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5G NR Numerology Selection

  • Writer: Venkateshu Kamarthi
    Venkateshu Kamarthi
  • 5 hours ago
  • 10 min read

Introduction

Unlike 4G LTE, which relied on a fixed  Subcarrier Spacing (SCS) and a static  subframe duration, 5G New Radio (NR) introduces a flexible OFDM numerology frame structure scaling as Δf=15×2^μ kHz.

Selecting the optimal numerology parameter (μ∈{0,1,2,3,4}) governs a direct trade-off between coverage geometry, PHY-layer latency, Doppler resilience, and hardware processing overhead.

1. Fundamentals of 5G Flexible Numerology

3GPP TS 38.211 specifies the mathematical foundation for scalable subcarrier spacing:


Δf=15×2^μ kHz, where μ is the numerology configuration index.

Physical Layer Scaling Relations

Tsymbol=1/Δf=(66.67 μs)/2^μ 
TCP ≈(4.69 μs)/2^μ     (Normal CP)
Nslots, subframe & μ =2^μ  where 1subframe=1 ms
Tslot= (1 ms)/2^μ = 14 OFDM symbols /2^μ

μ

SCS (kHz)

Slot duration

Normal CP (µs)

Max cell radius

Primary domain

0

15

1.00 ms

~4.69 µs

~1.40 km

Sub-3 GHz FDD

1

30

0.50 ms

~2.34 µs

~0.70 km

2.3–4.9 GHz TDD

2

60

0.25 ms

~1.17 µs

~0.35 km

FR1/FR2 bridge

3

120

0.125 ms

~0.59 µs

~0.17 km

FR2 mmWave

4

240

0.0625 ms

~0.29 µs

~0.08 km

FR2 SSB search

2. RF Trade-offs: Coverage vs. Latency vs. Mobility

A. Cell-Edge Coverage (The +3 dB Thermal Noise Penalty)

Thermal noise power per Resource Block (RB) is calculated as:

NRB =k⋅T⋅BRB * NF 
Where:
	k=1.38×10^(-23) J/K (Boltzmann's constant)
	T=290K (N0=-174dBm/Hz)
	BRB =12×Δf (12 subcarriers per RB)
	"NF"=Receiver Noise Figure (typically 5 dB for UE Uplink)

Noise Floor per RB Comparison

SCS

RB bandwidth

Noise floor

Delta vs 15 kHz

15 kHz

180 kHz

−121.45 dBm

—

30 kHz

360 kHz

−118.44 dBm

+3.01 dB

      

·     15 kHz SCS ( RB BW):

NRB,15 =-174+10log10⁡(180,000)=-121.45dBm

  • 30 kHz SCS ( RB BW):

NRB,30=-174+10log10⁡(360,000)=-118.44dBm

It degrades the Uplink SINR by 3dB, directly shrinking the link budget margin and limiting maximum uplink distance.

Impact on Coverage: Moving a power-limited UE (transmitting at ) from  to  SCS increases the thermal noise floor per RB by . This degrades the Uplink SINR by , directly shrinking the link budget margin and limiting maximum uplink distance.

B. Multipath Delay Spread & Inter-Symbol Interference (ISI)

The Cyclic Prefix (CP) acts as a buffer against delay spread caused by signal reflections:

Maximum Un-aliased Path Difference (Δd)=c×TCP

  • 15 kHz SCS (Tcp=4.69us):

    Δd=(3×10^8m/s)×(4.69×10^(-6)s)=1.407km

  • 30 kHz SCS (Tcp=2.34us):

    Δd=(3×10^8 m/s×(2.34×10^(-6)s)=0.702km


                       MULTIPATH PROPAGATION & CP FIT    


   - If Delay Spread <= CP Duration  --> Zero ISI (Orthogonality Maintained)

   - If Delay Spread >  CP Duration  --> ISI Degradation & EVM Floor Spikes

When multipath delay spread exceeds Tcp , adjacent symbols spill into each other, inducing Inter-Symbol Interference (ISI) and creating an Error Vector Magnitude (EVM) floor that severely degrades the modulation scheme (e.g., dropping 64QAM down to QPSK).

C. Phase Noise and High Doppler Tracking

At higher RF carrier frequencies (fc), local oscillator phase noise density increases significantly, causing Inter-Carrier Interference (ICI).       

