Sensing-Communication Trade-Off in ISAC

• Sensing-communication trade-off is the balance of sharing physical-layer resources for both environmental inference and data transmission in ISAC systems.
• Recent research employs information and estimation theory to define Pareto frontiers, quantifying trade-offs across metrics like MSE, detection probability, and throughput.
• Practical solutions use waveform design, resource allocation, and deep learning to dynamically manage the trade-off in multi-user and variable network conditions.

The sensing-communication trade-off refers to the fundamental and often inevitable tension arising in systems that jointly use physical-layer resources (time, frequency, space, power, waveform shape) for both active sensing and data transmission. Such systems—which include integrated sensing and communication (ISAC) transceivers as foundational elements of 6G networks—must balance the conflicting requirements of maximizing information transfer and optimizing environmental inference. Recent research has formalized, quantified, and characterized these trade-offs using tools from information theory, estimation theory, optimization, and practical transceiver algorithms. Modern frameworks provide mathematically precise Pareto boundaries delineating the achievable joint performance in terms of metrics such as mutual information, mean squared error (MSE), detection probability, coverage, and system throughput.

1. Information-Theoretic Foundations and General Formulations

Early and ongoing research has grounded the sensing-communication trade-off in multi-objective information theory, notably via the capacity-distortion and related “rate-error” or “rate-detection-exponent” regions (Xiong et al., 2023, Choi et al., 2023, Xiong et al., 2022, Chang et al., 2022). A canonical formulation considers a channel supporting simultaneous message transmission and state estimation:

$$\mathcal{R}_{C,D} = \left\{ (R, D): \, \exists\,p_X, \quad R\le I(X;Y_c), \ \mathbb{E}[d(S,\widehat{S})]\le D, \ \mathbb{E}[b(X)]\le B \right\}$$

with $R$ the per-channel-use reliable communication rate, $D$ the expected sensing distortion for state $S$, $b(X)$ a resource constraint, and $I(X;Y_c)$ the mutual information for communications. Optimizing over $p_X$ (the input distribution or waveform ensemble) traces the Pareto frontier, showing for each distortion $D$ the maximum achievable $R$ and vice versa.

Several refinements stem from this template:

• For channel discrimination or detection, the distortion $D$ is replaced by an error exponent $E$ (Wu et al., 2022), or by a Cramér–Rao bound (CRB) for parameter estimation (Xiong et al., 2022).
• For Gaussian systems, this region can be described analytically, yielding “CRB–rate” or “rate–MSE” curves with explicit boundary points (Choi et al., 2023, Xiong et al., 2022).

A central insight is that for nearly all nontrivial ISAC channels, maximizing communication rate requires high-entropy or stochastic inputs, while optimizing sensing metrics favors deterministic, structured waveforms or covariances—an archetype termed the deterministic–random trade-off (DRT) (Xiong et al., 2023, Yu et al., 4 Jul 2024).

2. Structural Properties: Pareto Frontiers and Regime Decomposition

The achievable region for joint sensing–communication is strictly Pareto-optimal: any attempt to improve one metric (e.g., MSE, probability of detection) beyond a certain point necessarily sacrifices the other (e.g., rate).

Key zone decompositions appear across theoretical and empirical results:

• Communication saturation: Most resources favor data delivery; sensing performance plateaus with marginal “free” improvements until a threshold.
• Sensing saturation: Most resources allocated to probing; communications rate can increase with minimal sensing loss up to a limit.
• Adversarial (“balanced”) zone: Both metrics trade off sharply and must be simultaneously optimized (Li et al., 2021). Any “balanced” system-optimality point—one not at a corner—always lies in this zone and is characterized by necessary Lagrangian KKT conditions:

$w_A \,\frac{dA}{dN_s} + w_R \,\frac{dR}{dN_s} = 0$

(as in (Li et al., 2021)), where $w_A, w_R$ are metric weights.

• Resource partitioning law: In canonical models, communication mutual information (CMI) scales linearly with allocated resource units, while the sensing MSE often falls inversely with assigned resources (Yu et al., 4 Jul 2024). Pareto boundary points are obtained by sweeping a scheduling or resource-allocation parameter.

The table below summarizes common regimes, as seen in (Li et al., 2021):

Zone	Dominant Resource	Performance Slope
Comm. saturation	Communication	$R\approx R_{\max}$, sensing improves slowly
Adversarial (balanced)	Both (mixed)	$dA/dN_s > 0,\ dR/dN_s < 0$
Sensing saturation	Sensing	$A\approx A_{\max}$, rate improves slowly

3. Waveform, Resource, and Codebook Design Principles

The trade-off is ultimately governed by the waveform structure and how system resources are partitioned and modulated. Several core phenomena and methods emerge:

