ISAC Tradeoffs: Complexity, PAPR, Doppler Resolution

The Three Constraints

OTFS-ISAC inherits three performance-complexity tradeoffs from the OTFS architecture:

  1. Complexity: joint processing vs separate radar + comms.
  2. PAPR: peak-to-average power ratio, relevant for RF front ends.
  3. Doppler resolution: frame duration TT vs latency.

Each dimension affects deployment decisions. This section quantifies each and positions OTFS against OFDM-ISAC and chirp-based alternatives.

Theorem: OTFS-ISAC vs OFDM-Hybrid-ISAC Complexity

For the same (W,T,f0)(W, T, f_0) budget, the compute complexity of OTFS-ISAC vs OFDM-with-pulse-Doppler (time-multiplexed ISAC):

  • OTFS-ISAC: O(MNlog⁡(MN)⋅Titer)≈5MNlog⁡(MN)O(MN \log(MN) \cdot T_{\text{iter}}) \approx 5MN \log(MN).
  • OFDM-pulse-Doppler: O(MNlog⁡(M)⋅NPRI)≈2MNlog⁡(M)O(MN \log(M) \cdot N_{\text{PRI}}) \approx 2 MN \log(M) (for NPRI=NN_{\text{PRI}} = N).

Ratio: OTFS is ∼2×\sim 2\times more expensive than pure OFDM pulse-Doppler due to the log⁡(N)\log(N) factor in the 2D FFT. But OTFS-ISAC delivers simultaneous data + sensing, while OFDM pulse-Doppler sacrifices data during sensing.

Normalized per-unit-of-"ISAC-output" (data + sensing combined): OTFS is roughly 3×3\times cheaper than OFDM-ISAC because it avoids the mode-switching overhead.

Naively, OTFS looks more complex due to the 2D FFT. But comparing "ISAC output per operation": OTFS delivers both data and sensing per operation; OFDM delivers only one at a time. The comparison requires normalizing by the utility of the computation.

For systems where data and sensing are both required (automotive, ISAC for 6G URLLC), OTFS is significantly more efficient in the "joint output per compute unit" metric.

Proof
OTFS compute count

Wigner + SFFT: 2MNlog⁡(MN)2 MN \log(MN) per frame. LCD: 3⋅MNlog⁡(MN)3 \cdot MN \log(MN) for 3 iterations. Super-resolution: ∼MN\sim MN (local optimization). Total: ∼5MNlog⁡(MN)\sim 5 MN \log(MN) per frame.

OFDM-ISAC time-multiplexed

Data mode: MNlog⁡(M)MN \log(M) per frame (standard OFDM). Radar mode: MNlog⁡(MN)MN \log(MN) for pulse-Doppler processing. If split 50-50: ∼MNlog⁡(M)+MNlog⁡(MN)/2≈1.5MNlog⁡(M)\sim MN \log(M) + MN\log(MN)/2 \approx 1.5 MN \log(M).

Ratio

OTFS / OFDM = 5MNlog⁡(MN)/1.5MNlog⁡(M)≈3.3log⁡(N)/log⁡(M)5 MN \log(MN) / 1.5 MN \log(M) \approx 3.3 \log(N)/\log(M). At typical M=512,N=16M = 512, N = 16: ratio ≈3.3⋅4/9=1.5\approx 3.3 \cdot 4/9 = 1.5. OTFS is ∼1.5×\sim 1.5\times the compute, but delivers 2x the ISAC output (both modes). Net: OTFS more efficient per unit of output. ■\blacksquare

Theorem: OTFS vs OFDM-ISAC PAPR

For OTFS with i.i.d. QAM data symbols, the peak-to-average power ratio (PAPR) at the time-domain waveform output scales as PAPROTFS  ≈  log⁡(MN) dB at 99.9% CCDF.\text{PAPR}_{\text{OTFS}} \;\approx\; \log(MN) \text{ dB at 99.9\% CCDF}. For OFDM with same data: PAPROFDM≈log⁡(M) dB\text{PAPR}_{\text{OFDM}} \approx \log(M) \text{ dB}. At (M,N)=(64,16)(M, N) = (64, 16): PAPROTFS≈10\text{PAPR}_{\text{OTFS}} \approx 10 dB, PAPROFDM≈6\text{PAPR}_{\text{OFDM}} \approx 6 dB.

For dedicated pulse-Doppler radar (chirp-type waveform): PAPR≈0\text{PAPR} \approx 0 dB (constant envelope).

OTFS has higher PAPR than OFDM, not lower. This is the price of the DD-domain spreading. Requires back-off at the PA, reducing effective transmit power by 4-6 dB at typical saturation points.

OTFS's time-domain signal is a sum of MNMN complex exponentials with random phases — a classical Gaussian-PAPR signal with log⁡(MN)\log(MN) dB peaks. OFDM is the same but with MM exponentials. OTFS pays a ∼4\sim 4 dB PAPR penalty for the extra spreading factor.

Mitigation: PAPR-reduction techniques developed for OFDM apply directly to OTFS — clipping, tone reservation, selective mapping. None eliminate the PAPR penalty entirely.

Proof
Gaussian limit

For i.i.d. data and large MNMN, the waveform samples are approximately CN(0,1)\mathcal{CN}(0, 1) by CLT.

PAPR from extreme value

max⁡t∣s(t)∣2\max_t |s(t)|^2 for MNMN iid complex Gaussians: E[max⁡]∼log⁡(MN)\mathbb{E}[\max] \sim \log(MN) (Gumbel distribution). Hence PAPR≈log⁡(MN)\text{PAPR} \approx \log(MN) dB.

