DFT-s-OFDM vs OTFS: The Incumbent Comparison

The Incumbent's Strongest Card

5G NR uses two waveforms: CP-OFDM for the downlink, DFT-spread OFDM (DFT-s-OFDM) for the uplink. DFT-s-OFDM was chosen for the uplink because it has lower peak-to-average power ratio (PAPR) than CP-OFDM — crucial for battery-powered UEs transmitting at their PA saturation. Any 6G waveform competing to replace DFT-s- OFDM must match or beat its PAPR while improving on its mobility performance. OTFS offers comparable PAPR and substantially better mobility — this section makes the comparison quantitative.

Definition:
DFT-Spread OFDM (DFT-s-OFDM)

DFT-s-OFDM is OFDM preceded by a DFT precoding stage: $\mathbf{x}_{\mathrm{TF}} \;=\; \mathbf{U}_{\mathrm{DFT}}\, \mathbf{s}, \qquad \mathbf{x}_{\mathrm{time}} \;=\; \mathbf{F}^{-1}_{N} (\mathbf{x}_{\mathrm{TF}} \otimes \mathbf{pilot\_mask}),$ where $\mathbf{U}_{\mathrm{DFT}}$ is an $M$ -point DFT applied to the data symbols before OFDM mapping.

Effect: DFT-spreading converts the multicarrier OFDM signal into a single-carrier-like waveform in the time domain, reducing PAPR from $\sim 8$ - $10$ dB (CP-OFDM) to $\sim 4$ - $6$ dB.

Mobility behavior: same as CP-OFDM — the DFT precoding does not help with Doppler. Still suffers ICI at high mobility.

Sensitivity: slightly more sensitive to frequency offset than CP-OFDM due to the precoding.

Theorem: PAPR Comparison: OTFS, DFT-s-OFDM, CP-OFDM

For QPSK data symbols and frame size $MN \geq 256$ , the 99%-tile PAPR is:

CP-OFDM: 10-11 dB.
DFT-s-OFDM: 5-6 dB.
OTFS: 7-8 dB.
Single-carrier (DFT-s): 5 dB.

Interpretation: OTFS PAPR is $\sim 2$ dB higher than DFT-s-OFDM. For UE-side transmission at mmWave (where PA back-off matters), this is a real cost — $\sim 2$ dB less effective Tx power. However, OTFS maintains full rate under high Doppler where DFT-s-OFDM suffers ICI-induced SINR loss. Net trade-off depends on application.

The PAPR hierarchy reflects the waveform structure:

Single-carrier: envelope is the QAM constellation, bounded.
DFT-s-OFDM: approximates single-carrier via DFT pre-spreading.
OTFS: 2D pulse shape in time; partial PAPR reduction from DD spreading but not as aggressive as DFT.
CP-OFDM: sum of $N$ random subcarriers (central limit theorem).

OTFS's 2 dB penalty over DFT-s-OFDM is the price for DD-domain processing. In contexts where PAPR matters more than mobility (indoor URLLC), DFT-s-OFDM wins. For mobility applications (V2X, LEO, HST), OTFS's mobility gain outweighs the PAPR cost.

Proof

OTFS time-domain signal

After ISFFT and Heisenberg transform: $\mathbf{x}_{\mathrm{time}} = \mathbf{F}^{-1} \mathbf{U}_{\mathrm{ISFFT}} \mathbf{s}$ where $\mathbf{U}_{\mathrm{ISFFT}}$ is the 2D DFT for the DD grid.

PAPR of unitary mix

Unitary mixing of i.i.d. QPSK: central-limit theorem applies for $N$ large, PAPR $\sim \log(MN)$ + constant.

DFT-spread PAPR

DFT pre-spreading localizes energy into a single-carrier-like signal. Standard result: PAPR $\sim 5$ dB for QPSK.

OTFS vs DFT-s

OTFS has two-dimensional spreading; less aggressive PAPR reduction than one-dimensional DFT. Gap: $\sim 2$ dB. $\blacksquare$

Key Takeaway

OTFS pays a 2 dB PAPR cost over DFT-s-OFDM. This matters for UE-side mmWave uplink. For mobility applications (where OTFS delivers orders-of-magnitude better BER), the cost is absorbed in the overall link budget. For low-mobility URLLC, DFT-s-OFDM remains the right choice.

Definition:
Dual-Waveform 6G Air Interface

A dual-waveform 6G air interface offers two PHY choices to the scheduler:

OFDM (including DFT-s): for low-mobility, low-latency scenarios. Sub-6 GHz cellular, static URLLC.
OTFS: for high-mobility, high-Doppler, sensing-heavy scenarios. V2X, LEO, HST, mmWave ISAC.

The scheduler picks per-slot based on UE speed, link type, and service requirements. UEs support both PHYs in hardware (common ISFFT + FFT pipeline); software routing handles the waveform selection.

Benefit: no rigid waveform choice. Each UE-session gets the best waveform for its current context. No "chop off the hands" decision.

Cost: UE hardware must support both PHYs. Compute overhead $\sim 1.5\times$ single-waveform.

Theorem: Dual-Waveform Performance

For a 6G deployment with mixed UE mobility profile (30% static, 50% vehicular, 20% high-mobility), a dual-waveform scheduler achieves aggregate throughput $R_{\text{dual}} \;\geq\; 0.95 \cdot \max(R_{\mathrm{OFDM-only}}, R_{\mathrm{OTFS-only}}),$ within 5% of the oracle-optimal per-UE choice.

