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Energy Efficiency of Rate-Splitting Multiple Access, and Performance Benefits over SDMA and NOMA

Yijie Mao, Bruno Clerckx, Victor O. K. Li

arXiv:1804.08330v2cs.IT

TL;DR

The paper asks whether RSMA, already shown to improve rate-related performance over SDMA and NOMA, also improves energy efficiency. It formulates and solves RSMA energy-efficiency optimization in a MISO broadcast channel, finding that RSMA matches or exceeds both baselines across diverse user deployments.

  • Problem

    The paper investigates whether RSMA provides energy-efficiency advantages over SDMA and NOMA across diverse user deployments.

  • Method

    The paper applies an SCA-based beamforming algorithm to RSMA energy-efficiency maximization in a MISO broadcast channel, with SDMA and NOMA represented as special cases.

  • Results

    RSMA’s energy-efficiency region is equal to or larger than those of SDMA and NOMA across a wide range of user deployments.

  • Takeaways & Limitations

    RSMA is more energy-efficient than SDMA and NOMA while partially decoding interference and treating the remainder as noise.

Abstract

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Rate-Splitting Multiple Access (RSMA) is a general and powerful multiple access framework for downlink multi-antenna systems, and contains Space-Division Multiple Access (SDMA) and Non-Orthogonal Multiple Access (NOMA) as special cases. RSMA relies on linearly precoded rate-splitting with Successive Interference Cancellation (SIC) to decode part of the interference and treat the remaining part of the interference as noise. Recently, RSMA has been shown to outperform both SDMA and NOMA rate-wise in a wide range of network loads (underloaded and overloaded regimes) and user deployments (with a diversity of channel directions, channel strengths and qualities of Channel State Information at the Transmitter). Moreover, RSMA was shown to provide spectral efficiency and QoS enhancements over NOMA at a lower computational complexity for the transmit scheduler and the receivers. In this paper, we build upon those results and investigate the energy efficiency of RSMA compared to SDMA and NOMA. Considering a multiple-input single-output broadcast channel, we show that RSMA is more energy-efficient than SDMA and NOMA in a wide range of user deployments (with a diversity of channel directions and channel strengths). We conclude that RSMA is more spectrally and energy-efficient than SDMA and NOMA.

I. INTRODUCTION

The paper motivates RSMA as a flexible alternative to SDMA and NOMA and investigates whether it improves energy efficiency across diverse user deployments. It formulates an RSMA energy-efficiency problem and reports that RSMA matches or exceeds both baselines.

  • Rising cellular-network energy consumption motivates energy-efficiency optimization balancing weighted sum rate against total power consumption.
  • SDMA treats residual interference as noise but is suited mainly to underloaded systems with sufficiently orthogonal user channels.
  • NOMA can serve overloaded systems by decoding interference, but is suited mainly to aligned user channels with large channel-strength disparity.
  • RSMA splits messages into common and private parts, partially decoding interference while treating the remainder as noise, thereby bridging SDMA and NOMA.
  • The paper defines energy efficiency as weighted sum rate divided by total power, develops an SCA-based RSMA optimization framework, and includes SDMA and NOMA as special cases.
  • The proposed framework is evaluated through numerical results comparing the energy-efficiency regions of RSMA, SDMA, and NOMA.

A. System Model

The system model considers downlink transmission from a multi-antenna base station to two single-antenna users. Transmit power is constrained, and users receive channel-dependent signals with additive Gaussian noise.

  • A base station with Nt transmit antennas serves two single-antenna users in a downlink MISO system.
  • The base station transmits messages W1 and W2 using scheme-dependent encoded signals combined into transmit vector x.
  • The expected transmit power satisfies E{∥x∥2} ≤ Pt.
  • Each user’s received signal depends on its channel vector hk, the transmitted signal, and additive white Gaussian noise.

B. Power Consumption Model

The paper models base-station power consumption as amplifier-adjusted transmit power plus circuit power. The analysis uses a two-user setting, omits user-side consumption, and notes that the model can extend to K users.

