nrPRACHOFDMModulate

Generate PRACH OFDM modulated waveform

Syntax

[waveform,info] = nrPRACHOFDMModulate(carrier,prach,grid)

[waveform,info] = nrPRACHOFDMModulate(carrier,prach,grid,'Windowing',samples)

Description

[waveform,info] = nrPRACHOFDMModulate(carrier,prach,grid) generates waveform, a physical random access channel (PRACH) time-domain waveform, by performing orthogonal frequency-division multiplexing (OFDM) modulation of PRACH carrier resource array grid for carrier configuration parameters carrier and PRACH configuration parameters prach. The function also returns info, a structure containing OFDM information.

[waveform,info] = nrPRACHOFDMModulate(carrier,prach,grid,'Windowing',samples) specifies the number of time-domain samples over which the function applies raised cosine windowing and overlapping of OFDM symbols.

Examples

Generate PRACH OFDM Modulated Waveform

Generate a PRACH waveform by performing OFDM modulation of a resource array that contains PRACH symbols.

Specify carrier configuration parameters.

carrier = nrCarrierConfig;

Configure PRACH for format A1.

prach = nrPRACHConfig('ConfigurationIndex',106,'SubcarrierSpacing',15);

Generate PRACH symbols and map to a PRACH slot resource grid.

sym = nrPRACH(carrier,prach);
ind = nrPRACHIndices(carrier,prach);
grid = nrPRACHGrid(carrier,prach);
grid(ind) = sym;

Generate the PRACH OFDM waveform by modulating the grid. Display PRACH OFDM information.

[waveform,info] = nrPRACHOFDMModulate(carrier,prach,grid);
disp(info)

                   Nfft: 1024
             SampleRate: 15360000
    CyclicPrefixLengths: [152 0 144 0 144 0 152 0 144 0 144 0 0 0]
           GuardLengths: [0 0 0 0 0 0 0 0 0 0 0 0 0 144]
          SymbolLengths: [1x14 double]
           OffsetLength: 0
              Windowing: 72

Generate PRACH OFDM Modulated Waveform with Custom Windowing

Generate a PRACH OFDM modulated waveform by modulating a carrier containing PRACH symbols, specifying the number of samples over which the modulator applies windowing and overlapping of OFDM symbols.

Specify carrier configuration parameters, specifying a subcarrier spacing of 60 kHz.

carrier = nrCarrierConfig('SubcarrierSpacing',60);

Configure and generate PRACH symbols and map to a PRACH slot resource grid.

prach = nrPRACHConfig('FrequencyRange','FR2','SubcarrierSpacing',60,'DuplexMode','TDD');
sym = nrPRACH(carrier,prach);
ind = nrPRACHIndices(carrier,prach);
grid = nrPRACHGrid(carrier,prach);
grid(ind) = sym;

Generate the PRACH OFDM waveform by modulating the grid, specifying the number of time domain samples over which the PRACH OFDM modulator applies windowing and overlapping of OFDM symbols.

samples = 80;
[waveform,info] = nrPRACHOFDMModulate(carrier,prach,grid,'Windowing',samples);

Input Arguments

carrier — Carrier configuration parameters

nrCarrierConfig object

Carrier configuration parameters for a specific OFDM numerology, specified as an nrCarrierConfig object. Only these object properties are relevant for this function.

NSizeGrid — Number of RBs in carrier resource grid

52 (default) | integer from 1 to 275

Number of RBs in the carrier resource grid, specified as an integer from 1 to 275. The default value of 52 corresponds to the maximum number of RBs of a 10 MHz carrier with 15 kHz SCS.

Data Types: double

SubcarrierSpacing — Subcarrier spacing in kHz

15 (default) | 30 | 60 | 120 | 240

Subcarrier spacing in kHz, for all channels and reference signals of the carrier, specified as 15, 30, 60, 120, or 240.

