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Full-Duplex Communication for ISAC: Joint Beamforming and Power Optimization
Zhenyao He, Wei Xu, Hong Shen, Derrick Wing Kwan Ng, Yonina C. Eldar, Xiaohu You
TL;DR
The paper addresses joint beamforming and power optimization for FD ISAC, where radar sensing and uplink/downlink communication share resources and create tightly coupled interference. It derives closed-form receive beamformers and uses iterative optimization methods, reporting improved power and spectral efficiency over HD communication-based ISAC, especially under favorable residual-SI and sensing conditions.
Problem
Existing ISAC beamforming designs commonly combine FD sensing with HD communication, leaving joint FD radar, downlink, and uplink optimization under shared resources challenging because of coupled signals and interference.
Method
The paper derives closed-form optimal radar and uplink receive beamformers, then optimizes BS transmit beamforming and uplink-user power using rank relaxation, SCA, and a low-complexity alternative for a special case.
Results
The optimized FD communication-based ISAC substantially improves power efficiency and spectral efficiency over conventional ISAC with HD communication; its sum rate is nearly doubled when residual SI power is relatively low.
Takeaways & Limitations
FD capability for both sensing and communication provides the reported largest performance gains when residual self-interference is low and sensing requirements are less restrictive.
Abstract
from arXiv · showhide
Beamforming design has been widely investigated for integrated sensing and communication (ISAC) systems with full-duplex (FD) sensing and half-duplex (HD) communication. To achieve higher spectral efficiency, in this paper, we extend existing ISAC beamforming design by considering the FD capability for both radar and communication. Specifically, we consider an ISAC system, where the BS performs target detection and communicates with multiple downlink users and uplink users reusing the same time and frequency resources. We jointly optimize the downlink dual-functional transmit signal and the uplink receive beamformers at the BS and the transmit power at the uplink users. The problems are formulated under two criteria: power consumption minimization and sum rate maximization. The downlink and uplink transmissions are tightly coupled due to both the desired target echo and the undesired interference received at the BS, making the problems challenging. To handle these issues in both cases, we first determine the optimal receive beamformers, which are derived in closed forms with respect to the BS transmit beamforming and the user transmit power, for radar target detection and uplink communications, respectively. Subsequently, we invoke these results to obtain equivalent optimization problems and propose efficient iterative algorithms to solve them by using the techniques of rank relaxation and successive convex approximation (SCA), where the adopted relaxation is proven to be tight. In addition, we consider a special case under the power minimization criterion and propose an alternative low complexity design. Numerical results demonstrate that the optimized FD communication-based ISAC brings tremendous improvements in terms of both power efficiency and spectral efficiency compared to the conventional ISAC with HD communication.
I. INTRODUCTION
ISAC shares spectrum and hardware for sensing and communication, but prior FD radar designs paired sensing with HD communication. This paper formulates joint FD communication-based ISAC optimization for coupled downlink and uplink transmissions.
- ISAC integrates sensing and communication by sharing spectral resources and reusing hardware, addressing demands for reliable sensing and efficient wireless communication.
- Prior ISAC studies considered FD radar reception while integrating communication only in either the downlink or uplink under HD operation.
- The proposed system lets the BS detect a point target and serve multiple downlink and uplink users concurrently over the same time-frequency resources.
- The paper jointly optimizes the downlink dual-functional transmit signal, BS receive beamformers, and uplink-user transmit powers under power-minimization and sum-rate-maximization criteria.
- Optimal radar and uplink receive beamformers are derived in closed form, enabling equivalent problems solved iteratively with rank relaxation and SCA, with tight relaxation.
- An alternative low-complexity design for a special power-minimization case achieves almost the same performance as the SCA-based method while significantly reducing computational complexity.
B. Radar and Communication SINR
The BS receives uplink signals and target echoes alongside downlink-dependent interference, so radar and communication SINRs include coupled interference terms. Linear receive beamformers define the radar and uplink detection metrics.
- Radar target-detection performance is measured by radar SINR because detection probability generally increases monotonically with output SINR.
- The BS receive signal contains desired target reflection, uplink communication signals, and downlink-dependent interference from environmental interferers and residual self-interference.
- The radar SINR is more complicated than prior downlink-only expressions because uplink transmission introduces signal-dependent interference and coupling.
- Linear receive beamformers are applied to the BS signal to recover each uplink user's data and obtain the corresponding receive SINR.
- Downlink-user SINR follows from the downlink signal model, while the considered users do not cancel interference from the dedicated radar signal.
C. Problem Formulation
The paper formulates FD ISAC design under power minimization and sum-rate maximization, while accounting for coupled communication and sensing constraints. It also establishes extensions to multiple targets and proceeds toward closed-form receiver-based solution methods.
- C. Problem Formulation: The optimization variables include BS transmit beamforming, uplink transmit powers, and receive beamformers.
