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User-Centric 5G Cellular Networks: Resource Allocation and Comparison with the Cell-Free Massive MIMO Approach

Stefano Buzzi, Carmen D'Andrea, Alessio Zappone

arXiv:1803.02261v1cs.ITcs.NI

TL;DR

The paper addresses how to extend CF Massive MIMO to multiple-antenna APs and MSs while avoiding channel estimation at the MSs, and compares CF with a user-centric alternative. It proposes channel-inversion beamforming and power-allocation strategies, finding that UC generally outperforms CF, especially on the uplink, while using less backhaul.

  • Problem

    Extending CF Massive MIMO to multiple-antenna MSs is nontrivial because MSs perform no channel estimation, while serving every MS from every AP can waste resources on distant, low-SINR links.

  • Method

    The paper compares CF and UC with multiple-antenna APs and MSs, proposes channel-inversion beamforming without MS channel estimation, and develops sum-rate- and minimum-rate-maximizing power allocation.

  • Results

    UC generally outperforms CF, especially on the uplink; under sum-rate maximization, CF can outperform UC, but the difference is rather limited.

  • Takeaways & Limitations

    Limiting each MS’s serving APs can improve achievable rate-per-user for most users while requiring less backhaul bandwidth than CF.

Abstract

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Recently, the so-called cell-free (CF) Massive MIMO architecture has been introduced, wherein a very large number of distributed access points (APs) simultaneously and jointly serve a much smaller number of mobile stations (MSs). The paper extends the CF approach to the case in which both the APs and the MSs are equipped with multiple antennas, proposing a beamfoming scheme that, relying on the channel hardening effect, does not require channel estimation at the MSs. We contrast the CF massive MIMO approach with a user-centric (UC) approach wherein each MS is served only by a limited number of APs. Since far APs experience a bad SINR, it turns out that they are quite unhelpful in serving far users, and so, the UC approach, while requiring less backhaul overhead with respect to the CF approach, is shown here to achieve better performance results, in terms of achievable rate-per-user, for the vast majority of the MSs in the network. Furthermore, in the paper we propose two power allocation strategy for the uplink and downlink, one aimed at maximizing the overall data-rate and another aimed at maximizing system fairness.

I. INTRODUCTION

The paper extends distributed CF Massive MIMO to multiple-antenna APs and MSs, compares it with a less backhaul-intensive UC architecture, and proposes power-control strategies for rate and fairness.

  • Motivation: Distributed Massive MIMO spreads antennas over a large area, improving shadow-fading diversity and coverage probability at the cost of increased backhaul requirements.The distributed layout also alleviates the cell-edge problem and can improve service uniformity.
  • CF architecture: CF Massive MIMO uses many distributed APs that jointly serve users through a CPU-connected backhaul, without cells or cell boundaries.The backhaul carries downlink data symbols and uplink sufficient statistics, while beamformers are computed locally.
  • Contributions: The paper compares CF and UC when both APs and MSs have multiple antennas, addressing the challenge that MSs perform no channel estimation.Its beamforming scheme exploits channel hardening to support coherent data reception at the MSs.
  • UC motivation: Serving every MS from every AP can waste power and computation on distant links with very low SINR.The UC approach instead assigns each MS only nearby APs and was previously shown to provide higher achievable rate-per-user for most users with less backhaul bandwidth.
  • Contributions: Two power-allocation strategies target overall data-rate maximization and minimum-rate maximization for fairness in both uplink and downlink.The study contrasts these strategies with uniform power allocation and evaluates CF and UC under pilot-matched estimation and perfect CSI.

III. THE COMMUNICATION PROTOCOL FOR THE CF AND UC APPROACHES

Both architectures use sequential uplink training, downlink transmission, and uplink transmission within the channel coherence interval. APs estimate channels from pilots, but non-orthogonal inter-user pilots create pilot contamination.

  • Protocol phases: The communication protocol has three sequential phases: uplink training, downlink data transmission, and uplink data transmission.Their total duration must remain within the channel coherence time.
  • Uplink training: During uplink training, MSs transmit pilots that APs use for channel estimation in both CF and UC approaches.The pilot length τp must be shorter than the coherence interval τc.
  • Uplink training: Each AP estimates all MS channel matrices using simple pilot-matched single-user estimation and knowledge of MS transmit powers.The received training observations include thermal noise and out-of-cell interference.
  • Pilot contamination: Pilot sequences are orthogonal across antenna dimensions for each user but non-orthogonal across different users because τp ≥ KNMS is often impractical.Consequently, the channel estimate is impaired by both noise and other users’ pilots.

B. Downlink data transmission

In downlink transmission, APs use channel-inversion beamforming based on their channel estimates, while MSs decode without channel estimation by combining hardened channel observations.

