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Rate-Splitting Multiple Access to Mitigate the Curse of Mobility in (Massive) MIMO Networks

Onur Dizdar, Yijie Mao, Bruno Clerckx

arXiv:2102.06405v2cs.ITmath.IT

TL;DR

Existing power-allocation studies address specific system cases and do not account for CSIT degradation from mobility and latency. This paper derives an ergodic sum-rate lower bound and a closed-form power allocation for RSMA. Simulations report that RSMA maintains multi-user connectivity under mobility, unlike conventional MU-MIMO strategies whose performance collapses.

  • Problem

    Prior work leaves open practical RSMA power allocation for arbitrary antenna and user counts under CSIT degradation from mobility and latency.

    Source: A. Related Work · p. 2

  • Method

    The paper derives an ergodic sum-rate lower bound for mobile RSMA and a closed-form power-allocation coefficient that maximizes it.

    Source: §VI · p. 13

  • Results

    RSMA maintains multi-user connectivity under mobility, while SDMA and conventional MU-MIMO performance collapses.

    Source: B. Contributions · p. 3

  • Takeaways & Limitations

    For mobile multi-antenna systems, RSMA's partial decoding and treatment of remaining interference as noise support reliable multi-user connectivity.

    Source: §VI · p. 13

Abstract

from arXiv · show

Rate-Splitting Multiple Access (RSMA) is a flexible and robust multiple access scheme for downlink multi-antenna wireless networks. RSMA relies on multi-antenna Rate-Splitting (RS) at the transmitter and Successive Interference Cancellation (SIC) at the receivers. In this work, we study the performance of RSMA under the practical important setup of imperfect Channel State Information at Transmitter (CSIT) originating from user mobility and latency in the network. First, we derive a lower bound on the ergodic sum-rate of RSMA for an arbitrary number of transmit antennas, number of users, user speeds and transmit power. Then, we study the power allocation between common and private streams and obtain a closed-form solution for the optimal power allocation that maximizes the obtained lower bound. The proposed power allocation greatly reduces precoder design complexity for RSMA. By Link-Level Simulations (LLS), we demonstrate that RSMA with the proposed power allocation is robust to degrading effects of user mobility and has significantly higher performance compared to conventional multi-user (massive) Multiple-Input Multiple-Output (MIMO) strategies. The work has important practical significance as results demonstrate that, in contrast to conventional multi-user (massive) MIMO whose performance collapse under mobility, RSMA can maintain reliable multi-user connectivity in mobile deployments.

I. INTRODUCTION

Mobility and latency make CSIT outdated, challenging multi-user connectivity, while prior RSMA power-allocation work did not address arbitrary system sizes under mobility. This paper develops an RSMA power-allocation approach and reports robust multi-user connectivity under mobility compared with conventional MU-MIMO.

I. INTRODUCTION

  • Mobility and feedback latency cause outdated CSIT, which degrades SDMA and makes maintaining multi-user connectivity a challenge.Processing delay can exceed channel coherence time even at 30 km/h, making CSIT inaccurate for multi-user beamforming.Source: §I · p. 1
  • RSMA splits user messages into common and private parts, partially decodes interference, and treats the remainder as noise using SIC.The common message is decoded by all users, alongside separately encoded private streams.Source: §I · p. 2

A. Related Work

  • Earlier studies addressed specific antenna or user counts or optimization frameworks unsuitable for practical implementation, leaving mobility- and latency-related CSIT degradation unaddressed.The resulting interference terms complicate analytical design of practical power-allocation algorithms.Source: A. Related Work · p. 2

B. Contributions

  • The paper derives an ergodic sum-rate lower bound and a closed-form power-allocation coefficient for arbitrary antenna counts, user counts, transmit power, and user speed.The coefficient maximizes the derived lower bound for the approximated ergodic sum-rate.Source: B. Contributions · p. 3
  • RSMA maintains multi-user connectivity under mobility, while SDMA and conventional MU-MIMO performance collapses.The reported benefits span small- and large-scale MIMO deployments and small and large user counts.Source: B. Contributions · p. 3

II. SYSTEM MODEL

The system is a K-user MISO broadcast channel using 1-layer RSMA. The transmitter uses delayed channel information for precoding, while receivers decode a common stream before their private streams.

II. SYSTEM MODEL

  • Each user message is split into common and private parts; the common parts are combined into one message, while each user retains a private stream.The common and private streams are independently encoded and linearly precoded.Source: §II · p. 3
  • The power-allocation coefficient t distributes transmit power between the common and private precoders; setting t = 1 disables the common stream and reduces the scheme to uniform-power SDMA.The private streams use zero-forcing precoders with equal power allocation, and the common precoder is modeled as a random beamformer.Source: §II · pp. 3–4
  • Receivers decode the common message while treating private streams as noise, cancel it by SIC, then decode their own private stream with other private streams as noise.Each user's decoded message combines its common and private parts.Source: §II · pp. 3–4
  • The transmitter uses the previous channel observation for precoding because CSI reports are delayed, making its CSIT outdated under mobility.The channel model represents the current channel using a time-correlated prior channel and an error term; the correlation depends on Doppler and the CSI-report interval.Source: §II · p. 4

III. LOWER BOUND FOR THE ERGODIC SUM-RATE

This section derives a tractable lower bound for the approximated ergodic sum-rate of 1-layer RSMA under mobility-related imperfect CSIT. The bound combines private- and common-stream rate bounds and supports power allocation analysis.