Consequence: a dual-waveform 6G is within a few percent of the best possible outcome. The scheduler overhead (deciding which PHY) is small compared to the gain. This is the natural 6G design: offer both, switch based on context.

The point is that neither OFDM nor OTFS dominates all scenarios. A scheduler that picks the right one per UE, per slot, achieves near-optimal throughput. The overhead of supporting two waveforms (UE hardware, scheduler complexity) is modest compared to the gain of matching waveform to channel.

Proof

Per-UE optimal choice

For each UE, pick the waveform that maximizes per-UE rate given current channel. Oracle knows channel perfectly; scheduler approximates with measurements.

Aggregate

Total rate = $\sum_k R_k(\text{best waveform})$ . Scheduler error: $\sim 5\%$ from imperfect choice.

Sub-optimality

Single-waveform: rate $= \sum_k R_k(\text{fixed waveform})$ . Inferior UEs drag the sum down.

Ratio

$R_{\text{dual}}/\max(R_{\mathrm{OFDM}}, R_{\mathrm{OTFS}}) \geq 0.95$ for realistic mobility mix. $\blacksquare$

Waveform Head-to-Head

Feature	CP-OFDM	DFT-s-OFDM	OTFS
Max mobility	~400 km/h	~400 km/h	Unlimited
PAPR (99%-tile)	10-11 dB	5-6 dB	7-8 dB
Frame size	14 symbols/slot	14 symbols/slot	Arbitrary
Compute	FFT + CP	FFT + DFT + CP	ISFFT + FFT
ISAC	Poor	Poor	Natural
Standardization	5G NR baseline	5G NR uplink	6G candidate
Commercial (2024)	Mature	Mature	Research/prototype

Example: Waveform Selection for a Mixed Cell

A 6G cell serves 100 UEs: 40 static (indoor), 40 vehicular (30- 100 km/h), 20 HST (300-500 km/h). For each, identify the optimal waveform.

Solution

Static UEs (40)

Low Doppler, low PAPR concerns. DFT-s-OFDM optimal (uplink) or CP-OFDM (downlink). Common choice.

Vehicular UEs (40)

Moderate Doppler. At 28 GHz: $\nu \sim 3$ kHz. Fits OFDM numerology $\mu = 2$ ( $\Delta f = 60$ kHz). Either OFDM or OTFS works; OFDM is simpler.

HST UEs (20)

High Doppler: $\nu \sim 25$ kHz at 28 GHz. Exceeds OFDM $\mu = 3$ ceiling. OTFS mandatory.

Scheduler choice

Dual-waveform scheduler:

40 static + 40 vehicular → OFDM (80%).
20 HST → OTFS. Rate: OFDM UEs at 1 Gbps, HST UEs at 500 Mbps. Aggregate: $\sim 95$ Gbps. Single-waveform (OFDM only): HST UEs at 100 Mbps (severely degraded). Aggregate: $\sim 82$ Gbps. Single-waveform (OTFS only): static/vehicular at 950 Mbps (slight PAPR penalty). Aggregate: $\sim 93$ Gbps. Dual-waveform beats both single-waveform choices.

PAPR CCDF: CP-OFDM, DFT-s-OFDM, OTFS

Plot the complementary CDF (probability PAPR exceeds $x$ ) for three waveforms. Sliders: frame size $MN$ , QAM order.

Parameters

\log_2 MN

Modulation

🔧Engineering Note

Dual-Waveform Deployment Pattern

Expected 6G deployment pattern for dual-waveform:

UE hardware: supports both OFDM and OTFS PHYs. Shared FFT/ISFFT pipeline saves silicon. Software selects per-session.

BS hardware: same. All 6G gNBs support both PHYs from Rel. 21.

Scheduler: new RRC signaling indicates per-UE waveform choice. Default: operator-configured (usually OFDM for low-mobility, OTFS for high-mobility). Adaptive switching at RRC reconfiguration (every few seconds) or per-slot (milliseconds).

Migration: Rel. 20 adds OTFS signaling; Rel. 21 adds waveform switching primitives. 2028-2030 UEs support both natively. Legacy 5G UEs: OFDM-only, still served.

Real-world distribution (2030+):

Urban dense: 80% OFDM, 20% OTFS.
Highway / HST: 30% OFDM, 70% OTFS.
LEO / rural NTN: 5% OFDM, 95% OTFS.
Industrial IoT: 95% OFDM, 5% OTFS.

Practical Constraints

•
UE hardware: both PHYs (shared FFT pipeline)
•
Scheduler: per-UE waveform choice via RRC
•
Migration path: dual-mode from Rel. 21
•
2030+: dual-waveform is the baseline

Common Mistake: No Waveform Is Universally Best

Mistake:

Assuming OTFS should replace OFDM everywhere. Despite OTFS's mobility advantages, OFDM wins in simplicity, PAPR, and standardization maturity for 50-80% of scenarios.

Correction:

Frame the 6G decision as which scenarios need OTFS, not "should OTFS replace OFDM". The answer: high-mobility, NTN, ISAC, V2X. These are 20-30% of 6G use cases. The remaining 70-80% stays with OFDM. Dual-waveform 6G is the realistic outcome.

The 6G Vision and Its Demands Multi-Domain Multiple Access with OTFS