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Energy-Efficient Waveform Design for ISAC Systems: An Ambiguity-Domain QoS Perspective
Ngoc-Son Duong, Trung-Hieu Nguyen, Quang-Truong Can
TL;DR
The paper addresses minimum-energy ISAC waveform design with localized AF-SINR sensing QoS, per-user communication SINR, and PAPR constraints. It proposes FP-SCA for the resulting nonconvex problem, with simulations showing requirement satisfaction and preserved local ambiguity suppression.
Problem
The problem is to minimize ISAC transmit power while satisfying localized sensing QoS, per-user communication QoS, and practical PAPR requirements.
Method
The method uses AF-SINR for weighted local mainlobe-to-sidelobe-plus-noise sensing QoS and solves the nonconvex design with FP-SCA.
Results
The proposed waveform satisfies the stated requirements while preserving localized ambiguity suppression in the local delay-Doppler region.
Takeaways & Limitations
The design jointly shapes sensing and communication waveforms while minimizing transmit power under a PAPR constraint.
Abstract
from arXiv · showhide
Integrated sensing and communication (ISAC) requires transmit waveforms that simultaneously preserve communication quality, provide reliable sensing, and remain compatible with practical radio-frequency front ends. This paper considers a discrete-time ISAC waveform design problem that minimizes transmit power from the perspective of a novel metric termed the ambiguity-domain sensing signal-to-interference-plus-noise ratio (AF-SINR). The proposed AF-SINR quantifies the ratio between the desired ambiguity-function mainlobe power and the weighted aggregate sidelobe leakage plus noise within a local delay-Doppler region of interest, thereby providing a localized and noise-aware sensing-QoS measure. To enable ISAC operation, the waveform is further required to satisfy per-user effective communication-SINR constraints, while a peak-to-average power ratio (PAPR) constraint is imposed to facilitate practical implementation. The resulting energy-minimization problem is nonconvex due to the fractional QoS expressions, quartic ambiguity terms, and waveform-dependent PAPR constraint. To address this challenge, we propose a fractional-programming successive-convex-approximation (FP-SCA) algorithm. Simulation results verify that the proposed method satisfies all requirements while preserving localized ambiguity suppression over the local delay-Doppler region.
I. INTRODUCTION
The paper formulates energy-efficient ISAC waveform design around a localized, noise-aware AF-SINR sensing QoS while retaining communication and practical transmitter constraints.
- Motivation: ISAC waveforms must jointly control communication quality and the temporal, spectral, and spatial structure of sensing signals.This is particularly relevant for OFDM systems and practical radio-frequency front ends.
- AF-SINR sensing QoS: AF-SINR addresses the limitations of sidelobe-only metrics by balancing desired mainlobe power against weighted local sidelobe leakage and noise.The metric is defined over a prescribed delay-Doppler region of interest excluding the origin.
- Problem and contribution: The proposed design minimizes transmit power subject to AF-SINR, per-user communication-SINR, and PAPR constraints.The sensing metric has a matched-filter mainlobe-to-leakage-plus-noise interpretation.
- Solution approach: An FP-SCA algorithm combines quadratic transforms and affine ambiguity-function approximations to produce successive second-order cone subproblems.The method targets fractional sensing and communication QoS constraints in the nonconvex waveform design.
- Paper scope: The paper develops a discrete-time waveform model, ambiguity-domain sensing metric, minimum-energy formulation, algorithm, and numerical evaluation.The paper is organized around modeling, algorithm development, comparisons, and conclusions.
B. Communication QoS
The communication model represents each user's useful response and waveform-dependent residual interference through effective vectors and matrices, then imposes per-user SINR targets.
- Effective communication model: Each user has an effective desired-response vector whose projection onto the waveform represents the useful communication component.The model avoids explicitly representing a conventional multiuser precoder and symbol vector.
- Effective communication model: An interference-response matrix aggregates waveform-dependent residual interference across multiple effective interference components.The resulting interference power is defined from the collected interference responses.
- Communication SINR: The communication SINR is formed from the desired signal power, aggregate interference power, and effective user noise power.The effective noise may include thermal noise.
- Communication SINR: Channel coefficients, fixed beamformers, and waveform-projection operators are absorbed into known effective response quantities.These quantities may be obtained through channel estimation and predetermined transceiver processing.
- Communication QoS constraint: Communication QoS is enforced by requiring each user’s modeled SINR to exceed its prescribed target γk.The target is specified separately for each user.
C. PAPR constraint
The waveform design includes a low-PAPR requirement to improve transmitter efficiency and avoid severe nonlinear distortion while preserving amplitude flexibility.
- Motivation: Low PAPR helps the power amplifier operate closer to saturation, improving energy efficiency without severe nonlinear distortion.The paper treats low PAPR as important for both communication and sensing performance.
- PAPR definition: The discrete-time PAPR constraint limits each sample’s squared magnitude relative to the waveform’s average energy.The constraint is part of the practical waveform design requirements.
- PAPR design trade-off: The parameter ρ trades envelope regularity against design flexibility, with ρ = 1 corresponding to constant-modulus signaling.Smaller ρ improves hardware compatibility but restricts amplitude degrees of freedom.
