Why NR Needs Flexible Numerology
LTE uses a single numerology: 15 kHz subcarrier spacing (SCS), 1 ms subframe, 0.5 ms slot, 7 symbols per slot (normal CP). This one-size-fits-all approach works for sub-6 GHz macro deployments but cannot serve the diverse requirements of 5G -- from sub-1 GHz wide-area coverage to 52.6 GHz mmWave short-range links, and from best-effort broadband to sub-millisecond URLLC.
3GPP therefore defined a scalable OFDM numerology in 3GPP TS 38.211 clause 4.2, parameterized by the index mu (representing Greek letter mu). Each mu value doubles the subcarrier spacing, halves the symbol and slot durations, and maintains orthogonality with other numerologies. This article provides the complete numerology tables, explains bandwidth parts, details mini-slot configurations, and works through URLLC latency calculations step by step.
Complete NR Numerology Table
The fundamental relationship is: SCS = 2^mu x 15 kHz. All timing parameters scale accordingly.
| Parameter | mu=0 | mu=1 | mu=2 | mu=3 | mu=4 |
|---|---|---|---|---|---|
| Subcarrier spacing (kHz) | 15 | 30 | 60 | 120 | 240 |
| OFDM symbol duration (us) | 66.67 | 33.33 | 16.67 | 8.33 | 4.17 |
| Normal CP duration (us) | 4.69 | 2.34 | 1.17 | 0.59 | 0.29 |
| Extended CP duration (us) | 16.67 | -- | 4.17 | -- | -- |
| Symbols per slot | 14 | 14 | 14 (NCP) / 12 (ECP) | 14 | 14 |
| Slot duration (ms) | 1.0 | 0.5 | 0.25 | 0.125 | 0.0625 |
| Slots per subframe (1 ms) | 1 | 2 | 4 | 8 | 16 |
| Slots per frame (10 ms) | 10 | 20 | 40 | 80 | 160 |
| Applicable frequency range | FR1 | FR1 | FR1 + FR2 | FR2 | FR2 (SSB only) |
Key notes from 3GPP TS 38.211 clause 4.2 and 4.3.2:
- mu=0 (15 kHz) is used for sub-3 GHz deployments and serves as the backward-compatible numerology matching LTE.
- mu=1 (30 kHz) is the dominant choice for FR1 (sub-7.125 GHz) deployments worldwide, balancing throughput and latency.
- mu=2 (60 kHz) bridges FR1 and FR2, and is the only numerology that supports extended CP (12 symbols per slot), useful for large delay-spread channels and broadcast (per 3GPP TS 38.211 clause 4.2, Table 4.2-1).
- mu=3 (120 kHz) is the primary data numerology for FR2 (24.25--52.6 GHz mmWave).
- mu=4 (240 kHz) is restricted to SS/PBCH block (SSB) in FR2 for initial access and synchronization only. It is not used for data transmission.
Frame Structure
The NR frame structure is defined in 3GPP TS 38.211 clause 4.3.1:
- Frame: 10 ms duration, always. Contains 10 subframes of 1 ms each.
- Subframe: 1 ms duration, always (numerology-independent reference).
- Slot: Duration = 1 / (2^mu) ms. A slot contains 14 symbols (normal CP) or 12 symbols (extended CP, mu=2 only).
- Half-frame: 5 ms, used for TDD DL/UL switching period alignment.
The slot is the basic scheduling unit in NR. Unlike LTE where the TTI (Transmission Time Interval) is fixed at 1 ms, NR's TTI equals one slot duration and scales with the numerology. This is the primary mechanism for latency reduction at higher SCS values.
Bandwidth Parts (BWP)
A Bandwidth Part is a contiguous set of PRBs on a given numerology within a carrier, defined in 3GPP TS 38.211 clause 4.4.5 and configured via 3GPP TS 38.331 clause 6.3.2 (BWP-Downlink and BWP-Uplink IEs).
Each UE can be configured with up to 4 DL BWPs and 4 UL BWPs, but only one DL and one UL BWP are active at any time. BWPs enable:
- UE power saving: A device can operate on a narrow BWP (e.g., 20 MHz) during low-activity periods, then switch to a wide BWP (e.g., 100 MHz) for high-throughput transfers.
- Mixed numerology: Different BWPs on the same carrier can use different SCS values.
