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Performance of Network-Assisted Full-Duplex for Cell-Free Massive MIMO

Dongming Wang, Menghan Wang, Pengcheng Zhu, Jiamin Li, Jiangzhou Wang, Xiaohu You

arXiv:1905.11107v1cs.ITmath.IT

TL;DR

Cross-link interference complicates flexible duplexing in large-scale networks. This paper proposes NAFD for cell-free massive MIMO and derives deterministic sum-rate equivalents while introducing genetic-algorithm user scheduling. The reported comparisons favor half-duplex RAUs over CCFD massive MIMO and GAS over random scheduling.

  • Problem

    Cross-link interference in large-scale networks challenges flexible duplexing, including uplink and downlink operation.

    Source: §I · p. 2

  • Method

    The paper models NAFD for cell-free massive MIMO, derives sum-rate equivalents for uplink MMSE and downlink ZF/RZF, and proposes GAS to mitigate uplink-to-downlink interference.

    Source: §VII · p. 23

  • Results

    NAFD with half-duplex RAUs achieves higher spectral efficiency than CCFD massive MIMO, and GAS yields higher sum-rate than random user scheduling.

    Source: §VII · p. 23

  • Takeaways & Limitations

    GAS is a scheduling option for alleviating uplink-to-downlink interference in cell-free massive MIMO with NAFD.

    Source: §VII · p. 23

Abstract

from arXiv · show

Network assisted full-duplex (NAFD) is a spatial-division duplex technique for future wireless networks with cell-free massive multiple-input multiple-output (CF massive MIMO) network, where a large number of remote antenna units (RAUs), either using half-duplex or full-duplex, jointly support truly flexible duplex including time-division duplex, frequency-division duplex and full duplex on demand of uplink and downlink traffic by using network MIMO methods. With NAFD, bi-directional data rates of the wireless network could be increased and end-to-end delay could be reduced. In this paper, the spectral efficiency of NAFD communications in CF massive MIMO network with imperfect channel state information (CSI) is investigated under spatial correlated channels. Based on large dimensional random matrix theory, the deterministic equivalents for the uplink sum-rate with minimum-mean-square-error (MMSE) receiver as well as the downlink sum-rate with zero-forcing (ZF) and regularized zero-forcing (RZF) beamforming are derived. Numerical results show that under various environmental settings, the deterministic equivalents are accurate in both a large-scale system and system with a finite number of antennas. It is also shown that with the downlink-to-uplink interference cancellation, the uplink spectral efficiency of CF massive MIMO with NAFD could be improved. The spectral efficiencies of NAFD with different duplex configurations such as in-band full-duplex, and half-duplex are compared. With the same total numbers of transmit and receive antennas, NAFD with half-duplex RAUs offers a higher spectral efficiency. To alleviate the uplink-to-downlink interference, a novel genetic algorithm based user scheduling strategy (GAS) is proposed. Simulation results show that the achievable downlink sum-rate by using the GAS is greatly improved compared to that by using the random user scheduling.

I. INTRODUCTION

Flexible duplexing in large-scale wireless networks is challenged by cross-link interference, while prior spatial-duplex designs also leave spatial degrees of freedom underused. The paper proposes NAFD for cell-free massive MIMO and analyzes its spectral efficiency under imperfect CSI and spatial correlation.

I. INTRODUCTION

  • NAFD unifies flexible duplex and existing duplexing methods, with a general model that includes CCFD massive MIMO, CoMPflex, hybrid full-duplex, half-duplex, and full-duplex C-RAN.Source: §I · pp. 2–3
  • NAFD with half-duplex RAUs performs best among half-duplex RAUs, CCFD-CRAN, and CCFD massive MIMO as RAU density increases.The comparison identifies half-duplex RAUs as the best-performing of the three schemes.Source: §I · p. 3
  • Large-dimensional random matrix theory yields deterministic sum-rate equivalents for uplink MMSE and downlink ZF or RZF under imperfect CSI and spatial correlation.The analysis considers MMSE joint detection after downlink-to-uplink interference cancellation.Source: §I · p. 3
  • The deterministic equivalents approximate spectral efficiency using statistical channel knowledge, without requiring the actual channel realization.Source: §I · p. 3
  • Numerical simulations show that the deterministic equivalents are accurate in both large-scale systems and systems with finite antenna counts.Source: §I · p. 3
  • The proposed low-complexity genetic algorithm-based user scheduling strategy targets uplink-to-downlink interference.Source: §I · p. 3

II. SYSTEM MODEL

NAFD uses distributed RAUs and centralized processing to support flexible uplink and downlink duplexing. The model accounts for the interference and power constraints involved in simultaneous transmission and reception.

