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Rate-Splitting Multiple Access for Multi-Antenna Joint Radar and Communications

Chengcheng Xu, Bruno Clerckx, Shiwa Chen, Yijie Mao, Jianyun Zhang

arXiv:2103.07914v1eess.SPcs.IT

TL;DR

The paper addresses how multi-antenna DFRC can jointly support communication and radar beampattern design while managing their interference. It proposes RSMA-based transmission and ADMM optimization, finding that RSMA improves the WSR–beampattern tradeoff and can eliminate the need for an additional radar sequence and SIC.

  • Problem

    The paper studies how to share multi-antenna DFRC resources between downlink communication and radar beampattern design while managing interference.

  • Method

    The framework splits messages into common and private streams, jointly precodes them with an optional radar sequence, and optimizes WSR and beampattern MSE using ADMM.

  • Results

    RSMA-assisted DFRC achieves a better WSR–beampattern tradeoff than SDMA-assisted DFRC, FDRC, and, under stated conditions, TDRC; with RSMA, radar-sequence modes have the same tradeoff.

  • Takeaways & Limitations

    RSMA’s common stream manages communication-user and radar–communication interference while fulfilling beampattern requirements, removing the need for an additional radar sequence and SIC.

Abstract

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Dual-Functional Radar-Communication (DFRC) system is an essential and promising technique for beyond 5G. In this work, we propose a powerful and unified multi-antenna DFRC transmission framework, where an additional radar sequence is transmitted apart from communication streams to enhance radar beampattern matching capability, and Rate-Splitting Multiple Access (RSMA) is adopted to better manage the interference. RSMA relies on multi-antenna Rate-Splitting (RS) with Successive Interference Cancellation (SIC) receivers, and the split and encoding of messages into common and private streams. We design the message split and the precoders of the radar sequence and communication streams to jointly maximize the Weighted Sum Rate (WSR) and minimize the radar beampattern approximation Mean Square Error (MSE) subject to the per antenna power constraint. An iterative algorithm based on Alternating Direction Method of Multipliers (ADMM) is developed to solve the problem. Numerical results first show that RSMA-assisted DFRC achieves a better tradeoff between WSR and beampattern approximation than Space-Division Multiple Access (SDMA)-assisted DFRC with or without radar sequence, and other simpler radar-communication strategies using orthogonal resources. We also show that the RSMA-assisted DFRC frameworks with and without radar sequence achieve the same tradeoff performance. This is because that the common stream is better exploited in the proposed framework. The common stream of RSMA fulfils the triple function of managing interference among communication users, managing interference between communication and radar, and beampattern approximation. Therefore, by enabling RSMA in DFRC, the system performance is enhanced while the system architecture is simplified since there is no need to use additional radar sequence and SIC. We conclude that RSMA is a more powerful multiple access for DFRC.

I. INTRODUCTION

The paper develops a multi-antenna DFRC framework that combines RSMA with dual-functional communication and radar transmission. It jointly designs message splitting and precoding to balance communication WSR against radar beampattern approximation error.

  • Motivation: Spectrum congestion motivates integrated DFRC systems that use shared resources for radar sensing and communication.The paper positions DFRC as an alternative to separate radar and communication operation in congested bands.
  • Prior work: Earlier dual-functional designs embed information in radar waveforms or use communication streams and probing signals, but some approaches face communication-rate limitations or rely on ZF-based designs.Embedding information in radar pulses can limit rates by the pulse repetition frequency, while later systems jointly design precoders for beampattern and SINR objectives.
  • Proposed architecture: RSMA splits each user message into common and private parts, encoding them into a common stream decoded by all users and private streams decoded by their intended users.The proposed transmitter linearly precodes these streams together with the radar sequence.
  • Proposed architecture: The proposed DFRC simultaneously transmits precoded information streams and a radar sequence to serve downlink users and probe targets within the same frequency band.The radar sequence contains no user messages and its waveform is assumed predesigned; the paper focuses on its precoder.
  • Optimization: An ADMM-based iterative framework addresses the joint non-convex optimization of WSR maximization and beampattern-approximation MSE minimization.Majorization-Minimization is used to solve non-convex subproblems within ADMM iterations.
  • Evaluation: The study compares RSMA-assisted DFRC with SDMA-assisted DFRC, TDRC, and FDRC to evaluate WSR–beampattern tradeoffs.TDRC and FDRC use orthogonal time or frequency resources, whereas DFRC performs both functions in shared resources.