- C. Problem Formulation: The joint design optimizes transmit variables under two criteria: total power minimization with SINR guarantees, and sum-rate maximization under power budgets and a radar SINR constraint.
- C. Problem Formulation: For power minimization, the objective is total transmit power subject to minimum uplink, downlink, and radar SINR requirements.
- C. Problem Formulation: For sum-rate maximization, the system maximizes aggregate uplink and downlink rates with limited transmit power while enforcing minimum radar SINR.
- C. Problem Formulation: Both formulations are nonconvex, with tightly coupled optimization variables that make globally optimal solutions difficult to obtain by polynomial-time methods.
- C. Problem Formulation: In multi-target sensing, M radar receive beamformers replace the single radar SINR constraint with M individual target constraints.
- C. Problem Formulation: The solution strategy first determines closed-form optimal receive beamformers, substitutes them into the power-minimization problem, and then applies SCA to the equivalent formulation.
A. Closed-Form Solutions to Receive Beamformer
The paper eliminates receiver optimization through SINR-maximizing closed-form receive beamformers, then solves the remaining transmit design using rank relaxation and SCA. The relaxation is shown to be tight, while the resulting iterative procedure converges to a KKT point.
- A. Closed-Form Solutions to Receive Beamformer \b: The radar and uplink receive beamformers are selected to maximize their corresponding SINRs, reducing required transmit power without affecting unrelated user SINRs.
- A. Closed-Form Solutions to Receive Beamformer \b: The optimal receive beamformers have closed-form expressions determined by BS transmit beamforming and uplink-user transmit powers.
- B. Solutions to Transmit Beamforming and Power \b: After substituting the closed-form receivers, the remaining problem optimizes BS transmit beamforming and uplink powers using an equivalent formulation.
- B. Solutions to Transmit Beamforming and Power \b: Rank relaxation removes beamformer rank constraints, and SCA constructs convex surrogate problems by first-order Taylor lower bounds for the remaining DC constraints.
- B. Solutions to Transmit Beamforming and Power \b: The iterative convex subproblem is solved with standard convex optimization tools, and the procedure converges to a Karush-Kuhn-Tucker point.
- B. Solutions to Transmit Beamforming and Power \b: Although Gaussian randomization can recover rank-one beamformers with computational cost and performance loss, the paper constructs rank-one solutions without performance loss.
- B. Solutions to Transmit Beamforming and Power \b: Algorithm 1 alternates convex updates of transmit variables and closed-form updates of the receive beamformers until convergence.
C. Special Case of Uplink Communication Only
For the uplink-only special case, the paper replaces the general SCA-based design with an alternating low-complexity method. Its SOCP subproblem yields lower computational cost while retaining nearly identical performance.
- C. Special Case of Uplink Communication Only: The special case removes downlink communication, uses the downlink signal only for target detection, and still optimizes uplink transmission.
- C. Special Case of Uplink Communication Only: The simplified problem removes downlink-communication optimization, allowing an alternative algorithm with dramatically lower computational complexity than the SCA method.
- C. Special Case of Uplink Communication Only: The low-complexity method alternates receive-beamformer updates with optimization of the downlink covariance and uplink powers.
- C. Special Case of Uplink Communication Only: For fixed receive beamformers, the transmit-variable subproblem can be formulated as an SDP and equivalently solved as an SOCP with lower computational complexity.
- C. Special Case of Uplink Communication Only: The receive beamformers are obtained in closed form, while the SOCP introduces auxiliary variables to compute the remaining optimal solution.
- C. Special Case of Uplink Communication Only: The alternating algorithm has a nonincreasing power objective and is guaranteed to converge because its solution set is compact.
- C. Special Case of Uplink Communication Only: Algorithm 2 updates receive beamformers, solves the SOCP, and repeats until convergence.
- C. Special Case of Uplink Communication Only: Compared with Algorithm 1, Algorithm 2 has lower per-iteration complexity while achieving similar convergence speed and performance.
IV. JOINT FD ISAC DESIGN FOR SUM RATE MAXIMIZATION
The sum-rate maximization problem is generally NP-hard, so the paper first determines optimal receivers and then develops an effective iterative algorithm.
- IV. JOINT FD ISAC DESIGN FOR SUM RATE MAXIMIZATION: The sum-rate maximization problem is generally NP-hard, even for communication-only systems, motivating receiver elimination followed by iterative optimization.
A. Problem Reformulation
The reformulation substitutes optimal receive beamformers and equivalent SINR expressions, then introduces auxiliary variables to establish an equivalent optimization problem.
- Optimal receive beamformers and equivalent SINR expressions rewrite the original problem into a tractable reformulated form.
- Real-valued auxiliary variables uk ≥ 0 and matrices Vl ≜ vlvH are introduced in the reformulation.