OFDM comparison

Same argument with MM samples: PAPROFDM≈log⁡(M)\text{PAPR}_{\text{OFDM}} \approx \log(M) dB. OTFS loses by factor log⁡(N)\log(N) dB.

Chirp

Dedicated chirp: constant envelope. PAPR = 0 dB. Dedicated radar wins on PAPR; loses on data rate. ■\blacksquare

Key Takeaway

OTFS has 4+ dB higher PAPR than OFDM. The DD spreading that enables the thumbtack ambiguity and sparse channel also inflates the waveform's peak values. This is a real cost: PA must be backed off, effective transmit power reduced, range shortened. Mitigations (clipping, tone reservation) recover 1-2 dB. The remaining ∼2\sim 2-33 dB penalty is the structural cost of the OTFS approach — and must be factored into link budgets.

PAPR CCDF: OTFS vs OFDM vs Chirp

Plot the complementary CDF of PAPR for OTFS, OFDM, and dedicated chirp waveforms on the same time-bandwidth product. OTFS is roughly 4 dB worse than OFDM at 99.9%99.9\% CCDF. Chirp is 0 dB PAPR (constant envelope). This is the structural PAPR penalty of OTFS compared to OFDM and to dedicated radar.

Parameters
64
16
1000

Theorem: Latency-Doppler Resolution Tradeoff

OTFS's Doppler resolution Δv=c/(2Tf0)\Delta v = c/(2 T f_0) directly couples frame duration TT to velocity accuracy. For URLLC applications with latency requirement L≤1L \leq 1 ms:

  • Maximum T=L=1T = L = 1 ms.
  • Δv=c/(2⋅10−3⋅f0)\Delta v = c/(2 \cdot 10^{-3} \cdot f_0) — at 5 GHz: 30 m/s (poor); at 28 GHz: 5.4 m/s; at 77 GHz: 1.9 m/s.

For relaxed-latency sensing (L∼10L \sim 10 ms):

  • T=10T = 10 ms.
  • Δv=3\Delta v = 3 m/s at 5 GHz, 0.54 m/s at 28 GHz, 0.19 m/s at 77 GHz.

At higher carrier (mmWave), the latency-Doppler tradeoff relaxes: TT can be small without sacrificing velocity resolution. This is a structural advantage of mmWave ISAC.

Doppler resolution depends on both observation time TT and carrier f0f_0. At fixed TT, higher f0f_0 gives finer velocity resolution. For URLLC, short TT is mandatory — mmWave provides the carrier frequency that keeps velocity resolution acceptable.

For 6G URLLC automotive ISAC (latency < 1 ms, fine velocity): 77 GHz is appropriate. Sub-6 GHz is adequate only for longer- latency applications (100 ms-scale ranging for positioning, not real-time tracking).

Proof
Doppler resolution formula

Δv=c/(2Tf0)\Delta v = c/(2 T f_0). Inverse proportional to TT.

Latency constraint

L=Tframe=T+TprocessingL = T_{\text{frame}} = T + T_{\text{processing}}. For short LL, TT is bounded above by LL.

Joint bound

At given LL, maximum T=LT = L. So Δv≥c/(2Lf0)\Delta v \geq c/(2 L f_0). For fine Δv\Delta v at short LL: need high f0f_0. ■\blacksquare

OTFS-ISAC vs Competitors: Three Tradeoffs

MetricOTFS-ISACOFDM time-multiplexed ISACChirp + OFDM hybrid
Computational complexity (per 1 ISAC-output)Low (∼MNlog⁡MN\sim MN\log MN)High (mode switching)Medium
PAPRHigh (∼log⁡MN\sim \log MN dB)Low (∼log⁡M\sim \log M dB)Low (0 dB chirp mode)
Doppler resolution at LL = 1 msSame as OFDMSameN/A (chirp = short pulse)
Data rate during sensing100%0% (radar mode)50% (time-shared)
Joint CRLB achievementYesYes (in radar mode)Yes
Standardization path6G nativeLegacy 5G + extensionDedicated radar + data
⚠️Engineering Note

Why mmWave Is the ISAC Sweet Spot

mmWave carrier frequencies (24-77 GHz for 5G FR2, 80-180 GHz for 6G) are naturally suited for OTFS-ISAC:

  1. Doppler resolution scales with f0f_0: velocity accuracy improves 8-fold from 3.5 GHz to 28 GHz. Essential for cm/s-level tracking.
  2. Large bandwidth available: W=100W = 100 MHz - 2 GHz typical, giving cm-level range resolution.
  3. Short wavelength: sub-cm range geometry, matching fine-motion applications (gesture, health).
  4. OTFS Doppler robustness: high f0f_0 means high velocity, which stresses OFDM; OTFS handles it natively.

As of 2026, the only OTFS-ISAC deployments under active research are at mmWave (automotive 77 GHz, gesture 60 GHz, health 60-120 GHz). Sub-6 GHz ISAC exists but is limited to long-latency positioning applications.

Practical Constraints
  • •

    mmWave ISAC: fine velocity resolution, short wavelength

  • •

    Sub-6 GHz ISAC: positioning only (not real-time tracking)

  • •

    6G FR3 (7-24 GHz): middle ground, emerging band for ISAC

Joint Delay-Doppler Estimation and Data DetectionApplications: Automotive, UAV, Healthcare