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Making Cell-Free Massive MIMO Competitive With MMSE Processing and Centralized Implementation

Emil Björnson, Luca Sanguinetti

arXiv:1903.10611v2cs.ITeess.SP

TL;DR

Cell-free mMIMO lacks a comprehensive comparison of AP cooperation levels and processing choices under practical fading and combining conditions. This paper analyzes four implementations and finds that MMSE-based processing, especially in a centralized architecture, provides the strongest supported performance and fronthaul trade-off, while nonlinear decoding adds little.

  • Problem

    Existing cell-free mMIMO comparisons emphasized small cells and local MR processing, leaving the most competitive implementation under general practical conditions unresolved.

  • Method

    The paper analyzes four AP-cooperation levels using achievable uplink SE expressions for spatially correlated fading, imperfect CSI, arbitrary AP antenna numbers, and receive combining schemes.

  • Results

    Local MMSE processing substantially outperforms MR and can roughly double SE per UE, while centralized Level 4 increases SE and reduces fronthaul signaling.

  • Takeaways & Limitations

    MMSE-based schemes should replace MR for cell-free mMIMO, with centralized Level 4 preferred because it combines higher SE with lower fronthaul signaling.

Abstract

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Cell-free Massive MIMO is considered as a promising technology for satisfying the increasing number of users and high rate expectations in beyond-5G networks. The key idea is to let many distributed access points (APs) communicate with all users in the network, possibly by using joint coherent signal processing. The aim of this paper is to provide the first comprehensive analysis of this technology under different degrees of cooperation among the APs. Particularly, the uplink spectral efficiencies of four different cell-free implementations are analyzed, with spatially correlated fading and arbitrary linear processing. It turns out that it is possible to outperform conventional Cellular Massive MIMO and small cell networks by a wide margin, but only using global or local minimum mean-square error (MMSE) combining. This is in sharp contrast to the existing literature, which advocates for maximum-ratio combining. Also, we show that a centralized implementation with optimal MMSE processing not only maximizes the SE but largely reduces the fronthaul signaling compared to the standard distributed approach. This makes it the preferred way to operate Cell-free Massive MIMO networks. Non-linear decoding is also investigated and shown to bring negligible improvements.

I. INTRODUCTION

Cell-free mMIMO replaces exclusive cell service with distributed APs jointly serving users, but its competitiveness depends strongly on cooperation and receive processing. The paper develops a four-level taxonomy and analytical framework to compare these designs with cellular mMIMO and small cells.

  • Motivation: Cell-free mMIMO uses many distributed APs connected to a CPU to jointly serve users without cell boundaries.The APs can support coherent joint transmission and reception in a Network MIMO fashion.
  • Motivation: Cell-free mMIMO offers macro diversity, whereas cellular mMIMO benefits from channel hardening and spatial interference suppression but can disadvantage cell-edge users.
  • Contributions: The paper introduces four implementation levels spanning fully centralized to fully distributed AP cooperation.Level 4 gathers pilot and data signals at the CPU; Levels 3 and 2 use increasingly simplified centralized decoding after local processing.
  • Contributions: The framework covers spatially correlated fading, imperfect CSI, multi-antenna APs, and arbitrary heuristic or optimized receive combining.It enables numerical evaluation of performance and fronthaul costs across the implementations.
  • Related work: Previous work largely used distributed local MR processing, which the paper identifies as basically the worst way to operate cell-free networks.

A. Pilot Transmission and Channel Estimation

Uplink pilots are transmitted over orthogonal sequences that may be reused by multiple users, enabling local AP channel estimation but creating pilot contamination. The APs then receive payload signals and cooperate through fronthaul-connected CPU processing.

