Dual-domain ISAC Waveforms Overview

• Dual-domain ISAC waveforms are signaling strategies that exploit both frequency-time and delay-Doppler domains to achieve concurrent radar sensing and digital communication.
• They use techniques like superposition, separability, and optimization to enhance performance metrics such as sidelobe suppression and delay estimation accuracy.
• Practical implementations in full-duplex systems, MIMO-OFDM/OTFS platforms, and WD-NOMA architectures demonstrate their effectiveness for next-generation integrated networks.

Dual-domain ISAC (Integrated Sensing and Communication) waveforms are a class of signaling strategies that explicitly leverage separability, superposition, or optimization across two fundamental domains—typically frequency-time (FT, or equivalently time and frequency), and delay-Doppler (DD)—to provide simultaneous radar and communication functionalities. The dual-domain concept enables separation, coordination, or interference management between sensing and communications by waveform design or processing in their respective (often nearly orthogonal) representations. This paradigm underpins recent breakthroughs in full-duplex ISAC, self-interference cancellation, superposed waveform design, and integrated MIMO-OFDM/OTFS/AFDM platforms.

1. Foundations and Dual-Domain Definitions

Dual-domain ISAC waveforms are defined by their exploitation of two mathematically conjugate (Fourier-paired or affine-paired) domains for joint sensing and communication. Dominant strategies include: (a) embedding communication symbols in the FT (DFT-based/OFDM)/space, and radar-specific features or pilots in the DD domain, (b) superposing signals in FT and DD domains prior to time-domain transmission, or (c) leveraging orthogonal domains for full-duplex or non-orthogonal-multiple-access (NOMA) separation.

In “Integrated Sensing and Communication System via Dual-Domain Waveform Superposition,” an OFDM signal is synthesized in the FT domain for communication, then a very low-power DD-domain impulse is superposed, expanding the effective sensing bandwidth far beyond the nominal OFDM allocation without harming communications. This approach achieves substantial delay estimation (range) Cramér–Rao bound (CRB) improvement versus legacy approaches (Tagliaferri et al., 2022). Similarly, “Enabling Full Duplex ISAC Leveraging Waveform Domain Separability” employs OFDM for communications and AFDM for radar. The time-domain OFDM signal is mapped through a discrete affine Fourier transform (DAFT) to the affine (DD-like) domain, where it appears white, allowing efficient self-interference (SI) cancellation in full-duplex operation (Arous et al., 14 Oct 2025).

2. System Architectures and Signal Models

Dual-domain ISAC frameworks encompass a diversity of architectural instantiations:

• Superposition in FT/DD: The overall transmit signal is $x(t) = x_{\rm com}(t) + \alpha\, x_{\rm sen}(t)$, with $x_{\rm com}(t)$ an FT-domain (OFDM) communication waveform and $x_{\rm sen}(t)$ a DD-domain (e.g., impulse or chirp) sensing signal, $\alpha$ selected for regulatory compliance and negligible communication penalty (Tagliaferri et al., 2022).
• Partitioned Frame Architectures: OFDM is used for communication bursts, AFDM/OTFS or chirp (FMCW) is used for sensing, with per-block parameters or modulator kernel changes effecting the domain switch (Arous et al., 14 Oct 2025, Huang et al., 2 Feb 2026). The transmitter inserts short guard intervals to preserve phase continuity when alternating domains.
• Modulation Mappings: DD-domain (OTFS/ODDM/AFDM) is mapped to time-frequency or directly to time via a succession of (I)SFFT and Heisenberg or DAFT transforms. Spatial modulation (SSK) in LEO satellite ISAC systems supports flexible waveform selection (sinusoid or chirp) per symbol, providing reconfigurability and hardware simplicity (Ngoufo et al., 17 Jul 2025).
• Waveform-domain NOMA (WD-NOMA): In monostatic uplink ISAC, AFDM/OTFS waveforms are transmitted in the uplink (user to base station), while OFDM is used for downlink and sensing. The OFDM echo appears as AWGN in the affine domain, enabling straightforward MMSE detection and efficient joint radar/comm processing (Zhu et al., 11 Nov 2025).

3. Mathematical and Algorithmic Frameworks

Superposition and Scaling

FT-domain OFDM and DD-domain impulses are combined after domain transformation, with careful power scaling:

• Sensing signals are attenuated by $30$–$40$ dB below communication signals per subcarrier, maintaining OOB emission compliance.
• Sensing CRB improves in proportion to the square of the sensing bandwidth, $B_{\rm sen}^2$, which can greatly exceed communication allocations because of the low per-bin power of the sensing component (Tagliaferri et al., 2022).

Dual-Domain SIC and Separability

• Application of DAFT transforms projects OFDM signals into the affine domain, where they become “white” and can be subtracted as noise, drastically simplifying SI cancellation in full-duplex ISAC (Arous et al., 14 Oct 2025).
• Windowing and time-domain spreading further localize residual SI in the delay-Doppler map, improving target detection RMSE and $P_D$ (probability of detection).

Joint Optimization for Dual-Domain Performance

• ODDM-FMCW combines data and sensing pilot frames in the DD domain and reconstructs them with matched-filter and DFT/IDFT techniques to extract channel/sensing information and achieve low-PAPR signaling (Huang et al., 2 Feb 2026).
• MIMO-OFDM SLP frameworks utilize symbol-level constructive interference constraints and quartic (ambiguity- or ISL-based) cost functions—optimized using MM, ADMM, or Riemannian conjugate-gradient methods—to guarantee both radar sidelobe suppression and communication QoS (Li et al., 2024, Li et al., 15 Mar 2025, Li et al., 2023).
• DRIP (Dual beam-similarity awaRe ISAC with controlled PAPR) extends these principles to multi-slot, multi-target designs, using block cyclic coordinate-descent to balance radar and communication metrics under PAPR and similarity constraints (Wang et al., 2024).