- The constraints uk ≤ γ̄com,UL_k remain active at optimality, establishing equivalence between problems (34) and (35).
B. Proposed Solution
The proposed solution applies successive convex approximation to nonconvex objective and SINR constraints, solving convex subproblems iteratively. Convergence yields a KKT point, while rank-one solutions can be recovered without performance loss.
- Nonconcave objective terms and coupled radar and communication constraints make the reformulated optimization problem nonconvex.
- Downlink rate approximation: The downlink achievable rate is lower-bounded by linearizing one concave logarithm term with a first-order Taylor expansion.
- Constraint approximation: Existing successive-convex-approximation constraints are reused to construct convex subsets for the radar and communication constraints.
- Uplink SINR approximation: Auxiliary variables xk split a fractional SINR constraint into two constraints, enabling convex approximation after replacing xk^2 with its first Taylor expansion.
- Iterative algorithm: Each iteration solves a convex optimization problem globally, updates the approximation variables, and repeats within the SCA framework.
- Convergence and recovery: Iterative solution of problem (42) converges to a KKT point, and rank-one matrices are recovered without performance loss; the procedure is designated Algorithm 3.
V. SIMULATION RESULTS
Simulations evaluate the proposed algorithms under power-minimization and sum-rate-maximization settings, including convergence, beampatterns, and comparisons with HD and sensing/communication-only benchmarks. The results show effective sensing and communication beamforming, lower power than HD mode, and nearly doubled sum rate at relatively low residual SI.
- Convergence and complexity: Both Algorithm 1 and Algorithm 2 typically converge within 6 iterations, while Algorithm 2 has lower per-iteration complexity and the same objective value in the special case.The complexity advantage is verified for the special case with L = 0.
- Radar beampattern: Algorithm 1 allocates transmit main beams toward the target and downlink users while placing deep nulls toward interferers and uplink users.The receive beampattern also suppresses directions whose reflected or transmitted signals interfere with radar sensing.
- Communication beampattern: The communication beampattern validates the design by steering beams toward downlink users and producing patterns nearly identical to the communication-only scheme.For uplink reception, nulls are placed toward the target, interferers, and the other uplink user when they cause decoding interference.
- Sum-rate maximization: The proposed FD ISAC scheme nearly doubles sum rate relative to HD mode at relatively low SI power, while increasing radar SINR requirements reduce sum rate through a communication-radar trade-off.The FD advantage is also observed when comparing sum rate against the radar SINR threshold.
VI. CONCLUSION
The paper jointly optimizes FD communication-based ISAC for transmit-power minimization and sum-rate maximization, deriving closed-form receive beamformers and SCA-based algorithms. A low-complexity power-minimization design achieves almost identical performance, while simulations show advantages over HD communication.
- The study jointly optimizes an FD communication-based ISAC system under transmit-power minimization and sum-rate maximization.
- Closed-form optimal receive beamformers are derived, followed by SCA-based optimization of BS transmit beamforming and user transmit power.
- A low-cost power-minimization solution has much lower computational complexity than SCA while achieving almost identical performance.
- Simulations verify the algorithms and show tremendous advantages of FD communication-based ISAC over prior ISAC frameworks with HD communication.
APPENDIX A PROOF OF PROPOSITION 1
The appendix derives closed-form receive beamformers by recognizing the radar and uplink communication SINR maximizations as generalized Rayleigh quotient problems. It then develops the tightness proof for the relaxed optimization formulation using semidefinite-program duality and KKT conditions.
- The optimal uplink receive beamformer follows from maximizing the uplink communication SINR as a generalized Rayleigh quotient.
- The optimal radar receive beamformer is obtained by applying the generalized Rayleigh quotient to the radar SINR expression.
- The relaxation proof is divided into showing feasibility of the constructed solution and identical objective values relative to the relaxed solution.
- Because the problem is a convex SDP satisfying Slater’s condition, zero duality gap makes its KKT conditions necessary and sufficient for optimality.
- The KKT conditions establish the required rank property, enabling the relaxed matrix V0 to be expressed as V0 = v0v0^H.
APPENDIX D PROOF OF PROPOSITION 2
The appendix converts the rank-one formulation into second-order cone constraints and an SOCP for a special low-complexity power-minimization design. It also defines the HD comparison problems and averages downlink and uplink objectives for the TDD system.
- The rank-one matrix V0 is represented as V0 = v0v0^H, with phase rotation imposed without loss of optimality.
- The radar SINR constraint is transformed into a second-order cone, and analogous operations produce SOCs for communication SINR constraints.
- Introducing an auxiliary variable converts the power-minimization formulation into the SOCP in (33).
- The HD benchmark omits uplink interference from radar SINR and adjusts rate constraints so FD and HD minimum average rates are identical.
- The TDD system’s average power consumption and achievable rate are obtained by averaging the optimized downlink and uplink objective values.