Joint Sensing & Communication Optimization

• Joint Sensing and Communication Optimization is a framework that integrates resource allocation for both wireless communication and sensing to achieve optimal trade-offs.
• It employs techniques such as MIMO/OFDM waveform design, adaptive beamforming, and iterative algorithms to balance information transfer with environmental sensing.
• Practical implementations rely on hybrid hardware, dynamic windowing, and machine learning to meet constraints like QoS, latency, interference, and security.

Joint Sensing and Communication Optimization refers to the integrated design and resource allocation of communication and sensing functionalities in wireless systems, leveraging shared spectrum, hardware, and signal processing to achieve a globally optimal trade-off between information transfer and environment perception. The optimization considers system-level variables such as waveform, beamforming, bandwidth, power allocation, and time/frequency resources, subject to quality of service (QoS), reliability, latency, interference, security, and application-specific constraints. This field spans theoretical foundations, architectures, and algorithmic frameworks across diverse platforms including MIMO/MU-MIMO, OFDM, vehicular, UAV-based, backscatter, distributed sensor, and cognitive radio networks.

1. Mathematical Foundations and Trade-off Characterization

A central element of joint sensing and communication optimization is the characterization of the fundamental resource trade-offs. For a generic shared hardware system, the total system bandwidth $B_{\mathrm{tot}}$ and RF power $P_{\mathrm{tot}}$ are partitioned between communication ($B_c,P_c$) and sensing ($B_s,P_s$), subject to $B_c+B_s=B_{\mathrm{tot}}$ and $P_c+P_s=P_{\mathrm{tot}}$. The achievable communication rate and sensing accuracy are then modeled as

$$\begin{aligned} R(B_c,P_c) &= B_c \log_2\left(1+\frac{P_c}{N_0 B_c}\right), \ S(B_s,P_s) &\approx \kappa P_s B_s^2, \end{aligned}$$

where $S$ reflects the inverse of ranging mean squared error under CRB scaling. The Pareto-optimal trade-off between $R$ and $S$ is given by parameterizing $B_c=\beta B_{\mathrm{tot}}$, $P_c=\beta P_{\mathrm{tot}}$ for $\beta\in[0,1]$, producing a boundary of achievable pairs $(R(\beta), S(\beta))$ (Li, 2020).

The canonical weighted-sum optimization is

$$\max_{B_c, P_c} \; \alpha R(B_c,P_c) + (1-\alpha)S(B_s,P_s)$$

with the resources split accordingly. For classical JCS, bandwidth allocation is strictly zero-sum, while power sharing is nearly non-interfering due to the radar echo’s dual utility, confirming efficient power usage but strong spectral tension (Li, 2020).

State-dependent channels, such as in systems with generalized feedback, further allow formulation of the capacity-distortion function $C(D)=\sup\{R : (R, D) \text{ achievable}\}$ with optimal input laws obtained via Lagrangian/KKT analysis and iterative Blahut-Arimoto-type algorithms (Kobayashi et al., 2018).

2. System Architectures and Modeling Paradigms

Modern joint optimization problems are instantiated across diverse architectures:

MIMO/OFDM Platforms: Dual-functional waveform optimization integrates communication and radar sensing within MIMO-OFDM, targeting either the entire frequency band or subsets of subcarriers for JCAS to maximize the communication throughput subject to sensing performance bounds. This involves hybrid architectures, resource block allocation, and beamspace partitioning (Nguyen et al., 2023, Ni et al., 2020).

Vehicular and Mobile Networks: In vehicular THz networks, each service provider vehicle (SPV) chooses to operate either in communication or sensing mode, associating with subsets of target vehicles. The design variables include service-mode assignments and user/target associations, subject to SINR and exclusivity constraints (Li et al., 2023).

UAV/Distributed Topologies: Multi-UAV ISAC systems require joint beamforming and trajectory design, with constraints on CRB for sensing accuracy, transmit power, and mobility, leading to nonconvex, dynamic programs (Tun et al., 21 Mar 2025).

Backscatter and IoT: In B-ISAC systems, joint beamforming simultaneously optimizes the UE communication rate under strict constraints on tag detection probability and power, exploiting probing streams and joint covariance control (Zhao et al., 4 Sep 2024).

Cognitive Wideband and Subcarrier Partitioning: Wideband CR-enabled JCS systems dynamically partition subcarriers between communication-only and joint communication-sensing roles, with alternating optimization of transmit/receive beamformers and sensing waveform covariance (Galappaththige et al., 22 Mar 2025).

A summary table of common paradigms is provided:

Architecture	Typical Variables	Principal Constraints
MIMO/OFDM (DFRC)	$\{\mathbf{W}_k\}$, subcarrier set $\mathcal{J}$	Power, sensing beampattern, rate
Vehicular SPV	Mode selection, association	SINR, mapping exclusivity
UAV-assisted ISAC	Beamforming, 3D trajectory	CRB, energy, collision
B-ISAC/Backscatter	Tx/Rx beamforming	Detection probability, power
Wideband CR JCS	Subcarrier allocation, beams	Interference, QoS, power

3. Algorithmic Approaches

A broad range of algorithmic strategies are employed, driven by the non-convexity and the hybrid combinatorial/continuous nature of the optimization problems:

Graph Neural Networks (Vehicular SPV)

A heterogeneous node/edge-type GNN encodes spatial, connectivity, and interference context in dynamic topologies. The model employs layered message-passing to generate multi-label scores for assignment, with final binary decision derived via QCP solvers (Li et al., 2023).