B. Different Modes of Radar Sequence

The framework supports three radar-sequence modes and both RSMA and SDMA operation. It also compares integrated transmission with time- and frequency-orthogonal radar-communication baselines.

  • Radar-sequence modes: With the radar sequence disabled, its precoder power is zero and the mode is called DFRC without radar sequence.This mode is represented by δc = 0 and Pr = 0.
  • Radar-sequence modes: With radar sequence and SIC, users know the prestored sequence and cancel its interference before decoding information streams.This mode is represented by δc = 0 while the radar sequence remains transmitted.
  • Radar-sequence modes: Without SIC, the transmitted radar sequence is treated as interference when users decode information streams.This mode is represented by δc = 1.
  • Multiple access: SDMA-assisted DFRC is obtained by disabling the common stream, while the radar-sequence mode remains independently selectable.The baseline sets Pc = 0 and compares multiple-access methods under the same radar-sequence options.
  • Orthogonal baselines: TDRC separates radar and communication in time, allocating fractions α and 1 − α of operation to the base station and MIMO radar.Each function uses the working power budget Pt during its assigned interval.
  • Orthogonal baselines: FDRC separates radar and communication in frequency, splitting total power as PR + PC = Pt and avoiding radar–communication interference through frequency orthogonality.RSMA is enabled for FDRC communication streams.

2) Frequency-Division Radar-Communication:

The section defines communication and radar metrics for DFRC design and describes how RSMA rates account for common and private streams under different radar-sequence modes.

  • Metrics: WSR measures communication performance, while beampattern-approximation MSE represents radar performance in the DFRC design.These metrics jointly formulate the transmission-design optimization problem.
  • Radar-sequence modes: The radar sequence is either treated as interference when δc = 1 or fully removed from each user's received signal when δc = 0.The unified index δc captures both radar-sequence processing modes.
  • RSMA rate construction: The common-stream rate is limited by the minimum decoding rate across users and is divided among users as common-rate portions Ck.Each user's total achievable rate combines its common-rate portion and private-stream rate.
  • SDMA comparison: For SDMA-assisted DFRC, setting all Ck to zero leaves only private-stream rates in the WSR.This gives the corresponding SDMA WSR expression from the RSMA formulation.
  • Radar metric: Desired beampattern approximation is used to represent radar performance, with the target generated from radar prior knowledge and array settings.The target incorporates azimuth angles of interest and the antenna-array configuration.

C. Problem Formulation

The proposed DFRC problem jointly optimizes RSMA message splitting and stream precoders for communication rate and radar-beampattern accuracy under per-antenna constraints. An ADMM framework decomposes the non-convex problem into alternating updates.

  • C. Problem Formulation: The objective jointly maximizes WSR and minimizes beampattern-approximation MSE using a regularization parameter λ ∈ [0, 1].The variables include the message split and the precoders for communication streams and radar sequence.
  • C. Problem Formulation: The formulation enforces common-stream decodability at every user and equal transmit average power across antennas.The common-rate vector is c = [C1, C2, . . . , CK]^T.
  • C. Problem Formulation: Applying the variable settings in Table I produces SDMA-assisted baseline problems for different radar-sequence modes.The baselines are obtained directly from the proposed formulation.
  • IV. ADMM-BASED FRAMEWORK FOR SOLVING THE PROBLEM: Because the logarithmic WSR, quartic MSE, and equality power constraint are non-convex, the problem is decomposed into alternating communication and radar sub-problems.The alternating procedure seeks a local optimal solution.
  • IV. ADMM-BASED FRAMEWORK FOR SOLVING THE PROBLEM: The ADMM formulation collects the optimization variables into v and uses selection matrices and vectors to represent precoders, rates, and common-rate portions.The construction includes pvec = vec(P) and Ck = e_k^T v.
  • IV. ADMM-BASED FRAMEWORK FOR SOLVING THE PROBLEM: The reformulated objective separates communication and radar terms with feasible-set indicator functions gc(v) and gr(u).The radar indicator corresponds to the per-antenna power constraint.
  • IV. ADMM-BASED FRAMEWORK FOR SOLVING THE PROBLEM: The auxiliary power condition improves convergence robustness without changing the original problem because it is always satisfied when the equality constraint holds.The ADMM updates iteratively update v, u, and the scaled dual variable d.
  • IV. ADMM-BASED FRAMEWORK FOR SOLVING THE PROBLEM: Algorithm 1 solves the intractable formulation through successive v-, u-, and d-updates, using WMMSE for v and MM for u.Primal and dual residuals determine the iterative stopping conditions.

