5G NR Numerology: Understanding Subcarrier Spacing and Resource Elements

The provided source material focuses exclusively on technical aspects of 5G New Radio (NR) numerology within the telecommunications industry. It defines numerology as a set of configurable parameters—specifically subcarrier spacing, cyclic prefix length, slot duration, and frame structure—that define the physical layer waveform characteristics for wireless communication. Unlike previous generations like LTE, which used a fixed numerology, 5G NR introduces multiple numerologies to support a wide variety of services, frequency bands, and deployment scenarios.

This flexibility is essential for supporting diverse use cases, ranging from enhanced mobile broadband (eMBB) and ultra-reliable low-latency communications (URLLC) to massive machine-type communications (mMTC). The source material details how numerology allows the network to adapt to specific application requirements, such as low power for IoT devices or high data rates for video streaming and virtual reality.

Defining 5G NR Numerology

Numerology in 5G New Radio (NR) is defined by the subcarrier spacing in the frequency domain. According to 3GPP TS 38.211, there are five distinct numerologies specified, each corresponding to a specific subcarrier spacing (Δf). The subcarrier spacing is calculated using the formula:

Δf = 15 kHz × 2μ

Where μ (mu) represents the numerology index, taking values of 0, 1, 2, 3, or 4 depending on the frequency of operation and the specific use case.

The introduction of multiple numerologies allows different parts of the network, or even different users within the same cell, to use different configurations simultaneously. This is a fundamental departure from LTE, which used a fixed 15 kHz subcarrier spacing. The ability to adjust subcarrier spacing enables 5G to efficiently handle low-latency high-throughput communications as well as long-range, low-power links required for IoT applications.

Subcarrier Spacing and Resource Elements

A Resource Element (RE) is the fundamental unit of the physical layer grid, defined by one subcarrier in the frequency domain and one symbol in the time domain. The subcarrier spacing directly determines the bandwidth of the Resource Element. Conversely, the duration of the symbol (excluding the cyclic prefix) is inversely proportional to the subcarrier spacing; higher subcarrier spacing results in shorter symbol duration.

Multiple subcarriers in the frequency domain and multiple symbols in the time domain create a grid of Resource Elements. This grid is fundamental to mapping physical channels and signals. Orthogonal Frequency Division Multiplexing (OFDM) is the underlying technology that divides the configured spectrum into numerous closely spaced subcarriers that can communicate at the same time. These subcarriers are orthogonal (non-overlapping), providing high spectral efficiency and strong multipath fading mitigation.

The Five Numerologies and Their Characteristics

The source material outlines five specific numerologies, each tailored for specific frequency ranges and application requirements. These configurations impact bandwidth, symbol duration, cyclic prefix length, and slot duration.

Numerology μ = 0

Subcarrier Spacing: 15 kHz
Symbol Duration: 66.7 μs
Cyclic Prefix Duration: 4.7 μs
Slot Duration: 1.0 ms
Typical Use Case: Compatible with LTE, low frequency bands (FR1). This configuration supports one slot per subframe.

Numerology μ = 1

Subcarrier Spacing: 30 kHz
Symbol Duration: 33.3 μs
Cyclic Prefix Duration: 2.3 μs
Slot Duration: 0.5 ms
Typical Use Case: Sub-6 GHz (FR1), Enhanced Mobile Broadband (eMBB). This configuration supports two slots per subframe.

Numerology μ = 2

Subcarrier Spacing: 60 kHz
Symbol Duration: 16.7 μs
Cyclic Prefix Duration: 1.2 μs (Normal CP) or 4.13 μs (Extended CP)
Slot Duration: 0.25 ms
Typical Use Case: mmWave (FR2), low latency. This configuration supports four slots per subframe. Notably, 60 kHz spacing supports both normal and extended CP types.

Numerology μ = 3

Subcarrier Spacing: 120 kHz
Symbol Duration: 8.33 μs
Cyclic Prefix Duration: 0.59 μs
Slot Duration: 0.125 ms
Typical Use Case: mmWave (FR2), ultra-low latency (URLLC). This configuration supports eight slots per subframe.

Numerology μ = 4

Subcarrier Spacing: 240 kHz
Symbol Duration: 4.17 μs
Cyclic Prefix Duration: 0.29 μs
Slot Duration: 0.0625 ms
Typical Use Case: Very high frequency mmWave (FR2). This configuration supports sixteen slots per subframe.

