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NOMA Empowered Integrated Sensing and Communication
Zhaolin Wang, Yuanwei Liu, Xidong Mu, Zhiguo Ding, Octavia A. Dobre
TL;DR
The paper addresses ISAC when correlated channels or overload limit conventional spatial degrees of freedom by proposing NOMA-ISAC with SIC and superimposed sensing-communication signals. A double-layer penalty-based SCA algorithm solves its beamforming design, and numerical results show better performance than conventional ISAC in highly correlated underloaded and overloaded regimes.
Problem
The central problem is integrating sensing with communication when correlated channels or overload limit conventional ISAC’s spatial degrees of freedom.
Method
NOMA-ISAC uses a dual-functional BS, superimposed communication signals for simultaneous sensing, SIC for interference mitigation, and a double-layer penalty-based SCA algorithm for beamforming design.
Results
NOMA-ISAC outperforms conventional ISAC in the underloaded regime with highly correlated channels and in the overloaded regime.
Takeaways & Limitations
In the overloaded regime, NOMA-ISAC performs close to the ideal ISAC system while providing high-quality communication and sensing.
Abstract
from arXiv · showhide
A non-orthogonal multiple access (NOMA) empowered integrated sensing and communication (ISAC) framework is investigated. A dual-functional base station serves multiple communication users employing NOMA, while the superimposed NOMA communication signal is simultaneously exploited for target sensing. A beamforming design problem is formulated to maximize the weighted sum of the communication throughput and the effective sensing power. To solve this problem, an efficient double-layer penalty-based algorithm is proposed by invoking successive convex approximation. Numerical results show that the proposed NOMA-ISAC outperforms the conventional ISAC in the underloaded regime experiencing highly correlated channels and in the overloaded regime.
I. INTRODUCTION
The paper introduces NOMA-ISAC to address communication and sensing challenges under highly correlated channels and overloaded conditions. It uses superimposed NOMA signals, SIC, and beamforming optimization to improve the communication-sensing trade-off.
- Motivation: Conventional ISAC can fail when highly correlated channels or overload create severe inter-user interference and insufficient spatial DoFs.Under these conditions, even communication-only requirements may be unsatisfied, making sensing integration generally impossible.
- Motivation: NOMA multiplexes users in the power domain and uses SIC to mitigate inter-user interference while providing extra DoFs.It can serve more users than conventional multiple access techniques and achieve higher spectral efficiency.
- Contribution: The paper proposes a NOMA-ISAC framework that simultaneously uses the transmitted superimposed signal for communication and sensing.SIC is exploited for inter-user interference mitigation.
- Contribution: The beamforming problem maximizes a weighted sum of communication throughput and effective sensing power subject to communication-rate and radar-specific constraints.The non-convex problem is addressed using a double-layer penalty-based algorithm based on successive convex approximation.
- Results: Under high spatial correlation or system overload, NOMA-ISAC achieves a better performance trade-off than conventional ISAC.The result is reported for both the underloaded regime with highly correlated channels and the overloaded regime.
II. SYSTEM MODEL AND PROBLEM FORMULATION
The system model comprises a dual-functional multi-antenna base station serving single-antenna users and radar targets through superimposed NOMA transmission. User ordering and SIC determine the achievable communication rates and total throughput.
- A. System Model: The NOMA-ISAC system uses a dual-functional BS with an N-antenna ULA, K single-antenna users, and M radar targets.Users and targets are indexed by K = {1, ..., K} and M = {1, ..., M}.
- 1) Communication Model:: The BS transmits superimposed signals w_i s_i to all users, where w_i is the beamformer for user i.The received signal at user k is modeled using the combined transmitted signals and noise.
- 1) Communication Model:: User indexes increase with large-scale channel strength, with user 1 weakest and user K strongest.The model distinguishes large- and small-scale fading and includes circularly symmetric complex noise.
- 1) Communication Model:: User k decodes and removes interference from weaker users j < k using SIC, while treating stronger-user interference j > k as noise.This decoding order determines the achievable rate of each decoded symbol.
- 1) Communication Model:: For k ≠ K, each user symbol must also be decodable at stronger users j > k to enable SIC.The overall achievable rate accounts for these decoding requirements.
- 1) Communication Model:: At user K, SIC eliminates interference from all other users before determining its achievable rate.The users’ communication throughput is then obtained from their achievable rates.
2) Sensing Model:
The sensing model reuses communication waveforms and designs their covariance to provide effective target-direction sensing while controlling target separability through cross-correlation.
