Block, since number of resource blocks isNRB=M/ 12.Nmust be a multiple of the number of symbols in a subframe,L, whereLis 14 for normal cyclic prefix and 12 for extended cyclic prefix.

Data Types:double
Complex Number Support:Yes

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 fieldenb.Windowing, if present.

Data Types:double

Output Arguments

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OFDM modulated waveform, returned as a numeric matrix of sizeT-by-P, wherePis the number of antennas andTis the number of time-domain samples.T=K× 30720 / 2048 ×NfftwhereNfftis the IFFT size andK子帧的数量吗the inputgrid.Nfftis a function of the number of resource blocks (NRB), as shown in the following table.

NRB Nfft
6 128
15 256
25 512
50 1024
75 2048
100 2048

In general,Nfftis the smallest power of 2 greater than or equal to12*NRB/0.85. It is the smallest FFT that spans all subcarriers and results in a bandwidth occupancy,12*NRB/Nfft, of no more than 85%.

Data Types:double
Complex Number Support:Yes

OFDM modulated waveform information, returned as a structure.infocontains the following fields.

Time-domain waveform sampling rate, returned as a scalar.SamplingRate= 30.72 MHz / 2048 ×Nfft.

Data Types:double

Number of FFT points, returned as a scalar power of 2.Nfftis 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/Nfft) of no more than 85%.

Data Types:uint32

Number of time-domain samples over which the function applies windowing and overlapping of OFDM symbols, returned as a nonnegative integer.

Data Types:int32

Cyclic prefix length (in samples) of each OFDM symbol in a subframe.

info.Nfft CyclicPrefixLengths
forCyclicPrefix = 'Normal' forCyclicPrefix = 'Extended'
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]

Note

Forinfo.Nfft< 2048,info.CyclicPrefixLengthsare theCyclicPrefixLengthsforinfo.Nfft= 2048 scaled byinfo.Nfft/ 2048.

Data Types:uint32

Data Types:struct

Algorithms

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Windowing

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/

ForWindowing=Nsamples, the cyclic prefix added to the nominal OFDM symbol extends byNadditional samples.

This extended waveform is windowed by pointwise multiplication in the time domain with a raised cosine window, which applies a taper to the firstNand lastNsamples, with all other values being 1. Theyvalues in the firstNsamples are:

y = 1 2 ( 1 − sin ( π N + 1 − 2 i 2 N ) ) , where i = 1 … N

The values in the lastNsamples are the same values in reverse order.

The windowed OFDM symbols are then overlapped by commencing transmission of each windowed OFDM symbolNsamples 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.

Processing

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 and whether the cyclic prefix length is normal or extended. The number of samples is chosen in accordance with themaximumvalues implied by TS 36.101[1], Tables F.5.3-1, and F.5.4-1.

Number of resource blocks (NRB) Windowing samples for normal cyclic prefix Windowing samples for extended cyclic prefix
6 4 4
15 6 6
25 4 4
50 6 6
75 8 8
100 8 8

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.

References

[1] 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 History

Introduced in R2014a

See Also

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