D. Problem formulation
The paper formulates minimum-energy waveform design under sensing, communication, and PAPR constraints, then transforms fractional QoS conditions for iterative conic optimization.
- D. Problem formulation: The waveform energy minimization problem is formulated with the stated sensing, communication, and PAPR requirements.The formulation targets a feasible waveform with minimum transmit energy.
- D. Problem formulation: The formulation therefore combines minimum-energy optimization with iterative handling of fractional sensing and communication constraints.The supplied formulation and transformation steps jointly define the optimization structure.
- D. Problem formulation: The resulting problem is nonconvex mainly because AF-SINR contains quartic terms.The paper therefore develops a conic method for obtaining a feasible solution.
- A. Quadratic transform for QoS ratios: At each iteration, an auxiliary variable is updated for the sensing QoS ratio using a quadratic-transform step.The update is based on a cited quadratic-transform theorem.
- A. Quadratic transform for QoS ratios: A corresponding auxiliary variable is updated for each user’s communication QoS ratio.The communication transformation parallels the sensing transformation.
- A. Quadratic transform for QoS ratios: Fixing the auxiliary variables converts the fractional QoS requirements into difference-of-quadratic expressions.This transformation enables the subsequent successive-convex-approximation procedure.
B. Local ambiguity approximation
The method locally approximates complex quadratic ambiguity samples with affine expressions, enabling conic modeling of sidelobe terms and successive approximations of sensing and communication QoS constraints.
- B. Local ambiguity approximation: Each ambiguity sample is a complex quadratic form in the waveform vector.
- B. Local ambiguity approximation: The local model combines the current iterate and candidate waveform to create an affine complex expression.
- B. Local ambiguity approximation: The affine model enables a conic representation of the aggregate sidelobe term.
- B. Local ambiguity approximation: Because delay-Doppler operators may be non-Hermitian, the approximation is applied locally and sequentially.
- B. Local ambiguity approximation: The resulting local approximations are used for the sensing and communication QoS constraints.
C. PAPR successive convex approximation
The PAPR constraint is replaced with a successive-convex-approximation surrogate as part of the convexified waveform-design subproblem.
- C. PAPR successive convex approximation: An affine lower bound at the current iterate supports the convex approximation of a nonconvex term.
- C. PAPR successive convex approximation: The method introduces a PAPR surrogate for the waveform-dependent constraint.
- C. PAPR successive convex approximation: After convexifying the cost function and constraints, the original problem becomes a convex subproblem.
E. Feasibility restoration
The algorithm restores feasibility after local approximation updates by rechecking the original QoS constraints and scaling candidates to the required positive power.
- E. Feasibility restoration: The local ambiguity model is not a global inner approximation for arbitrary non-Hermitian Qq.
- E. Feasibility restoration: The algorithm solves each convex subproblem, normalizes the resulting waveform, and recomputes the relevant ambiguity and communication quantities.
- E. Feasibility restoration: The restored power is selected from the required AF-SINR and user communication powers.
- E. Feasibility restoration: The restored candidate maintains its PAPR while preserving the original AF-SINR and communication-SINR requirements.
A. Simulation Configuration
The simulations compare proposed ISAC and radar-only designs under fixed waveform, QoS, and PAPR settings, then vary sensing requirements to evaluate transmit-power behavior. The proposed design preserves localized ambiguity suppression while satisfying communication constraints.
- The setup serves K = 3 users with waveform length N = 32, reference γAF = 16 dB, communication target γk = 20 dB, and PAPR threshold ρ = 1.5.
- Both designs reduce transmit power and stabilize after four iterations, while the proposed ISAC design reaches the same final power as radar-only.The PAPR constraint becomes active at convergence for both designs.
- The proposed waveform retains low sidelobes in the protected delay-Doppler region, though its region of interest is slightly brighter than radar-only.The difference reflects allocation of waveform degrees of freedom to communication QoS.
- Transmit power increases monotonically with γAF, and larger filter noise produces higher power costs.
- At low γAF, communication constraints can make proposed ISAC require more power than radar-only; as γAF increases, the power gap decreases and curves converge.
4) Transmit-power requirement under varying communication-QoS targets:
When communication-QoS targets vary, sensing determines a low-target power floor, while increasingly stringent communication requirements eventually dominate and make the curves nearly converge. The conclusion reports that the proposed design preserves localized ambiguity suppression while satisfying all constraints.
- At low communication-QoS requirements, transmit power remains approximately constant because the AF-SINR constraint dominates.
- Larger matched-filter noise coefficients raise the sensing-induced power floor by increasing the energy needed to compensate for AF-SINR denominator noise.
- As γC increases, communication constraints activate and required transmit power rises; lower-noise curves begin rising earlier because their sensing floors are lower.
- At sufficiently stringent communication-QoS targets, the curves nearly converge because communication requirements primarily determine transmit power.
- The proposed waveform preserves localized ambiguity suppression while satisfying AF-SINR, communication-QoS, and PAPR constraints.