PaperlayerView exact revision on arXiv

Source-linked AI summary

Energy-Efficient Power Control in Cell-Free and User-Centric Massive MIMO at Millimeter Wave

Mario Alonzo, Stefano Buzzi, Alessio Zappone, Ciro D'Elia

arXiv:1903.11365v1eess.SPcs.IT

TL;DR

This paper addresses energy-efficient power control for cell-free and user-centric massive MIMO at millimeter-wave frequencies, where channel modeling and allocation are complicated by correlated channels and non-convex optimization. It develops clustered channel modeling, low-complexity hybrid beamforming, and power-control methods, finding improved performance over uniform allocation and practical benefits for user-centric operation.

  • Problem

    Millimeter-wave cell-free and user-centric massive MIMO require energy-efficient power allocation despite correlated channels and a non-concave global energy-efficiency objective.

  • Method

    The paper combines a multiuser clustered millimeter-wave channel model with uplink channel estimation, low-complexity hybrid analog-digital beamforming, and successive lower-bound maximization for power allocation.

  • Results

    The proposed power optimization method outperforms uniform power allocation, while the analyzed cell-free and user-centric architectures remain effective under hybrid beamforming and imperfect channel state information.

  • Takeaways & Limitations

    User-centric operation with each access point serving one user generally performs better than serving three users in the considered practical dense-deployment scenario.

  • Takeaways & Limitations

    With an idle-access-point circuit-power model, the global energy-efficiency function becomes non-differentiable, so convergence does not guarantee first-order optimality.

Abstract

from arXiv · show

In a cell-free massive MIMO architecture a very large number of distributed access points simultaneously and jointly serves a much smaller number of mobile stations; a variant of the cell-free technique is the user-centric approach, wherein each access point just serves a reduced set of mobile stations. This paper introduces and analyzes the cell-free and user-centric architectures at millimeter wave frequencies, considering a training-based channel estimation phase, and the downlink and uplink data transmission phases. First of all, a multiuser clustered millimeter wave channel model is introduced in order to account for the correlation among the channels of nearby users; second, an uplink multiuser channel estimation scheme is described along with low-complexity hybrid analog/digital beamforming architectures. Third, the non-convex problem of power allocation for downlink global energy efficiency maximization is addressed. Interestingly, in the proposed schemes no channel estimation is needed at the mobile stations, and the beamforming schemes used at the mobile stations are channel-independent and have a very simple structure. Numerical results show the benefits granted by the power control procedure, that the considered architectures are effective, and permit assessing the loss incurred by the use of the hybrid beamformers and by the channel estimation errors.

I. INTRODUCTION

The paper extends cell-free and user-centric massive MIMO to mmWave frequencies, motivated by wide bandwidths, dense distributed deployment, path diversity, and energy-efficiency requirements. It introduces a correlated multiuser channel model, practical beamforming and training procedures, and global-energy-efficiency resource allocation.

  • Motivation: MmWave massive MIMO combines large antenna arrays with wide bandwidths available over short distances.The paper motivates mmWave operation as a future wireless technology while noting its distinct propagation and hardware challenges.
  • Motivation: Distributed access points alleviate the cell-edge problem and provide path diversity against frequent mmWave blockages.The architecture replaces a few co-located massive arrays with many densely deployed APs having smaller arrays.
  • Contributions: The paper is the first to consider cell-free and user-centric massive-MIMO deployments at mmWave while maximizing global energy efficiency.The study focuses on resource allocation strategies for these architectures and reports earlier results indicating that user-centric operation generally outperforms cell-free operation.
  • Contributions: A multiuser clustered mmWave channel model captures channel correlation among nearby users by sharing scatterers across AP–MS links.The paper also studies hybrid analog-digital partial-ZF beamforming at APs and channel-independent 0-1 beamforming at MSs.
  • Communication protocol: The communication protocol comprises uplink training, downlink data transmission, and uplink data transmission.APs estimate channels from mobile-station pilots before using those estimates for data processing.
  • Mobile-station beamforming: Each mobile station uses a simple channel-independent 0-1 beamformer that divides its antennas into disjoint groups and sums each group’s received samples.APs use channel estimates and TDD reciprocity to approximately align the summed samples in phase.

A. Uplink training

Uplink training lets mobile stations transmit pilots so that access points can estimate the effective channels used for subsequent processing. The paper uses structured pilots and an LMMSE estimation procedure implemented through an iterative beamforming-related algorithm.

  • Pilot transmission: During uplink training, mobile stations transmit pilot sequences that enable each access point to estimate the channels.The training phase length τp must be shorter than the channel coherence time τc.
  • Pilot design: Each mobile station’s pilot matrix has orthogonal rows, while pilots assigned to different mobile stations need not be mutually orthogonal.Full pilot orthogonality would avoid pilot contamination but limit the accommodated product KP relative to the coherence interval.
  • Signal model: The received training signal at each access point is modeled as a sum of effective user channels plus thermal noise.The effective channel is represented by Sk,m = Hk,mLk, and the noise entries are modeled as independent complex Gaussian samples.
  • Channel estimation: The LMMSE estimator vectorizes the received training matrix and processes it with a matrix derived from the channel statistics.The estimator is obtained by setting the mean-square-error gradient with respect to the estimator matrix to zero.
  • Algorithm: The beamforming-related implementation uses block coordinate descent with an initialization, alternating updates, and termination at convergence or a maximum iteration count.The listed algorithm updates the relevant variables iteratively after initializing the RF component.