V. ALGORITHMS FOR SOLVING ADMM UPDATES

The ADMM communication update is handled with WMMSE, which converts the rate terms into augmented WMSE expressions and repeatedly solves a convex QCQP after updating equalizers and weights.

  • V. ALGORITHMS FOR SOLVING ADMM UPDATES: The v-update and u-update remain challenging, so the framework uses WMMSE for v and an MM-based algorithm for u.These methods are embedded within each ADMM iteration.
  • WMMSE-based v-update: The WMMSE derivation first represents all optimization variables in v and rewrites the intended-stream SINRs, rates, and augmented WMSEs.The common stream is decoded before the private stream after removing the decoded common stream.
  • WMMSE-based v-update: The common and private stream estimations use equalizers, with the private-stream equalizer applied after common-stream cancellation.The resulting MSEs support the rate-WMMSE reformulation.
  • WMMSE-based v-update: After optimizing equalizers and weights, rate-WMMSE relationships reformulate the v-update into a tractable problem.The reformulation follows from first-order optimality conditions.
  • WMMSE-based v-update: With fixed weights and equalizers, the reformulated problem is a convex QCQP over pvec and c that can be solved efficiently.The WMMSE iterations update weights, equalizers, and precoders until convergence.
  • WMMSE-based v-update: The WMMSE procedure initializes and updates WSR using the current precoders and common-rate allocation, then repeats QCQP-based precoder updates.Algorithms 1 and 2 provide the surrounding ADMM and WMMSE procedures.

B. MM-based Algorithm for u-update

The MM-based u-update majorizes the quartic radar objective into tractable subproblems and iteratively reconstructs the radar-related variables until convergence.

  • B. MM-based Algorithm for u-update: The u-update is formulated through an MM approach after defining the radar-related variable pu = Dp u.The ADMM subproblem is rewritten into a tractable form before majorization.
  • B. MM-based Algorithm for u-update: The quartic formulation motivates an iterative MM method because it is difficult to relax tightly.The method follows the cited MM approach and uses Lemma 1 for majorization.
  • B. MM-based Algorithm for u-update: Lemma 1 upper-bounds a quadratic form using a dominating Hermitian matrix, enabling majorization of the radar objective.This produces a surrogate that can be minimized iteratively.
  • B. MM-based Algorithm for u-update: The algorithm constructs a linear majorization of the quartic objective at the current iterate and solves the resulting majorized problem.The construction uses the desired beampattern levels and current ADMM variables.
  • B. MM-based Algorithm for u-update: The majorized subproblem separates entries of the auxiliary vector and obtains closed-form solutions for the split variables.The radar variable u is recovered through the inverse transformation.
  • B. MM-based Algorithm for u-update: The MM iterations continue until convergence, with initialization available from semi-definite relaxation.The first K output elements are copied from the preceding v-update because they do not participate in the u-optimization.

C. Computational Complexity Analysis

The proposed ADMM-based framework has polynomial per-iteration complexity, dominated by WMMSE and MM subroutines.

  • Each ADMM iteration runs the WMMSE algorithm and the MM-based algorithm.These two procedures constitute the iteration-level complexity.
  • O([(K + 2)(Nt)]^3) is the complexity of WMMSE-AO and the MM-based iteration for the proposed DFRC.Both complexities arise from interior-point QCQP solving or largest-eigenvalue computation.
  • O([(K + 2)(Nt)]^3) is the per-iteration complexity of the proposed DFRC ADMM framework.The no-radar-sequence variant has complexity O([(K + 1)(Nt)]^3).

VI. NUMERICAL RESULTS

Numerical experiments evaluate RSMA-assisted DFRC, emphasizing its advantages over SDMA and the role of the common stream, with TDRC and FDRC as baselines.

  • The numerical results validate RSMA-assisted DFRC against SDMA-assisted DFRC, TDRC, and FDRC baselines.The evaluation focuses on RSMA’s advantages in DFRC and the contribution of its common stream.

A. Settings of Numerical Experiments

The experiments use an eight-antenna ULA, four users, three targets, specified power and noise budgets, and RMSE-based comparisons with IBR diagnostics.