- 2) Sensing Model:: Communication waveforms are exploited for radar target sensing, requiring the transmitted-signal covariance matrix to satisfy sensing requirements.The covariance matrix is the sensing-design variable.
- 2) Sensing Model:: Effective sensing power is the probing-signal power in target directions and is maximized using prior target information.Target directions are represented by θ_m and their steering vectors by a(θ_m).
- 2) Sensing Model:: The steering vector depends on the carrier wavelength λ and antenna spacing d.These parameters define the array response used for target-direction sensing.
- 2) Sensing Model:: Similar sensing power is desired across target directions so that each target can be fairly tracked.The model also expects low cross-correlation between transmitted signals at distinct target directions.
- 2) Sensing Model:: The cross-correlation between directions θ_k and θ_p is measured by |a^H(θ_k)R_w a(θ_p)| for distinct targets.Its mean-squared value summarizes cross-correlation across the M^2−M target pairs.
- 2) Sensing Model:: Unlike conventional ISAC, NOMA-ISAC combines spatial-DoF-based mitigation with SIC for inter-user interference.This supplies extra DoFs when spatial DoFs are limited, supporting communication performance and sensing integration.
B. Problem Formulation
The beamforming formulation balances communication throughput and effective sensing power under user-rate, radar, power, and cross-correlation constraints. Because the resulting problem is non-convex, the paper uses an iterative SCA-based solution.
- B. Problem Formulation: The objective maximizes a weighted sum of communication throughput and effective sensing power while satisfying minimum user rates and radar requirements.The weights control the communication-sensing performance trade-off.
- B. Problem Formulation: The formulation enforces minimum communication rates, similar sensing power across target directions, and a constant per-antenna transmit-power constraint.The total transmit power is denoted by P_t.
- B. Problem Formulation: A mean-squared cross-correlation constraint imposes an upper bound on correlation among target-direction sensing signals.This constraint represents a radar-specific requirement.
- B. Problem Formulation: The achievable-rate expression is neither convex nor concave, making the objective non-concave and the minimum-rate constraint non-convex.Quadratic covariance forms also make the sensing constraints non-convex.
- B. Problem Formulation: The paper proposes an efficient iterative algorithm based on successive convex approximation to obtain a suboptimal solution.The global optimum is challenging to obtain for the formulated problem.
III. PROPOSED SOLUTION
The proposed solution uses an SCA-based double-layer penalty algorithm to address the non-convex beamforming problem while obtaining feasible rank-one solutions. The algorithm progressively handles rank-one constraints and balances objective performance against penalty reduction.
- The method develops an SCA-based double-layer iterative algorithm for the non-convex optimization problem.
- The algorithm avoids reconstruction drawbacks associated with semidefinite relaxation, which can cause performance loss and fail to preserve feasibility.
- The rank-one constraint is transformed into a penalty term using the difference between the nuclear and spectral norms.For a positive semidefinite matrix, the difference is zero for rank one and positive otherwise.
- Successive convex approximation replaces the non-convex penalty component with a first-order Taylor upper bound, yielding a quadratic semidefinite program solvable by CVX.
- The penalty factor η is initialized large and gradually reduced to obtain an overall suboptimal solution while controlling throughput and sensing-power optimization.If η approaches zero, the penalty can dominate the objective and prevent a good solution for throughput and effective sensing power.
- The stated complexity is O(IoIi(K^6.5N^6.5 log(1/e))), with Io and Ii denoting outer- and inner-layer iteration counts.
IV. NUMERICAL RESULTS
The numerical evaluation studies NOMA-ISAC with a four-antenna ULA, multiple users and radar targets, correlated Rayleigh-fading channels, and specified power, noise, path-loss, and algorithm parameters.
- The simulation uses a BS with a ULA of N = 4 antennas serving K = 2 or 6 users and tracking M = 2 radar targets.
- User channels follow Rayleigh fading with path loss Λk(dB) = 32.6 + 36.7 log10(dk), based on a 3GPP propagation environment.
- Users are equally spaced between 50 m and 200 m from the BS, and spatial correlation between users follows t^|i−j| for t ∈ [0, 1].
- The simulations set Rmin = 1 bit/s/Hz, Pdiff = 10, ξ = 10, η = 10^5, ε1 = 10^-2, and ε2 = 10^-4.
