# lteULFrameOffset

PUSCH DM-RS uplink subframe timing estimate

## Description

example

offset = lteULFrameOffset(ue,chs,waveform) performs synchronization using PUSCH DM-RS signals for the time-domain waveform, waveform, given UE-specific settings, ue, and PUSCH configuration, chs.

The returned value offset indicates the number of samples from the start of the waveform, waveform, to the position in that waveform where the first subframe containing the DM-RS begins.

offset provides subframe timing; frame timing can be achieved by using offset with the subframe number, ue.NSubframe. This information is consistent with real-world operation, since the base station knows when, or in which subframe, to expect uplink transmissions.

example

[offset,corr] = lteULFrameOffset(ue,chs,waveform) also returns a complex matrix corr, which is the signal used to extract the timing offset.

## Examples

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Synchronization and demodulation of transmission which has been delayed by 5 samples.

Initialize waveform and insert a 5 sample delay.

ue = lteRMCUL('A3-2');
waveform = lteRMCULTool(ue,[1;0;0;1]);
tx = [zeros(5,1); waveform];

Determine offset and demodulate the waveform.

offset = lteULFrameOffset(ue,ue.PUSCH,tx)
offset = 5

View the correlation peak for a delayed transmit waveform. The transmission contains PUSCH demodulation reference signal (DM-RS) symbols available for estimating the waveform timing.

UE Configuration

Configure UE-specific settings and generate the transmit waveform.

ue = lteRMCUL('A3-2');
tx = lteRMCULTool(ue,[1;0;0;1]);

Determine Offset

Calculate timing offset and return the correlations for the transmit waveform and for a delayed version of the transmit waveform.

[~,corr] = lteULFrameOffset(ue,ue.PUSCH,tx);
txDelayed = [zeros(6,1); tx];
[offset,corrDelayed] = lteULFrameOffset(ue,ue.PUSCH,txDelayed);

Plot the correlation data before and after delay is added. Zoom in on the x-axis to view correlation peaks.

plot(corr)
hold on
plot(corrDelayed)
hold off
xlim([0 100])

Correct the timing offset and demodulate the received waveform.

## Input Arguments

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UE-specific settings, specified as a scalar structure with the following fields.

Parameter FieldRequired or OptionalValuesDescription
NULRBRequired

Scalar integer from 6 to 110

Number of uplink resource blocks. (${N}_{\text{RB}}^{\text{UL}}$)

NCellIDRequired

Integer from 0 to 503

Physical layer cell identity

NSubframeRequired

0 (default), nonnegative scalar integer

Subframe number

CyclicPrefixULOptional

'Normal' (default), 'Extended'

Cyclic prefix length

NTxAntsOptional

1 (default), 2, 4

Number of transmission antennas.

HoppingOptional

'Off' (default), 'Group', or 'Sequence'

Frequency hopping method.

SeqGroupOptional

0 (default), integer from 0 to 29

PUSCH sequence group assignment (ΔSS).

Only used if NDMRSID or NPUSCHID is absent.

CyclicShiftOptional

0 (default), integer from 0 to 7

Number of cyclic shifts used for PUSCH DM-RS (yields ${n}_{DMRS}^{\left(1\right)}$).

NPUSCHIDOptional

0 (default), nonnegative scalar integer from 0 to 509

PUSCH virtual cell identity. If this field is not present, NCellID is used for group hopping sequence-shift pattern initialization.

See footnote.

NDMRSIDOptional

0 (default), nonnegative scalar integer from 0 to 509

DM-RS identity for cyclic shift hopping (${n}_{ID}^{csh_DMRS}$). If this field is not present, NCellID is used for cyclic shift hopping initialization.

See footnote.

1. The pseudorandom sequence generator for cyclic shift hopping is initialized according to NDMRSID, if present — otherwise it is initialized according to the cell identity NCellID and the sequence group assignment SeqGroup. Similarly, the sequence-shift pattern for group hopping is initialized according to NPUSCHID, if present — otherwise it is initialized according to NCellID and SeqGroup.

Data Types: struct

PUSCH configuration, specified as a scalar structure with the following fields.

Parameter FieldRequired or OptionalValuesDescription
PRBSetRequired

Integer column vector or two-column matrix

0-based physical resource block indices (PRBs) for the slots of the current PUSCH resource allocation. As a column vector, the resource allocation is the same in both slots of the subframe. As a two-column matrix, it specifies different PRBs for each slot in a subframe.

NLayersOptional

1 (default), 2, 3, 4

Number of transmission layers.

DynCyclicShiftOptional

0 (default), integer from 0 to 7

Cyclic shift for DM-RS (yields ${n}_{DMRS}^{\left(2\right)}$).

OrthCoverOptional

'Off' (default), 'On'

Applies ('On'), or does not apply ('Off'), orthogonal cover sequence w (Activate-DMRS-with OCC).

The following field is required only when ue.NTxAnts is set to 2 or 4.
PMIOptional

0 (default), nonnegative scalar integer from 0 to 23.

Scalar precoder matrix indication (PMI) to be used during precoding

See lteULPMIInfo.

Data Types: struct

Time-domain waveform, specified as a numeric matrix. waveform must be a NS-by-NR matrix, where NS is the number of time-domain samples and NR is the number of receive antennas. waveform should be at least one subframe long and contain the DM-RS signals.

Generate waveform by SC-FDMA modulation of a resource matrix using the lteSCFDMAModulate function, or by using one of the channel model functions, lteFadingChannel, lteHSTChannel, or lteMovingChannel.

Data Types: double
Complex Number Support: Yes

## Output Arguments

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Offset number of samples, returned as a scalar integer. This output is the number of samples from the start of the waveform to the position in that waveform where the first subframe containing the DM-RS begins. offset is computed by extracting the timing of the peak of the correlation between waveform and internally generated reference waveforms containing DM-RS signals. The correlation is performed separately for each antenna and the antenna with the strongest correlation is used to compute offset.

Note

offset is the position of mod(max(abs(corr),LSF)), where LSF is the subframe length.

Signal used to extract the timing offset, returned as a complex-valued numeric matrix. corr has the same dimensions as waveform.