5G NR Frame Structure
Numerology, Slots & Timing Scaling Forensics
1. The Mathematical Foundation: Numerology () Scaling
The defining characteristic of 5G NR is Flexible Numerology. In legacy 4G LTE, the Subcarrier Spacing (SCS) was locked at . This was optimal for sub-3GHz coverage but fundamentally limited for high-frequency or low-latency operations. 5G NR introduces the concept of an exponential scaling factor .
The Scaling Law
As increases, the subcarrier spacing doubles, and the symbol duration shrinks by half. This relationship is governed by the Inverse Fourier Transform physics: .
| Index () | SCS () | Slot Time | Primary Spectrum | Use Case |
|---|---|---|---|---|
| 0 | 15 | 1000 μs | Sub-3 GHz | Coverage / FDD Coexistence |
| 1 | 30 | 500 μs | 3.5 GHz (n78) | eMBB Standard |
| 2 | 60 | 250 μs | 5 GHz / URLLC | Industrial Automation |
| 3 | 120 | 125 μs | 28 GHz (FR2-1) | Fixed Wireless Access |
| 4 | 240 | 62.5 μs | 71 GHz (FR2-2) | Intra-Data Center |
2. The Resource Grid Physics: RE, PRB & REG
The 5G NR resource grid is a 2D mapping of time and frequency. Every unit of allocation must be precisely defined to ensure orthogonality and prevent inter-carrier interference.
Resource Element (RE)
The smallest physical unit. 1 Subcarrier x 1 OFDM Symbol. In a 256-QAM scheme, a single RE carries 8 bits of information.
RE = (k, l) \quad \text{where } k \in \text{Freq}, l \in \text{Time}Physical Resource Block (PRB)
Consists of 12 consecutive subcarriers. Unlike LTE, there is no fixed time-domain length for a PRB; it spans the duration of the allocation (typically 1 slot).
PRB_{BW} = 12 \cdot 15 \cdot 2^\mu\,\text{kHz}For a carrier at (30kHz), the number of PRBs is calculated as:
Flexible Numerology Simulator
Subframe (1ms) Slot Scaling Analysis
Scientific Context: As Carrier Spacing (SCS) doubles, the slot duration halves. In mmWave ($\mu=3$), we have 8 slots per millisecond, allowing the gNodeB to make scheduling decisions every 125 microseconds—essential for self-driving vehicles and high-speed industrial robotics.
Fig 2.1: Dynamic 5G NR Slot Structure Simulation
3. Channel Coding Evolution: LDPC & Polar Codes
5G NR abandons the Turbo Codes used in 3G/4G in favor of a more modern, hardware-parallelizable coding suite. This shift was necessary to handle the 20Gbps+ peak rates of 5G.
LDPC for Data (PDSCH/PUSCH)
Low-Density Parity-Check (LDPC) codes are used for all shared data channels. Unlike Turbo codes, which are inherently serial, LDPC decoding can be fully parallelized in silicon (ASICs). 3GPP defines two base graphs (BG1 for large blocks/high rates, BG2 for small blocks/low rates) to optimize the parity matrix.
Polar Codes for Control (PDCCH/PBCH)
For short blocks like control signaling, Polar codes are superior. They "polarize" the bit channels into perfectly reliable or completely unreliable states. By only transmitting information on the "frozen" reliable channels, Polar codes can reach the Shannon Limit for short block lengths.
4. Synchronization & Initial Access: The SSB Beam-Sweep
In a beamformed network, a base station doesn't just broadcast; it "sweeps." The Synchronization Signal Block (SSB) is the mechanism for this. An SSB consists of the PSS, SSS, and PBCH (Master Information Block).
The SSB Burst Pattern
Up to number of SSBs are transmitted in a window. Each SSB is mapped to a different spatial beam.
- Sub-3 GHzL = 4 beams
- 3-6 GHzL = 8 beams
- mmWave (FR2)L = 64 beams
A UE measures the RSRP of each beam and reports back the best SSB index during the RACH procedure, allowing the gNodeB to "lock on" to the user's location.
5. Bandwidth Parts (BWP): Dynamic Power Forensics
In LTE, devices had to monitor the entire carrier. In 5G, with 400MHz carriers, this would drain a battery in minutes. Bandwidth Parts (BWP) solve this by allowing the UE to see only a slice of the spectrum.
Initial BWP
Used for RACH and RRC connection setup. Usually narrow (e.g., 20MHz) for compatibility.
Active BWP
The current operating slice. Can be switched via DCI signaling in under .
Default BWP
The "fallback" slice. If no data activity occurs, the UE retunes here to save energy.
6. HARQ Timing Forensics: K0, K1, K2 Logic
Timing in 5G is no longer deterministic. It is Dynamic. The relationship between control, data, and feedback is defined by three primary offsets.
DCI to DL Data
Offset between PDCCH (Control) and PDSCH (Data). In high-performance 5G, (Self-contained slot).
DL Data to ACK/NACK
The "Processing Budget." Defines how many slots the UE has to decode data and send feedback on the PUCCH.
DCI to UL Data
Offset between the UL Grant and the actual PUSCH transmission from the UE.
7. TDD Slot Formats: The 61 Flavors
5G NR doesn't just have UL/DL; it has Flexible (F) symbols. This allows for Dynamic TDD, where a cell can change its uplink/downlink ratio based on demand.
8. Phase Tracking Reference Signals (PTRS)
At high frequencies (mmWave), Phase Noise becomes a critical bottleneck. PTRS is a new reference signal introduced in 5G NR to track the common phase error (CPE) in the time domain. Unlike DMRS which is sparse in time, PTRS is inserted into every OFDM symbol to allow the receiver to compensate for oscillator jitter.