PHASE NOISE & SUBCARRIER SPACING


  The maximum tolerable Doppler shift without severe ICI is roughly a fraction of the SCS:

f(D,max)=(v/c)*fc ≤ η⋅Δf (where η≈0.05 to 0.10)

  • For a train moving at v=300km/h  (83.33m/s) on a 3.5Ghz carrier:

    fD=[83.33/(3×10^8)]×(3.5×10^9)≈972.2Hz

  • 15 kHz SCS: Frequency offset ratio 972.2/15000 = 6.48% (High ICI Risk)

  • 30 kHz SCS: Frequency offset ratio 972.2/30000= 3.24% (Safe Margin)


3. Real-World Operator Case Studies

                  GLOBAL OPERATOR NUMEROLOGY PROFILE           

Operator

Band

Numerology

Use Case

AT&T / Dish

n71/n70 (low-band FDD)

u=0 (15 kHz)

Max coverage

Reliance Jio

n28 (700 MHz FDD)

u=0 (15 kHz)

Rural coverage

Jio / Airtel

n77/n78 (3.5 GHz TDD)

u=1 (30 kHz)

High capacity

Rakuten Mobile

n257 (28 GHz mmWave)

u=3 (120 kHz)

Ultra-low latency

Case 1: Reliance Jio (India)

Tier

Band

Duplex / Bandwidth

SCS

Role

Tier 1

n28 (700 MHz)

FDD, 10 MHz

15 kHz

Coverage anchor

Tier 2

n78 (3.5 GHz)

TDD, 100 MHz

30 kHz

Capacity layer

Tier 3

n257 (28 GHz)

TDD, 800 MHz

120 kHz

FWA / hotspot density

Low-Band Layer: n28 (10Mhz FDD)

  • SCS: 15Khz(u=0)

  • RBs Allocated: 52 RBs

  • Engineering Rationale: Maximizes rural link margin and indoor penetration. 15Khz  SCS minimizes thermal noise floor per RB (-121.45dBm) and provides a 4.69us CP duration to absorb long delay spreads in open terrain.

Mid-Band Layer: n78 ( 100Mhz TDD)

  • SCS: 30Khz (u=1)

  • RBs Allocated: 273 RBs

  • Engineering Rationale: Balances baseband FFT processing complexity (Nfft=2048) with lower transmission latency (0.5ms slot) and high phase noise tolerance on 3.5Ghz active antenna units (AAUs).

mmWave Layer: n257 (800Mhz TDD via 8x100 MHz CA)

  • SCS: 120khz (u=3)

  • RBs Allocated: 66 RBs per 100Mhz component carrier

  • Engineering Rationale: Deployed for Fixed Wireless Access (FWA). A  0.125ms slot time yields low air-interface latency, while 120khz subcarriers resist the heavy phase noise inherent to 28Ghz  local oscillators.

Case 2: AT&T & Dish/Boost Spectrum (USA)

AT&T Low-Band: n70/n71 / n5 ( 10Mhz - 20Mhz FDD)

  • SCS:15khz  (u=0)

  • Engineering Rationale: Designed to maximize cell radius in rural highway coverage corridors.

Dish Network Greenfield: n70 ( 25Mhz FDD Block)

  • SCS: 15Khz (u=0)

  • Carrier Layout: Split into distinct 5G carriers (10Mhz + 15Mhz) using 15Khz SCS to align with Cloud-RAN processing constraints and maintain link budget balance.

AT&T C-Band: n77 (80Mhz -120MhzTDD)

  • SCS: 30Khz(u=1)

  • RBs Allocated: 217 RBs (80Mhz) or 273 RBs (100Mhz)

  • Engineering Rationale: Uses Massive MIMO (64T64R) beamforming gain to offset the +3.01dB noise floor penalty of 30khz SCS, restoring the link budget match with underlying 15Khz LTE/5G low-bands.

Case 3: Bharti Airtel & Vodafone Idea (India)

Layer

Band

Bandwidth

SCS

Role

Mid-band

n78 (3.5 GHz)

100 MHz

30 kHz

High capacity

Refarmed low/mid-band

n3 (1800 MHz) / n1 (2100 MHz)

—

15 kHz

Coverage continuity

  • n78 ( 100Mhz TDD): Configured with 30khz SCS (273 RBs).

  • Refarmed FDD Bands (n1, n3, n8): Dynamic Spectrum Sharing (DSS) or pure NR using 15Khz SCS to maintain inter-operability and matching frame boundaries with existing 4G LTE deployments.

