OFDM Numerology

5G NR defines a scalable OFDM numerology based on the formula Δf = 15 × 2^μ kHz, where μ is the numerology index (0–4). This creates subcarrier spacings of 15, 30, 60, 120, and 240 kHz.

• μ=0 (15 kHz): Baseline numerology, identical to LTE, for sub-6 GHz macro coverage.
• μ=1 (30 kHz): Balanced option for urban deployments and initial 5G NR rollouts.
• μ=2 (60 kHz): Enables low-latency URLLC services with shorter symbol duration.
• μ=3 (120 kHz): Designed for mmWave bands (FR2) above 24 GHz.
• μ=4 (240 kHz): Reserved for very high mmWave bands with extreme bandwidths.

Larger subcarrier spacing reduces OFDM symbol duration proportionally, providing robustness against phase noise at higher carrier frequencies.

The cyclic prefix (CP) duration scales inversely with subcarrier spacing to maintain multipath resilience. 5G NR supports two CP types:

• Normal CP: The default for all numerologies. At 15 kHz, the CP is 4.7 μs (symbol 0: 5.2 μs), sufficient for typical urban delay spreads up to ~1.4 km.
• Extended CP: Available only for μ=2 (60 kHz), providing a longer guard interval of 16.67 μs for high-dispersive environments like large-cell rural deployments or broadcast services.

The CP overhead remains constant across numerologies at approximately 7%, preserving spectral efficiency while adapting to channel conditions.

Numerology directly determines the slot duration and the number of slots per subframe:

• A slot always contains 14 OFDM symbols (normal CP) or 12 symbols (extended CP).
• At μ=0 (15 kHz): 1 slot/subframe, slot duration = 1 ms.
• At μ=1 (30 kHz): 2 slots/subframe, slot duration = 0.5 ms.
• At μ=2 (60 kHz): 4 slots/subframe, slot duration = 0.25 ms.
• At μ=3 (120 kHz): 8 slots/subframe, slot duration = 0.125 ms.

Mini-slots (2, 4, or 7 OFDM symbols) enable ultra-low-latency transmissions by preempting ongoing slot-based scheduling, critical for URLLC services requiring sub-millisecond round-trip times.

Numerology selection is constrained by the operating frequency range to balance performance and implementation complexity:

• FR1 (410–7125 MHz): Supports μ=0, 1, 2. The 15 kHz and 30 kHz spacings dominate commercial deployments, with 60 kHz used for specific low-latency applications.
• FR2 (24.25–52.6 GHz): Supports μ=2, 3. The 120 kHz spacing is standard for mmWave, providing resilience against phase noise from high-frequency local oscillators.
• FR2-2 (52.6–71 GHz): Supports μ=3, 4. The 240 kHz spacing addresses extreme phase noise and enables bandwidths up to 400 MHz per component carrier.

This mapping ensures that subcarrier spacing is sufficiently wide relative to the Doppler shift and phase noise experienced at each band.

Numerology enables dynamic Bandwidth Part (BWP) switching, a key 5G NR power-saving feature:

• A UE can be configured with up to 4 BWPs per serving cell, each with a different numerology and bandwidth.
• The network can switch the active BWP via DCI signaling or timers, adapting the UE's numerology to instantaneous traffic demands.
• Example: A UE monitoring a wide BWP at 30 kHz for high-throughput downloads can switch to a narrow BWP at 15 kHz during inactivity, reducing baseband processing power.

BWP adaptation decouples the UE's instantaneous bandwidth from the carrier bandwidth, allowing efficient support of diverse device capabilities within a single wideband carrier.

5G NR supports mixed numerology transmission on the same carrier, enabling simultaneous services with different latency and throughput requirements:

• Different BWPs or component carriers can operate with independent numerologies, sharing the same RF front-end.
• Guard bands between numerologies prevent inter-numerology interference caused by the loss of orthogonality between subcarriers with different spacings.
• In the time domain, slot boundaries align at the 1 ms subframe level across all numerologies, simplifying scheduling and enabling TDD cross-link interference management.

This flexibility allows a single gNB to concurrently serve eMBB (15/30 kHz), URLLC (60 kHz), and mMTC (15 kHz) traffic classes.

A blind OFDM detection method that exploits the autocorrelation introduced by the cyclic prefix. By correlating the received signal with a delayed copy of itself at the useful symbol length, the receiver can estimate symbol timing and fractional carrier frequency offset without prior knowledge of the numerology.

• Directly leverages the CP duration defined by the numerology
• Normal CP vs. Extended CP produce distinct correlation lag profiles
• Foundational technique for blind parameter estimation