# lteNPRACH

## Description

`[`

generates `waveform`

,`info`

,`resourceGrid`

] = lteNPRACH(`ue`

,`chs`

)`waveform`

, a time-domain narrowband physical random access
channel (NPRACH) frequency-division duplexing (FDD) waveform for user equipment (UE)
settings `ue`

and channel transmission configuration
`chs`

. The function also returns `info`

, a structure
containing NPRACH information, and `resourceGrid`

, an NPRACH resource
grid.

## Examples

### Generate NPRACH FDD Waveform

Generate an NPRACH waveform for specified UE settings and channel transmission configuration.

Specify the narrowband physical layer cell identity and subcarrier spacing.

ue = struct('NNCellID',0,'NBULSubcarrierSpacing','15kHz');

Specify the NPRACH format, periodicity, subcarrier offset, number of subcarriers, and number of preamble repetitions.

chs = struct('NPRACHFormat','0','Periodicity',80, ... 'SubcarrierOffset',0,'NumSubcarriers',12,'NRep',1);

Generate the NPRACH waveform, NPRACH information, and resource grid.

[waveform,info,grid] = lteNPRACH(ue,chs);

## Input Arguments

`ue`

— UE-specific settings

structure

UE-specific settings, specified as a structure containing these fields.

Field | Required or Optional | Values | Description | Data Type |
---|---|---|---|---|

`NNCellID` | Required | Integer in the interval [0, 503] | Narrowband physical layer cell identity. | `double` |

`NBULSubcarrierSpacing` | Required | `'3.75kHz'` , `'15kHz'` | Narrowband internet of things (NB-IoT) uplink subcarrier spacing. To set
a subcarrier spacing of 3.75 kHz, specify this field as
`'3.75kHz'` . To set a subcarrier spacing of 15 kHz, specify
this field as `'15kHz'` . | `char` , `string` |

`Windowing` | Optional | Nonnegative integer, default value depends on NPRACH preamble format in accordance with section F.5.F of [1] | Number of time-domain samples over which the function applies windowing and overlapping of OFDM samples. If you do not specify
this field, this function returns the | `double` |

**Data Types: **`struct`

`chs`

— Channel transmission configuration

structure

Channel transmission configuration, specified as a structure containing these fields.

Field | Required or Optional | Values | Description | Dependencies | Data Types |
---|---|---|---|---|---|

`NPRACHFormat` | Required | `'0'` , `'1'` ,
`'2'` | NPRACH preamble format | Not applicable | `char` , `string` |

`Periodicity` | Required | `40` , `80` , `160` ,
`240`
(since R2024b), `320` ,
`640` , `1280` , `2560` ,
`5120` | NPRACH resource periodicity, in milliseconds | If you set the If you set the
| `double` |

`SubcarrierOffset` | Required | `0` , `2` , `6` ,
`12` , `18` , `24` ,
`34` , `36` , `42` ,
`48` , `54` , `60` ,
`72` , `78` , `84` ,
`90` , `102` ,
`108` | Frequency location of the first subcarrier allocated to NPRACH | If you set the If you set
the | `double` |

`NumSubcarriers` | Required | `12` , `24` , `36` ,
`48` , `72` , `108` ,
`144` | Number of subcarriers allocated to NPRACH | If you set the If you set the
| `double` |

`NRep` | Required | `1` , `2` , `4` ,
`8` , `16` , `32` ,
`64` , `128` | Number of NPRACH repetitions | Not applicable | `double` |

`StartTime` | Optional | `8` (default), `16` ,
`32` , `64` , `128` ,
`256` , `512` ,
`1024` | NPRACH starting time, in milliseconds | Not applicable | `double` |

`NInit` | Optional | `0` (default), integer in the interval [0,
`NumSubcarriers` – 1] | Initial subcarrier for NPRACH | Not applicable | `double` |

`NPRACHPower` | Optional | `0` (default), real-valued scalar | NPRACH power scaling, in decibels | Not applicable | `double` |

**Data Types: **`struct`

## Output Arguments

`waveform`

— Time-domain NPRACH FDD waveform

complex-valued column vector

Time-domain NPRACH FDD waveform, returned as a complex-valued column vector of
length (`chs`

