Rate-Splitting Multiple Access for Multi-Antenna Joint Radar and Communications with Partial CSIT: Precoder Optimization and Link-Level Simulations

I. INTRODUCTION

• The paper motivates radar-communications spectrum sharing by scarce sub-10 GHz resources and the need to operate radar and wireless systems simultaneously while managing interference.Source: §I · p. 1
• Prior DFRC work often assumes perfect CSIT and ideal Gaussian signaling with infinite constellation size and code length; RSMA-based DFRC with partial CSIT had not been studied.The paper identifies a further gap: beampattern approximation error is often not related to conventional radar metrics such as RMI and CRB.Source: §I · p. 2

A. Contributions

• The paper extends earlier RSMA-based DFRC work to partial CSIT, studies ergodic sum-rate performance, and includes a model for communication-user mobility.The earlier common-stream approach under perfect CSIT is not possible with the uncertainty introduced by partial CSIT.Source: A. Contributions · pp. 2–3
• An ADMM-based algorithm jointly targets communication AWSR under QoS constraints and transmit-beampattern MSE, using SAA and WMMSE for the AWSR subproblem and SDR for the MSE subproblem.The design considers different degrees of CSIT inaccuracy.Source: A. Contributions · p. 3
• RSMA-based DFRC provides the best reported results for radar and communications versus SDMA- and NOMA-based DFRC, with greater resilience to CSIT errors and flexibility under QoS constraints.It also approximates the desired directional radar beampattern.Source: A. Contributions · p. 3
• The paper reports that minimizing beampattern MSE also maximizes RMI and minimizes CRB, and that RSMA-based DFRC improves radar performance on these metrics.Source: A. Contributions · p. 3
• Link-level simulations with finite-length polar codes and finite-size QAM corroborate RSMA's superiority for joint radar sensing and communications while exposing losses from finite-length modulation and coding.Source: A. Contributions · p. 3

II. DFRC MODEL

• The system combines an RSMA communications module with a monostatic MIMO radar, using an N-antenna uniform linear array for transmission and radar-echo reception while jointly optimizing precoders.It serves K downlink users and tracks multiple radar targets.Source: §II · p. 3

A. RSMA-based DFRC Signal Model

• Each user message is split into common and private parts, jointly encoded with other users’ common parts or separately as private streams, then linearly precoded.The precoder contains a common-stream vector and one private-stream vector per user.Source: A. RSMA-based DFRC Signal Model · p. 3
• The transmitted communication signal also serves as the MIMO radar probing signal, so radar covariance design reduces to optimizing the precoder matrix.The model uses independent signals combined linearly, and the same signal is used for radar sensing.Source: A. RSMA-based DFRC Signal Model · p. 3
• Users decode the common stream while treating private streams as noise, cancel it with SIC, then decode their own private stream amid the remaining private-stream interference.The common-stream rate must be decodable by every user, and its rate is partitioned among users’ common message parts.Source: A. RSMA-based DFRC Signal Model · p. 4

B. Baseline SDMA-based DFRC and NOMA-based DFRC Signal Models

• SDMA allocates no power to the common-stream precoder, whereas NOMA superposes user data streams and applies SIC in an order based on effective scalar channel strengths.At each NOMA user, streams earlier in the decoding order are decoded and removed.Source: B. Baseline SDMA-based DFRC and… · p. 4

C. Channel Model

• The transmitter has only an estimate of the user channels and its conditional error distribution, while receiver channel information is assumed perfect.The model represents actual channels, estimates, and estimation errors separately, with Gaussian channel and error distributions.Source: C. Channel Model · p. 4

A. Communications Metric: Average Weighted Sum-Rate

• AWSR weights each user’s common and private average rates, with the common rate constrained by the weakest users’ common-stream rate.Under partial CSIT, the paper uses average rates over the conditional error distribution to represent expected performance.Source: A. Communications Metric: Average… · p. 4

B. Radar Sensing Metric: Beampattern Mean Squared Error

• Beampattern MSE measures deviation from a scaled desired beampattern across azimuth-angle grid points, using the transmit covariance and array steering vectors.The desired pattern is highly directional toward target directions of interest.Source: B. Radar Sensing Metric: Beampattern… · pp. 4–5