Data Types: double

CyclicPrefix — Cyclic prefix length

'normal' (default) | 'extended'

Cyclic prefix length, specified as one of these options.

• 'normal' — Use this value to specify normal cyclic prefix. This option corresponds to 14 OFDM symbols in a slot.

• 'extended' — Use this value to specify extended cyclic prefix. This option corresponds to 12 OFDM symbols in a slot. For the numerologies specified in TS 38.211 Section 4.2, extended cyclic prefix length applies for only 60 kHz subcarrier spacing.

Data Types: char | string

prach — PRACH configuration parameters

nrPRACHConfig object

PRACH configuration parameters, specified as an nrPRACHConfig object. The function uses only these properties of this input.

FrequencyRange — Frequency range

'FR1' (default) | 'FR2'

Frequency range, specified as 'FR1' or 'FR2'.

Use this property together with the DuplexMode property to specify these PRACH configuration tables from TS 38.211.

• To specify Table 6.3.3.2-2, set FrequencyRange to 'FR1' and DuplexMode to 'FDD' or 'SUL'.

• To specify Table 6.3.3.2-3, set FrequencyRange to 'FR1' and DuplexMode to 'TDD'.

• To specify Table 6.3.3.2-4, set FrequencyRange to 'FR2' and DuplexMode to 'TDD'.

Data Types: char | string

DuplexMode — Duplex mode for uplink transmission

'FDD' (default) | 'TDD' | 'SUL'

Duplex mode for uplink transmission, specified as one of these values:

• 'FDD' — Use this value to specify frequency division duplex (FDD) mode for paired spectrum.

• 'TDD' — Use this value to specify time division duplex (TDD) mode for unpaired spectrum.

• 'SUL' — Use this value to specify supplementary uplink.

Use this property together with the FrequencyRange property to specify these PRACH configuration tables from TS 38.211:

• To specify Table 6.3.3.2-2, set FrequencyRange to 'FR1' and DuplexMode to 'FDD' or 'SUL'.

• To specify Table 6.3.3.2-3, set FrequencyRange to 'FR1' and DuplexMode to 'TDD'.

• To specify Table 6.3.3.2-4, set FrequencyRange to 'FR2' and DuplexMode to 'TDD'.

Data Types: char | string

ConfigurationIndex — Time resource of PRACH preamble

27 (default) | integer from 0 to 255

Time resource of PRACH preamble, specified as an integer from 0 to 255. This property specifies a configuration index from Tables 6.3.3.2-2 to 6.3.3.2-4 in TS 38.211. Properties FrequencyRange and DuplexMode determine the actual configuration table to consider.

This property is the higher layer parameter prach-ConfigurationIndex.

Data Types: double

SubcarrierSpacing — Subcarrier spacing for PRACH in kHz

1.25 (default) | 5 | 15 | 30 | 60 | 120

Subcarrier spacing for the PRACH in kHz, specified as 1.25, 5, 15, or 30 for frequency range FR1 and 60 or 120 for frequency range FR2.

Set this property in relation to the preamble format property Format. To identify valid preamble format and subcarrier spacing combinations, see the LongPreambleFormats and ShortPreambleFormats fields of the Tables property. For more information, see Table 6.3.3.1-1 for long preambles and Table 6.3.3.1-2 for short preambles.

Data Types: double

NPRACHSlot — PRACH slot number

0 (default) | nonnegative integer

PRACH slot number, specified as a nonnegative integer. You can set NPRACHSlot to a value larger than the number of slots per frame. For example, you can set this value using transmission loop counters in a MATLAB^® simulation. In this case, you might have to ensure that the property value is modulo the number of slots per frame in a calling code.

Data Types: double

grid — PRACH resource grid

complex array

PRACH resource grid, specified as a K-by-L-by-P complex array.

• K is the number of subcarriers equal to (carrier.SubcarrierSpacing / prach.SubcarrierSpacing) × carrier.NSizeGrid × 12

• L is the number of OFDM symbols and depends on the PRACH preamble format.

