Ferkans — Interactive Telecom Tutor

A Head-to-Head Comparison

Sections 1-3 established the ambiguity-function framework and derived the key resolution theorems. This section compares OTFS and OFDM as radar waveforms head-to-head across the relevant performance metrics: range resolution, velocity resolution, sidelobe level, unambiguous region, CRLB. The conclusion: OTFS simultaneously wins on velocity resolution and matches OFDM on range resolution, without compromising data throughput. OFDM requires dedicated pulse-Doppler processing to match OTFS.

OTFS vs OFDM Radar: Full Comparison

Metric	OTFS	OFDM (single sym)	OFDM (pulse-Doppler)
Range resolution $\Delta R$	$c/(2W)$	$c/(2W)$	$c/(2W)$
Velocity resolution $\Delta v$	$c/(2 T f_0)$	$\infty$	$c/(2 T_{\text{dwell}} f_0)$
Ambiguity shape	Thumbtack	Ridge (in $\nu$ )	Thumbtack (after $N_{\text{PRI}}$ pulses)
Peak sidelobe (unwindowed)	$-13$ dB (localized)	$-13$ dB (along ridge)	$-13$ dB (localized)
Data during sensing?	Yes (ISAC)	Yes (ISAC)	No (dedicated radar mode)
Preserves data rate?	Yes	Yes (per symbol)	No
CRLB range accuracy	$c/(2W\sqrt{2\rho})$	Same	Same
CRLB velocity accuracy	$c/(2Tf_0\sqrt{2\rho})$	$\infty$	Same as OTFS at equal dwell
Detection algorithm	2D DFT on DD grid	1D DFT per symbol	2D DFT over time × frequency
Recommended use	6G ISAC, automotive	Range-only OFDM	Dedicated radar

Theorem: Quantitative Resolution Gap Between OTFS and OFDM-single-Symbol

At equal time-bandwidth product $TW$ , OTFS and OFDM-pulse-Doppler achieve the same range and velocity resolution. However:

Per-OFDM-symbol OFDM radar has velocity resolution $\Delta v_{\text{OFDM}} = c/(2 T_{\text{sym}} f_0)$ where $T_{\text{sym}} = 1/\Delta f$ . For typical 5G NR ( $T_{\text{sym}} = 33\mu$ s), $\Delta v \approx 900$ m/s — useless for any practical radar.
OTFS achieves $\Delta v = c/(2 T f_0)$ where $T = N T_{\text{sym}}$ is the full frame duration. Factor $N$ better.
OFDM pulse-Doppler with $N_{\text{PRI}} = N$ pulses achieves $\Delta v_{\text{PRI}} = c/(2 N T_{\text{PRI}} f_0)$ . Matches OTFS if $T_{\text{PRI}} = T_{\text{sym}}$ and $N_{\text{PRI}} = N$ — but this is dedicated radar mode with no data.

The structural advantage: OTFS integrates the $N$ -symbol time extension into the waveform itself; OFDM pulse-Doppler requires switching to a dedicated radar mode. ISAC is the unification of data+sensing that OTFS offers natively.

OFDM per-symbol thinks "range only" because its ambiguity is a ridge along Doppler. OFDM-pulse-Doppler thinks "range and Doppler, in separate modes": first send data, then send radar pulses. OTFS thinks "data and Doppler, simultaneously": the data grid is the Doppler resolution cell.

Quantitatively: given a fixed communications resource budget of $(W, T)$ , OTFS hits the information-theoretic resolution limits for both range and Doppler; OFDM hits them only for range, and would need to sacrifice data for Doppler.

Proof

OFDM per-symbol Doppler

An OFDM symbol of duration $T_{\text{sym}}$ has Doppler resolution $1/T_{\text{sym}}$ . At typical 5G NR values this is coarse (600 Hz - 30 kHz).

OTFS frame Doppler

OTFS frame duration is $N T_{\text{sym}}$ . Doppler resolution: $1/(N T_{\text{sym}}) = 1/T$ . Factor $N$ improvement.

Equivalence with OFDM-PRI

OFDM with $N$ sequentially-transmitted pulses can also use duration $N T_{\text{sym}}$ for Doppler processing. Same Doppler resolution as OTFS. Distinction: those $N$ pulses are pure radar, not data-bearing.