- Spectrum sharing: Operators can partition a carrier into BWPs serving different device classes.
| BWP Configuration | SCS (kHz) | Bandwidth (MHz) | PRB Count | Typical Use Case |
|---|---|---|---|---|
| Default BWP (narrow) | 15 | 5 | 25 | Paging, idle-mode monitoring, RedCap |
| Active BWP (mid) | 30 | 40 | 106 | Standard eMBB user |
| Active BWP (wide) | 30 | 100 | 273 | Peak-rate eMBB, carrier aggregation |
| URLLC BWP | 30 | 20 | 51 | Low-latency industrial control |
| FR2 BWP | 120 | 400 | 264 | mmWave high-throughput |
| RedCap BWP (R17) | 15 | 20 | 100 | Wearables, sensors (per TS 38.300 cl. 4.4a) |
BWP switching is triggered by DCI (Downlink Control Information) format 1_1 or 0_1 carrying a BWP indicator field, or by a BWP inactivity timer expiring (returning the UE to the default BWP). The switching time is defined in 3GPP TS 38.133 clause 8.6 and ranges from 0.5 ms (Type 1, within same SCS) to 2 ms (Type 2, different SCS requiring RF retuning).
Mini-Slot: Sub-Slot Scheduling for URLLC
A mini-slot is a scheduling allocation shorter than a full 14-symbol slot, defined in 3GPP TS 38.214 clause 5.1.2.1 (DL) and clause 6.1.2.1 (UL). Mini-slots enable transmission at the next available OFDM symbol boundary rather than waiting for a slot boundary.
Valid mini-slot lengths (SLIV configurations):
| Symbols | Duration at SCS 30 kHz (us) | Duration at SCS 120 kHz (us) | Primary Use |
|---|---|---|---|
| 2 | 71.4 | 17.9 | URLLC DL/UL, minimum latency |
| 4 | 142.9 | 35.7 | URLLC with moderate payload |
| 7 | 250.0 | 62.5 | Half-slot scheduling |
| 14 | 500.0 | 125.0 | Full slot (reference) |
The Start and Length Indicator Value (SLIV) in DCI encodes both the starting symbol (S) and the length in symbols (L). For L <= 7, SLIV = 14 x (L - 1) + S. For L > 7, SLIV = 14 x (14 - L + 1) + (14 - 1 - S). The gNB scheduler uses mini-slots to immediately preempt ongoing slot-based transmissions when a URLLC packet arrives, per the pre-emption indication in DCI format 2_1 (defined in 3GPP TS 38.212 clause 7.3.1.2.1).
Worked Example 1: URLLC One-Way Latency Calculation
Calculate the minimum one-way user-plane latency for a URLLC DL transmission using SCS = 30 kHz and 2-symbol mini-slot.
Step 1: Frame alignment delay.In the worst case, the packet arrives just after a symbol boundary and must wait for the next one. Average alignment delay = 0.5 x symbol duration = 0.5 x 33.33 us = 16.67 us.
Step 2: DCI processing (scheduling grant).The UE must decode the PDCCH carrying DCI format 1_0 or 1_1. Processing time is defined in 3GPP TS 38.214 Table 5.3-1 as N1 symbols. For mu=1, N1 = 13 symbols for processing capability 1, or N1 = 4.5 symbols for processing capability 2.
Using capability 2: 4.5 x 33.33 us = 150 us.
Step 3: PDSCH transmission.2 symbols x 33.33 us = 66.67 us.
Step 4: PDSCH processing + HARQ feedback.UE decodes PDSCH and prepares HARQ-ACK. Processing time per TS 38.214 Table 5.3-2 for capability 2: N1 = 4.5 symbols = 150 us.
Step 5: Sum one-way (DL only, no HARQ retransmission).16.67 + 150 + 66.67 + 150 = 383.3 us = 0.38 ms.
This is well within the 1 ms one-way target for URLLC per 3GPP TR 38.913 clause 7.2. Adding UPF processing (~0.1 ms) and fronthaul delay (~0.1 ms), the total is approximately 0.58 ms.
Worked Example 2: Throughput Calculation per Slot
Calculate the peak throughput of a single NR carrier with mu=1 (30 kHz SCS), 100 MHz bandwidth, 4x4 MIMO, 256QAM.
Step 1: PRBs per carrier.Per 3GPP TS 38.101-1 Table 5.3.2-1: 100 MHz at SCS 30 kHz = 273 PRBs.
Step 2: Subcarriers per slot.273 PRBs x 12 subcarriers/PRB = 3,276 subcarriers.
Step 3: REs per slot.3,276 subcarriers x 14 symbols = 45,864 REs. Subtract ~14% overhead (DMRS, PDCCH, SSB, CSI-RS): usable REs = 45,864 x 0.86 = 39,443 REs.