III. LOWER BOUND FOR THE ERGODIC SUM-RATE

  • The rate analysis assumes equal power across zero-forcing private precoders and allocates fraction t of total power to them, with the remainder assigned to the common stream.The private-rate and common-rate contributions are bounded separately before being combined.Source: §III · pp. 4–5
  • The section derives a lower bound for the approximated ergodic sum-rate of 1-layer RSMA, combining bounds for the private-stream rates and the common-stream rate.The resulting bound is for the approximated ergodic sum-rate (AESR), and its tightness is assessed by simulations.Source: §III · pp. 4–5, A. Lower Bound for PK · p. 6
  • Identical user-channel second-order statistics simplify the derivation and yield a closed-form optimal power coefficient, while the lower-bound derivation extends to users with different statistics.Equal private-stream power is also described as common in MU-MIMO literature and practical systems.Source: §III · p. 4, A. Lower Bound for PK · p. 6
  • Simulations show that RSMA achieves significant sum-rate gain even with random beamformers for the common streams.Source: §III · p. 4

B. Lower Bound for eRc(t)

This subsection derives a lower bound for the approximated ergodic rate of the common stream. The result contributes to the overall lower bound for the 1-layer RSMA sum-rate under mobility-related imperfect CSIT.

B. Lower Bound for eRc(t)

  • The approximated ergodic rate of the common stream is lower-bounded, and this bound is combined with the private-stream bound to obtain an overall sum-rate bound.The common-rate derivation uses an approximation to a random variable and Jensen's inequality.Source: B. Lower Bound for eRc(t) · p. 7
  • The resulting overall lower bound applies to 1-layer RSMA with imperfect CSIT due to mobility and can be extended to users with different second-order channel statistics.Source: B. Lower Bound for eRc(t) · p. 7

IV. CLOSED-FORM SOLUTION FOR THE OPTIMAL POWER ALLOCATION

The section seeks a closed-form power-allocation coefficient that maximizes the lower bound on the ergodic sum-rate. It motivates this approach by noting that exhaustive search is unsuitable for practical systems.

IV. CLOSED-FORM SOLUTION FOR THE OPTIMAL POWER ALLOCATION

  • The target is the power-allocation coefficient that maximizes the ergodic sum-rate lower bound.Source: §IV · p. 7
  • Exhaustive search over the lower bound is considered unsuitable for practical systems, motivating a closed-form solution.Source: §IV · p. 7

A. Derivation

The derivation uses a high-transmit-power asymptotic assumption to simplify the lower bound, then optimizes the power-allocation coefficient subject to a feasibility condition.

A. Derivation

  • Assuming P_t → ∞, the derivation uses Lemma 4 to rewrite the lower-bound expression before optimizing the allocation coefficient t.The supplied lemma passage gives only a partial expression for β.Source: A. Derivation · p. 7
  • Setting the derivative of the rewritten lower bound with respect to t to zero yields the candidate allocation.Source: A. Derivation · p. 8
  • The algorithm restricts the candidate to t_opt ∈ (0, 1] using a feasibility condition, then gives the resulting allocation in (39).The displayed formula in the supplied passage is incomplete.Source: A. Derivation · p. 8

B. Asymptotic Analysis

The asymptotic analysis examines how the allocation coefficient behaves at extreme CSIT quality and for small or large user counts. It finds that low CSIT quality favors increasing common-stream power as transmit power rises, while perfect CSIT yields no common-stream allocation.

B. Asymptotic Analysis

  • For K = 2 at low CSIT quality, t_opt depends only on transmit power and approaches zero as P → ∞.Source: B. Asymptotic Analysis · p. 8
  • For large K, the allocation condition is approximated as 1.78 < P + 1, and the resulting algorithm likewise has t_opt → 0 as P → ∞.The supplied algorithm expression is incomplete.Source: B. Asymptotic Analysis · p. 8
  • At asymptotically low CSIT quality, the common-stream power share increases with transmit power, with its allocation threshold depending on transmit power and user count.The analysis also considers K = 2 and large K cases.Source: B. Asymptotic Analysis · pp. 8–9
  • With perfect CSIT, t_opt = 1, so no power is allocated to the common stream; the passage attributes this to ZF precoding cancelling multi-user interference.Source: B. Asymptotic Analysis · p. 9

V. SIMULATION RESULTS

The simulations assess both ergodic sum-rate and practical link-level throughput, comparing RSMA with SDMA and testing the proposed allocation against exhaustive search.