  • Beamforming: After channel estimation, APs treat the estimates as true channels and apply channel-inversion beamforming for downlink transmission.The scheme aims to enable data reception without information about the instantaneous channel at the MS.
  • Beamforming: The precoder for each AP-MS link is structured using the user’s multiplexing order and a fixed matrix construction.The multiplexing order Pk denotes the number of simultaneous data streams for user k.
  • CF downlink: In CF operation, every AP communicates with every MS, so each MS receives signal contributions from all APs.The received vector also includes thermal noise and out-of-cluster interference.
  • MS decoding: MSs perform no channel estimation because the fixed beamformer structure partitions observations into groups and coherently sums entries within each group.This decoding relies on the channel-hardening-based observation structure rather than channel-dependent beamformers at the MS.

2) UC massive MIMO architecture:

The UC architecture assigns each AP a limited set of nearby MSs using channel-strength measures, reducing the scope of AP–MS communication. The received signal combines contributions from serving APs with noise and out-of-cluster interference, after which each MS forms a soft data estimate.

  • AP–MS association: Each AP can select associated MSs using estimated-channel Frobenius norms, either by thresholding against the average or by retaining the N strongest channels.The paper uses the latter strongest-channel strategy in its numerical results.
  • AP–MS association: The set K(m) contains the MSs served by AP m, while M(k) contains the APs communicating with user k.These sets define the user-centric serving relationships.
  • Received signal: The user’s observable vector consists of signal contributions from the communicating APs together with thermal noise and out-of-cluster interference.The noise and interference are modeled as independent complex Gaussian variables.
  • Data detection: Each MS obtains a soft estimate of its downlink data symbols from the received observation.The soft estimate is formed at the MS after observing its received vector.

C. Uplink data transmission

During uplink transmission, each MS sends data using a predefined trivial beamformer without channel estimation. APs receive the transmitted vectors and, in the CF case, form and forward soft estimates to the CPU without transmitting channel estimates.

  • Uplink transmission: MSs transmit uplink data using a trivial beamformer because they do not perform channel estimation.The MS antennas are partitioned into disjoint subsets, with each subset transmitting the same data symbol.
  • Uplink transmission: The signal received at each AP is an N_AP-dimensional vector containing the uplink contributions from the MSs.The received vector is indexed by AP m and time sample n.
  • CF processing: In CF MIMO, every AP forms per-user statistics for all K MSs before forwarding them to the CPU.This reflects the CF assumption that all APs participate in decoding every user.
  • CF processing: The AP computes the statistics through a defined channel-related matrix and sends the resulting soft estimates to the CPU.The CPU then forms soft estimates of the transmitted data vectors.
  • Backhaul: Only soft data estimates, rather than channel estimates, are transmitted from APs to the CPU over the backhaul.This avoids propagating channel estimates through the backhaul.

2) UC massive MIMO architecture:

The UC uplink decoder restricts each AP to the MSs in its association set, reducing backhaul traffic relative to CF processing. Downlink power control then optimizes sum rate or minimum user rate under per-AP power and nonnegativity constraints, using successive lower-bound maximization for non-concave problems.

  • UC versus CF processing: In UC processing, AP m computes decoding statistics only for MSs in K(m), and the CPU forms soft estimates from these restricted contributions.The CF case is recovered when every AP serves all K users.
  • UC versus CF processing: UC reduces backhaul overhead because each AP sends soft estimates only for its associated MSs.CF requires every AP to contribute estimates for every MS.
  • Downlink power control: Downlink power coefficients η_k,m determine the power transmitted by AP m for MS k, and η collects all KM downlink powers.The coefficients are optimized subject to AP-level power limits.
  • Downlink power control: The paper optimizes downlink powers for either system sum rate or minimum users’ rate under maximum per-AP power constraints and nonnegative powers.These are separate fairness and aggregate-rate objectives.
  • Optimization challenge: Both power-control problems have non-concave objectives and KM optimization variables, creating challenges for direct solution.The paper therefore applies successive lower-bound maximization.

A. Successive lower-bound maximization

Successive lower-bound maximization combines alternating optimization with sequential convex programming to handle difficult non-concave subproblems. Under stated assumptions, it preserves monotonic improvement and yields first-order optimality properties while remaining computationally feasible.

  • Alternating optimization: The method partitions variables into blocks and cyclically optimizes one block at a time while fixing the others.This decomposes the original problem into blockwise subproblems.
  • Optimality properties: Iterative block optimization monotonically improves the objective and converges to a first-order optimal point when each subproblem has a unique solution and the feasible set is separable.These are the assumptions given for the alternating-optimization guarantee.
  • Sequential convex programming: When block subproblems are difficult, sequential convex programming replaces them with a sequence of easier maximization problems.This improves feasibility but does not guarantee global solution of each subproblem.
  • Optimality properties: The sequential approach retains monotonic objective improvement and reaches KKT first-order optimality for the original problem under suitable lower-bound conditions.Its applicability depends on constructing lower bounds satisfying the required properties.
  • Method rationale: Successive lower-bound maximization retains the optimality properties of alternating optimization even when subproblems are not globally solved, under similar assumptions.This is the method’s principal theoretical rationale.