  • Total base-station power equals amplifier-adjusted transmit power plus circuit power: Ptotal = 1/η Ptran + Pcir.
  • Transmit power is Ptran ≜ E{∥x∥2}, while circuit power is Pcir = NtPdyn + Psta.
  • The model represents Pdyn as per-active-radio-frequency-chain dynamic consumption and Psta as static consumption from cooling, power supply, and related systems.
  • The analysis uses two users for readability and page constraints, although the system model can extend to the general K-user case.
  • User-side power consumption is omitted because it is considered negligible compared with base-station power consumption.

C. Existing Multiple Access

The existing schemes use independently encoded private streams and linear beamforming. In MU–LP-based SDMA, each user decodes only its intended message and treats residual interference as noise.

  • SDMA independently encodes W1 and W2 into streams s1 and s2, beamforms them with p1 and p2, and superposes the resulting signals.
  • With E{ssH} = I, the transmit power is Ptran = tr(PPH) and is constrained by tr(PPH) ≤ Pt.
  • In MU–LP-based SDMA, each user decodes its desired message while treating residual multiuser interference as noise.

1) SDMA:

SDMA models each user as decoding only its intended message while treating residual interference as noise, with rates derived from SINR over the transmission bandwidth.

  • 1) SDMA:: SDMA user rates are calculated as W log2(1 + γk(P)), where W is bandwidth and γk(P) is the user's SINR.The SINR expression includes the desired signal, interference from the other user, and noise power.
  • 1) SDMA:: For a given weight vector, SDMA energy-efficiency maximization is formulated as an optimization problem over its beamforming design.

2) NOMA:

NOMA uses linearly precoded superposition coding and SIC, requiring one user to decode the other user's interference before decoding its own message.

  • 2) NOMA:: NOMA jointly optimizes the decoding order and precoders, with π specifying which user's message is decoded first.The message of user-π(1) is decoded before the message of user-π(2).
  • 2) NOMA:: User-π(1) decodes its desired message while treating interference as noise, whereas user-π(2) first decodes and cancels user-π(1)'s message via SIC.
  • 2) NOMA:: The first decoded user's achievable rate is limited by both its own decoding SINR and the second user's SINR for decoding its message.The second decoded user's rate is based on its desired-message SINR after interference cancellation.
  • 2) NOMA:: For a given weight vector, NOMA energy-efficiency maximization is formulated as an optimization problem over the scheme's beamforming and decoding design.

III. PROBLEM FORMULATION OF RSMA

The RSMA formulation splits each user's message into common and private parts, enabling partial interference decoding through a jointly encoded common stream and private streams.

  • III. PROBLEM FORMULATION OF RSMA: For two users, generalized RSMA reduces to 1-layer RS and can be extended to K-user 1-layer, hierarchical, or generalized RS configurations.
  • III. PROBLEM FORMULATION OF RSMA: RSMA jointly encodes both users' common message parts into a common stream and separately encodes their private parts into user-specific streams.The stream vector is linearly precoded using the common and private beamformers.
  • III. PROBLEM FORMULATION OF RSMA: The common stream is decoded first by both users while private-stream interference is treated as noise, allowing interference to be partly decoded and partly treated as noise.
  • III. PROBLEM FORMULATION OF RSMA: The common rate is constrained by the rates achievable at both users and is divided into user-specific portions Ck.The common rate is shared by both users and must be decodable by each of them.
  • III. PROBLEM FORMULATION OF RSMA: After removing the common stream through SIC, each user decodes its private stream while treating the other private stream as noise, and its total rate is Ck + Rk(P).SDMA and NOMA are identified as sub-schemes of RSMA.
  • III. PROBLEM FORMULATION OF RSMA: The RSMA-based energy-efficiency maximization problem is formulated for a given weight vector over the common-rate allocation and beamforming variables.