4. Performance Metrics and Trade-offs

Key metrics in dual-domain ISAC design include:

• Integrated Sidelobe Level (ISL): Measures total off-peak power in the ambiguity function (range/Doppler sidelobe suppression). Dual-domain optimization achieves ISL suppression up to $45$ dB below communications-only designs and rivals radar-only baselines (Li et al., 2024).
• Cramér–Rao Bound (CRB): Range and velocity CRBs benefit from increased sensing bandwidth, as in FT/DD superposition schemes ($\sim$20 dB lower than OFDM) (Tagliaferri et al., 2022).
• Bit Error Rate (BER): Not compromised at typical SNRs because communication processing can project out or ignore low-power sensing signals, or exploits AWGN-like sensing interference in the appropriate domain (Tagliaferri et al., 2022, Arous et al., 14 Oct 2025, Huang et al., 2 Feb 2026).
• PAPR: Joint designs (e.g., ODDM-FMCW, DRIP) tightly regulate PAPR to ensure efficient nonlinear amplifier operation (Wang et al., 2024, Huang et al., 2 Feb 2026).
• Spectral Efficiency, Target Detection Probability, RMSE, and Complexity: Algorithms achieve near-radar-only detection accuracy, minimal SE penalty, and efficient FPGA/DSP real-time execution (Tagliaferri et al., 2022, Li et al., 2024, Arous et al., 14 Oct 2025).

Trade-offs involve communication data rate versus radar/AF shaping, DoF allocation between the two domains, and hardware complexity versus sensing precision. For parameters (e.g., power split $x_{\rm com}(t)$0, similarity radius $x_{\rm com}(t)$1, or shaping Lagrange multipliers), tuning yields a Pareto frontier between communication and radar performance.

Table: Representative Performance Gains

Method / Metric	ISL Suppression	Range CRB Gain	Comm Penalty	PAPR Relief	Added Complexity
FT/DD superposition	~20 dB	~20 dB	negligible	n/a	$x_{\rm com}(t)$2s FPGA / SDR
Dual-domain SLP-OFDM	40–45 dB	matches radar	<1 dB	enforced	Iter. QCQP/ADMM
ODDM-FMCW	matches pilot	at CRB	at genie CSI	tunable	Matched filter + DFT
DRIP (space-time)	43–48 dB peak	n/a	variable	tunable	Cyclic-coord. desc.

5. Experimental and Practical Considerations

Prototypes demonstrate the real-world viability of dual-domain ISAC:

• USRP (mmWave, 28 GHz, 1024-tone) boards realize FT/DD superposed waveforms, achieving −17 dB sidelobes (vs −11 dB unshaped), PAPR reduction (8.2 vs 10.5 dB), and accurate SNR, BER, and delay-resolution performance (Pu et al., 14 May 2025, Tagliaferri et al., 2022).
• MIMO-OFDM SLP implementations run real-time convex solvers, fitting strict per-sample and per-antenna constraints (Li et al., 2024, Li et al., 15 Mar 2025).
• AFDM/OTFS systems deliver WD-NOMA uplink with full SI rejection and improved BER via domain-selective SIC (Zhu et al., 11 Nov 2025).

Key engineering aspects:

• Sensing per-bin power must be low to satisfy adjacent-channel mask requirements and preserve demodulator operation.
• Tuning of filter shapes, frame guards, and windowing iterations can flexibly balance SI suppression/complexity.
• Constant-modulus or PAPR-limited signaling is vital for PA linearity, especially in mmWave hardware.

6. Comparisons and Relation to Classical Schemes

Classical ISAC approaches (e.g., pure OFDM, time-division alternation) are limited by regulatory bandwidth, inflexible resource partitioning, or poor radar ambiguity properties due to comms waveform randomness. Dual-domain designs, by jointly controlling the waveform in two domains, overcome these limitations:

• Bandwidth expansion for radar is feasible without harming communications (e.g., $x_{\rm com}(t)$3 over OFDM allocation in NR hardware) (Tagliaferri et al., 2022).
• Sensing and comms can be performed simultaneously and without mutual degradation by leveraging domain separability (WD-NOMA, full-duplex) (Arous et al., 14 Oct 2025, Zhu et al., 11 Nov 2025).

7. Open Directions and Future Extensions

Open research areas include:

• Near-field dual-domain ISAC, extending from classical far-field delay-Doppler or FT domains to spherical wavefront and volumetric shaping (Wang et al., 2024).
• Wideband and hybrid-analog/digital implementations with massive MIMO or hybrid RF chain architectures.
• Machine learning for parameter selection, using data-driven methods to optimize trade-off coefficients (e.g., $x_{\rm com}(t)$4 in DRIP) in complex propagation and interference environments.
• Adaptive frame/beam/domain switching, where software-defined radios toggle domains or waveform parameters dynamically according to mission or network demands (Ngoufo et al., 17 Jul 2025).

Dual-domain ISAC waveform design thus represents a foundational shift in the signal processing and optimization of future wireless and radar networks, offering resource-efficient, interference-immune, and high-resolution joint sensing-communication functionalities. The concept is rapidly evolving, with significant demonstrations already in both simulation and hardware, and forms a critical pillar of 6G and beyond wireless platforms.