nrTimingEstimate

Practical timing estimation

Syntax

[offset,mag] = nrTimingEstimate(carrier,waveform,refGrid)

[offset,mag] = nrTimingEstimate(carrier,waveform,refInd,refSym)

[offset,mag] = nrTimingEstimate(waveform,nrb,scs,initialNSlot,refGrid)

[offset,mag] = nrTimingEstimate(waveform,nrb,scs,initialNSlot,refInd,refSym)

[offset,mag] = nrTimingEstimate(___,Name,Value)

Description

[offset,mag] = nrTimingEstimate(carrier,waveform,refGrid) performs practical timing estimation by cross-correlating input waveform waveform with a reference waveform. The function obtains the reference waveform by modulating reference resource grid refGrid using orthogonal frequency division multiplexing (OFDM). carrier specifies the parameters for the OFDM modulation. The function returns the estimated timing offset, offset, and the estimated impulse response magnitude, mag, for each receive antenna in the input waveform, summed across all reference signal ports.

[offset,mag] = nrTimingEstimate(carrier,waveform,refInd,refSym) obtains the reference waveform by modulating a reference resource grid containing reference symbols refSym at locations refInd and using the OFDM modulation specified by carrier.

[offset,mag] = nrTimingEstimate(waveform,nrb,scs,initialNSlot,refGrid) obtains the reference waveform by modulating reference resource grid refGrid and using OFDM modulation that spans nrb resource blocks at subcarrier spacing scs and initial slot number initialNSlot.

[offset,mag] = nrTimingEstimate(waveform,nrb,scs,initialNSlot,refInd,refSym) obtains the reference waveform by modulating a resource grid containing reference symbols refSym at locations refInd and using the OFDM modulation specified by nrb, scs, and initialNSlot.

[offset,mag] = nrTimingEstimate(___,Name,Value) specifies options by using one or more name-value pair arguments in addition to the input arguments in any of the previous syntaxes.

Examples

Estimate Timing Offset for TDL-C Channel Transmission

Generate primary synchronization signal (PSS) symbols for physical layer cell identity number 42.

ncellid = 42;
pssSym = nrPSS(ncellid);

Obtain resource element indices for the PSS.

pssInd = nrPSSIndices();

Create a resource grid containing the generated PSS symbols.

nrb = 20;
scs = 15;
carrier = nrCarrierConfig('NSizeGrid',nrb,'SubcarrierSpacing',scs);
txGrid = nrResourceGrid(carrier);
txGrid(pssInd) = pssSym;

OFDM modulate the resource grid.

txWaveform = nrOFDMModulate(carrier,txGrid);

Transmit the waveform through a TDL-C channel model by using a sample rate of 7.68 MHz.

ofdmInfo = nrOFDMInfo(carrier);
channel = nrTDLChannel;
channel.SampleRate = ofdmInfo.SampleRate;
channel.DelayProfile = 'TDL-C';
rxWaveform = channel(txWaveform);

Estimate timing offset for the transmission by using the PSS symbols as reference symbols. The OFDM modulation of the reference symbols uses initial slot number 0.

initialNSlot = 0;
offset = nrTimingEstimate(rxWaveform,nrb,scs,initialNSlot,pssInd,pssSym);

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

• SubcarrierSpacing

• NSlot

• CyclicPrefix

waveform — Received waveform

T-by-N_R complex matrix

Received waveform, specified as a T-by-N_R complex matrix.

• T is the number of time-domain samples.

• N_R is the number of receive antennas.

Data Types: single | double
Complex Number Support: Yes

refGrid — Predefined reference grid

K-by-N-by-P complex array

Predefined reference grid, specified as a K-by-N-by-P complex array. refGrid can span multiple slots.

• K is the number of subcarriers equal to nrb × 12.

• N is the number of OFDM symbols in the reference grid.

• P is the number of reference signal ports.

Data Types: single | double
Complex Number Support: Yes

refInd — Reference symbol indices

integer matrix

Reference symbol indices, specified as an integer matrix. The number of rows equals the number of resource elements. You can specify all indices in a single column or distribute them across several columns. The number of elements in refInd and refSym must be the same but their dimensionality can differ. The function reshapes refInd and refSym into column vectors before mapping them into a reference grid: refGrid(refInd(:)) = refSym(:).

The elements of refInd are 1-based linear indices addressing a K-by-L-by-P resource array.

• K is the number of subcarriers equal to nrb × 12.

• L is the number of OFDM symbols in a slot. L is 12 or 14, depending on the cyclic prefix length specified in the cpl input or the CyclicPrefix property of the carrier input.

• P is the number of reference signal ports, inferred from the range of values in refInd.

Data Types: double

refSym — Reference symbols

complex matrix

Reference symbols, specified as a complex matrix. The number of rows equals the number of resource elements. You can specify all symbols in a single column or distribute them across several columns. The number of elements in refInd and refSym must be the same but their dimensionality can differ. The function reshapes refInd and refSym into column vectors before mapping them into a reference grid: refGrid(refInd(:)) = refSym(:).