Case 4: Rakuten Mobile & Deutsche Telekom (Japan & Europe)

Rakuten Mobile (Japan)

  • n77 (100Mhz TDD at 3.8Ghz ): Configured with 30Khz SCS (273 RBs). Operated entirely within an open RAN (O-RAN) Cloud-DU environment. The 30Khz SCS option reduces lower PHY layer task processing rates from 1000 subframes/sec to 2000 slots/sec, which fits x86 server hardware pipelines efficiently.

  • n257 ( 400Mhz mmWave): Configured with 120Khz SCS.

Deutsche Telekom (Germany)

  • n1 ( 20Mhz FDD DSS): Uses 15Khz SCS to share the physical layer grid directly with LTE Band 1.

  • n78 (90Mhz TDD): Uses 30Khz SCS (245 RBs) to optimize throughput across suburban and dense urban topologies.

4. Comprehensive Mathematical Derivations & Calculations

Peak PHY Data Rate Equation (3GPP TS 38.306)

Where:

  • J: Number of aggregated component carriers

  • vlayers: MIMO layers ( 4 for DL, 2 for UL)

  • Qm: Modulation order (6 for 64QAM, 8 for 256QAM )

  • f: Scaling factor (1)

  • Rmax=948/1024=0.92578 (Code rate)

  • Nprb: Allocated Resource Blocks

  • Ts,u = 10^-3/14.2^u= (OFDM symbol duration)

  • OH: Overhead scaling factor (0.14 for Sub-6 GHz DL, 0.18 for mmWave DL)

Scenario Calculations:  20Mhz Bandwidth at 15Khz  vs  30Khz SCS

           20 MHz BANDWIDTH ALLOCATION MATRIX          

SCS

RB count

Used bandwidth

Guard band

Spectral efficiency

15 kHz

106 RBs

19.08 MHz

920 kHz

95.4%

30 kHz

51 RBs

18.36 MHz

1.64 MHz

91.8%

Transmission Bandwidth Configuration (3GPP TS 38.101-1)

For  20Mhz Channel Bandwidth:

  • 15kHz SCS (μ=0): NRB =106 RBs ⟹Used BW=106×180kHz=19.08MHz

  • 30 kHz SCS (μ=1): NRB =51 RBs ⟹Used BW=51×360kHz=18.36MHz

1. Peak Downlink Throughput Calculation (Single Carrier)

Parameters: 4 Layer MIMO (v=4), 256QAM (Qm=8), Overhead OH=0.14.

  • Option A: 20MHz Bandwidth with 15kHz SCS

    Ts,0=10^(-3)/(14⋅2^0)=71.428 μs REs per second=(106×12)/(71.428×10^(-6) )=17,808,000RE/s Peak Rate_15=10^(-6)⋅(4×8×1.0×0.92578×17,808,000×(1-0.14))=453.33Mbps

Option B: 20Mhz Bandwidth with 30Khz SCS

Ts,1=10^(-3)/(14⋅2^1 )=35.714 μs REs per second=(51×12)/(35.714×10^(-6) )=17,136,000 RE/s Peak Rate_30=10^(-6)⋅(4×8×1.0×0.92578×17,136,000×(1-0.14))=436.22Mbps


Analysis: In a narrow 20MHz channel, 30kHz SCS reduces peak throughput by ≈3.78%. This reduction happens because wider subcarrier channels leave larger spectral guard bands at the channel edges, reducing available active RBs (51 RBs vs. 106 RBs).

2. Link Budget & SINR Mapping at Cell Edge

System Assumptions:

  • Max UE Uplink Tx Power (Ptx) = +23dBm

  • Path Loss (PL) = 130dB

  • Base Station Receiver NF = 5dB

  • Prx =23dBm-130dB=-107dBm

SINR Results:

  • 15kHz SCS:

    • Noise_15=-121.45+5=-116.45dBm

    • SINR _15=-107-(-116.45)=+9.45dB

  • 30kHz SCS:

    • Noise_30=-118.44+5=-113.44dBm

    • SINR_30=-107-(-113.44)=+6.44dB

3. BLER & HARQ Throughput Penalty

    LINK BUDGET CORRIDOR AT CELL EDGE

This traces the full link budget from transmitter to outcome at cell edge: +23 dBm Tx power minus 130 dB path loss lands you at −107 dBm received signal — that number is fixed regardless of numerology, since it's purely a function of RF propagation.