II. SYSTEM MODEL

  • Distributed RAUs jointly serve uplink and downlink users in the same time-frequency resources, with the CPU coordinating their transmit and receive roles according to network traffic.The architecture can scale to many RAUs and supports dynamic TDD, flexible FDD, and full duplex.Source: §II · pp. 4–5
  • NAFD cancels downlink-to-uplink interference at the CPU and can mitigate uplink-to-downlink interference through user scheduling or cancellation at user equipment.Full-duplex RAUs can handle intra-RAU self-interference in the analog domain, while the CPU cancels residual inter-RAU interference digitally.Source: §II · p. 4

A. Transmission Model

  • The transmission model includes uplink and downlink channels, inter-RAU and user-to-user interference, and a per-RAU transmit-power constraint.The paper adopts the per-RAU constraint as more practical than the conventional sum-power constraint.Source: A. Transmission Model · pp. 5–6

B. Channel Model

The paper models spatially correlated channels with imperfect CSI and derives deterministic approximations for downlink ergodic sum-rates under RZF and ZF precoding. For RZF, the approximation uses statistical channel information rather than actual channel realizations.

B. Channel Model

  • Spatially correlated channels are modeled with deterministic matrices that characterize pathloss and antenna-level correlation, while the channel estimates are imperfect.The model also includes channels between transmitting and receiving RAUs and between uplink and downlink users.Source: B. Channel Model · pp. 6–7

III. DETERMINISTIC EQUIVALENT SUM-RATE FOR DOWNLINK

  • Under imperfect CSI and independent spatial correlations, the paper derives deterministic approximations of downlink ergodic sum-rates for RZF and ZF precoding.The derivation considers a large-system regime with system dimensions growing at fixed ratios.Source: §III · p. 7, A. Regularized Zero-Forcing Precoding · p. 8

A. Regularized Zero-Forcing Precoding

  • Because user-side successive interference cancellation depends on inter-user channel capacity and uplink data rate and has high implementation complexity, the paper studies user scheduling to mitigate uplink-to-downlink interference.The analysis also identifies noise and interference as factors reducing downlink sum-rate.Source: A. Regularized Zero-Forcing Precoding · pp. 10–11
  • For RZF, the downlink ergodic sum-rate can be approximated from statistical channel knowledge without the actual channel realization.Theorem 1 gives the approximation under its stated assumptions as the system dimensions grow.Source: A. Regularized Zero-Forcing Precoding · pp. 8, 11

B. Zero-Forcing Precoding

The paper derives a deterministic equivalent for the downlink ergodic sum-rate under ZF precoding. It relates ZF to RZF as the zero-regularization case and reports a higher sum-rate for RZF than ZF.

B. Zero-Forcing Precoding

  • Under Assumptions 1–3, Theorem 2 gives a deterministic equivalent for the downlink ergodic sum-rate with ZF precoding as system dimensions grow.The ZF sum-rate is derived by taking the regularization parameter toward zero.Source: B. Zero-Forcing Precoding · pp. 11, 13
  • RZF achieves higher sum-rate than ZF, and ZF is obtained from RZF by setting the regularization parameter α to zero.The paper states that the RZF sum-rate can be maximized by choosing the regularization parameter.Source: B. Zero-Forcing Precoding · pp. 11, 13

IV. DETERMINISTIC EQUIVALENT SUM-RATE FOR UPLINK

The uplink analysis uses CPU-side cancellation of downlink-to-uplink interference followed by MMSE detection, accounting for residual interference caused by imperfect CSI. It derives deterministic equivalents for the residual-interference-plus-noise covariance and uplink sum-rate.

