5G NR Numerology: The One Parameter That Shapes the Whole Air Interface

Why this is the first thing to learn

Almost every number in the NR physical layer — symbol length, slot length, cyclic prefix, how many resource blocks fit in a carrier, how often the UE has to blind-decode — is derived from one integer, μ (mu). Learn how μ works and half of this chapter becomes arithmetic.

The mental model: gears on a bicycle

OFDM splits the band into many narrow subcarriers. The subcarrier spacing (SCS) is the distance between them, and it sets the OFDM symbol length: a subcarrier of spacing Δf needs a symbol of length 1/Δf to stay orthogonal to its neighbours.

Think of the SCS as a gear:

• Low gear (15 kHz) — long symbols (66.7 µs). Lots of "torque" against multipath: the cyclic prefix can be long, so the signal survives big cells and long echoes. But everything moves slowly: a slot is a full millisecond.
• High gear (120 kHz) — short symbols (8.3 µs). Fast: a slot is 125 µs, so latency is low, and the short symbol shrugs off the phase noise and Doppler that grow with carrier frequency. But the cyclic prefix is short, so it only works where echoes are short — small cells, mmWave.

LTE had one gear (15 kHz) because it lived in a narrow range of frequencies and cell sizes. NR runs from 410 MHz to 52.6 GHz (and beyond), from rural macro cells to indoor mmWave hot-spots. No single gear fits, so NR gives you five, and — the clever part — makes them mesh.

The mechanics

Subcarrier spacing is defined as

Δf = 2^μ × 15 kHz ,   μ ∈ {0, 1, 2, 3, 4}

Everything else follows (normal cyclic prefix):

Two invariants make this table easy to reconstruct:

1. Symbols per slot is always 14 (normal CP). So as the symbol halves, the slot halves.
2. The subframe (1 ms) and frame (10 ms) never change. So the number of slots per subframe is simply 2^μ.

Which SCS is allowed where (TS 38.104 / 38.101): FR1 data uses 15, 30 or 60 kHz; FR1 SSB uses 15 or 30 kHz. FR2 data uses 60 or 120 kHz; FR2 SSB uses 120 or 240 kHz. Rel-17 added μ = 5 and 6 (480 and 960 kHz) for the 52.6–71 GHz range (FR2-2); treat those as 5G-Advanced extras.

Why powers of two — the meshing gears

The factor 2^μ is not just tidy. It guarantees that symbol boundaries line up across numerologies: every 15 kHz symbol boundary coincides with every second 30 kHz boundary, every fourth 60 kHz boundary, and so on. That is what allows:

• Mixed numerologies on one carrier (different bandwidth parts with different SCS) without the two grids drifting apart.
• A 15 kHz SSB on a 30 kHz data carrier — the UE can translate between the two grids with a fixed offset.
• Scheduling across numerologies (a PDCCH at one SCS scheduling a PDSCH at another) with clean slot alignment.

If the spacings were, say, 15 / 20 / 25 kHz, none of this would work.

What each choice really trades

The design rule of thumb that falls out: choose the smallest SCS whose CP still covers the delay spread and whose subcarrier still tolerates the phase noise. That lands on 15/30 kHz in FR1 and 120 kHz in FR2.

A worked example

An operator has 100 MHz in n78 (3.5 GHz). Options: 30 kHz gives 273 RBs (98.28 MHz used), 0.5 ms slots and a 2.34 µs CP — enough for typical urban delay spread. 15 kHz cannot fill a 100 MHz carrier (max 50 MHz at 15 kHz, because the FFT would exceed 4096 points), and 60 kHz would shorten the CP to 1.17 µs, too short for macro cells. So the answer is 30 kHz — which is why almost every mid-band NR network on earth runs μ = 1.

Common confusions

Spec pointers

Recap

Interview questions

The questions below are drawn from this topic and phrased the way they tend to come up. Try each one out loud before revealing the answer.