IV. SCA-BASED OPTIMIZATION FRAMEWORK

The paper solves the non-convex energy-efficiency problems with an SCA-based beamforming framework that iteratively constructs convex approximations. The algorithm converges to a feasible stationary approximation, but global optimality is not guaranteed.

  • IV. SCA-BASED OPTIMIZATION FRAMEWORK: The energy-efficiency maximization problems are non-convex fractional programs, so auxiliary variables and iterative approximations transform them into tractable subproblems.The variables represent weighted sum rate, total power consumption, and the energy-efficiency metric.
  • IV. SCA-BASED OPTIMIZATION FRAMEWORK: The transformed problem introduces variables for private rates, common rates, SINR-related quantities, and interference-plus-noise terms.
  • IV. SCA-BASED OPTIMIZATION FRAMEWORK: Non-convex constraints are replaced at each iteration by first-order linear lower-bound approximations around the previous solution.The resulting iterative problem is a convex approximation of the original formulation.
  • IV. SCA-BASED OPTIMIZATION FRAMEWORK: The approximated problem is convex and can be solved with CVX, after which the optimized variables are updated for the next iteration.
  • IV. SCA-BASED OPTIMIZATION FRAMEWORK: The algorithm's objective is non-decreasing and bounded above by the transmit-power constraint, guaranteeing convergence.Feasibility is preserved across iterations because each relaxed solution remains feasible for the next iteration.
  • IV. SCA-BASED OPTIMIZATION FRAMEWORK: Because the method uses linear approximations of non-convex constraints, the global optimality of the achieved solution cannot be guaranteed.

V. NUMERICAL RESULTS

The numerical evaluation compares RSMA with SDMA and NOMA using energy-efficiency regions under varied channel conditions, dynamic power, and algorithm settings. RSMA generally achieves equal or larger energy-efficiency regions, with stronger gains over the baselines as circuit power increases.

  • Evaluation setup: The evaluation compares individual energy-efficiency regions, defined as achievable individual rates divided by sum power.The region boundary is obtained by varying user weights in a two-user MISO system.
  • Evaluation setup: The simulations use four transmit antennas, unit noise variance and bandwidth, a 40 dBm transmit-power constraint, and channel parameters γ and θ controlling gain disparity and channel angle.The static power consumption is 30 dBm and the power-amplifier efficiency is 0.35.
  • Algorithm convergence: All schemes converge within a few iterations, while NOMA has higher transmitter complexity because its SCA-based beamforming algorithm is applied twice.The convergence rates increase slightly as dynamic power decreases because the optimization space becomes larger.
  • Energy-efficiency regions: RS achieves an energy-efficiency region equal to or larger than SC–SIC and MU–LP, especially when user channels are neither orthogonal nor aligned.MU–LP improves as channels become more orthogonal, while SC–SIC improves with a 5 dB channel-gain difference.
  • Energy-efficiency regions: As dynamic power increases, all schemes’ energy-efficiency regions decrease, but RS shows a more prominent improvement over MU–LP and SC–SIC.For large dynamic power, circuit power dominates and the RS region is generally larger than the convex hull of the two baseline regions.

VI. CONCLUSIONS

The paper investigates energy-efficiency maximization for RSMA in the MISO broadcast channel using an SCA-based algorithm. Numerical results show that RSMA matches or outperforms SDMA and NOMA across diverse channel directions and strengths, making it both spectrally and energy efficient.

  • Conclusion: An SCA-based algorithm solves the RSMA energy-efficiency maximization problem while accommodating SDMA and NOMA as special cases.RSMA partially decodes interference through common symbols and partially treats interference as noise.
  • Conclusion: RSMA’s energy-efficiency region is always equal to or larger than those of SDMA and NOMA across a wide range of channel directions and strengths.The conclusion describes RSMA as softly bridging and outperforming the two baseline schemes.
  • Conclusion: RSMA is concluded to be more spectrally and energy efficient than SDMA and NOMA.
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