A. Downlink-to-Uplink Interference Cancellation and Joint MMSE detection

B. A Deterministic Equivalent for Uplink Sum-rate

  • Theorem 3 provides a deterministic equivalent for the residual-interference-plus-noise covariance, which can be approximated using statistical channel information without actual channel realizations.The covariance approximation can simplify its computation.Source: B. A Deterministic Equivalent for… · pp. 14–15
  • Under Assumption 4, Theorem 4 gives a deterministic equivalent for the uplink ergodic sum-rate with an MMSE receiver as system dimensions grow.The expression accounts for residual interference and noise after imperfect downlink-to-uplink cancellation.Source: B. A Deterministic Equivalent for… · pp. 15–16
  • Improving channel-estimation accuracy for links between transmitting and receiving RAUs improves uplink spectral efficiency.The paper also describes its results as unified formulas encompassing special cases such as massive MIMO full duplex and C-RAN-based full duplex.Source: B. A Deterministic Equivalent for… · pp. 16–17
  • The paper states that its deterministic equivalents are analytical and easier to compute than ergodic results requiring time-consuming Monte Carlo simulations.The derived formulas account for spatial correlation, large-scale fading, imperfect CSI, and imperfect interference cancellation.Source: B. A Deterministic Equivalent for… · p. 17

V. USER SCHEDULING

The section formulates user grouping to minimize uplink-to-downlink interference and proposes GAS as a heuristic alternative to exhaustive search, which is impractical at CF massive MIMO scale.

V. USER SCHEDULING

  • The grouping assigns users waiting for service to L groups, with each user served only once.The groups together form the universal set of uplink and downlink users.Source: §V · pp. 17–18
  • A downlink user can cancel uplink interference when the interfering link's capacity is at least the uplink user's data rate.The scheduling conditions distinguish interference that remains from interference that is cancelled.Source: §V · pp. 17–18
  • Exhaustive search over all users is prohibitively large and cannot be implemented in practice.The search complexity grows with the full user search space in CF massive MIMO.Source: §V · p. 18
  • GAS is proposed to minimize uplink-to-downlink interference through user scheduling in CF massive MIMO with NAFD.The formulation groups waiting uplink and downlink users, while the objective couples the users across the full set.Source: §V · pp. 17–18
  • GAS selects candidate groupings with probability inversely proportional to their calculated uplink-to-downlink interference, then applies genetic operators and validates the group constraints.The algorithm stops when interference reaches a satisfactory, stable value or the iteration limit is reached.Source: §V · pp. 18–19

VI. SIMULATIONS AND DISCUSSIONS

The simulations report improved downlink sum-rate with GAS versus random scheduling and higher spectral efficiency for NAFD than CCFD alternatives. They also assess deterministic-equivalent accuracy across system sizes and channel settings.

VI. SIMULATIONS AND DISCUSSIONS

  • NAFD offers greater spectral efficiency than massive MIMO CCFD and C-RAN CCFD in the reported comparison.Source: §VI · p. 19
  • GAS improves achievable downlink sum-rate compared with random user scheduling.The simulation compares the two scheduling schemes in CF massive MIMO with NAFD.Source: §VI · p. 19

A. Accuracy of the Deterministic Equivalent Results

B. Comparison between NAFD and CCFD

The comparison finds higher spectral efficiency for NAFD than for massive-MIMO CCFD and C-RAN CCFD, and reports that GAS improves downlink sum-rate over random scheduling. The paper also concludes that half-duplex NAFD RAUs are more spectrally efficient than CCFD massive MIMO.

B. Comparison between NAFD and CCFD

  • NAFD is more spectrally efficient than both massive-MIMO CCFD and C-RAN CCFD, with spectral efficiency increasing as antenna count M grows.The paper attributes the advantage over co-located massive MIMO to distributed RAUs' more advantageous placement, which can yield additional power gains and macro diversity.Source: B. Comparison between NAFD and CCFD · p. 21

C. Comparison between GAS and Random User Scheduling

  • The proposed GAS groups simultaneous uplink and downlink users to mitigate UL-to-DL interference, generally placing them geographically apart.In some cases, close users are grouped when the uplink interference is large enough for the downlink users to perform successive interference cancellation.Source: C. Comparison between GAS and Random… · p. 22
  • GAS achieves higher downlink sum-rate than random user scheduling in NAFD, and the reported rate decreases as uplink SNR increases for both schemes.The comparison uses fixed downlink SNR ρdl = 5dB.Source: C. Comparison between GAS and Random… · p. 23, Figure 9 · p. 23