  • For long formats, L = prach.PRACHDuration.

  • For short format C0, L = 7.

  • For all other short formats, L = 14.

    For more information on PRACH preamble formats, see TS 38.211 Tables 6.3.3.1-1 and 6.3.3.1-2 [1].

• P is the number of transmit antennas.

Data Types: double
Complex Number Support: Yes

samples — Number of time-domain samples for OFDM symbol windowing and overlapping

nonnegative integer (default depends other input values) | []

Number of time-domain samples over which the function applies raised cosine windowing and overlapping of OFDM symbols, specified as a nonnegative integer or [].

If you do not specify this input, or if you specify it as [], the function sets this input to the maximum value E that does not impact error vector magnitude (EVM) tests, as specified in TS 38.101-1 Annex F.5.5 and TS 38.101-2 Annex F.5.5. E is equal to value of floor((N_CP − W) × info.Nfft ⁄ N_{FFT, nominal}), where N_CP, W, and N_{FFT, nominal} are the values in the table columns labeled "Cyclic prefix length", "EVM window length", and "FFT size", respectively.

Data Types: double

Output Arguments

waveform — PRACH OFDM modulated waveform

complex-valued matrix

PRACH OFDM modulated waveform, returned as a complex-valued matrix of size T-by-P.

• T is the number of time domain samples in the waveform for the current slot, equal to the value of info.OffsetLengths + sum(info.SymbolLengths).

  The NPRACHSlot property of the prach input determines the current slot.

• P is the number of transmit antennas.

Data Types: double
Complex Number Support: Yes

info — OFDM information

structure

OFDM information, returned as a structure containing these fields.

Fields	Values	Description
Nfft	Positive integer	Number of FFT points
SampleRate	Positive integer	Waveform sample rate
CyclicPrefixLengths	1-by-N vector of nonnegative integers, where N is the number of OFDM symbols in a PRACH slot	Cyclic prefix lengths of each OFDM symbol, in samples
GuardLengths	1-by-N vector of positive integers, where N is the number of OFDM symbols in a PRACH slot	Guard lengths of OFDM symbols, in samples
SymbolLengths	1-by-N vector of nonnegative integers, where N is the number of OFDM symbols in a PRACH slot	OFDM symbol lengths, in samples
OffsetLength	Nonnegative integer	Length, in samples, of the initial time offset between the start of the configured PRACH slot period to the start of the cyclic prefix
Windowing	Nonnegative integer	Number of time-domain samples over which the function applies raised cosine windowing and overlapping of OFDM symbols

For long formats, for which the LRA property of the prach input is 839, the first slot of a PRACH preamble can occur part of the way through the nominal PRACH slot period. In this case, the function increases the value of the OffsetLength field, which ensures that the OFDM waveform spans the entire active PRACH preamble. To balance these slots with the nominal PRACH slot period, some inactive PRACH slots have OFDM waveforms that are shorter than the nominal PRACH slot period. The function conveys this by returning the CyclicPrefixLengths and GuardLengths fields as [], corresponding to no OFDM symbols, and setting the OffsetLength field equal to the number of empty subframes required.

Data Types: struct

References

[1] 3GPP TS 38.211. “NR; Physical channels and modulation.” 3rd Generation Partnership Project; Technical Specification Group Radio Access Network.

[2] 3GPP TS 38.101-1. “NR; User Equipment (UE) radio transmission and reception; Part 1: Range 1 Standalone.” 3rd Generation Partnership Project; Technical Specification Group Radio Access Network.

[3] 3GPP TS 38.101-2. “NR; User Equipment (UE) radio transmission and reception; Part 2: Range 2 Standalone.” 3rd Generation Partnership Project; Technical Specification Group Radio Access Network.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

The samples input argument must be compile-time constant. Include {coder.Constant('Windowing'),coder.Constant(samples)} in the -args value of the codegen function. For more information, see the coder.Constant (MATLAB Coder) class.