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Scalable Cell-Free Massive MIMO Systems

Emil Björnson, Luca Sanguinetti

arXiv:1908.03119v2cs.ITeess.SP

TL;DR

Cell-Free Massive MIMO must retain cooperative gains while avoiding the computational and fronthaul growth of network-wide processing. The paper uses dynamic cooperation clustering to build scalable access, clustering, combining, and precoding methods. The proposed methods outperform maximum-ratio processing and approach the performance of unscalable alternatives.

  • Problem

    Original Cell-Free Massive MIMO has computational complexity and fronthaul requirements that grow with the number of UEs, limiting practical scalability.

  • Method

    The paper exploits dynamic cooperation clustering to create scalable algorithms for access, pilot assignment, cluster formation, channel estimation, combining, and precoding.

  • Results

    The proposed scalable distributed LP-MMSE and centralized P-MMSE processing outperform maximum-ratio processing, while the scalable framework achieves nearly the spectral efficiency of unscalable solutions.

  • Takeaways & Limitations

    Scalable Cell-Free Massive MIMO can retain much of the performance of unscalable processing while keeping per-AP complexity and signaling finite as the number of UEs grows.

Abstract

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Imagine a coverage area with many wireless access points that cooperate to jointly serve the users, instead of creating autonomous cells. Such a cell-free network operation can potentially resolve many of the interference issues that appear in current cellular networks. This ambition was previously called Network MIMO (multiple-input multiple-output) and has recently reappeared under the name Cell-Free Massive MIMO. The main challenge is to achieve the benefits of cell-free operation in a practically feasible way, with computational complexity and fronthaul requirements that are scalable to large networks with many users. We propose a new framework for scalable Cell-Free Massive MIMO systems by exploiting the dynamic cooperation cluster concept from the Network MIMO literature. We provide a novel algorithm for joint initial access, pilot assignment, and cluster formation that is proved to be scalable. Moreover, we adapt the standard channel estimation, precoding, and combining methods to become scalable. A new uplink and downlink duality is proved and used to heuristically design the precoding vectors on the basis of the combining vectors. Interestingly, the proposed scalable precoding and combining outperform conventional maximum ratio processing and also performs closely to the best unscalable alternatives.

I. INTRODUCTION

Cell-Free Massive MIMO uses distributed APs to jointly serve UEs, but early implementations require network-wide coordination that makes fronthaul and computation unscalable. This paper applies dynamic cooperation clustering to develop scalable access, clustering, and signal-processing methods while retaining much of the performance of unscalable alternatives.

  • Coherent transmission from multiple APs can improve received power without increasing total transmit power and can outperform serving each UE from one AP.
  • Early Network MIMO assumed network-wide CSI and transmission to all UEs, creating impractical fronthaul signaling and computational complexity.
  • User-centric cooperation serves each UE through its best AP subset, requiring APs to cooperate with different AP groups across UEs and resources.
  • Original Cell-Free Massive MIMO connected all APs to one CPU, so per-AP complexity and fronthaul grew linearly or faster with the number of UEs.
  • The paper develops scalable initial access, pilot assignment, cluster formation, combining, and precoding by exploiting the DCC framework.
  • Numerical results show the scalable framework achieves almost the same spectral efficiency as state-of-the-art unscalable solutions and outperforms maximum-ratio processing.

A. Pilot Transmission and Channel Estimation

Pilot transmission assigns a fixed set of orthogonal pilots to accessing UEs, after which APs estimate channels for data processing. Pilot sharing creates contamination that reduces estimation quality and induces correlated estimates, while the original all-UE processing model motivates scalable alternatives.

  • A. Pilot Transmission and Channel Estimation: The network uses τp mutually orthogonal pilot signals, with τp constant independent of K, and assigns pilots when UEs access the network.
  • A. Pilot Transmission and Channel Estimation: MMSE channel estimation uses the pilot observation and channel statistics, with the statistical matrix precomputed at each AP.
  • A. Pilot Transmission and Channel Estimation: Pilot contamination from UEs sharing a pilot reduces estimation quality and correlates their channel estimates, producing additional interference.
  • A. Pilot Transmission and Channel Estimation: The original Cell-Free Massive MIMO model has all APs simultaneously serve all UEs in uplink and downlink, using network-wide processing.
  • A. Pilot Transmission and Channel Estimation: Maximum-ratio combining uses each served AP's local channel estimate, while collective combining aggregates the AP-level processing for uplink decoding.
  • A. Pilot Transmission and Channel Estimation: Downlink transmission uses AP-specific precoders and UE power allocations to form the received signal.

B. The Scalability Issue

Scalability requires finite per-AP complexity and resource requirements as the number of UEs grows. The original cell-free architecture violates these requirements, motivating a DCC-based implementation framework.