V. SIMULATION RESULTS

  • Monte Carlo simulations compare RSMA using the proposed coefficient from (39) with exhaustive search over the lower bound to assess near-optimality.Source: §V · p. 9
  • The sum-rate study compares RSMA and SDMA using the proposed power-allocation methods to assess their performance difference.Source: §V · p. 9
  • Link-level simulations use a practical transceiver architecture and realistic 3GPP channel model to compare RSMA and SDMA throughput.Source: §V · p. 9

A. Sum-Rate Performance

The simulations find that RSMA outperforms SDMA, and that the closed-form allocation performs near the exhaustive-search solution. As SNR rises, RSMA avoids the sum-rate saturation seen with SDMA.

A. Sum-Rate Performance

  • The lower-bound-maximizing coefficient is almost identical to the coefficient maximizing actual ergodic sum-rate, supporting near-optimality of the proposed low-complexity algorithm.The lower bound captures ergodic sum-rate behavior as system parameters vary.Source: A. Sum-Rate Performance · p. 9
  • RSMA maintains non-saturating sum-rate performance as SDMA saturates in the interference-limited SINR regime, while closed-form and exhaustive-search allocation perform similarly across the considered cases.The comparison uses user speeds of 20 km/h and 30 km/h, a 2.5 ms CSI acquisition delay, and a 3.5 GHz operating frequency.Source: A. Sum-Rate Performance · p. 9, Figure 3 · p. 10
  • Both allocation methods distribute power similarly between common and private streams, with the common-stream share increasing as SNR rises.The stream-rate plots cover two scenarios.Source: A. Sum-Rate Performance · p. 10, Figure 4 · p. 10

B. Link-Level Simulations

Link-level simulations show that RSMA with the proposed power allocation remains robust as user speed increases, while SDMA’s sum-rate and throughput decline and saturate. The simulations also extend the evaluation to multiple-receive-antenna users, where RSMA performs significantly better than SDMA despite a suboptimal allocation.

B. Link-Level Simulations

  • The link-level evaluation uses finite-alphabet modulation, finite-length polar coding, and AMC, with channels generated using the 3GPP Urban Macro-Cell model.The simulations use CP-OFDM at 3.5 GHz with a 10 ms CSI acquisition delay.Source: B. Link-Level Simulations · pp. 11–12
  • As user speed increases, RSMA limits performance degradation while SDMA’s sum-rate and throughput drop significantly and its performance saturates with SNR.RSMA’s sum-rate and throughput continue increasing with SNR without saturating.Source: Figure 7 · p. 12, B. Link-Level Simulations · pp. 12–13
  • With multiple receive antennas, RSMA significantly outperforms SDMA, although its throughput is non-monotonic because the allocation is suboptimal in this setting.The simulations use nt = 64, nr = 4, and K = 8 with different common- and private-stream counts.Source: Figure 8 · p. 12, B. Link-Level Simulations · p. 13
  • The closed-form power allocation performs close to exhaustive search across the simulated user speeds and SNR values.The authors describe the proposed algorithm as achieving near-optimal performance.Source: B. Link-Level Simulations · p. 12

VI. CONCLUSION

  • The conclusion recommends RSMA for mobile MIMO connectivity because it partially decodes interference while treating the remainder as noise.The paper reports theoretical bounds and link-level simulations supporting RSMA’s robustness to mobility relative to SDMA.Source: §VI · p. 13

APPENDIX A PROOF OF LEMMA 1

The appendix approximates sums of correlated Gamma random variables by moment matching, then uses Gamma approximations and independence assumptions to derive a CDF approximation for the SINR-related random variable.

APPENDIX A PROOF OF LEMMA 1

  • The proof approximates a sum of correlated Gamma random variables with a Gamma random variable by matching the first two moments.The component variables may have different scales.Source: Appendix A · p. 13

APPENDIX B PROOF OF LEMMA 2

  • Using the approximation from Lemma 1, the proof approximates Qk2 with a Gamma random variable and then approximates Yk under numerator-denominator independence.The resulting approximation is expressed as a CDF.Source: Appendix B · pp. 13–14
  • Assuming the Yk variables are independent, the proof approximates the CDF of Y from the CDF of Yk.The stated CDF combines the individual terms across K users.Source: Appendix B · p. 14

APPENDIX C PROOF OF LEMMA 4

The proof simplifies terms in the expression for β using recurrence relations and series identities. Under the stated high-power and small-argument approximations, it substitutes the resulting expression to obtain equation (35).

APPENDIX C PROOF OF LEMMA 4

  • For the β term that depends on P and t, the proof applies a recurrence relation under the assumption Pt → ∞.The derivation begins from relation (51).Source: Appendix C · p. 14
  • The proof expands an expression using a finite harmonic-series approximation and the solution for an alternating geometric series.It also invokes properties of the remaining terms and assumes exE1(x) ≈ −γ − ln(x) as x → 0.Source: Appendix C · p. 14
  • Substituting the resulting approximation for β yields equation (35).Source: Appendix C · p. 14
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