C. Problem Formulation

• The joint RadCom optimization is formulated for a given channel estimate under partial CSIT.The formulation’s design balances average weighted sum-rate and radar beampattern MSE.Source: C. Problem Formulation · p. 5
• The regularization parameter λ prioritizes communications through AWSR maximization or radar sensing through MSE minimization.The allocation vector contains user portions of the common-stream average rate.Source: C. Problem Formulation · p. 5
• The formulation requires the common stream to be decodable by all users and the common-rate allocation entries to remain positive.It also enforces a positive scaling factor.Source: C. Problem Formulation · p. 5
• A constant-modulus constraint is imposed at each transmit antenna to avoid power-amplifier saturation in practical scenarios.The constraint appears alongside the common-rate and scaling-factor constraints.Source: C. Problem Formulation · p. 5
• An optional QoS constraint guarantees a minimum average rate for each user.The minimum rate is denoted by R̄_th,k.Source: C. Problem Formulation · p. 5

D. Other Conventional Radar Sensing Metrics

• Radar mutual information measures performance using the target-dependent sensing channel and received signal, and maximizing it is equivalent to maximizing transmit beampattern gain toward the target.The sensing channel incorporates target parameters including reflection, delay, and velocity.Source: 1) Radar Mutual Information · p. 5

2) Cramér-Rao Bound:

• The total Cramér-Rao Bound is the Frobenius norm of the inverse Fisher Information Matrix for estimating target complex gain, delay, and velocity.The parameter vector contains the real and imaginary parts of target gain, delay, and velocity.Source: 2) Cram´er-Rao Bound · p. 5
• Minimizing total CRB is equivalent to maximizing the smallest eigenvalue of the Fisher Information Matrix, which depends on target-direction transmit beampattern gain.The passage also relates minimizing the largest eigenvalue of the CRB matrix to that maximization.Source: 2) Cram´er-Rao Bound · p. 5

IV. PRECODER OPTIMIZATION WITH PARTIAL CSIT

• The non-convex precoder optimization problem is addressed with an ADMM algorithm extending prior perfect-CSIT DFRC work to partial CSIT.The optimization is reformulated using vectors that collect the design variables and auxiliary variables.Source: §IV · pp. 5–6
• The ADMM reformulation expresses user common and private average rates through selected components of the precoder variables.The reformulated objective separates functions of the precoder-variable vector and auxiliary vector.Source: §IV · p. 6
• The algorithm solves the reformulated problem through iterative updates, with the v- and u-updates specified as its component steps.The scaled dual variable and penalty parameter are used in the ADMM updates.Source: §IV · p. 6

A. AWSR Maximization Sub-problem

• Partial CSIT makes problem (18) stochastic, so Sample Average Approximation converts it to a deterministic problem.The method adapts the approach proposed in.Source: A. AWSR Maximization Sub-problem · p. 6

1) Sample Average Approximation:

• For each estimated channel, the method samples normalized CSIT errors and uses the resulting channel realizations and common and private rates to estimate average rates through sample average functions.Source: 1) Sample Average Approximation · p. 6
• As the sample count M increases, solutions to the SAA AWSR-maximization problem converge to solutions of the original stochastic problem.The precoder is fixed across the M realizations, and the average-power constraint is relaxed to a convex inequality.Source: 1) Sample Average Approximation · p. 6

• The general approach covers 1-layer RSMA with K users and can be extended to multiple SIC layers following.Source: 2) Weighted Minimum Mean Squared Error… · p. 6
• Users decode the common stream first, then reconstruct it and cancel it to detect their private stream.Source: 2) Weighted Minimum Mean Squared Error… · p. 6
• The approach relates common and private stream rates to their MMSEs, then defines augmented weighted MSEs for the streams.Source: 2) Weighted Minimum Mean Squared Error… · p. 7
• Under partial CSIT, average rate-WMMSE relationships are expectations over the conditional channel-error distribution, approximated by sample average functions.Source: 2) Weighted Minimum Mean Squared Error… · p. 7
• The SAA AWSR problem is reformulated using these average rate-WMMSE relationships, with a transformed common-rate variable.Source: 2) Weighted Minimum Mean Squared Error… · p. 7

• Although the SAA-WMSE problem is jointly non-convex, it is convex in each of W, G, and P when the other two are fixed, enabling Alternating Optimization.Source: 3) Alternating Optimization (AO)… · p. 7
• Each iteration updates the MMSE-optimal weights and equalizers for the previous precoder, then uses the resulting sample averages to form a convex QCQP for the precoder update.Source: 3) Alternating Optimization (AO)… · pp. 7–8
• The resulting SAA AR-WMMSE-AO procedure is summarized in Algorithm 1.Source: 3) Alternating Optimization (AO)… · p. 8