  • Scalability requires finite per-AP complexity and resource requirements for channel estimation, data processing, fronthaul signaling, and power control as K →∞.
  • The original Cell-Free Massive MIMO architecture is unscalable because AP computation, fronthaul signaling, and non-trivial network-wide power optimization grow without bound with K.APs process channel estimates, signals, data, and optimization variables for all UEs.
  • The proposed framework starts from DCC and fills in missing implementation details, including initial access, pilot assignment, and channel estimation.
  • Per-AP complexity and fronthaul can remain finite as K →∞, while total requirements scale with the number of APs L.
  • DCC represents cooperation through diagonal matrices that determine which AP antennas may transmit to and decode signals from each UE.

A. Uplink and Downlink Data Transmissions

Dynamic cooperation clustering restricts each UE’s serving and detection APs while retaining a cell-free architecture. A bounded number of served UEs per AP makes processing and fronthaul scalable, and the paper develops access, pilot, and clustering procedures accordingly.

  • DCC lets each UE use an AP subset, allowing overlapping cooperation clusters rather than disjoint network-wide clusters.
  • A sufficient scalability condition is that each AP serves a constant number of UEs as K →∞.
  • Under this condition, each AP computes channel estimates and precoding or combining vectors, and exchanges fronthaul data, for only a bounded UE set.
  • The proposed implementation jointly handles initial access, pilot assignment, and cooperation-cluster formation while limiting AP service load and guaranteeing that all UEs are served.
  • Each AP serves at most one UE per pilot sequence, fixing channel-estimation and signal-processing complexity even when all N antennas are used.

A. Algorithm for Joint Initial Access, Pilot Assignment, and Cluster Formation

The proposed access procedure assigns each UE a Master AP and pilot, then forms its serving cluster through neighboring-AP decisions. The resulting channel-estimation and processing design keeps per-AP complexity scalable while supporting centralized combining and achievable-SE analysis.

  • Access procedure: Each UE appoints a Master AP responsible for downlink transmission and uplink decoding coordination before pilot assignment and cluster formation.
  • Access procedure: The Master AP assigns the pilot with the least observed pilot contamination and informs neighboring APs that it will serve the new UE.
  • Access procedure: Neighboring APs serve the UE if they are unused on its pilot or if its channel is better than that of their currently served UE.
  • Access procedure: The access procedure can be repeated when UEs move or network membership changes, including reassignment to a new Master AP.
  • Channel estimation and scalability: Each AP estimates only channels for UEs in its serving set, so initial access and pilot assignment have complexity independent of K as K grows.
  • Channel estimation and scalability: Perfect synchronization is assumed, although neighboring-AP synchronization and UE synchronization with its Master AP make the dominant signal-model terms accurate.
  • Centralized combining: Centralized combining sends AP signals or local estimates to a CPU, which can evaluate achievable spectral-efficiency bounds for arbitrary combining vectors.
  • Centralized combining: MMSE combining maximizes instantaneous SINR but is unscalable with K, whereas P-MMSE retains bounded interference modeling and scalable complexity.

2) Distributed combining:

Distributed combining lets each AP form local estimates using only its locally available channel information, then forwards soft estimates to a CPU. LP-MMSE provides a scalable alternative to local MMSE, while MR admits closed-form evaluation but is simpler.

  • Each AP computes local estimates for its served UEs and sends them to the CPU for final decoding.
  • Distributed fronthaul requires τ_u|D_l| complex scalars per coherence block, upper bounded by τ_uτ_p and therefore independent of K.
  • The distributed uplink uses a use-and-then-forget bound because the CPU lacks the channel estimates required by centralized analysis.
  • Local combining vectors depend only on channel estimates and statistics available at the same AP.
  • LP-MMSE restricts processing to UEs served by each AP, making its complexity scalable because |D_l| ≤ τ_p independently of K.
  • LP-MMSE requires an N × N matrix inverse per UE instead of the N|M_k| × N|M_k| inverse required by centralized P-MMSE.
  • MR combining permits closed-form expectations, whereas LP-MMSE expectations can be computed using Monte Carlo simulations.

C. Downlink Data Transmission

The downlink analysis derives achievable spectral-efficiency expressions and an uplink-downlink duality, then uses uplink combiners to construct scalable downlink precoders. The hardening bound may be loose when APs have few antennas.

  • The downlink achievable-SE analysis uses the hardening bound for the distributed cooperation signal model.
  • Each normalized precoder has unit expected squared norm, while ρ_i denotes the total transmit power allocated to UE i.
  • Downlink SE depends on all UEs’ precoding vectors, so jointly optimizing them is not scalable.
  • The proved duality shows that uplink-achievable SINRs are also achievable downlink through suitable power-control coefficients and normalized precoders.
  • Downlink SE generally differs from uplink SE because duality power control is unscalable and uplink and downlink power constraints differ.
  • Selecting downlink precoders from uplink combiners transfers scalability from the uplink design to the downlink when based on available channel estimates.
  • The hardening bound can be loose in Cell-Free Massive MIMO with relatively small N, depending on the combining scheme.

1) Centralized precoding:

Centralized precoding uses uplink channel estimates and reciprocity to construct downlink precoders from uplink combiners. A distributed alternative lets APs compute precoders locally and reduces fronthaul signaling.

