What is 5G NR numerology and why are there multiple subcarrier spacings?

5G NR defines multiple numerologies (subcarrier spacings) to handle different deployment scenarios. At sub-6 GHz (macro cells with large delay spreads), 15 kHz or 30 kHz spacing is used with long CP durations (4.69 or 2.34 microseconds) to handle multipath from distant reflectors. At mmWave (28 GHz, 39 GHz), the delay spread is shorter but the Doppler shift is higher (due to higher carrier frequency), so 120 kHz or 240 kHz spacing is used with shorter symbols (8.33 or 4.17 microseconds) that are more robust to phase rotation from Doppler. Wider subcarrier spacing also means wider bandwidth per numerology: 120 kHz spacing with 3300 subcarriers gives 396 MHz channel bandwidth, enabling the multi-Gbps peak rates that 5G promises.

Why does OFDM have high PAPR?

An OFDM signal is the sum of hundreds or thousands of independently modulated subcarriers. When many subcarriers happen to align in phase at the same instant, their voltages add constructively, producing a peak that is much higher than the average. For N subcarriers, the theoretical maximum PAPR is 10 log10(N). With 1024 subcarriers: PAPR can reach 30 dB, though statistically peaks above 10 to 12 dB are rare. This high PAPR requires the PA to operate well below its compression point (backed off), reducing efficiency. Techniques to reduce PAPR include clipping (with filtering to remove out-of-band distortion), tone reservation (dedicating some subcarriers to peak cancellation), and DFT-spread OFDM (used in 5G uplink) which pre-codes the data to reduce peak excursions.

Signal Processing

OFDM

Q: How does OFDM handle multipath?

In a wideband single-carrier system, a reflected signal arriving 1 microsecond late causes severe inter-symbol interference if the symbol duration is also around 1 microsecond (as it would be at 1 Mbps symbol rate). OFDM solves this by dividing the channel into N narrowband subcarriers, each with N times longer symbol duration. With 1024 subcarriers in a 20 MHz channel, each subcarrier is 19.5 kHz wide with a symbol duration of 51.2 microseconds. A 1-microsecond delay spread is only 2 percent of the symbol duration, not 100 percent. The cyclic prefix (CP) is a copy of the end of the symbol prepended to the beginning. If the CP duration exceeds the maximum delay spread of the channel, all multipath echoes arrive within the CP window and the useful symbol period remains interference-free.

Orthogonal Frequency-Division Multiplexing

A 20 MHz WiFi channel carries data at 1.2 Gbps using WiFi 6. A single carrier at that bandwidth would need symbol durations of less than 1 microsecond, making it devastated by indoor multipath reflections arriving 50 to 200 nanoseconds late. OFDM solves this by splitting the 20 MHz channel into 256 subcarriers, each only 78.125 kHz wide. Each subcarrier's symbol lasts 12.8 microseconds: long enough that a 200 ns multipath echo is just 1.6% of the symbol, causing negligible interference. The cyclic prefix absorbs the remaining distortion. The IFFT at the transmitter and FFT at the receiver implement this entire scheme with a single matrix operation, making 256 parallel narrowband channels as computationally cheap as one wideband channel.

Category: Signal Processing

Implementation: IFFT (TX) / FFT (RX)

Challenge: High PAPR (8 to 12 dB)

OFDM Parameters Across Standards

Standard	Subcarrier Δf	FFT Size	Symbol Duration	CP Duration	Max BW
WiFi 6 (802.11ax)	78.125 kHz	256 / 512 / 1024 / 2048	12.8 μs	0.8 / 1.6 / 3.2 μs	160 MHz
LTE (4G)	15 kHz	128 to 2048	66.7 μs	4.69 / 16.67 μs	20 MHz
5G NR μ=0	15 kHz	Up to 4096	66.7 μs	4.69 μs	50 MHz
5G NR μ=1	30 kHz	Up to 4096	33.3 μs	2.34 μs	100 MHz
5G NR μ=3	120 kHz	Up to 4096	8.33 μs	0.59 μs	400 MHz
DVB-T2	0.558 to 4.46 kHz	1k to 32k	224 μs to 3.6 ms	1/128 to 1/4	8 MHz

Subcarrier spacing & symbol duration:
T_symbol = 1 / Δf
15 kHz: T = 66.7 μs. 120 kHz: T = 8.33 μs

CP requirement:
T_CP > τ_max (max channel delay spread)

Theoretical max PAPR:
PAPR_max = 10·log₁₀(N) dB
256 subcarriers: 24 dB max (typical: 8 to 10 dB at 0.1% probability)

Common Questions

Frequently Asked Questions

How does OFDM handle multipath?

Divides the channel into N narrow subcarriers, each with N× longer symbol duration. Multipath echoes become a tiny fraction of the symbol. Cyclic prefix absorbs remaining ISI. If CP > max delay spread, zero intersymbol interference.

Why multiple 5G NR numerologies?

Sub-6 GHz: large delay spread needs longer CP (15/30 kHz spacing). mmWave: shorter delay but higher Doppler needs shorter symbols (120/240 kHz). Wider spacing also enables wider channels (120 kHz × 3300 = 396 MHz = multi-Gbps).

Why high PAPR?

Sum of N independent subcarriers. Occasional phase alignment creates peaks. PAPR up to 10·log(N). Mitigation: clipping+filtering, tone reservation, DFT-spread OFDM (5G uplink). PA must back off 8 to 10 dB, reducing efficiency.

Related Terms

← Notch Filter Oscillator →

Waveform Design

OFDM Parameter Calculator

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