Numerology in the context of 5G refers to the various configurations of subcarrier spacing and other parameters that are designed to meet different performance and deployment requirements. In 5G, the term "numerology" encapsulates the flexibility and scalability of the system, allowing it to cater to a wide range of use cases from enhanced mobile broadband (eMBB) to ultra-reliable low latency communication (URLLC) and massive machine type communication (mMTC).
5G Numerology Overview
The different numerologies in 5G are primarily characterized by their subcarrier spacing (Δ𝑓), which is a critical factor in defining the symbol duration and cyclic prefix length. These parameters are key to optimizing performance for different scenarios.
Subcarrier spacing is the frequency spacing between adjacent subcarriers in an orthogonal frequency-division multiplexing (OFDM) system. The subcarrier spacing determines the bandwidth of each subcarrier and impacts the overall bandwidth, latency, and performance of the wireless system.
The subcarrier spacing is given by the formula: Δ𝑓=2𝑛×15kHz, where 𝑛 is an integer.
The 5G standard defines multiple numerologies, each suited to specific deployment and service requirements. The most common numerologies in 5G include:
5G technology introduces a flexible framework for designing systems with various subcarrier spacings and bandwidths, known as numerology. This flexibility allows 5G to cater to a wide range of deployment scenarios, from low-frequency bands (FR1) to high-frequency millimeter-wave bands (FR2).
Basic System Model for 5G Communication
The basic 5G communication system involves a transmitter and a receiver. Here's how they work:
Transmitter:
OFDM Modulation using IFFT: Converts data into a form suitable for transmission.
Cyclic Prefix (CP) Insertion: Adds a small section of data at the beginning of each symbol to prevent data overlap and interference.
Receiver:
Cyclic Prefix Removal: Removes the added cyclic prefix.
OFDM Demodulation using FFT: Converts the received data back to its original form.
Mathematical Representation
For each data subcarrier, the system can be expressed as:
𝑏𝑖=ℎ𝑖𝑎𝑖+𝑛𝑖
Where:
ℎ𝑖: Channel effect on the signal.
𝑎𝑖: Transmitted signal.
𝑛𝑖: Noise.
System Dimensioning for 5G-NR (25 MHz)
Baseband Bandwidth
Total bandwidth: 25 MHz
Usable bandwidth: 24.75 MHz
Guard band: 0.25 MHz
This is the total frequency range the system can use for communication. Out of the 25 MHz total bandwidth, 24.75 MHz is usable, with a 0.25 MHz guard band to avoid interference.
Subcarrier Spacing
Subcarrier spacing: 30 kHz
Each subcarrier is spaced 30 kHz apart, which determines how data is divided across the available bandwidth.
Total Subcarriers Required
To find the number of subcarriers, divide the usable bandwidth by the subcarrier spacing:
𝑁𝑐=24.75 MHz/30 kHz = 825
FFT Size
The FFT size is chosen based on the total number of subcarriers and is usually a power of 2 for computational efficiency. Here, it's 1024. 𝑁 = 1024
OFDM Symbol Duration
The duration of each OFDM symbol is the inverse of the subcarrier spacing:
𝑇𝑢=1/30 kHz ≈33.3 𝜇𝑠
Sampling Rate
The sampling rate is the product of the FFT size and subcarrier spacing:
𝑓𝑠=1024×30 kHz =30.72 MHz
This is the rate at which the system samples the signal.
What is Phase Noise?
Phase noise refers to small, rapid variations in the phase of a signal caused by imperfections in the local oscillator or other components of the transmitter and receiver. These variations appear as noise in the frequency domain and can disrupt the precise timing of the signal.
Impact on OFDM Systems
In Orthogonal Frequency-Division Multiplexing (OFDM), phase noise is particularly detrimental because OFDM relies on maintaining precise phase relationships between subcarriers. Here’s how phase noise affects OFDM systems:
Signal Jitter: Phase noise manifests as jitter or fluctuations in the signal phase, which leads to errors during demodulation. This can cause a significant degradation in the quality of the received signal.
Inter-Carrier Interference (ICI): Phase noise can cause interference between subcarriers, known as Inter-Carrier Interference (ICI). ICI reduces the orthogonality between subcarriers, making it harder to distinguish between them.
The flexibility in 5G numerology allows the technology to be highly adaptable, catering to a wide range of use cases and deployment scenarios. By selecting appropriate numerologies, network operators can optimize their systems for performance, latency, and coverage, thereby meeting the diverse requirements of modern wireless communication.
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