NOMA-Aided Joint Radar and Multicast-Unicast Communication Systems

I. INTRODUCTION

• Radar occupies substantial spectrum, while sharing it with communications is also relevant to applications such as autonomous vehicles that need radar sensing and reliable information exchange.The introduction cites weather radar bands below 10 GHz and mmWave radar for collision avoidance and high-resolution imaging.Source: §I · p. 1

A. State-of-the-art

• RCC research manages mutual interference between separate radar and communication systems, whereas DFRC uses a common platform and can reduce hardware cost.The cited DFRC work spans beam-pattern design, communication requirements, waveform design, and communication-performance improvements.Source: 1) Studies on RCC · p. 2, 2) Studies on DFRC · p. 2

B. Motivations and Contributions

• Prior CRSS work considered unicast communication and treated the radar target as detection-only, leaving NOMA's interplay with CRSS and its potential performance gain unstudied.The introduction identifies mixed multicast-unicast service and simultaneous communication with and detection of the radar target as the motivation for this work.Source: B. Motivations and Contributions · p. 2
• The single-pair BB NOMA framework uses different beamformers for multicast and unicast, maximizing unicast rate subject to multicast-rate and radar-pattern requirements.Its non-convex beamformer problem is addressed with a penalty-based iterative algorithm targeting a stationary point.Source: B. Motivations and Contributions · p. 3
• The multi-pair CB NOMA framework superimposes each pair's multicast and unicast messages at different power levels over a common beamformer and jointly optimizes beamforming and power allocation.The objective is the sum unicast rate subject to each pair's multicast-rate requirement and radar-pattern accuracy for multiple R-user targets.Source: B. Motivations and Contributions · p. 3
• The proposed NOMA-aided schemes achieve higher unicast performance than conventional-transmission benchmarks, with larger gains under more relaxed radar beam-pattern constraints.The schemes also support multicast-unicast communication while constructing a high-quality radar beam pattern.Source: B. Motivations and Contributions · p. 3

C. Organization and Notation

• The paper proceeds from a single-pair BB NOMA framework and unicast-rate optimization to a multi-pair CB NOMA framework and sum-rate optimization, followed by numerical results and conclusions.The notation section defines conventions for scalars, vectors, matrices, and common matrix operations.Source: C. Organization and Notation · p. 3

A. System Model

• The single-pair system has one MIMO DFRC base station, one R-user, and one C-user, with multicast intended for both users and unicast only for the C-user.The paper presents the mixed transmission as an integration of communication with radar detection.Source: A. System Model · pp. 3–4

1) BB NOMA-aided MU-Communication Model:

• BB NOMA multiplexes multicast and unicast signals in the power domain using different beamformers, with the C-user decoding multicast first and subtracting it before decoding unicast.The R-user detects multicast while treating unicast as noise, and the multicast rate is limited by the lower of the two users' rates.Source: 1) BB NOMA-aided MU-Communication Model · p. 4

2) BB NOMA-aided Radar Detection Model:

• The superimposed communication symbols are also radar probing snapshots, so radar beam-pattern design is equivalent to designing the transmitted signal's covariance matrix.The transmit beam pattern depends on the antenna-array steering vector, detection angle, antenna spacing, and carrier wavelength.Source: 2) BB NOMA-aided Radar Detection Model · p. 4
• NOMA's power sharing supports the R- and C-users' rate requirements, while separate beamformers add degrees of freedom for radar beam-pattern design.Successive interference cancellation removes inter-signal interference for the C-user's unicast transmission, at the cost of additional signal-processing complexity.Source: 2) BB NOMA-aided Radar Detection Model · p. 4

B. Problem Formulation

• The radar-only ideal beam pattern supplies a benchmark for measuring radar performance loss in the joint radar-communication design.Its minimum beam-pattern error is obtained from a convex least-squares problem; the joint design seeks to maximize C-user unicast rate while meeting multicast-rate and radar-pattern requirements.Source: B. Problem Formulation · p. 5
• The optimization constrains joint-system beam-pattern error relative to the radar-only minimum by a maximum tolerable mismatch ratio.The model assumes a total base-station power constraint, which the paper says provides more beamformer-design degrees of freedom than a per-antenna constraint.Source: B. Problem Formulation · p. 5