  • Pilot assignment: The network uses τp mutually orthogonal pilots, with pilot reuse when K > τp.UEs sharing a pilot are collected in the set Pk.
  • Channel estimation: Each AP correlates its received pilot signal with the associated pilot to obtain a sufficient statistic for channel estimation.
  • Channel estimation: The MMSE channel estimate and its estimation error are modeled as independent complex Gaussian vectors.
  • Pilot contamination: Pilot-sharing users create mutual interference called pilot contamination, which degrades system performance.
  • Payload transmission: During payload transmission, each AP receives the superposition of all users’ information signals plus receiver noise.The APs forward or process these observations using their fronthaul-connected cooperation architecture.

A. Level 4: Fully Centralized Processing

Level 4 centralizes pilot processing, channel estimation, and data detection at the CPU by forwarding AP observations over the fronthaul. Its general achievable-SE analysis permits arbitrary combining and identifies MMSE combining as SINR-optimal, while computational complexity remains a practical trade-off.

  • Architecture: Level 4 forwards all AP pilot and data signals to the CPU, which performs channel estimation and data detection.Each AP sends τcN complex scalars per coherence block for its pilot and received-data signals.
  • Architecture: The CPU forms collective channel estimates from all AP observations and selects a combining vector using the joint estimates.
  • Achievable SE: The Level 4 achievable SE is a capacity lower bound valid under imperfect CSI and arbitrary receive combining.The expression is evaluated through an effective instantaneous SINR and expectations over channel estimates.
  • MMSE processing: MMSE combining maximizes the instantaneous SINR and consequently minimizes the conditional mean-squared error.
  • Trade-offs: MMSE combining requires an LN × LN matrix inverse, creating higher computational complexity than heuristic alternatives.ZF and RZF reduce inversion size but can substantially reduce SE for low-SNR users.

B. Level 3: Local Processing & Large-Scale Fading Decoding

Level 3 combines local AP processing with CPU-side statistical weighting, extending LSFD to arbitrary combining schemes. It offers optimized SINR but requires substantial statistical signaling and relies on channel hardening for its stated SE expression.

  • Local processing and LSFD: Each AP locally combines received signals into UE estimates, which the CPU linearly combines using LSFD weights.The CPU optimizes the weights using channel statistics rather than instantaneous channel estimates.
  • Local processing and LSFD: L-MMSE combining minimizes each AP’s local mean-square error while inverting an N × N matrix instead of an LN × LN matrix.Even with single-antenna APs, L-MMSE differs from MR through a non-deterministic scaling factor.
  • Achievable SE: The Level 3 achievable SE is valid for arbitrary combining schemes and channel estimators, but its approximation requires channel hardening.When AP antenna counts are relatively small, the expression can underestimate achievable performance.
  • Achievable SE: The deterministic weighting vector that maximizes the effective SINR follows from the generalized Rayleigh-quotient structure.The optimized weights yield the maximum value stated in the corresponding corollary.
  • Contribution and cost: Level 3 extends prior LSFD analyses by supporting arbitrary combining rather than only MR combining.Its signaling includes per-coherence-block local estimates plus statistical parameters whose total count grows quadratically with L and K.

C. Level 2: Local Processing & Simple Centralized Decoding

Level 2 retains local combining but uses simple centralized decoding with fixed equal weights, avoiding the statistical-parameter exchange required by optimized LSFD. Its performance can remain substantially below Level 3.

  • Simple centralized decoding: Level 2 sets the CPU weighting vector to equal weights, ak = [1/L … 1/L]T, after receiving local AP estimates.Any local combining vector and channel estimator can be used.
  • Achievable SE: The Level 2 achievable SE follows directly from the Level 3 expression with equal CPU weights.The effective SINR is defined through expectations over all sources of randomness.
  • Performance limitation: Tests with statistical weight choices akl = β_lk^ν retained a large performance gap to Level 3.The passage identifies further research in this direction as necessary.
  • Signaling and implementation: Unlike Level 3, Level 2 requires no statistical parameters at the CPU while exchanging the same number of complex scalars per coherence block.With MR and single-antenna APs, it reduces to the previously considered small-cell-related case.

