RF Theory › OFDM & 5G NR

OFDM & 5G NR

OFDM is the modulation underlying WiFi, LTE, and 5G NR. Understanding subcarrier orthogonality, cyclic prefix, PAPR, and the 5G numerology framework is essential for any RF engineer working on modern wireless systems.

01 — Motivation

Why OFDM?

OFDM solves inter-symbol interference (ISI) in wideband channels by splitting the channel into hundreds of narrow subcarriers, each experiencing flat (non-selective) fading — allowing simple one-tap equalisation per subcarrier.

OFDM Key Advantage
If subcarrier spacing Δf ≪ coherence bandwidth Bcoh = 1/(5·τrms)
→ each subcarrier sees flat fading → trivial 1-tap equalisation

Example: Urban τrms=1 μs → Bcoh=200 kHz
5G NR 15 kHz SCS (200 kHz ≫ 15 kHz) → each SC is flat faded ✓
02 — Orthogonality

Subcarrier Orthogonality

Subcarriers are orthogonal when spaced at Δf = 1/Tu — at the peak of each subcarrier, all others are exactly zero. This is implemented using IFFT at the transmitter and FFT at the receiver.

Figure 1 — OFDM subcarrier spectra (5 shown). Each subcarrier is a sinc function. At each subcarrier peak, all others are zero — orthogonality ensures no inter-carrier interference.

IFFT / FFT Implementation

OFDM IFFT / FFT
TX: x[n] = (1/N)·Σ X[k]·ej2πkn/N   (IFFT, N-point)
RX: X̂[k] = Σ y[n]·e−j2πkn/N   (FFT, N-point)

Δf = 1/Tu = BW/N  ·  Tu = N/BW = useful symbol duration
03 — Cyclic Prefix

Cyclic Prefix

The CP copies the last N_cp samples of each OFDM symbol and prepends them. As long as T_cp ≥ τ_max (maximum channel delay spread), there is zero ISI and zero ICI. The CP converts linear convolution into circular convolution — exactly what the FFT assumes.

Cyclic Prefix
Tcp ≥ τmax  ·  CP overhead = Tcp/(Tu+Tcp) × 100%
5G NR Normal CP (15 kHz SCS): Tcp = 4.69 μs → 6.7% overhead
Extended CP: Tcp = 16.67 μs — for large cells / high delay spread

CP Length vs Environment

EnvironmentTypical τmax5G NR SCS
Indoor office0.1–0.3 μs60 kHz (T_cp=1.17 μs) ✓
Urban macro1–3 μs15 kHz (T_cp=4.69 μs) ✓
Rural / large cell3–10 μs15 kHz Extended CP ✓
mmWave indoor0.01–0.05 μs120 kHz (T_cp=0.29 μs) ✓
CP eats throughput: Normal CP is 6.7% overhead for 15 kHz SCS. Wider SCS (60/120 kHz) has shorter absolute CP but smaller relative overhead — mmWave 5G has lower relative CP overhead.
04 — PAPR

The PAPR Problem

When N subcarriers align in phase, their voltages add — peak power is N× average. This forces PAs to back off from P1dB, reducing efficiency.

PAPR
PAPR = Ppeak/Pavg = max|x[n]|² / E[|x[n]|²]
Statistical PAPR (99.9% CCDF): ≈ 8–12 dB for large N
LTE/5G NR: PAPR ≈ 10–12 dB  ·  Single carrier QPSK: PAPR ≈ 0–3.5 dB

PAPR Reduction Techniques

TechniquePAPR ReductionUsed In
Clipping & Filtering3–5 dBWiFi APs, small cells
DPD (Digital Pre-Distortion)Allows 3–5 dB less back-off5G base stations
DFT-s-OFDM (SC-FDMA)PAPR ≈ 3–4 dB vs 10 dB OFDM5G NR UL, LTE UL
5G UL uses DFT-s-OFDM — reduces PAPR to ~3 dB, extending handset battery life. Downlink uses CP-OFDM since base station PA efficiency is managed via DPD.
05 — 5G NR Numerology

5G NR Numerology (μ)

5G NR uses scalable subcarrier spacing: Δf = 2μ × 15 kHz. Different μ values are optimised for different frequency ranges and environments.

