Numerology — The single index μ that sets subcarrier spacing and slot length

5G Systems Notes · Concept map · Numerology Route · Live ↗ · Hierarchy · Index · All concepts · Hub

The grid and its units

This page is the explanation. numerology, live is the working half — the same quantities computed by 5G Simulation/ while the page loads, so they cannot drift from what is written here.

Where it sits

Sits atLevel 4 of the hierarchy · The grid and its units · explained
Learn firstSubcarrier · Slot · Cyclic prefix — 5 concepts in the full chain, see the paths
UnlocksPoint A · URLLC and eMBB
Primary clauseTS 38.211 §4.2, Table 4.2-1
Used innr-frame-structure 46 · nr-pdsch 11 · nr-srs 7 · index 2 · ref-core 1 · ref-session 1
Scanned from the notes at page load and joined with terms.json; nothing on this card is typed by hand.

What it is

Numerology is the single index $\mu$ that sets everything about the time-frequency grid: subcarrier spacing is $2^{\mu} \times 15$ kHz, and the slot length is $1/2^{\mu}$ ms.

Seven values, 0 to 6, giving 15 to 960 kHz (TS 38.211 Table 4.2-1). One number decides the trade that runs through the whole system:

Wider spacing means shorter symbols, so shorter slots and lower latency, and more tolerance of frequency error and phase noise — which is why high bands use it. Narrower spacing means longer symbols, so a longer cyclic prefix for the same overhead fraction, and better tolerance of echoes — which is why wide-area cells use it.

Only $\mu = 2$ has the extended cyclic prefix as an option.

Read on

The full treatment is in nr-frame-structure — this page is the definition and the map reference; that note is where the subject is actually developed.

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Before this concept, the hierarchy says to learn the following — the full chain, in order:

To understand Numerology (level 4) you first need 5 other concepts. Read them in this order — everything on one line can be read in any order, but no line before the one above it:
Level Learn these
0 Subcarrier
1 OFDM
2 OFDM symbol
3 Cyclic prefix · Slot
Immediately before Numerology: Subcarrier, Slot, Cyclic prefix.
Keep going — where this sits on the route
The route is every concept in the folder ordered by level, so nothing here needs anything after it. Computed at page load from terms.json; the same numbering as the route page.
5G Systems Notes · Concept map · Numerology Top · Concept map · Hub