lteNPRACH

Generate NPRACH FDD waveform

Since R2021a

Syntax

[waveform,info,resourceGrid] = lteNPRACH(ue,chs)

Description

[waveform,info,resourceGrid] = lteNPRACH(ue,chs) generates 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 Windowing field of the info output as a function of the NBULSubcarrierSpacing field. This behavior compromises between the effective duration of the cyclic prefix (and therefore the channel delay spread tolerance) and the spectral characteristics of the transmitted signal (not considering any additional FIR filtering). For NPRACH preamble format 2, the function sets the default value such that the ratio of cyclic prefix length to windowing length is the same as that of NPRACH preamble format 1.	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 NPRACHFormat field to '0' or '1', you cannot set this field to 5120. If you set the NPRACHFormat field to '2', you cannot set this field to 240.	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 NPRACHFormat field to '0' or '1', you cannot set this field to 6, 42, 48, 54, 60, 72, 78, 84, 90, 102, or 108. If you set the NPRACHFormat field to '2', you cannot set this field to 2 or 34.	double
NumSubcarriers	Required	12, 24, 36, 48, 72, 108, 144	Number of subcarriers allocated to NPRACH	If you set the NPRACHFormat field to '0' or '1', you cannot set this field to 72, 108, or 144. If you set the NPRACHFormat field to '2', you cannot set this field to 12, 24, or 48.	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:

1. 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.

2. 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].

3. 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 Ts, where Ts 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 Ts.	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.