VII. CONCLUSIONS

  • Large-dimensional random matrix theory yields deterministic equivalents for uplink sum-rate with MMSE reception and downlink sum-rate with RZF or ZF precoding under imperfect CSI and spatial correlation.The paper investigates NAFD spectral efficiency in CF massive MIMO under these channel conditions.Source: §VII · p. 23
  • Simulations report that the analytical results provide reliable performance predictions in both large-scale systems and systems with finite antenna counts.The comparison between NAFD and CCFD uses RZF downlink precoding and MMSE uplink reception.Source: B. Comparison between NAFD and CCFD · p. 21, §VII · p. 23
  • The conclusion reports that half-duplex NAFD RAUs offer a more spectrally efficient solution than CCFD massive MIMO.The comparison subsection also reports NAFD's advantage over CCFD C-RAN.Source: §VII · p. 23

APPENDIX A IMPORTANT LEMMAS

Appendix A introduces five lemmas as mathematical groundwork for the later derivations. The supplied passages name matrix-inversion and resolvent identities and state assumptions for random-matrix lemmas.

APPENDIX A IMPORTANT LEMMAS

  • Five lemmas provide the mathematical basis for the subsequent derivations.The appendix also includes a matrix inversion lemma and a resolvent identity.Source: Appendix A · pp. 23–24
  • The random-matrix lemmas specify conditions including bounded spectral norms, large matrix dimension, and random vectors with zero mean and finite eighth-order moments.The passages also describe independence conditions for the random vectors and matrices.Source: Appendix A · p. 24
  • A further lemma states a resolvent identity for two invertible matrices.The appendix labels the identity as Lemma 5.Source: Appendix A · p. 24

APPENDIX B PROOF OF THEOREM 2

Appendix B proves Theorem 2 by deriving deterministic equivalents under the stated assumptions. The supplied proof passages identify the downlink ZF sum-rate expression as the endpoint.

APPENDIX B PROOF OF THEOREM 2

  • The derivation proceeds under Assumptions 1–3 and the large-system limit.The proof passages state that the deterministic equivalents for component terms are derived before the final expression.Source: Appendix B · pp. 24–26
  • The proof substitutes intermediate expressions to obtain the result for an earlier equation.The supplied passage identifies this step as deriving the result in (B-7) from (B-8), (B-9), and (B-10).Source: Appendix B · p. 26
  • The proof derives the deterministic equivalent for the downlink sum-rate under ZF precoding.It combines results from Lemmas 6, 7, and 8 to obtain the expression for Rdl,zf,sum.Source: Appendix B · p. 26

APPENDIX C PROOF OF THEOREM 3

Appendix C derives deterministic equivalents for the residual interference-and-noise covariance matrix in the proof of Theorem 3. It also invokes the RZF precoding definition in deriving an intermediate equivalent.

APPENDIX C PROOF OF THEOREM 3

  • The passage proceeds to derive a deterministic equivalent for wH, referring to the vector in (13) and then applying Lemma 1 in the derivation.Source: Appendix C · p. 27
  • An intermediate deterministic equivalent is obtained using the definition of RZF precoding.The proof refers to the term rzf,kAnwrzf,k.Source: Appendix C · p. 27
  • The proof derives deterministic equivalents for the covariance matrix of residual interference and noise.The stated result is given in equation (56), with the nth diagonal element of Σ in (57).Source: Appendix C · p. 28

APPENDIX D PROOF OF THEOREM 4

Appendix D derives the deterministic equivalent of the uplink sum-rate with an MMSE receiver under Assumption 4 as the antenna dimension grows. It obtains the result by deriving equivalents for the terms in the uplink SINR and combining them into the final expression.

APPENDIX D PROOF OF THEOREM 4

  • The derivation proceeds by finding deterministic equivalents for the three terms of the uplink SINR and combining them to form its approximation.The proof identifies the SINR in (53) and states that the three terms are derived separately.Source: Appendix D · p. 28
  • Under Assumption 4, as N → ∞, Lemmas 9, 10, and 11 are used to derive a deterministic equivalent.Source: Appendix D · pp. 28, 29, 31
  • The proof derives the deterministic equivalent of the MMSE-receiver uplink sum-rate, with the final expression given in (64).The derivation uses the deterministic equivalent of the uplink SINR as N → ∞.Source: Appendix D · p. 31
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