nrTimingEstimate

Practical timing estimation

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Syntax

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

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

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

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

[offset,mag] = nrTimingEstimate(___,'CyclicPrefix',cpl)

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

Description

example

[offset,mag] = nrTimingEstimate(waveform,nrb,scs,initialSlot,refInd,refSym) performs practical timing estimation by cross-correlating the input waveform waveform with a reference waveform. The function obtains the reference waveform by modulating a reference resource grid containing reference symbols refSym at locations refInd using orthogonal frequency division multiplexing (OFDM). The OFDM modulation spans nrb resource blocks at subcarrier spacing scs and initial slot number initialSlot. The function returns the estimated timing offset offset and the estimated impulse response magnitude mag for each receive antenna in the input waveform.

[offset,mag] = nrTimingEstimate(waveform,nrb,scs,initialSlot,refGrid) specifies a predefined reference resource grid refGrid.

[offset,mag] = nrTimingEstimate(carrier,waveform,refInd,refSym) specifies carrier configuration parameters.

[offset,mag] = nrTimingEstimate(carrier,waveform,refGrid) specifies a carrier resource grid.

[offset,mag] = nrTimingEstimate(___,'CyclicPrefix',cpl) specifies the cyclic prefix length for the OFDM modulation in addition to the input arguments in any of the previous syntaxes that do not include the carrier input.

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

Examples

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Estimate Timing Offset for TDL-C Channel Transmission

Open Live Script

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.

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

Input Arguments

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`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

`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`

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

Data Types: double

`initialSlot` — Zero-based initial slot number
nonnegative integer

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

Data Types: double

`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 one-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

`carrier` — Carrier configuration parameters
`nrCarrierConfig` object

Carrier configuration parameters for a specific OFDM numerology, specified as an nrCarrierConfig object. The function uses only these properties of this input.

`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

`NSlot` — Slot number
`0` (default) | nonnegative integer

Slot number, specified as a nonnegative integer. You can set NSlot 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 may have to ensure that the property value is modulo the number of slots per frame in a calling code.

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

`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

`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

`cpl` — 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, the extended cyclic prefix length only applies to 60 kHz subcarrier spacing.

Data Types: char | string

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

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

`'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 either a nonnegative integer greater than 127, or []. The value you specify must result in integer-valued cyclic prefix lengths and a maximum occupancy, defined as the value of (12 × N_RB)/Nfft, where N_RB is the number of resource blocks, of 100%.

If you do not specify this input, or if you specify 'Nfft',[], the function sets a default value satisfying these conditions.

The value of this input is an integer power of 2.
The maximum occupancy is 85%.
The minimum value of this input is 128.

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 specified in the SubcarrierSpacing property of the config input for the first function syntax, or the scs input for the other syntaxes.

Data Types: double

`'CarrierFrequency'` — Carrier frequency
`0` (default) | nonnegative scalar

Carrier frequency, in Hz, specified as the comma-separated pair consisting of 'CarrierFrequency' and a nonnegative scalar. This input corresponds to f₀, defined in Section 5.4 of [1].

Data Types: double

Output Arguments

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`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, 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™.

The nrb and scs inputs must be constant when you specify any name-value pair arguments. For example, to specify a subcarrier spacing of 30 kHz, include {coder.Constant(30)} in the -args value of the codegen function. For more information, see the coder.Constant (MATLAB Coder) class.

The 'SampleRate' name-value-pair argument cannot be used with function syntaxes that use the carrier input.

Documentation

nrTimingEstimate

Syntax

Description

Examples

Estimate Timing Offset for TDL-C Channel Transmission

Input Arguments

`waveform` — Received waveform
T-by-N_R complex matrix

`nrb` — Number of resource blocks
integer from 1 to 275

`scs` — Subcarrier spacing in kHz
`15` | `30` | `60` | `120` | `240`

`initialSlot` — Zero-based initial slot number
nonnegative integer

`refInd` — Reference symbol indices
integer matrix

`carrier` — Carrier configuration parameters
`nrCarrierConfig` object

`NSizeGrid` — Number of RBs in carrier resource grid
`52` (default) | integer from 1 to 275

