# Documentation

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# lteSCFDMAModulate

SC-FDMA modulation

## Syntax

``````[waveform,info] = lteSCFDMAModulate(ue,grid)``````
``````[waveform,info] = lteSCFDMAModulate(ue,grid,windowing)``````

## Description

example

``````[waveform,info] = lteSCFDMAModulate(ue,grid)``` performs IFFT calculation, half-subcarrier shifting, and cyclic prefix insertions. It optionally performs raised-cosine windowing and overlapping of adjacent SC-FDMA symbols of the complex symbols in the resource array, `grid`.For a block diagram that illustrates the steps in SC-FDMA modulation, see Algorithms. ```
``````[waveform,info] = lteSCFDMAModulate(ue,grid,windowing)``` allows control of the number of windowed and overlapped samples used in the time-domain windowing. If the value in `ue.Windowing` is present, it is ignored and the output, `info.Windowing`, equals `windowing`. ```

## Examples

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Perform SC-FDMA modulation of one subframe of random uniformly-distributed noise, using a 10MHz configuration.

```ue = struct('NULRB',50); dims = lteULResourceGridSize(ue); reGrid = reshape(lteSymbolModulate(randi([0,1],prod(dims)*2,1), ... 'QPSK'),dims); waveform = lteSCFDMAModulate(ue,reGrid); ```

## Input Arguments

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UE-specific settings, specified as a structure. `ue` contains the following fields.

Parameter FieldRequired or OptionalValuesDescription
`CyclicPrefixUL`Optional

`'Normal'` (default), `'Extended'`

Cyclic prefix length

`Windowing`Optional

Nonnegative scalar integer

Default value is absent.

The number of time-domain samples over which windowing and overlapping of SC-FDMA symbols is applied

See Note

### Note

If `ue.Windowing` is absent, `info.Windowing` returns a default value chosen as a function of `NRB` to 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). `ue.Windowing` must be even. With a value of zero, issues identified in the description of output, `grid`, concerning concatenation of subframes before SC-FDMA, modulation do not apply.

The number of samples used for windowing depends on the cyclic prefix length (normal or extended) and the number of resource blocks, and is chosen in accordance with the maximum values implied in TS 36.104, Tables E.5.1-1 and E.5.1-2 [1]. 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.

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

Data Types: `struct`

Resource grid, specified as an M-by-N-by-P numeric array array. The grid input contains M number of subcarriers, N number of SC-FDMA symbols, and P number of transmission antennas. The array contains resource elements (REs) for a number of subframes across all configured antenna ports, as described in Data Structures. Alternatively, it contains multiple such matrices concatenated to give multiple subframes (concatenation across the columns or 2nd dimension). The antenna planes in `grid` are each OFDM modulated to give the columns of `waveform`.

M must be a multiple of 12 REs per Resource Block, since number of resource blocks is NRB =M / 12. Dimension N must be a multiple number of symbols in a subframe L, where L=14 for normal cyclic prefix and L=12 for extended cyclic prefix. Dimension P must be (`1,2,4`).

The `grid` can span multiple subframes and windowing and overlapping is applied between all adjacent SC-FDMA symbols, including the last of one subframe and the first of the next. Therefore a different result is obtained than if `lteSCFDMAModulate` is called on individual subframes and then those time-domain waveforms concatenated. The resulting waveform in that case would have discontinuities at the start/end of each subframe. Therefore it is recommended that all subframes for SC-FDMA modulation first be concatenated before calling `lteSCFDMAModulate` on the resulting multi-subframe array. However, individual subframes can be OFDM modulated and the resulting multi-subframe time-domain waveform created by manually overlapping.

Data Types: `double`
Complex Number Support: Yes

Number of windowed and overlapped samples, specified as a positive scalar integer. This argument controls the number of windowed and overlapped samples used in time-domain windowing. If present, it is used for the SC-FMDA modulation (instead of `ue`.`Windowing`) and it is the value output for `info``.Windowing`.

Data Types: `double`

## Output Arguments

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SC-FDMA modulated waveform, returned as a numeric matrix of size T-by-P, where T is the number of time-domain samples and P is the number of transmission antennas. $T=K×30720/2048×{N}_{fft}$ where Nfft is the IFFT size and K is the number of subframes in the input `grid`. Nfft is a function of the Number of Resource Blocks (NRB).

NRB

Nfft

6

128

15

256

25

512

50

1024

75

2048

100

2048

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/Nfft) of no more than 85%.

Data Types: `double`
Complex Number Support: Yes

Information about SC-FDMA modulated waveform, returned as a scalar structure. `info` contains the following fields.

Sampling rate of time-domain waveform, `waveform`, returned as a positive numeric scalar. The sampling rate of the waveform is given by the equation: SamplingRate = 30.72 MHz / 2048 × NFFT.

Data Types: `double`

Number of FFT points, returned as a positive scalar integer.

Data Types: `double`

Number of time-domain samples over which windowing and overlapping of SC-FDMA symbols is applied, returned as a positive scalar integer.

Data Types: `double`

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

info.NfftCyclicPrefixLengths
for `CyclicPrefix = 'Normal'`for `CyclicPrefix = '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

As shown in this table, for `info``.Nfft` < 2048, `info``.CyclicPrefixLengths` are the `CyclicPrefixLengths` for `info``.Nfft` = 2048 scaled by `info``.Nfft` / 2048.

Data Types: `int32`

Data Types: `struct`

## Algorithms

The following diagram illustrates the processing performed by SC-FDMA modulation.

## References

[1] 3GPP TS 36.104. “Base Station (BS) radio transmission and reception.” 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA). URL: http://www.3gpp.org.