C. Proposed Solution

• The proposed double-layer penalty algorithm targets near-optimal rank-one solutions, avoiding the possible performance loss and feasibility failure of SDR reconstruction.SDR relaxes the rank-one constraint and may require Gaussian randomization to reconstruct a rank-one solution.Source: C. Proposed Solution · p. 5
• The method penalizes violations of rank-one equality constraints and gradually reduces the penalty factor from a large initial value.The penalty is based on the nuclear norm minus the spectral norm for each positive semidefinite matrix.Source: C. Proposed Solution · p. 6
• For a fixed penalty factor, successive convex approximation replaces non-convex terms with bounds and iteratively solves a convex problem.The inner iterations stop when the fractional objective reduction falls below a predefined threshold.Source: C. Proposed Solution · p. 6
• A larger penalty-update scaling factor can improve final performance by exploring more candidates, but requires more outer iterations.The scaling factor therefore trades performance against computational complexity.Source: 2) Outer Layer: Reducing the Penalty… · p. 6

3) Overall Algorithm and Complexity Analysis:

• The outer loop reduces the penalty factor until constraint violation falls below tolerance, while the inner loop repeats convex problem (16) until objective reduction is small.Algorithm 1 initializes feasible points and a penalty factor, then alternates these loops.Source: 3) Overall Algorithm and Complexity… · pp. 6–7
• The double-layer penalty algorithm is guaranteed to converge to a stationary point of the original problem.For a fixed penalty factor, the inner objective is monotonically non-increasing and the unicast rate is bounded by the BS transmit-power limit.Source: 3) Overall Algorithm and Complexity… · p. 6
• Repeatedly solving the standard SDP (16) accounts for the algorithm’s main computational complexity.The supplied complexity expression is incomplete, so no overall order is reported.Source: 3) Overall Algorithm and Complexity… · p. 6

III. CB NOMA-AIDED JOINT RAD-MU-COM SYSTEM

• The cluster-based framework serves multiple R&C pairs with a common beamformer per pair and multiple beamformers for detecting the R-user targets.Each pair receives a multicast message at both users and a unicast message only at its C-user.Source: §III · p. 7, A. System Model · p. 7

1) CB NOMA-aided MU-Communication Model:

• Unlike the single-pair beamformer-based structure, cluster-based NOMA multiplexes each pair’s multicast and unicast messages in the power domain over a common beamformer.The messages are intended for the R- and C-users in that pair.Source: 1) CB NOMA-aided MU-Communication Model · p. 7
• The formulation assumes equal numbers of R- and C-users, paired one-to-one; handling unequal numbers is left for future work.The framework is described for K R&C pairs.Source: 1) CB NOMA-aided MU-Communication Model · p. 7
• The C-user first decodes multicast while treating other signals as interference, then decodes unicast after SIC; the R-user detects only its intended multicast signal.The C-user’s post-SIC unicast rate and the pair’s multicast rate are defined separately.Source: 1) CB NOMA-aided MU-Communication Model · pp. 7–8

2) CB NOMA-aided Radar Detection Model:

• The cluster-based radar design uses K beamformers rather than the 2K required by the alternative BB structure, reducing complexity when K is large.The BB structure provides enhanced design degrees of freedom but requires separate multicast and unicast beamformers for each pair.Source: 2) CB NOMA-aided Radar Detection Model · p. 8

B. Problem Formulation

• The joint optimization maximizes the sum unicast rate across C-users subject to each pair’s multicast-rate requirement and radar beam-pattern accuracy for K targets.The beamformers and power-allocation factors are coupled, and the problem is non-convex.Source: B. Problem Formulation · p. 8

C. Proposed Solution

• For the non-convex problem, the method combines penalty-based rank-one enforcement with successive convex approximation and gradually reduces the penalty factor.Each inner iteration solves a convex optimization problem for the current penalty factor.Source: C. Proposed Solution · p. 9
• The double-layer procedure is guaranteed to converge to a stationary solution of the original joint optimization problem.The algorithm terminates when the equality constraints meet the predefined accuracy.Source: C. Proposed Solution · pp. 9–10

• Simulations use a half-wavelength ULA, LoS R-user channel, and Rayleigh C-user channel with path-loss models and distances of 1000 m and 100 m, respectively.The reference path loss is 40 dB.Source: §IV · p. 10
• 200 channel realizations are averaged, with receiver noise power set to −100 dBm.The initial penalty factors are 10^4, with inner-layer and equality-constraint termination thresholds of 10^-2 and 10^-5.Source: §IV · p. 10
• The desired radar beam pattern uses the true R-user angles and a beam width of 10° in the simulations.The radar-only system provides the performance benchmark.Source: §IV · p. 10