`.`

`Periodicity`

× `info`

`.`

`SamplingRate`

÷ 1000). The waveform consists of:

A period of zeros corresponding to the time,

`chs`

`.`

`StartTime`

, between the start of the transmission and the first frame occupied by an NPRACH symbol.The NPRACH transmission, defined in section 10.1.6.1 of [2] as a repetition of

`chs`

`.`

`NRep`

NPRACH preambles. An NPRACH preamble is a set of`info`

`.`

`P`

symbol groups. A symbol group is a sequence of`info`

`.`

`N`

identical symbols preceded by a cyclic prefix. The duration of an NPRACH preamble is a function of the preamble format as described in Table 10.1.6.1-1 of [2].A period of zeros corresponding to the time between the end of the transmission and the value of the

`chs`

`.`

`Periodicity`

input.

The function samples the waveform at the same sampling rate as for a narrowband
physical uplink shared channel (NPUSCH) waveform, defined by the
`NBULSubcarrierSpacing`

field of the `ue`

input.

For preamble formats 0 and 1, the function adds an additional 40 ms gap every 64 preambles. For preamble format 2, the function adds an additional 40 ms gap every 16 preambles.

For more information about NPRACH waveform generation, see the NB-IoT PRACH Waveform Generation example.

**Data Types: **`double`

**Complex Number Support: **Yes

`info`

— NPRACH resource information

structure

NPRACH resource information, returned as a structure containing these fields.

Field | Values | Description | Data Type |
---|---|---|---|

`Nfft` | Positive integer | Number of fast Fourier transform (FFT) points. | `double` |

`SamplingRate` | Positive scalar | Sampling rate, in Hz, of the time-domain waveform. | `double` |

`Windowing` | Nonnegative integer | Number of time-domain samples over which the function applies windowing and overlapping of OFDM symbols. | `double` |

`FrequencyLocation` | Row vector of nonnegative integers | Frequency location for all symbol groups in an NPRACH transmission. For
more information about NPRACH symbol groups, see the NB-IoT PRACH Waveform Generation example. The
kth element of this output represents the frequency
location of the kth symbol group. | `double` |

`K` | Positive integer | Ratio of uplink data to NPRACH subcarrier spacing. | `double` |

`NULSC` | Positive integer | Number of subcarriers for the specified uplink bandwidth. | `double` |

`PreambleParameters` | Structure | Random access preamble parameters for the specified preamble format and frame structure type 1, as specified in Table 10.1.6.1-1 of [2]. | `struct` |

`PreambleParameters`

Field

The `PreambleParameters`

field of this output contains these
fields.

Field | Values | Description | Data Type |
---|---|---|---|

`G` | Positive integer | Number of time-contiguous symbol groups. | `double` |

`P` | Positive integer | Total number of symbol groups. | `double` |

`N` | Positive integer | Number of symbols in a symbol group. | `double` |

`T_CP` | Positive integer | Cyclic prefix length, in multiples of
T_{s}, where
T_{s} is the basic time unit, defined
in section 4 of [2] as 1 ÷ (15000 × 2048) seconds. | `double` |

`T_SEQ` | Positive integer | Length of symbols in a symbol group, in multiples of
T_{s}. | `double` |

**Data Types: **`struct`

`resourceGrid`

— NPRACH resource grid

real-valued matrix

NPRACH resource grid, returned as a real-valued matrix of size
*K*-by-*L*, where:

*K*is the number of subcarriers.*L*is the number of NPRACH symbols that fit the value of`chs`

`.`

`Periodicity`

.

**Data Types: **`double`

## 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*. https://www.3gpp.org.

[2] 3GPP TS 36.211.
“Physical channels and modulation.” *3rd Generation Partnership Project;
Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio
Access (E-UTRA)*. https://www.3gpp.org.

## Version History

**Introduced in R2021a**

### R2024b: Generate NPRACH waveforms for 240 millisecond resource periodicity

You can now generate NPRACH waveforms for channel transmission configurations with an
NPRACH resource periodicity of 240 milliseconds. To use this feature, specify the
`Periodicity`

field of the `chs`

input as
`240`

. You must specify the `NPRACHFormat`

of
`chs`

as `0`

or `1`

.

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