D. Level 1: Small-Cell Network

Level 1 decodes each UE’s signal at a single AP, making the system fully distributed and effectively small-cell-like. The paper generalizes AP association and provides achievable SE expressions, including an exact treatment of pilot contamination.

  • Network operation: Level 1 performs decoding locally at one AP using local channel estimates, requiring no CPU signal exchange during decoding.The resulting architecture is fully distributed and essentially becomes a small-cell network.
  • AP association: The paper selects, for each UE, the AP that provides the highest SE, allowing arbitrary AP antenna counts and multi-UE service.This association is more complex than selecting by the largest large-scale fading coefficient.
  • Achievable SE: The Level 1 achievable SE is expressed for local decoding, with a closed-form special case when N = 1.The special case uses the local estimate ĥ_kl and accounts for the model’s interference terms.
  • AP association: Choosing the AP through SINR can match the complexity of large-scale-fading selection, but power optimization must also include AP association.This coupling arises because the SINR depends on transmit powers.
  • Achievable SE: The exact Level 1 expression agrees with earlier work only when pilot contamination is absent.The paper attributes the earlier discrepancy to conditioning errors in the interference-power calculation.
  • Numerical caveat: The Level 1 expression can become numerically unstable when ω_kl(1 + A_kl) or ω_klA_kl is small.The paper recommends using bounds for the exponential-integral product in that regime.

IV. CELL-FREE VERSUS CELLULAR MMIMO

The comparison evaluates uplink Cell-free mMIMO across cooperation levels and combining choices against Cellular mMIMO. It is motivated by the different strengths and weaknesses of the two network topologies.

  • Comparison scope: The study compares Cell-free mMIMO at different cooperation levels using MR or MMSE/L-MMSE combining against Cellular mMIMO.The comparison focuses on uplink performance.

A. Cellular mMIMO Setup

The cellular setup models correlated fading, pilot reuse, and uplink spectral efficiency with combining optimized by multi-cell MMSE. M-MMSE provides the strongest cellular baseline for comparison.

  • The cellular model uses Lc = 4 cells, Mc = 100 antennas per base station, and Kc = 10 user equipments per cell.
  • Spatial correlation matrices model correlated fading, while β captures large-scale fading from pathloss and shadowing.
  • Pilot reuse one assigns the same pilot to corresponding users in every cell, using τp = Kc mutually orthogonal pilots.
  • The achievable uplink SE is expressed through an effective SINR for each user.
  • Multi-cell MMSE combining maximizes the effective SINR, making M-MMSE the competitive cellular reference; other combiners provide lower SEs.

B. Simulation Setup and Propagation Model

The simulations compare cellular and cell-free networks with equal antenna counts under a common urban microcell propagation model. With MMSE-family processing, cell-free cooperation improves SE according to its cooperation level, while deployment geometry affects the balance among levels.

  • Both networks occupy the same 1 × 1 km area and use the same total antenna count, with either 400 single-antenna or 100 four-antenna cell-free APs.
  • The propagation model targets urban microcell deployments with APs roughly 10 m above ground and uses 2 GHz carrier-frequency assumptions.
  • Shadowing is correlated across users, while correlation between different APs is negligible because adjacent APs are separated by at least 50 m.
  • A common propagation model is applied to cellular and cell-free cases so observed differences reflect technology characteristics rather than propagation-model choices.
  • The simulations use spatially correlated arrays, 100 mW uplink power per user, 20 MHz bandwidth, and coherence blocks of τc = 200 channel uses.
  • At the 90% or 95% likely SE points, Level 4 gives the highest SE, while Level 1 remains preferable to Cellular mMIMO; Level 4 outperforms Cellular mMIMO for every user.
  • With L = 100 and N = 4, Level 4 loses SE from reduced macro diversity, while Level 1 improves through local interference suppression and becomes comparable to or better than Level 2.
  • With MR combining, cell-free performance suffers broadly: Level 2 is below small cells and Cellular mMIMO for every user, and even Level 4 does not outperform them.