• Subspace Trade-off (ST): The transmit covariance can be projected between sensing- and communication-optimal subspaces (e.g., beam steering) (Xiong et al., 2023, Xiong et al., 2022).
• Deterministic–Random Trade-off (DRT): Communication favors Gaussian or random codebooks, maximizing entropy and rate; sensing favors constant modulus or semi-unitary (deterministic) codebooks for maximizing Fisher information or detection statistics (Xiong et al., 2023, Yu et al., 4 Jul 2024). There is provably an operating point where the optimal input law is a convex mixture over at most two deterministic strategies, yielding a rate penalty versus communications-only optimal signaling (Xiong et al., 2023).
• Pareto-optimal resource allocation: In multi-carrier (OFDM) or time/frequency division systems, dynamic allocation (e.g., water-filling, slot partitioning) provides a tunable axis for balancing sensing and communication (Choi et al., 2023, Li et al., 2021).
• Constellation and beamforming shaping: Joint optimization of symbol alphabets and array weights can “carve out” the desired trade-off in metrics like KL divergence, bit error rate, and detection probability (Fei et al., 17 May 2024).
• Learning-based performance prediction: For black-box deep learning pipelines (e.g., radar-based motion classification), regression-fitted “learning curves” anchor the analytic mapping between resource allocation and sensing accuracy (Li et al., 2021).

4. Application Scenarios and Network-Level Trade-Offs

The trade-off manifests distinct features in various architectures:

• MIMO and Backscatter ISAC: Joint beamforming and power allocation, constrained by user communication needs and localization CRBs, yield Pareto-efficient sets through advanced convexification (fractional programming, LMIs) (Tian et al., 3 Jun 2024).
• Distributed/Ad hoc ISAC networks: In large random networks, stochastic geometry and scaling law analysis reveal that reducing per-node throughput by a function $g(n)$ improves sensing range by $g(n)^{\alpha_c/\alpha_s}$, highlighting a deep interplay between network density, power scaling, and S&C reach (Qiu et al., 14 Feb 2025).
• Finite blocklength ISAC: When codewords are short, the rate–MSE region exhibits a strong trade-off that vanishes as blocklength increases, approaching the classical decoupling of communication and estimation in the asymptotic regime (Shen et al., 2023).
• ISAC with blockage and fading: Channel blockage and fading directly shrink the feasible S&C region, and optimal signaling shifts to more isotropic or robust forms as blockage worsens (Mohajer et al., 7 Jan 2025).
• Multi-point/fusion based systems: By adaptive node mode switching and optimal fusion strategies, multi-view redundancy can expand the S–C trade-off frontier and allow for adaptive region spanning (Li et al., 2022).

5. Practical Solution Algorithms and Design Guidelines

To operationalize the trade-off, a range of optimization and signal design methodologies are deployed:

• Convexification techniques: Non-convex joint objectives become tractable via fractional programming, Schur complements, and semi-definite relaxations; this enables rigorous exploration and exploitation of the feasible set (Tian et al., 3 Jun 2024, Zou et al., 9 May 2024).
• Deep learning and adaptive methods: Neural-network-based constellations and reinforcement learning dynamically track and approach the trade-off boundary under environment uncertainty (Umra et al., 4 Nov 2025, Fei et al., 17 May 2024).
• Weighted-sum and scalarization: System designers select metric weights, tracing out the Pareto frontier and attaining solutions tailored to operational priorities (e.g., rapid detection vs maximal data rate) (Lu, 16 Oct 2024, Yu et al., 4 Jul 2024).
• Resource allocation in multi-user/multi-task settings: Optimal user scheduling, antenna selection (e.g., fluid antenna systems), and energy/slot partitioning enable flexible, context-aware operation (Zou et al., 9 May 2024, Li et al., 2021).
• Practical design rules: For example, in SISO ISAC links, blocklength and error probability set the “rate-loss” due to sensing, and codebook geometry (e.g., spherical cap vs full sphere) guides joint code design (Shen et al., 2023).

6. Implications, Limitations, and Future Directions

The sensing-communication trade-off is now a well-quantified and widely studied phenomenon, but several open challenges and insights remain:

• Unified metrics: Information-theoretic criteria (e.g., KL divergence and mutual information) provide yardsticks that unify communications and radar design (Yu et al., 4 Jul 2024, Fei et al., 17 May 2024), but practical and regulatory yardsticks may diverge.
• Scenario dependence: Performance boundaries depend on waveform choices, channel models, node cooperation (e.g., fusion), and environmental uncertainties; re-calibration is often required for new deployment environments (Li et al., 2021, Tian et al., 3 Jun 2024).
• Non-convex and finite-sample settings: For certain important metrics (e.g., detection probability under non-convex power metrics or finite-blocklength rates), the boundary requires intricate analysis or can only be approached using time-sharing/mixture strategies (Xiong et al., 2023, Shen et al., 2023).
• Scalable, adaptive, and data-driven trade-off management: The role of machine learning and RL for real-time adaptive trade-off navigation under non-stationary or adversarial disturbance is rapidly emerging (Umra et al., 4 Nov 2025).
• Network-level and scaling-law trade-offs: In large networks, the interaction of spatial reuse, interference, and physical limits, as well as control strategies for balancing metrics, remain active research areas (Qiu et al., 14 Feb 2025).
• Hardware and implementation constraints: Antenna selection, waveform shaping, and physical-layer adaptation must consider computational burden and compatibility with legacy systems (Zou et al., 9 May 2024, Fei et al., 17 May 2024).

The field continues to move toward fine-grained, adaptive operation, guided by rigorous characterization of the attainable trade-off regions and by the development of robust algorithmic controllers for optimal S&C balancing in heterogeneous environments.