μSCS (kHz)Tu (μs)Normal CP (μs)Slots/subframeUse Case
01566.74.691FR1, large cells (like LTE)
13033.32.342FR1 standard urban
26016.71.174FR1 and NR-U unlicensed
31208.330.598FR2 mmWave
42404.170.2916FR2 SSB reference signals only

Resource Grid

5G NR Resource Grid Hierarchy
RE = 1 subcarrier × 1 OFDM symbol (smallest unit)
RB = 12 subcarriers × 1 slot in frequency
Slot = 14 OFDM symbols (normal CP)
Subframe = 1 ms = 2μ slots  ·  Frame = 10 ms

100 MHz at μ=1 (30 kHz SCS): 275 RBs → 3300 active SCs
Peak DL (4 layers, 256-QAM): ≈ 3.2 Gbps

FR1 vs FR2

FeatureFR1 (sub-6 GHz)FR2 (mmWave, 24–52 GHz)
Max channel BW100 MHz400 MHz
SCS15, 30, 60 kHz60, 120 kHz
Antenna2–8 port MIMO64–256+ element massive MIMO
Peak DL speed~1–2 Gbps~4–10 Gbps
06 — RF Requirements

5G RF Chain Requirements

ParameterLTE 20 MHz5G NR FR1 100 MHz5G NR FR2 400 MHz
Noise floor (NF=7 dB)−94 dBm−87 dBm−81 dBm
ADC sample rate~30.72 Msps~245.76 Msps~983 Msps
LO phase noise @ 1 MHz−135 dBc/Hz−130 dBc/Hz−110 dBc/Hz
Wider BW = worse sensitivity: 5G NR 100 MHz noise floor is 7 dB higher than LTE 20 MHz. 5G compensates with massive MIMO beamforming gain (10–20 dB) and denser cells — not by improving NF.
07 — Massive MIMO

Massive MIMO & Beamforming

Beamforming Gain
Array gain = N (linear) = 10·log₁₀(N) dB for N-element coherent array
Beam HPBW ≈ 0.886·λ/(N·d) radians

64 elements: gain = +18 dB — offsets 18 dB mmWave path loss vs 3.5 GHz
HPBW at 28 GHz, N=64, d=λ/2: 2.8° pencil beam
Massive MIMO is why 5G works at mmWave. 28 GHz vs 3.5 GHz path loss is ~18 dB worse at same distance. A 64-element UE array recovers exactly 18 dB through beamforming.
Antenna Array Theory → Modulation & IQ → Phase Noise → RF Link Budget →
08 — Design Rules

OFDM / 5G Thumb Rules

#RuleConsequence
1Subcarrier spacing Δf = 1/TuWider SCS = shorter symbol = better for high Doppler and mmWave
2CP must exceed max delay spread τmaxUnder-sized CP → ICI and ISI, uncorrectable
3OFDM PAPR ≈ 10–12 dBPA back-off required; UL uses DFT-s-OFDM (~3 dB PAPR)
410× wider BW = 10 dB more noise5G 100 MHz is 7 dB noisier than LTE 20 MHz
5N elements → 10·log(N) dB array gain64 elements = 18 dB — makes mmWave viable
65G NR 1 RB = 12 subcarriers × 14 symbols275 RBs in 100 MHz at 30 kHz SCS
7EVM budget: phase noise + nonlinearity + IQ imbalanceFor 256-QAM (3.5%): allocate ≤1.5% each to main contributors

OFDM and 5G NR Physical Layer Fundamentals

Orthogonal Frequency Division Multiplexing (OFDM) is the foundation of every modern wireless standard — WiFi 4/5/6/6E/7, LTE, and 5G NR all use OFDM or a derivative. Splitting a wide channel into many narrow orthogonal subcarriers eliminates inter-symbol interference without complex time-domain equalisers.

5G NR Numerology — Why Scalable SCS Matters

5G NR introduces flexible numerology where subcarrier spacing scales as 15×2ᵘ kHz. At sub-6 GHz (FR1), 15 kHz and 30 kHz SCS provide the long symbol duration needed for urban macro cells. At mmWave (FR2), 120 kHz SCS gives shorter symbols — needed because mmWave delay spreads are shorter (indoor τ_max < 100 ns) but Doppler and phase noise are worse.

PAPR — The RF Engineer's Main OFDM Concern

OFDM's high PAPR (10–12 dB) forces PAs to operate at large back-off, drastically reducing efficiency. Digital pre-distortion (DPD) linearises the PA, allowing 3–5 dB less back-off. The uplink avoids this with DFT-spread OFDM (SC-FDMA), reducing UE handset PAPR to approximately 3 dB.