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nrTimingEstimate

Practical timing estimation

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.

example

[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

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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

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

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

  • T is the number of time-domain samples.

  • NR is the number of receive antennas.

Data Types: single | double
Complex Number Support: Yes

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

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

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

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

Data Types: double

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

Data Types: double

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.

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

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 × NRB)/Nfft, where NRB 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

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 Nfft × SCS.

  • Nfft 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

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

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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

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

  • T is the number of time-domain samples.

  • NR 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

Version History

Introduced in R2019b

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