Impact on Frame Structure and Slot Duration

The frame structure in 5G NR is defined by a radio frame duration of 10 ms. This frame consists of 10 subframes, each having a duration of 1 ms, similar to LTE. However, the composition of these subframes varies based on the numerology.

Each subframe consists of slots. The number of slots per subframe is determined by the numerology index μ. Specifically, there are 2μ slots per subframe. Consequently, the number of slots per frame is ten times the number of slots per subframe. For example, with μ = 2 (60 kHz), there are 4 slots per subframe, resulting in 40 slots per frame.

The slot duration is inversely related to the subcarrier spacing. As the subcarrier spacing increases, the slot duration becomes shorter. This shorter slot duration is critical for enabling lower latency transmissions, allowing 5G NR to efficiently support both high-throughput and low-latency applications.

Each slot can have either 14 OFDM symbols (normal CP) or 12 OFDM symbols (extended CP), with the exception of 60 kHz spacing which supports both types. All subcarrier spacing options generally support 14 OFDM symbols for normal CP. The extended CP is used in environments with significant delay spread to mitigate inter-symbol interference.

Cyclic Prefix and OFDM Enhancements

The cyclic prefix (CP) is a guard interval added to the beginning of each symbol to prevent inter-symbol interference (ISI) caused by multipath propagation. In 5G NR, the length of the cyclic prefix can be adjusted to suit different delay spreads and mobility scenarios. There are normal and extended cyclic prefix options. The extended version is utilized in environments with significant delay spread.

5G NR enhances OFDM to meet the challenges of a wide variety of deployment scenarios and frequency ranges. The benefits of using OFDM in 5G NR include:

High Spectral Efficiency: Minimal guard bands are required between subcarriers.
Multipath Resilience: Manages the effects of inter-symbol interference effectively.
Flexible Configuration: The subcarrier spacing (Δf) can be adjusted as detailed above.
Ability to Handle Wide Bandwidths: Functions well across both FR1 (sub-6 GHz) and FR2 (mmWave) systems.

Frequency Ranges and Deployment

5G NR is designed to support deployment across a wide range of frequencies. The 3GPP has defined two operating frequency ranges:

FR1 (Frequency Range 1): Corresponds to 450 MHz – 6,000 MHz.
FR2 (Frequency Range 2): Corresponds to 24,250 MHz – 52,600 MHz (mmWave).

The two frequency ranges vary significantly in characteristics due to the large gap in frequencies. Therefore, requirements for each FR are defined separately within the standards. 4G LTE standards were defined only for operating band FR1 under 6,000 MHz frequencies. The multiple numerologies in 5G allow it to operate efficiently in both ranges, supporting services from holograms and automated factories to self-driving cars.

Resource Element Mapping and Bandwidth

In 5G NR, 4096 FFT points are used, consisting of 3300 data subcarriers for a maximum bandwidth of 400 MHz. The relationship between subcarrier spacing, the number of Resource Blocks (RBs), and the channel bandwidth is a key aspect of the system design. A Resource Block consists of multiple subcarriers in frequency and symbols in time.

The flexibility of numerologies enables 5G to be efficiently used across different bandwidths and service requirements. By varying the subcarrier spacing, the system can optimize for either high data rates or long-range, low-power communication.

Comparison with LTE

The primary difference between 5G NR and LTE regarding numerology is the flexibility. LTE uses a fixed numerology with 15 kHz subcarrier spacing. 5G NR introduces the concept of multiple numerologies, allowing simultaneous use of different configurations within the same network. This allows 5G to support a much broader range of services and deployment scenarios than was possible with LTE.

The source material emphasizes that numerology is a fundamental concept in 5G NR that enables the network to be highly flexible and efficient. It is one of the key innovations that distinguishes 5G from previous generations of mobile technology. The ability to scale subcarrier spacing, slot duration, and cyclic prefix length allows the network to dynamically schedule resources and meet the specific demands of diverse applications, from low-power IoT sensors to ultra-fast mobile broadband and low-latency industrial applications.

Conclusion

The provided source material offers a detailed technical explanation of 5G NR numerology, focusing entirely on its definition, calculation, and application within telecommunications. It highlights the shift from fixed to flexible numerology as a cornerstone of 5G's ability to support diverse services. The five distinct configurations (μ = 0 to 4) allow for tailored subcarrier spacing, symbol duration, and slot structure to meet the specific needs of different frequency ranges (FR1 and FR2) and use cases (eMBB, URLLC, mMTC). This flexibility, built on an enhanced OFDM framework, provides the high spectral efficiency, multipath resilience, and low-latency capabilities required for next-generation wireless communication.