Riemannian and Manifold Optimization

For multi-carrier JCAS, maximizing communication rate under sensing constraints is framed on a complex hypersphere manifold. Gradients are computed with respect to the manifold’s tangent space, with iterative conjugate gradient steps and retraction for constraint satisfaction (Nguyen et al., 2023, Galappaththige et al., 22 Mar 2025).

Fractional Programming and Block Coordinate Descent

The sum-rate maximization with embedded SINR or CRB constraints is approached via fractional transforms (Lagrangian/quad. variable), followed by alternating optimization. For UAV networks, the beamforming step is solved via fractional programming and SDP, while trajectories are refined using DDPG, a deep reinforcement learning algorithm (Tun et al., 21 Mar 2025).

Alternating Convex and Successive Convex Approximation (SCA)

Problems with nonconvex SINR or detection constraints (e.g., B-ISAC) utilize quadratic transforms to recast objectives, with each iteration maximizing a surrogate and updating auxiliary variables. SCA linearly approximates the nonconvex parts, enabling iterative convex QCQP or SOCP updates convergent to stationary solutions (Zhao et al., 4 Sep 2024).

Evolutionary Algorithms with RL Operator Selection

Security-aware multi-objective problems in LAWN ISCC are addressed by embedding a DQN-based meta-controller within a multi-objective evolutionary algorithm, adaptively selecting variation operators to optimize Pareto dominance in the presence of secrecy rate, beampattern error, and AoI objectives (Wang et al., 3 Nov 2025).

Monotonic Optimization with Polyblock Approximation

In secure ISAC with time-split and beamforming, the system sum rate is globally maximized subject to secrecy and estimation error (CRLB) constraints through a nested monotonic program. Polyblock methods project candidate points, iteratively shrinking the feasible region, and are coupled with line search over time allocation (Xu et al., 2023).

4. Key Performance Metrics and Trade-off Analysis

Performance indicators are tailored to the application:

Rate/Accuracy Frontiers: Pareto curves plot communication rate (bit/s) versus sensing resolution (inverse MSE, e.g., $\kappa P_s B_s^2$), or sum-rate against CRB/MI for parameter estimation (Li, 2020, Ni et al., 2020, Nguyen et al., 2023).

Detection Probability and RMSE: For beamspace-based DFRC, windowing parameters are tuned to maximize probability of detection (PD) over the field of view, minimizing DOA RMSE and runtime for beam update (Raghavendra et al., 21 Dec 2024).

Reliability and Spectral Efficiency: In THz RIS-XR scenarios, situational map resolution, E2E latency reliability, and spectral efficiency gains are directly correlated with bandwidth and environmental sensing (Chaccour et al., 2021).

Secrecy Rate and AoI: Security-aware optimization in LAWNs utilizes secrecy sum-rate and average AoI as critical metrics, explicitly traded against beampattern fidelity (Wang et al., 3 Nov 2025).

Energy Minimization: In 6G joint location-communication, total power is minimized under communication and sensing throughput constraints, with subcarrier assignment informed by SINR weights (Zhang et al., 28 May 2024).

5. Hardware and Implementation Considerations

Joint optimization methods often require architectural adaptations for feasible deployment:

• Hybrid and Analog Arrays: Multibeam analog array optimization leverages phase-shift combinations and semidefinite relaxation for efficient multi-function support (Luo et al., 2020, Barneto et al., 2021).
• Windowing for Real-Time Adaptation: Amplitude-only parameterized windows (Kaiser, Chebyshev) are stored in lookup tables for sub-millisecond analog beamforming update, enabling robust DFRC performance under rapid resource fluctuation (Raghavendra et al., 21 Dec 2024).
• Resource Block and Subcarrier Adaptation: Modern systems split the OFDM subcarrier set adaptively, reserving subsets for JCAS to balance sensing and communication across time/frequency (Nguyen et al., 2023, Galappaththige et al., 22 Mar 2025).

6. Practical Guidelines and Observed Gains

• Subset Partitioning: Select low-rate subcarriers for JCAS functions to limit communication loss, empirical operational points at $J\approx K/4$ in multi-carrier systems yield substantial performance gains (Nguyen et al., 2023).
• Power/Bandwidth Allocation: Communication is power-tolerant but spectrally zero-sum with sensing, emphasizing spectral agility for higher performance (Li, 2020).
• Window Parameterization: In dynamic CR/DFRC systems, real-time adjustment of window parameters maintains sensing fidelity under strong communication priority (Raghavendra et al., 21 Dec 2024).
• Joint RL and Evolutionary Search: Adaptive operator selection via reinforcement learning in evolutionary frameworks outperforms static strategies for multi-metric balancing under security and latency constraints (Wang et al., 3 Nov 2025).
• **Integrated Mapping