What changes is which noise floor you're measuring against — pulling directly from the +3.01 dB penalty shown earlier: the 30 kHz noise floor sits 3 dB higher than 15 kHz (−113.44 vs −116.45 dBm), simply because wider subcarriers capture more thermal noise per RB.

That 3 dB gap in noise floor becomes a 3 dB gap in SINR (+9.45 dB vs +6.44 dB), and at the cell edge that's the difference between a clean link and one that dips into the SINR region where BLER climbs and HARQ retransmissions kick in. It's a concrete illustration of the coverage-vs-capacity trade-off: 30 kHz SCS's noise penalty isn't just an abstract number — at the edge of a cell it can directly cost you link reliability, which is why operators tend to keep low-band/edge coverage on 15 kHz and push 30 kHz+ to mid-band capacity layers, as shown in the tiered deployment tables above.

In a Rayleigh fading channel, the Block Error Rate (BLER) maps to the calculated SINR via an AWGN curve approximation:

SINR vs. BLER CURVES


  • At +9.45dB (15Khz SCS): The UE supports Modulation and Coding Scheme (MCS) 9 (16QAM, Coding Rate 0.43).

    Initial BLER≈1.2%⟹Effective Throughput ≈PHY Rate×(1-BLER)=98.8%

  • At +6.44dB  (30Khz SCS): The UE drops down to MCS 5 (QPSK, Coding Rate 0.37) to maintain link stability.

If forced to use MCS 9, the BLER spikes to 38.5%(approx).

Effective Throughput=PHY Rate×(1-0.385)=61.5%


The +3.01dB higher noise floor forces the network to drop to a lower MCS or suffer HARQ retransmissions, drastically reducing effective cell-edge throughput.

5. Network Optimization & Mitigation Strategies

When an operator deploys 30Khz SCS on Mid-band (n77/n78) or 120Khz on mmWave, coverage degradation can be mitigated using specific radio feature configurations.

#

Technique

Mechanism

Effect

1

Supplementary uplink (SUL)

n78 for downlink, n28 for uplink

Recovers uplink coverage lost to mid-band path loss

2

Uplink Tx switching

1T2R → 2T2R uplink

Adds transmit diversity/power to extend uplink reach

3

Massive MIMO beamforming

64T64R array, ~+18 dB gain

Focuses energy toward the UE, extending both DL and UL range

4

Adaptive frame structure

DSUUU slot layout

Rebalances slot allocation toward uplink-heavy traffic

Strategy 1: Supplementary Uplink (SUL) & Coverage Enhancement

SUL pairs a high-band TDD downlink (e.g., n78 at 3.5Ghz with 30Khz SCS) with a sub-1 GHz FDD uplink carrier (e.g., n83 or n28 at 700Mhz with 15Khz SCS).

SUPPLEMENTARY UPLINK (SUL) PATHS

Direction

Band

SCS

Duplex

Function

Downlink

3.5 GHz (n78)

30 kHz

TDD

High-rate DL data

Uplink (SUL)

700 MHz (n28)

15 kHz

FDD

Stable, extended-range UL

Technical Operation:

  1. Downlink: Transmitted on n78 (3.5Ghz) using 30Khz SCS to deliver wideband capacity (100Mhz).

  2. Uplink Switching: When the UE moves to the cell edge and its uplink path loss exceeds a configured threshold (RSRP <-108dBm), the gNB triggers a physical layer Uplink Switch to the SUL carrier (n28, 15Khz SCS).

  3. Gain Realization: Combining lower path loss at 700Mhz (~14dB lower than 3.5Ghz ) with the lower noise floor of  15Khz SCS ( 3dB lower) yields an overall Uplink Link Budget Gain of ~17dB .

Strategy 2: Dual Tx Uplink (2T4R / 2T2R Power Boosting)

Standard UEs operate in 1T4R mode (1 Tx antenna, 4 Rx antennas) limited to +23dBm (200mW) RF power output.

  1T4R Configuration: Tx Power = +23 dBm (200 mW)

  2T4R Dual Tx Mode : Tx Power = +23 dBm + +23 dBm = +26 dBm (400 mW)

  -------------------------------------------------------------------

  Net Uplink Coverage Gain = +3.0 dB (Directly Cancels 30 kHz SCS Penalty)

By enabling 2T4R Uplink Transmit Diversity or dual-layer PUSCH transmission (supported in 3GPP Rel-16):

  • The UE transmits via two independent Power Amplifiers (PAs) simultaneously.

  • Total transmit power increases to +26dBm (400mW).