• The single R-user is assumed to be located at 0° in the BB NOMA-aided system.Source: A. BB NOMA-Aided Joint Rad-MU-Com System · p. 10

• TDMA successively sends multicast and unicast messages over two slots with one common beamformer, whereas CBF-No-SIC sends them simultaneously with separate beamformers and no SIC.The common TDMA beamformer preserves an unchanged radar beam pattern; its transmit-SNR definition is motivated by the paper's optimization setting.Source: 1) Benchmark Schemes · pp. 10–11
• BB NOMA achieves the highest unicast rate; its advantage over CBF-No-SIC and TDMA grows as the allowable beam-pattern mismatch increases.SIC mitigates inter-signal interference relative to CBF-No-SIC, while power-domain sharing and separate beamformers outperform TDMA; TDMA nevertheless avoids interference and exceeds CBF-No-SIC.Source: 1) Benchmark Schemes · p. 11
• As the multicast-rate requirement rises, NOMA and CBF-No-SIC unicast rates fall, while TDMA remains nearly unchanged when the requirement is below its unicast rate.At low multicast requirements CBF-No-SIC can exceed TDMA, but at stricter requirements its interference-degraded rate falls below interference-free TDMA.Source: 1) Benchmark Schemes · pp. 11–12
• As transmit SNR rises, all schemes improve, but CBF-No-SIC becomes interference-limited while NOMA gains more than TDMA.The comparison is reported for a multicast requirement of 0.5 bit/s/Hz and beam-pattern mismatch of −10 dB.Source: 4) Unicast Rate Versus γp · p. 12

5) Beam Pattern of a Signal R-User and a Single C-User:

• In the single-pair setting, NOMA's transmit beam pattern closely approaches the radar-only pattern, while TDMA and CBF-No-SIC show more noticeable mismatch.At the same radar-pattern accuracy requirement, NOMA achieves higher communication performance than both benchmarks.Source: 5) Beam Pattern of a Signal R-User and… · p. 12, Figure 8 · p. 12

B. CB NOMA-Aided Joint MIMO Rad-MU-Com System

• The multiple-pair evaluation considers three R&C pairs, with R-users at −60°, 0°, and 60° and randomly paired C- and R-users.Source: B. CB NOMA-Aided Joint MIMO Rad-MU-Com… · p. 12, 1) Benchmark Scheme · p. 12

1) Benchmark Scheme:

• The multiple-pair benchmark uses TDMA, since CBF-No-SIC cannot use one common beamformer to deliver two different messages in this setting.The benchmark successively transmits unicast and multicast messages using different beamformers for each pair.Source: 1) Benchmark Scheme · p. 12
• CB NOMA's sum-rate advantage over TDMA grows with allowable beam-pattern mismatch; it also requires less transmit power for equal unicast performance and supports stricter mismatch constraints.The comparison reports that the NOMA advantage is more pronounced as γb increases.Source: 1) Benchmark Scheme · p. 13
• For the multiple-pair system, CB NOMA beats TDMA especially at small per-pair multicast requirements, and its sum-rate gain indicates suitability for heterogeneous rate requirements.Source: 1) Benchmark Scheme · p. 13, Figure 10 · p. 13

4) Beam Pattern of Multiple R-Users and Multiple C-Users:

• Both CB NOMA and TDMA approach the radar-only beam pattern while detecting three R-users, but NOMA achieves significantly higher communication performance than TDMA.The comparison uses K = 3 R&C pairs and a random channel realization.Source: Figure 11 · p. 13, 4) Beam Pattern of Multiple R-Users… · p. 13
• As K increases, the sum unicast rate first rises and then falls: added spatial DoFs help initially, but later multicast power demands reduce power available for unicast.The comparison considers K = 2, 3, 4, 5, and 6.Source: 5) Sum of Unicast Rate Versus K · pp. 13–14

V. CONCLUSIONS

• Numerical results show that the proposed NOMA-aided joint Rad-MU-Com schemes achieve higher unicast performance than benchmark schemes.The paper develops separate beamformer-based and cluster-based frameworks for single and multiple R&C pairs, respectively, with penalty-based iterative algorithms.Source: §V · p. 14
• The multiple-pair framework jointly designs beamformers and power allocation to maximize unicast performance while meeting multicast-rate and radar-pattern requirements.A penalty-based iterative algorithm seeks a near-optimal solution to the resulting non-convex optimization problem.Source: §V · p. 14