Step 4: Bits per RE.256QAM = 8 bits/symbol, 4 MIMO layers, coding rate 948/1024 = 0.926.
Bits per RE = 8 x 4 x 0.926 = 29.6 bits.
Step 5: Throughput per slot.39,443 REs x 29.6 bits = 1,167,513 bits = 1.168 Mbits per slot.
Slot duration = 0.5 ms, so throughput = 1.168 / 0.0005 = 2,335 Mbps per slot = ~2.34 Gbps.
For two slots per subframe (mu=1), the per-subframe throughput remains 2.34 Gbps (since slots are sequential, not parallel). Adding a second carrier via CA doubles this to 4.68 Gbps.
CP Length and Guard Band Considerations
The cyclic prefix (CP) absorbs multipath delay spread. Longer CP means more resilience to delay spread but reduces spectral efficiency (CP is overhead). The normal CP for mu=0 is 4.69 us, corresponding to a maximum supportable delay spread of approximately 4.69 us x 300 m/us = 1,407 m path-length difference -- adequate for macro cells.
For FR2 (mu=3, CP = 0.59 us), the maximum supportable delay spread corresponds to ~177 m path difference. This is sufficient for mmWave deployments where cells are small (50--200 m radius) and propagation is predominantly line-of-sight.
Extended CP (mu=2 only, 4.17 us) is specified for scenarios like:
- Large indoor venues with significant multipath (convention centers, airports).
- Single-Frequency Network (SFN) broadcast, where identical signals from multiple gNBs must be received constructively.
- High-speed rail at 3.5 GHz, where Doppler-induced timing variations require additional guard time.
Deutsche Telekom deployed mu=2 with extended CP for their 5G Broadcast trials at UEFA Euro 2024 stadiums, enabling SFN-mode delivery of live video to tens of thousands of devices simultaneously.
SK Telecom's commercial n78 network uses mu=1 (30 kHz SCS) for all data channels and mu=0 (15 kHz) for SSB and initial access on their sub-3 GHz n3 carrier. Their FR2 deployment on n257 (28 GHz) uses mu=3 (120 kHz) for both SSB and data, achieving slot durations of 0.125 ms that support their URLLC-grade stadium services with round-trip air-interface latency below 1 ms.
Numerology Selection Guidelines
| Deployment Scenario | Recommended mu | SCS (kHz) | Rationale |
|---|---|---|---|
| Rural macro, sub-1 GHz | 0 | 15 | Long CP for large cells, matches LTE coexistence |
| Urban macro, 1--7 GHz (FR1) | 1 | 30 | Balance of throughput and latency, dominant choice globally |
| Indoor/dense urban, 3.5 GHz | 1 or 2 | 30 or 60 | mu=2 for delay-spread-heavy environments |
| mmWave (24--52.6 GHz) | 3 | 120 | Handles Doppler and phase noise at mmWave |
| URLLC on FR1 | 1 | 30 | Mini-slot achieves sub-ms with mu=1 |
| URLLC on FR2 | 3 | 120 | 0.125 ms slot enables extreme low latency |
| V2X sidelink (FR1) | 1 | 30 | Defined in 3GPP TS 38.101-1 for sidelink |
Impact on Channel Estimation and Phase Noise
Higher SCS values increase robustness against phase noise, which scales with carrier frequency. At 28 GHz, oscillator phase noise can cause significant inter-carrier interference (ICI) with 15 kHz SCS, but is manageable at 120 kHz SCS because each subcarrier occupies a wider bandwidth relative to the phase-noise profile. This is a key reason why mu=3 is mandated for FR2 data -- not just for latency reduction.
Conversely, higher SCS increases sensitivity to timing advance errors and Doppler spread. For mu=3 at 28 GHz with a UE moving at 120 km/h, the Doppler shift is approximately 3.1 kHz -- about 2.6% of the 120 kHz SCS. This is within the 5% tolerance typically acceptable for coherent demodulation with DMRS-based channel estimation.
Summary
NR numerology is the foundation on which all 5G physical layer operations are built. The mu-based parameterization enables a single standard to serve frequency ranges from 410 MHz to 52.6 GHz, latency requirements from 100 ms to sub-0.5 ms, and device classes from RedCap sensors to 8-layer mmWave terminals. Mastering the numerology table, understanding BWP switching, and being able to calculate slot-level throughput and URLLC latency budgets are essential skills for 5G NR engineers and certification candidates.