  • This additional +3.0dB power boost cancels out the +3.01dB  thermal noise floor penalty caused by 30Khz SCS.

Strategy 3: Massive MIMO Beamforming Gain Matching

To compensate for coverage loss when using 30Khz SCS on mid-band spectrum, base stations deploy 64T64R Active Antenna Units (AAUs).


Beamforming Array Gain=10 log10⁡(Nelements)


  • Standard Macro Antenna (4T4R): Array Gain ~6dBi

  • Massive MIMO AAU (64T64R with 192 elements): Array Gain ~18dBi

    Net Coverage Advantage=+18 dBi - 6dBi =+12 dB Gain

This +12dB beamforming gain offsets both the 3.5Ghz  path loss penalty and the 30Khz  SCS noise floor penalty, creating an aligned cell footprint with existing 15Khz  low-band sites.

Strategy 4: Dynamic Slot Format & PUSCH Repetition Tuning

For coverage-constrained cells using 30Khz SCS, operators can optimize radio resource allocations through specific scheduling parameters:

  1. PUSCH Repetitions (3GPP Type A/B Repetition):

    • Configures the gNB to schedule PUSCH transmissions redundantly across 2, 4, or 8 consecutive slots.

    • Gain: Synthesizes slot aggregation at the physical layer, providing an effective energy-per-bit boost (Eb/N0 gain of 10log10(N) ~3dB to 6dB ) that offsets short 30Khz slot durations.

  2. Configuring Extended Cyclic Prefix (ECP):

    • Applied in heavy multipath environments (e.g., steep valleys, high-rise urban canyons).

    • Increases 60Khz SCS CP duration from 1.17us to 4.16us, eliminating multipath-induced ISI floors at the expense of one less symbol per slot (12 symbols vs 14 symbols).

6. Summary Matrix: RF Decision Framework

Use the following framework to select numerology based on carrier frequency, bandwidth, and operational requirements:

Frequency band

Bands

Channel BW

SCS

Deployment domain

Key RF mitigations

Sub-1 GHz

n5, n8, n28, n71

5–20 MHz

15 kHz (μ=0)

Rural / coverage anchor

None — native max coverage

1.7–2.6 GHz

n1, n3, n7, n41

10–40 MHz

15 kHz (μ=0)

FDD capacity / urban macro

Dynamic Spectrum Sharing (DSS), LTE rate matching

3.3–4.9 GHz

n77, n78, n79

40–100 MHz

30 kHz (μ=1)

Mid-band TDD / urban capacity

64T64R massive MIMO, SUL (sub-1 GHz UL), UE 2T4R

24–40 GHz

n257, n258, n260

100–400 MHz

120 kHz (μ=3)

mmWave / FWA / dense hotspot

Narrow analog beamforming, short site spacing (<200 m)

Key Engineering Rules:

  1. Never select 30Khz SCS for sub-2 GHz FDD carriers under 20Mhz bandwidth unless ultra-low air-interface latency (0.5ms) is strictly required, as guard-band overhead and the +3dB  thermal noise penalty reduce overall cell performance.

  2. Always deploy 30Khz  SCS for C-band (n77/n78) deployments over 40Mhz bandwidth. The 30Khz subcarrier spacing provides essential phase noise resilience and keeps baseband FFT sizes manageable (2048-point). Use Massive MIMO beamforming and Dual-Tx (2T4R) to recover the 3dB uplink noise floor difference.

  3. Deploy 120Khz  SCS for FR2 mmWave bands to resist local oscillator phase noise and maintain low latency (0.125ms slots). Compensate for high path loss using narrow high-gain beamforming antenna arrays.

 

References

1.      3GPP TS 38.211 – NR; Physical channels and modulation

2.      3GPP TS 38.101-1 – NR; User Equipment (UE) radio transmission and reception; Part 1: Range 1 Standalone (Sub-7 GHz)

3.      3GPP TS 38.104 – NR; Base Station (BS) radio transmission and reception

4.      3GPP TS 38.214 – NR; Physical layer procedures for data

5.      GSMA – 5G Spectrum Guide & Mid-Band Deployment Recommendations, https://www.gsma.com/spectrum/5g-spectrum-guide/

6.      5G NR Flexible Frame Structure & Numerology Design, https://www.qualcomm.com/research/5g

7.      Ericsson Technology Review – 5G NR Physical Layer & Coverage Enhancement Techniques, https://www.ericsson.com/en/reports-and-papers/ericsson-technology-review

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