  • The setup uses an Nt = 8 ULA with half-wavelength spacing, Pt = 20dBm, 0dBm user noise, four users, and three targets.The user channels are independent standard complex Gaussian vectors.
  • FDRC allocates the shared power budget equally between radar and communication functions, using Pt/2 for each.TDRC and FDRC serve as comparison baselines.
  • Communication precoders are initialized with MRC, while the radar precoder and d are random, and c starts as 1K×1.The desired beampattern is generated by a matching method.
  • The results report RMSE instead of MSE and distinguish RSMA- and SDMA-assisted DFRC modes by radar-sequence and SIC usage.The labels identify no-radar-sequence, radar-sequence without SIC, and radar-sequence with SIC variants.
  • WSR and beampattern MSE do not quantitatively depict dual-functional interference, motivating IBR and its lower bound LB-IBR.IBR measures interference leakage toward communication users for a unit-power beampattern.
  • LB-IBR removes pk using the precoder power constraint and evaluates the basic radar-to-communication interference level for SDMA-assisted DFRC without radar sequence.It provides an operating-environment interference measure independent of pk.

C. Beampattern Approximation Performance

The experiments compare beampattern and WSR tradeoffs across radar, orthogonal-resource, RSMA, and SDMA strategies under varied user channels, target locations, and user numbers.

  • C. Beampattern Approximation Performance: DFRC fully approximates the MIMO-radar beampattern and provides near 3dB gain over FDRC in Fig. 2(a).FDRC has half the power budget for radar.
  • C. Beampattern Approximation Performance: λ = 1 × 10^-6 yields near 1.8bps/Hz higher WSR and near 19.3dB higher RMSE, demonstrating the WSR–beampattern approximation tradeoff.The result is reported for the proposed DFRC in Fig. 2(b).
  • 1) RSMA Gain vs. Users’ Channels:: In Scenario-UC, RSMA-assisted DFRC without radar sequence outperforms FDRC by 0.8bps/Hz WSR at the same beampattern RMSE.It also surpasses TDRC when α is smaller than around 0.8.
  • 1) RSMA Gain vs. Users’ Channels:: Serving User-2&4 gives the largest RSMA-over-SDMA WSR gain, 1.2bps/Hz when RMSE≤1, while the gain nearly disappears for User-1&4.The comparison uses DFRC without radar sequence.
  • 1) RSMA Gain vs. Users’ Channels:: In Scenario-UC, higher LB-IBR at Target-1 corresponds to greater common-stream contribution to target detection and a larger RSMA tradeoff gain.The common stream contributes more when serving the higher-interference user pair.
  • 2) RSMA Gain vs. Target’s Location:: For Scenario-TL, RSMA-assisted DFRC without radar sequence outperforms FDRC and TDRC when α is smaller than around 0.8 and again mitigates radar-to-communication interference.Its tradeoff gain over SDMA varies across target locations.
  • 3) RSMA Gain vs. User Number:: For Scenario-UN, RSMA-assisted DFRC without radar sequence outperforms FDRC and SDMA, while its advantage over TDRC appears at smaller α as user number increases.The larger gain occurs in scenarios with higher LB-IBR.

4) RSMA Performance in Multi-target Detection:

In multi-target detection, RSMA-assisted DFRC outperforms the compared alternatives and achieves the same tradeoff with or without radar sequence. The common stream jointly manages communication and radar interference while fulfilling radar beampattern requirements.

  • RSMA-assisted DFRC without radar sequence outperforms FDRC and, in certain conditions, surpasses TDRC.
  • When RMSE≤1, radar sequence improves SDMA-assisted DFRC by around 0.4bps/Hz WSR, while SIC adds 1.1bps/Hz.
  • RSMA-assisted DFRC has the same tradeoff whether radar sequence is enabled or disabled, outperforming all SDMA-assisted systems, FDRC, and TDRC when α < 0.78.
  • With SIC, radar-sequence interference need not be zero-forced, enlarging the feasible region and improving SDMA-assisted DFRC performance.
  • RSMA’s common stream manages communication-user interference, radar-to-communication interference, and radar beampattern requirements, eliminating the need for an additional radar sequence and SIC.
  • The proposed ADMM framework converges to a good solution in around ten iterations for the evaluated DFRC designs.

APPENDIX PROOF OF (35)

The appendix proves inequality (35) using Rayleigh–Ritz properties, eigenvalue analysis, and the pseudo-inverse of a rank-deficient matrix.

  • The selection matrix Dp,k extracts the k-th user’s precoder block from the stacked precoder representation.
  • Rayleigh–Ritz quotient properties provide the inequality used to establish (35).
  • Because M is rank-deficient, its inverse is replaced by the pseudo-inverse M† in the derivation.
  • The proof derives eigenvalues of the relevant matrix products and concludes that (35) is satisfied.
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