Data Types: single | double
Complex Number Support: Yes

nrb — Number of resource blocks

integer from 1 to 275

Number of resource blocks, specified as an integer from 1 to 275.

Data Types: double

scs — Subcarrier spacing in kHz

15 | 30 | 60 | 120 | 240 | 480 | 960

Subcarrier spacing in kHz, specified as 15, 30, 60, 120, 240, 480, or 960.

Data Types: double

initialNSlot — Initial slot number

nonnegative integer

Initial slot number, 0-based, specified as a nonnegative integer. The function selects the appropriate cyclic prefix length for the OFDM modulation based on the value of initialNSlot modulo the number of slots per subframe.

Data Types: double

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: 'SampleRate','1e9' specifies a sample rate of 1×10⁹ Hz.

CyclicPrefix — Cyclic prefix length

'normal' (default) | 'extended'

Cyclic prefix length, specified as the comma-separated pair consisting of 'CyclicPrefix' and one of these values:

• '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, the extended cyclic prefix length only applies to 60 kHz subcarrier spacing.

Note

If you specify the carrier input, use the CyclicPrefix property of the carrier input to specify the cyclic prefix length. You cannot use this name-value pair argument together with the carrier input.

Data Types: char | string

Nfft — Number of FFT points

integer greater than 127 (default depends on other input values) | []

Number of fast Fourier transform (FFT) points, specified as the comma-separated pair consisting of 'Nfft' and a nonnegative integer greater than 127 or []. The value you specify must result in integer-valued cyclic prefix lengths and a maximum occupancy of 100%. The occupancy is defined as the value of (12 × N_RB)/Nfft, where N_RB is the number of resource blocks.

If you do not specify this input, or if you specify 'Nfft',[], the function sets an integer value greater than 127 as a default value for this input. The actual default value depends on other input values.

• If you do not specify the SampleRate input, or if you specify 'SampleRate',[], the function sets Nfft satisfying these conditions.

  • Nfft is an integer power of 2.

  • Nfft results in a maximum occupancy of 85%.

• If you specify the SampleRate input, the function sets Nfft satisfying these conditions.

  • Nfft results in integer-valued cyclic prefix lengths.

  • Nfft maximises the value of gcd (Nfft × SCS, SampleRate), where SCS is specified by the carrier.SubcarrierSpacing property or the scs input.

For more information, see Configure OFDM Sample Rate and FFT Size.

Data Types: double

SampleRate — Waveform sample rate

positive scalar (default depends on other input values) | []

Waveform sample rate, specified as the comma-separated pair consisting of 'SampleRate' and either a positive scalar or [].

If you do not specify this input, or if you specify 'SampleRate',[], then the function sets this input to the value of N_fft × SCS.

• N_fft is the value of the 'Nfft' input.

• SCS is the subcarrier spacing. Depending on the function syntax you use, SCS is specified by the carrier.SubcarrierSpacing property or the scs input.

For more information, see Configure OFDM Sample Rate and FFT Size.

Data Types: double

CarrierFrequency — Carrier frequency in Hz

0 (default) | real number

Carrier frequency in Hz, specified as the comma-separated pair consisting of 'CarrierFrequency' and a real number. This input corresponds to f₀, defined in TS 38.211 Section 5.4.

Data Types: double

Output Arguments

offset — Estimated timing offset in samples

nonnegative integer

Estimated timing offset in samples, returned as a nonnegative integer. The number of samples is relative to the first sample of the input waveform waveform.

Data Types: double

mag — Estimated impulse response magnitude

T-by-N_R real matrix

Estimated impulse response magnitude, for each receive antenna in the input waveform waveform, summed across all reference signal ports, returned as a T-by-N_R real matrix.

• T is the number of time-domain samples.

• N_R is the number of receive antennas.

mag inherits the data type of the input waveform.

Data Types: single | double

References

[1] 3GPP TS 38.211. “NR; Physical channels and modulation.” 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 'SampleRate' name-value argument must be compile-time constant for code generation. For example, when you call the function with 'SampleRate',15.36e6, include {coder.Constant('SampleRate'),coder.Constant(15.36e6)} in the -args value of the codegen function. For more information, see the coder.Constant (MATLAB Coder) class.

• If you specify the 'SampleRate' name-value argument, the nrb, scs input arguments and the 'Nfft' name-value argument must also be compile-time constants. For example, include also {coder.Constant(nrb)} and {coder.Constant(scs)} in the -args value of the codegen function.

• The 'SampleRate' name-value pair argument cannot be used together with the carrier input.

Version History

Introduced in R2019b

R2023a: Subcarrier spacing for FR2-2

The function now supports 480 kHz and 960 kHz subcarrier spacings, as defined in TS 38.211 Sections 4.2 and 4.3.

R2023a: C/C++ code generation updates

For C/C++ code generation, the limitation to specify 'CyclicPrefix', 'CarrierFrequency', or 'Nfft' name-value arguments as compile-time constants has been removed. However, if you specify the 'SampleRate' name-value argument, the 'Nfft' name-value argument must still be compile-time constant for code generation.