• The u-update sub-problem is reformulated using αu, pu, and Dp,k as components of the optimization variables.Source: B. MSE Minimization Sub-problem · p. 8
• Although the reformulated problem is originally non-convex, Semi-Definite Relaxation enables a convex expression.The relaxation introduces Rpu = pupH and applies Schur's complement.Source: B. MSE Minimization Sub-problem · p. 8
• The relaxation defines a Hermitian semidefinite matrix with Tr(Q) = Tr(Rpu) + 1, yielding the convex optimization problem.Source: B. MSE Minimization Sub-problem · p. 8

C. ADMM Algorithm

• ADMM iterations stop when both the primal residual r_t+1 and dual residual q_t+1 fall below threshold ν.Algorithm 2 summarizes the optimization procedure.Source: C. ADMM Algorithm · p. 8

C. EWSR vs. RMSE Trade-off and Average Precoder Power Distribution

• RSMA achieves the best EWSR–RMSE performance across CSIT qualities and surpasses SDMA when radar is prioritized under perfect CSIT.The EWSR–RMSE curves also compare communications-priority and radar-priority settings.Source: Figure 2 · p. 9, C. EWSR vs. RMSE Trade-off and Average… · pp. 9–10

A. Simulation Parameters

• The simulations average 200 channel realizations for an 8-antenna DFRC serving four users and tracking one radar target.The setup uses 20 dBm transmit power and a 0.1 bps/Hz QoS rate constraint per user.Source: A. Simulation Parameters · p. 9

B. Communication Users Mobility Model for Partial CSIT

• Partial CSIT models channel aging from user mobility and CSI-acquisition delay; the DFRC uses the previous channel estimate and tests 3 and 30 km/h.The channel sampling interval is 10 ms.Source: B. Communication Users Mobility Model… · p. 9

C. EWSR vs. RMSE Trade-off and Average Precoder Power Distribution

• At 30 km/h, RSMA allocates power only to the common and user-1 precoders, serving users 2–4 through the common stream.User 1 has the best channel conditions and can maximize its private rate after common-stream interference is removed through SIC.Source: Figure 3 · p. 9, C. EWSR vs. RMSE Trade-off and Average… · pp. 9–10
• Under high mobility and radar priority, SDMA raises user-1 precoder power by 20 dBm, yet RSMA and NOMA achieve twice its EWSR.The SDMA result reflects MUI from CSIT errors and the power needed to meet other users’ QoS constraints.Source: C. EWSR vs. RMSE Trade-off and Average… · p. 10
• NOMA is generally worst, except that at 30 km/h it performs similarly to RSMA; its multiple SIC layers lower sum DoF and constrain user-rate allocation.When radar is prioritized at high mobility, NOMA reduces user-1 power to limit MUI and preserve the minimum rate supported in SIC.Source: C. EWSR vs. RMSE Trade-off and Average… · p. 10

D. EWSR Trade-off with Conventional Radar Sensing Metrics

• EWSR trade-offs against RMI and CRB follow the RMSE trends, with differences under communications priority when 0° beampattern gain may fluctuate.The paper plots EWSR against RMI and CRB using the optimized precoders.Source: D. EWSR Trade-off with Conventional… · p. 10

E. Link-Level Simulations

• The link-level simulations adapt a 1-layer RSMA transceiver and use finite-alphabet modulation, polar coding, and adaptive modulation and coding.For rate selection, the simulations assume the DFRC knows the real channel after precoder optimization with partial CSIT.Source: E. Link-Level Simulations · pp. 10–11, Figure 6 · p. 11
• In link-level simulations, RSMA retains the best weighted-throughput–RMSE trade-off at both mobility levels, while NOMA performs worst because errors across three SIC layers suppress throughput.The practical modulation and coding results degrade relative to the theoretical Shannon bounds.Source: Figure 7 · p. 11, E. Link-Level Simulations · p. 11

VI. CONCLUSION

• RSMA provides a more robust, flexible QoS-compliant DFRC than SDMA and NOMA, and link-level results confirm its advantage despite finite-length modulation and coding.The conclusion also reports that minimizing beampattern MSE corresponds to maximizing RMI and minimizing CRB.Source: §VI · pp. 11–12