A. Convergence of Algorithm 1
The proposed algorithm rapidly converges to a stable objective while driving the penalty nearly to zero, producing feasible rank-one solutions. Smaller reduction factors accelerate convergence but yield lower objective values.
- A. Convergence of Algorithm 1: The objective value quickly converges to a stable value, while the penalty term approaches zero after several outer iterations.This behavior is observed for any tested reduction factor ε.
- A. Convergence of Algorithm 1: The convergence behavior indicates that the algorithm can find a feasible rank-one solution with high performance.
- A. Convergence of Algorithm 1: As ε decreases, convergence becomes faster but the objective value becomes lower, representing a speed–performance trade-off.
- A. Convergence of Algorithm 1: The simulations use ε = 0.2 to obtain a suitable balance between convergence speed and system performance.
B. Baseline
The baseline comparison evaluates conventional ISAC without NOMA against the proposed NOMA-ISAC using communication throughput and effective sensing power as the trade-off dimensions.
- B. Baseline: The conventional ISAC baseline excludes NOMA.
- B. Baseline: The achievable rate at user k is used in the conventional ISAC comparison.
- B. Baseline: The baseline throughput-maximization problem is formulated as maximizing Rb.
- B. Baseline: The sensing-target power problem can be solved using Algorithm 1 with the interference term in (20).
- B. Baseline: Figure 4 compares communication throughput against effective sensing power to show the performance trade-off.
C. Performance Trade-off
The performance trade-off between communication throughput and effective sensing power is evaluated for NOMA-ISAC and conventional ISAC under different spatial-correlation and loading conditions. NOMA-ISAC is especially advantageous in overloaded systems and highly correlated channels, while conventional ISAC performs better at low spatial correlation in the underloaded regime.
- Simulation setup: 400 random channel realizations evaluate underloaded (K = 2) and overloaded (K = 6) regimes.The simulations examine the effect of spatial correlation on both system configurations.
- Spatial correlation: The NOMA-ISAC performance is unaffected by the spatial factor because throughput is dominated by the strongest NOMA user.By contrast, conventional ISAC performance depends on spatial correlation, with its achievable area shrinking as correlation increases.
- Underloaded regime: In the underloaded regime, NOMA-ISAC outperforms conventional ISAC at high spatial correlation but performs worse when spatial correlation is low.This comparison describes the reversal in relative performance across correlation conditions.
- Overloaded regime: In the overloaded regime, NOMA-ISAC achieves a considerable gain over conventional ISAC, which increases with spatial correlation.Conventional ISAC cannot mitigate inter-user interference well with limited spatial DoFs, whereas SIC in NOMA-ISAC provides more DoFs for radar sensing.
- Implication: These results underscore the importance of NOMA when the ISAC system is overloaded or channels are highly spatially correlated.The comparison is made against conventional ISAC in both loading regimes and correlation conditions.
- Comparison with ideal ISAC: NOMA-ISAC has only a slight gap from ideal ISAC, while conventional ISAC has a significant gap between real and ideal performance.The NOMA-ISAC system can nearly achieve the communication and radar-sensing upper bounds simultaneously.
D. Transmit Beampattern
Transmit beampatterns are compared at a communication throughput of 13.5 bit/s/Hz for NOMA-ISAC and conventional ISAC. NOMA-ISAC preserves dominant sensing peaks in the overloaded regime, whereas conventional ISAC suffers severe leakage and sensing degradation.
- Setup: At 13.5 bit/s/Hz, transmit beampatterns are compared for NOMA-ISAC and conventional ISAC with t = 0.Both underloaded (K = 2) and overloaded (K = 6) regimes are considered.
- Overloaded regime: In the overloaded regime, NOMA-ISAC still achieves the dominant peaks, while conventional ISAC experiences severe power leakage in undesired directions.The leakage leads to significant sensing-performance degradation for conventional ISAC.
- Sensing implication: NOMA is important for guaranteeing sensing performance when the ISAC system is overloaded.The beampattern comparison provides an additional indication of the overloaded-regime advantage.
- Design and optimization: The proposed system maximizes a weighted sum of communication throughput and effective sensing power subject to user-rate and radar-specific requirements.A double-layer penalty-based algorithm obtains a suboptimal solution to the non-convex beamforming problem.
- Overall result: NOMA-ISAC achieves a better communication-sensing trade-off than conventional ISAC under overload or high channel spatial correlation.In the overloaded regime, its performance is close to ideal ISAC and can provide high-quality communication and sensing.