B. Sum-rate maximization

The downlink sum-rate problem is non-convex, so the paper uses sequential lower-bound maximization within an alternating optimization framework. The resulting algorithm monotonically improves and converges to a first-order stationary solution under stated conditions.

  • Problem formulation: Downlink sum-rate maximization is decomposed into access-point transmit-power blocks optimized alternately.Each block η_m contains the transmit powers of access point m, reducing the subproblem dimension to M transmit powers.
  • Sequential lower-bound method: The user-rate objective is non-concave, motivating a concave lower bound constructed from its difference-of-concave representation.The construction uses joint concavity of √xy, matrix monotonicity of log2|·|, summation-preserved concavity, and Taylor upper bounds.
  • Optimality properties: After each Algorithm 1 iteration, the sum-rate is not decreased, the objective sequence converges, and every limit point satisfies the KKT first-order conditions of Problem (34).These guarantees hold provided the additional assumptions of the sequential method are fulfilled at each iteration.

C. Minimum rate maximization

Minimum-rate maximization is reformulated with an auxiliary minimum-rate variable and solved through sequential convex approximations. Each resulting subproblem is convex, enabling an algorithm with properties similar to sum-rate maximization.

  • Problem reformulation: The non-differentiable minimum-rate objective is reformulated using an auxiliary variable t constrained by every user’s achievable rate.The reformulation imposes R_k(η_m, η_−m) ≥ t for all k = 1, . . . , K.
  • Sequential approximation: A sequential lower-bound approximation replaces each user-rate constraint with a tractable bound evaluated around the current block iterate.The approximate constraints use R̃_k(η_m, η_m,0, η_−m) ≥ t.
  • Algorithm: For any η_m,0, the approximate minimum-rate problem has a linear objective and convex constraints, so standard convex optimization solves it.The resulting procedure is specified as Algorithm 2.

V. UPLINK POWER CONTROL

For the uplink, the paper formulates sum-rate and minimum-rate power-control problems over users’ transmit powers and applies sequential optimization to both objectives. Because only K uplink variables exist, joint optimization is practically feasible.

  • Problem formulation: The uplink transmit-power vector eη collects the K mobile stations’ powers, which are constrained by individual maximum powers.Both sum-rate and minimum-rate objectives are formulated over this vector under per-user power limits.
  • Sequential optimization: Uplink user rates can be expressed as differences of two concave functions, enabling sequential lower-bound optimization.The concavity of g1 and g2 provides the required rate lower bounds for the sequential framework.
  • Computational structure: Unlike the downlink, the uplink has only K optimization variables, making a single variable block practical for joint optimization.The algorithms can nevertheless be extended to multiple variable blocks if desired.
  • Optimization procedures: Both uplink objectives use sequentially constructed auxiliary problems, and similar optimality properties to the downlink case hold.The paper gives separate auxiliary formulations for sum-rate and minimum-rate maximization.

VI. NUMERICAL RESULTS

The numerical study evaluates per-user and system sum-rates for CF and UC architectures under uniform, sum-rate-maximizing, and minimum-rate-maximizing power allocation. UC outperforms CF in most reported settings, especially on the uplink.

  • Simulation setup: The simulations use W = 20 MHz at f0 = 1.9 GHz, with N_AP = 4, N_MS = 2, and multiplexing order P_k = 2.Achievable per-user rate and uplink/downlink sum-rate are the performance measures.
  • Downlink results: Downlink CDFs compare CF and UC per-user rates under uniform, sum-rate-maximizing, and minimum-rate-maximizing power allocation.High-density settings use M = 80, K = 15, N = 6, τp = 16; low-density settings use M = 50, K = 5, N = 2, τp = 8.
  • Downlink results: UC outperforms CF in downlink under uniform and minimum-rate-maximizing allocation across both density scenarios.Under sum-rate-maximizing allocation, CF performs better, but the difference is rather limited; this behavior is also reflected in the sum-rate-versus-N experiment.
  • Uplink results: Uplink CDFs and sum-rate results show UC outperforming CF for every considered power-allocation strategy.The paper reports situations with many-fold improvement over CF, using maximum mobile-station power Pmax,k = 100 mW.

VII. CONCLUSIONS

The paper extends CF massive MIMO to multi-antenna APs and MSs, introduces two power-allocation strategies, and finds that UC generally outperforms CF, especially on the uplink.

  • The proposed channel-inverting beamforming scheme supports multi-antenna APs and MSs without requiring channel estimation at the MSs.
  • The paper contrasts CF with UC, where each AP decodes a pre-assigned number of MSs.
  • Two power-allocation strategies target sum-rate maximization and minimum-rate maximization for overall data-rate and fairness, respectively.
  • UC generally outperforms CF, especially on the uplink, including in many relevant practical situations.
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