Net outcome

At equal $(W, T)$ — i.e., equal time-bandwidth resources — OTFS and OFDM-pulse-Doppler match. But OTFS does this without sacrificing data rate; OFDM requires sacrificing data rate for Doppler. That's the difference. $\blacksquare$

Key Takeaway

OTFS is the natural ISAC waveform. For the same $(W, T)$ budget, OTFS matches OFDM-radar (dedicated pulse-Doppler mode) while simultaneously carrying data. OFDM can do ISAC only by compromising — either low-resolution velocity (per-symbol) or switching to radar-only mode (pulse-Doppler). OTFS has no such compromise: one waveform, both data and sensing, at the information-theoretic limits.

Side-by-Side: OTFS vs OFDM Ambiguity Shapes

Plot the ambiguity functions $|A_s(\tau, \nu)|^2$ of OTFS and OFDM (single symbol) as 2D heatmaps. OTFS: thumbtack at origin. OFDM: narrow ridge in $\tau$ , broad plateau in $\nu$ . Change parameters to see how the shapes respond.

Parameters

Subcarriers

M

64

OFDM symbols

N

16

Compare with OFDM single symbol

Example: Automotive ISAC Link Budget

An automotive ISAC system at $f_0 = 77$ GHz with $W = 100$ MHz, $T = 3$ ms, needs to detect a pedestrian at range 50 m with velocity 1.4 m/s (walking speed) and a truck at 100 m with velocity 25 m/s. Compute the OTFS resolutions and confirm detectability.

Solution

Range resolution

$\Delta R = c/(2W) = 1.5 \times 10^8/(2 \cdot 10^8) = 1.5$ m. Pedestrian vs truck: 50 m separation >> 1.5 m. Both resolvable in range.

Velocity resolution

$\Delta v = c/(2 T f_0) = 3 \times 10^8/(2 \cdot 3 \times 10^{-3} \cdot 7.7 \times 10^{10}) = 0.65$ m/s. Pedestrian (1.4 m/s) vs truck (25 m/s): 23.6 m/s separation >> 0.65 m/s. Resolvable.

CRLB at SNR 25 dB

$\rho = 316$ . $\sigma_R = 1.5/\sqrt{2\pi^2 \cdot 316} = 2.4$ cm. $\sigma_v = 0.65/\sqrt{2\pi^2 \cdot 316} = 0.01$ m/s. Pedestrian tracking: cm-level range, mm/s velocity. Excellent.

Data rate during sensing

$MN = 100 \text{MHz} \cdot 3 \text{ms}/(T_{\text{sym}})$ . At $T_{\text{sym}} = 33\,\mu$ s: $MN = 9000$ . QPSK data rate: $\sim 2 \cdot 9000/3\text{ms} = 6$ Mbps per link. Continuous ISAC — data flows while sensing happens.

⚠️Engineering Note

Three Operational Advantages Over OFDM-Radar

Single coherent observation: OTFS observes the scene for the full frame duration $T$ ; OFDM observes it per-symbol (short snapshot). OTFS gets $N$ -fold better Doppler resolution at the same data rate.
No mode switching: OTFS's ISAC is native — the transmit waveform is both data-bearing and radar-compatible. OFDM requires a scheduler to allocate some time for data, some for radar pulses. Mode switching introduces latency and fragmentation, detrimental for real-time applications.
Thumbtack ambiguity: even if OFDM used dedicated pulse- Doppler, its per-symbol ambiguity is a ridge — good range, poor velocity. OTFS's thumbtack at the full-frame level gives clean range-velocity detection without the ridge-sidelobe masking issue.

Consequence: OTFS ISAC achieves the radar performance of dedicated pulse-Doppler mode while running continuously at the data rate of OFDM. This is the basis for the 6G ISAC proposal.

Practical Constraints

•
OTFS integrates sensing at 0 data rate penalty
•
OFDM + pulse-Doppler: sacrificed data during radar mode
•
OTFS thumbtack: simultaneously good range and velocity

OTFS-ISAC Use Cases Compared

Application	$(W, T, f_0)$	$(\Delta R, \Delta v)$	OTFS advantage
Automotive CRUISE	(100 MHz, 3 ms, 77 GHz)	(1.5 m, 0.65 m/s)	Continuous ISAC, no radar mode
Gesture recognition	(500 MHz, 10 ms, 60 GHz)	(30 cm, 0.25 m/s)	Sub-second response
Indoor positioning	(50 MHz, 4 ms, 5 GHz)	(3 m, 7.5 m/s)	IoT-device tracking
UAV surveillance	(200 MHz, 10 ms, 28 GHz)	(75 cm, 0.54 m/s)	Simultaneous comms + detection
Healthcare monitoring	(2 GHz, 5 ms, 60 GHz)	(7.5 cm, 0.5 m/s)	Heart rate via Doppler

OFDM vs OTFS Radar: A Quantitative Comparison