  • The CPU computes normalized downlink precoders from uplink channel estimates using channel reciprocity.
  • Choosing a particular uplink combiner directly determines the corresponding downlink precoding scheme.
  • The CPU forms each AP’s downlink signal and sends it to that AP over the fronthaul for transmission.
  • Centralized precoding requires each AP to exchange τ_pN pilot scalars to the CPU and receive τ_dN downlink-signal scalars per coherence block.
  • APs can instead compute precoders locally from their served UEs’ channel estimates, reducing exchanged data to τ_d|D_l| complex scalars per coherence block.

2) Distributed precoding:

The scalable distributed precoding schemes are MR and LP-MMSE. LP-MMSE reduces interference and effective-gain variation compared with MR, supporting higher spectral efficiency under inter-user interference.

  • 2) Distributed precoding:: The two scalable distributed precoding options are classical MR and the newly considered LP-MMSE scheme.MR is also called conjugate beamforming and is standard in Cell-Free Massive MIMO.
  • 2) Distributed precoding:: LP-MMSE suppresses interference spatially when N > 1 by maximizing the ratio between desired signal power and interference caused to other served UEs.
  • 2) Distributed precoding:: MR and LP-MMSE have roughly the same mean channel gain, but MR has an exponential distribution with an infinite tail whereas LP-MMSE has small, compact support.The different gain distributions are associated with higher SE for LP-MMSE under inter-user interference.
  • 2) Distributed precoding:: LP-MMSE also reduces variations in the effective gain of desired and interfering channels, including when N = L = K = 1 with perfect CSI.

D. Uplink and Downlink Power Allocation

The paper uses heuristic power allocation because network-wide optimization is not scalable. UEs transmit at full power, while AP allocation schemes distribute power among served UEs under per-AP constraints.

  • D. Uplink and Downlink Power Allocation: Network-wide uplink power optimization is not scalable, so the paper uses a heuristic baseline in which every UE transmits at its maximum power P.The selected rule is p_i = P for i = 1, . . . , K.
  • D. Uplink and Downlink Power Allocation: Network-wide downlink optimization is not scalable as K →∞ because the number of optimization variables grows with the number of UEs.Scalable implementations therefore require heuristic power-allocation schemes.
  • D. Uplink and Downlink Power Allocation: Centralized precoding uses equal per-UE power ρ_i = ρ/τ_p, while distributed precoding adopts the power-allocation algorithm from [33].The centralized rule guarantees that AP power constraints are satisfied.
  • D. Uplink and Downlink Power Allocation: Both downlink schemes allocate more power to UEs with strong channels while guaranteeing non-zero power to every served UE.Each UE is served by at least one Master AP, ensuring non-zero transmit power and SE.

E. Network Topology

The proposed framework can be implemented across centralized, distributed, and edge-cloud topologies because only neighboring APs cooperate. Simulations show scalable processing remains competitive, with performance shaped by AP density, local antennas, interference mitigation, and power allocation.

  • E. Network Topology: The algorithms are largely transparent to network topology because cooperation occurs only among neighboring APs.The CPU represents centralized processing tasks rather than necessarily a physical unit.
  • E. Network Topology: CPU tasks can be distributed across local AP processors, with a UE’s Master AP handling tasks such as downlink encoding and uplink decoding.
  • E. Network Topology: Network-wide optimization can be implemented iteratively with dual decomposition, but slow convergence and extensive backhaul signaling make it impractical and unscalable.
  • E. Network Topology: APs can also be divided into disjoint sets connected to separate edge-cloud processors for centralized processing.
  • E. Network Topology: The simulations use 100 UEs in a 2 × 2 km square, comparing 400 single-antenna APs with 100 four-antenna APs.
  • E. Network Topology: 2.7× higher average UL SE is achieved by distributed LP-MMSE than MR, while scalable centralized P-MMSE achieves 89% of optimal centralized MMSE combining.The P-MMSE loss is attributed to limiting serving APs and using a suboptimal scalable cluster-formation algorithm.
  • E. Network Topology: Distributed LP-MMSE outperforms MR for 95% of UEs and matches it for the 5% most unfortunate UEs; LP-MMSE reaches 90% of genie-aided SE versus 60% for MR, while P-MMSE reaches 98%.
  • E. Network Topology: The framework achieves finite per-AP complexity and signaling as the number of UEs grows, with negligible performance loss for a given power-allocation policy.The proposed hierarchy is MR, distributed LP-MMSE, then centralized P-MMSE in performance.

APPENDIX

The appendix rewrites downlink SINR requirements as a matrix inequality and establishes feasibility of the resulting downlink power vector from feasible uplink conditions.

  • APPENDIX: The downlink SINR constraints are written in matrix form using a diagonal target-SINR matrix Γ and an interference matrix Σ.
  • APPENDIX: The downlink transmit-power vector ρ satisfies the SINR constraints when (Γ − Σ)ρ is bounded by the noise term.
  • APPENDIX: Feasibility follows when Γ − Σ is invertible, which the appendix states always holds when the corresponding uplink power vector is feasible.
  • APPENDIX: The proof then selects downlink powers according to the derived relation and verifies the total transmit-power condition by direct computation.
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