`SubcarrierSpacing` — Subcarrier spacing in kHz
`15` (default) | `30` | `60` | `120` | `240`

`NSlot` — Slot number
`0` (default) | nonnegative integer

`CyclicPrefix` — Cyclic prefix length
`'normal'` (default) | `'extended'`

`refSym` — Reference symbols
complex matrix

`refGrid` — Predefined reference grid
K-by-N-by-P complex array

`cpl` — Cyclic prefix length
`'normal'` (default) | `'extended'`

Name-Value Pair Arguments

`'Nfft'` — Number of FFT points
integer greater than 127 (default depends on other input values) | `[]`

`'SampleRate'` — Waveform sample rate
positive scalar (default depends on other input values) | `[]`

`'CarrierFrequency'` — Carrier frequency
`0` (default) | nonnegative scalar

Output Arguments

`offset` — Estimated timing offset in samples
nonnegative integer

`mag` — Estimated impulse response magnitude
T-by-N_R real matrix

References

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

See Also

Functions

Objects

5G Toolbox Documentation

Support

Documentation

nrTimingEstimate

Syntax

Description

Examples

Estimate Timing Offset for TDL-C Channel Transmission

Input Arguments

waveform — Received waveform T-by-NR complex matrix

nrb — Number of resource blocks integer from 1 to 275

scs — Subcarrier spacing in kHz 15 | 30 | 60 | 120 | 240

initialSlot — Zero-based initial slot number nonnegative integer

refInd — Reference symbol indices integer matrix

carrier — Carrier configuration parameters nrCarrierConfig object

NSizeGrid — Number of RBs in carrier resource grid 52 (default) | integer from 1 to 275

SubcarrierSpacing — Subcarrier spacing in kHz 15 (default) | 30 | 60 | 120 | 240

NSlot — Slot number 0 (default) | nonnegative integer

CyclicPrefix — Cyclic prefix length 'normal' (default) | 'extended'

refSym — Reference symbols complex matrix

refGrid — Predefined reference grid K-by-N-by-P complex array

cpl — Cyclic prefix length 'normal' (default) | 'extended'

Name-Value Pair Arguments

'Nfft' — Number of FFT points integer greater than 127 (default depends on other input values) | []

'SampleRate' — Waveform sample rate positive scalar (default depends on other input values) | []

'CarrierFrequency' — Carrier frequency 0 (default) | nonnegative scalar

Output Arguments

offset — Estimated timing offset in samples nonnegative integer

mag — Estimated impulse response magnitude T-by-NR real matrix

References

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™.

See Also

Functions

Objects

5G Toolbox Documentation

Support

`waveform` — Received waveform
T-by-N_R complex matrix

`nrb` — Number of resource blocks
integer from 1 to 275

`scs` — Subcarrier spacing in kHz
`15` | `30` | `60` | `120` | `240`

`initialSlot` — Zero-based initial slot number
nonnegative integer

`refInd` — Reference symbol indices
integer matrix

`carrier` — Carrier configuration parameters
`nrCarrierConfig` object

`NSizeGrid` — Number of RBs in carrier resource grid
`52` (default) | integer from 1 to 275

`SubcarrierSpacing` — Subcarrier spacing in kHz
`15` (default) | `30` | `60` | `120` | `240`

`NSlot` — Slot number
`0` (default) | nonnegative integer

`CyclicPrefix` — Cyclic prefix length
`'normal'` (default) | `'extended'`

`refSym` — Reference symbols
complex matrix

`refGrid` — Predefined reference grid
K-by-N-by-P complex array

`cpl` — Cyclic prefix length
`'normal'` (default) | `'extended'`

`'Nfft'` — Number of FFT points
integer greater than 127 (default depends on other input values) | `[]`

`'SampleRate'` — Waveform sample rate
positive scalar (default depends on other input values) | `[]`

`'CarrierFrequency'` — Carrier frequency
`0` (default) | nonnegative scalar

`offset` — Estimated timing offset in samples
nonnegative integer

`mag` — Estimated impulse response magnitude
T-by-N_R real matrix

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.