D. Revisiting “Cell-free Massive MIMO versus small cells”

Revisiting earlier small-cell comparisons shows that propagation assumptions, AP assignment, SE expressions, and receiver processing materially change the conclusions. L-MMSE and centralized processing deliver the strongest supported results, while nonlinear decoding adds little.

  • Earlier results favoring cell-free Level 2 over small cells used a three-slope propagation model and are reconsidered under alternative modeling and evaluation choices.
  • Improved AP assignment can reduce or reverse the apparent cell-free advantage: about 40% of users prefer another small cell, and improved SE expressions favor small cells for all users.
  • Replacing MR with L-MMSE makes Level 2 uniformly better than small cells, while Level 3 and Level 4 achieve still higher SE.
  • With max-min power control, Level 2 MR improves the weakest users, but Level 2 L-MMSE with full power gives 40% higher 95%-likely SE and 3× higher median SE.
  • MMSE-SIC guarantees every user at least the SE of MMSE combining regardless of decoding order, but its average sum-SE gain is only 1%.
  • Favorable propagation makes user channels nearly orthogonal, explaining why nonlinear processing is not needed in cell-free mMIMO.
  • Level 1 and Level 3 have roughly equal sum SE, Level 2 trails them, and the large Level 4 gap supports centralized implementation.

VI. A LOOK AT THE FRONTHAUL SIGNALING LOAD

The paper finds that centralized Level 4 can simultaneously improve spectral efficiency and reduce fronthaul signaling relative to distributed alternatives. For practical coherence blocks and typical user-to-antenna ratios, Level 4 is therefore strongly preferred, although serial fronthaul can make Levels 2 and 3 more viable.

  • Fronthaul comparison: Level 4 requires less signaling than distributed alternatives when N K < 1.This condition follows from the fronthaul formulas in Table I.
  • Fronthaul comparison: For typical Cell-free mMIMO, where τc/(τc−τp) ≈ 1 and K ≫ N, Level 4 requires much less signaling.
  • Fronthaul comparison: As τc →∞, Levels 2 and 3 require K/N = 10 times more fronthaul signaling than Level 4 in the considered setup.Level 4 requires more signaling when τc ≤11, but much less when τc becomes large, such as 100.
  • Fronthaul comparison: Level 2 and Level 3 expand each AP’s N-dimensional received vector into K-dimensional locally decoded outputs, increasing signaling when K ≥ N.
  • Caveat: The comparison assumes infinite-precision scalar sharing, while pilot signals may require higher bit resolution than data signals.Pilot signals are a minor fraction of total signaling, and channel estimates can be compressed relatively well.
  • Serial fronthaul: Serial fronthaul reduces the extreme-case signaling per coherence block from (τc−τp)KL to (τc−τp)K.Only one scalar per UE is transmitted over each fronthaul segment, so capacity does not grow with the number of APs sharing the connection.

APPENDIX A PROOF OF PROPOSITION 2

The appendix derives achievable spectral-efficiency expressions by modeling estimation errors and interference as an effective noise term. For Level 4, the received signal is treated as a multiple-access channel with colored noise, enabling pre-whitening and MMSE-SIC analysis.

  • Proof setup: The CPU treats the average channel gain as the deterministic channel because it lacks the channel estimates.
  • Proof setup: The interference-plus-noise term has zero mean and is uncorrelated with the desired signal, allowing an achievable SE bound to be applied.
  • Scalar derivation: Conditioning on the known channel estimate yields an achievable SE expression using a capacity lower bound.
  • Scalar derivation: The proof expands the effective interference variance using channel-estimate independence and pilot-contamination relations.
  • Level 4 derivation: For Level 4, the received signal is modeled as a multiple-access channel with colored noise, followed by pre-whitening and MMSE-SIC to obtain achievable sum SE.
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