4G/LTE - LTE NB

 

 

 

OFDM Signal Generation

 

As in normal LTE, LTE-NB downlink is using OFDM waveform as well. I put the LTE-NB OFDM waveform generation formula and LTE formula toghether for comparision. You may think there is a big difference between the two, but actually not so much difference. It looks like LTE OFDM formular is much more complicated.. but it just look like complicated. It just divided one formular into two terms (sections) to remove center subcarrier (DC carrier). But in LTE-NB, there is no DC removal part, so it can represent the whole formular in single term. In other words, in LTE k never gets to 0 (the formula is not defined at k = 0), but in LTE-NB the formula is defined at k = 0 as well.

Followings are the topics to be covered in this page.

How does the LTE-NB formula differ from the LTE formula ?

The picture below puts the two formulas one above the other. 36.211 clause 10.2.8 for LTE-NB is on top, and clause 6.12 for LTE is underneath. The green arrows point from each index rule to the resource element index it defines. Let's compare them term by term, because one small term carries the whole difference.

36.211 OFDM baseband formulas for LTE-NB in clause 10.2.8 and for LTE in clause 6.12

LTE splits the sum at k = 0 to skip the DC subcarrier. LTE-NB keeps a single sum and shifts every subcarrier by half a subcarrier spacing instead.

The shift sits in the exponent. LTE-NB uses (k + 1/2)Δf where LTE uses kΔf. With NscRB = 12, k runs from -6 to 5, so the subcarrier frequencies run from -5.5Δf to +5.5Δf. None of them lands on 0 Hz. So there is no DC subcarrier to skip, and the formula can be defined at k = 0, as the text above says.

LTE solves the same problem the other way. It keeps the subcarriers on the kΔf grid and leaves the DC subcarrier empty. That is why its sum has two parts, and why it needs two index rules, k(-) and k(+).

  • One sum instead of two : LTE-NB needs only one index rule, k(-) = k + ⌊NscRB/2⌋.
  • The half-subcarrier shift keeps DC empty : the 12 subcarriers sit at -5.5Δf to +5.5Δf around the carrier centre.
  • The sum covers one PRB : k runs over NscRB = 12 subcarriers, from -6 to 5.
  • The rest is the same as LTE : the cyclic prefix term NCP,lTs and the 15 kHz subcarrier spacing carry over unchanged.

Does every NB-IoT carrier use this formula ?

The formula in the picture is not the whole story in the current specification. 36.211 v19.3.0 clause 10.2.8 defines two formulas. Which one applies depends on how the NB-IoT carrier sits relative to the LTE cell.

The formula in the picture applies to an inband-DifferentPCI carrier, to a guardband or standalone carrier, and to a carrier configured by CarrierConfigDedicated-NB or DL-CarrierConfigCommon-NB. For the in-band cases, it covers every downlink channel and signal except NPRS. Every other case uses the second formula, and the main one is the inband-SamePCI anchor carrier.

The second formula counts the OFDM symbol from the start of the last even-numbered subframe. It also includes fNB-IoT, which is the frequency of the centre of the NB-IoT PRB minus the frequency of the centre of the LTE signal. So the phase of each NB-IoT resource element is tied to the LTE centre frequency, not to the centre of the NB-IoT PRB.

This matters in the same-PCI case. There the NB-IoT carrier shares the physical cell ID and the number of reference signal ports with the LTE cell. The NB-IoT signal therefore keeps the phase that the LTE OFDM signal gives the same resource elements, and the two signals stay consistent inside that PRB. The clause also states that only normal CP is supported for the NB-IoT downlink.

  • Two formulas in v19.3.0 : the half-subcarrier formula in the picture, and a second one tied to the LTE centre frequency.
  • inband-SamePCI uses the second formula : fNB-IoT carries the offset between the NB-IoT PRB and the LTE centre.
  • Guardband and standalone use the formula in the picture : these carriers have no surrounding LTE signal to stay aligned with.
  • Normal CP only : the NB-IoT downlink does not support extended CP.

Reference

[1] 3GPP TS 36.211 v19.3.0 - clause 6.12 and clause 10.2.8, OFDM baseband signal generation for LTE and for NB-IoT