B. Downlink data transmission

For downlink transmission, the access points first construct full-digital zero-forcing precoders from estimated effective channels and then decompose them into low-complexity hybrid beamformers. The analog beamformer is shared across users at each access point, while digital beamformers remain user-specific.

  • Full-digital precoding: After training, each access point constructs a zero-forcing precoder from the estimated effective channels of the served users.The precoding design begins by forming a matrix that collects the estimated effective channels.
  • Power normalization: The precoding matrices are normalized before downlink transmission.Normalization is specified for every user and access point.
  • Hybrid decomposition: Hybrid beamforming reduces RF-chain requirements below the number of transmit antennas, addressing mmWave hardware-complexity constraints.The hybrid structure decomposes the full-digital beamformer into baseband and analog components.
  • Hybrid architecture: The baseband beamformer is mobile-station-specific, whereas each access point uses one analog beamformer jointly for all served users.The analog matrix has constant-norm entries and is obtained through the block coordinate descent decomposition.
  • User-centric operation: In the user-centric approach, the decomposition input is formed only from beamformers associated with the mobile stations actually served by each access point.This distinguishes the user-centric construction from the all-user cell-free construction.

1) The CF approach:

The cell-free approach has every access point serve every mobile station, with power coefficients controlling AP-to-user transmissions and received signals formed from coherent multi-AP contributions plus noise. The resulting achievable rates support the paper’s power-allocation formulations.

  • Cell-free association: In the cell-free approach, every access point serves every mobile station.The transmitted signal from each AP contains data intended for all users, weighted by AP–user power coefficients.
  • Downlink signal model: The coefficient ηm,k represents the power used by access point m to transmit toward mobile station k.The received signal and achievable rate depend on the collection of all downlink powers.
  • Received signal: Each mobile station receives an NMS-dimensional signal containing the desired transmission, interference, and additive thermal noise.The noise is modeled as independent complex Gaussian with variance σ_z^2.
  • Detection: A soft estimate of the desired data symbol is formed at the mobile station from its received vector.The same estimation step is used after writing the cell-free received signal model.
  • Achievable rate: The achievable user rate is expressed using the covariance matrix of interference and then algebraically reformulated for optimization.The reformulated rate depends compactly on the vector η containing all downlink transmit powers.

C. Uplink data transmission

The uplink data-transmission phase sends each mobile station’s data vector to the access points, with transmit power represented explicitly in the received-signal model.

  • During uplink data transmission, the k-th mobile station transmits a P-dimensional data vector at each sample time.
  • The received signal at access point m includes the k-th mobile station’s uplink transmit power.

1) CF approach:

In the cell-free approach, access points process uplink observations and forward per-user statistics to the CPU, whose soft estimates coherently combine the desired signals from all access points.

  • Each access point forms a per-user statistic using the previously defined zero-forcing beamformer as a post-coder.
  • The access points send their processed vectors to the CPU through the backhaul link for soft data estimation.
  • Desired contributions associated with each uplink data symbol are coherently summed across access points.
  • Unlike the user-centric case, the cell-free case uses all access points for each mobile station by setting M(k)={1,2,...,M}.The same achievable-rate expression can therefore be applied to both architectures with this set definition.

III. GLOBAL ENERGY EFFICIENCY MAXIMIZATION

The paper addresses downlink and uplink global energy-efficiency power control through blockwise successive lower-bound maximization, producing tractable fractional subproblems and a convergent sequential algorithm.

  • The global energy-efficiency problem is difficult because its fractional objective has a non-concave numerator and KM optimization variables.
  • The method partitions transmit powers into access-point variable blocks and alternately optimizes one block while fixing the others.
  • Dinkelbach’s algorithm globally solves each resulting fractional subproblem after the approximate numerator becomes concave.
  • Algorithm 2 monotonically improves global energy efficiency and converges to a first-order optimal point of the original problem.

1) An alternative definition for the GEE on the downlink:

An alternative global-energy-efficiency definition models lower circuit consumption for idle access points, but the resulting indicator function makes the objective non-differentiable.

  • The baseline definition assumes circuit power is independent of each base station’s transmit power.
  • Idle access points can consume less circuit power because they switch to idle mode when not transmitting.
  • The alternative model halves circuit power when an access point radiates no power.
  • The indicator-based model is non-differentiable, so the algorithm retains monotonic improvement but loses its first-order optimality guarantee.A smooth sigmoid approximation can restore the first-order optimality property.

B. Uplink power control

The uplink global energy-efficiency problem has the same structure as the downlink problem, so it can use the same solution procedure while optimizing only K transmit powers. The paper also notes that sum-rate maximization can be treated as a special case and becomes standard convex optimization under perfect CSI with zero-forcing precoding.

  • Uplink global energy-efficiency maximization: The maximum transmit power constraint applies to each mobile station, with the same power assumed for all mobile stations for simplicity.The equal-power assumption can be relaxed.
  • Uplink global energy-efficiency maximization: The uplink global energy-efficiency maximization problem can be solved using the same procedure developed for the downlink.The two optimization problems have the same structure.
  • Uplink global energy-efficiency maximization: Only K transmit powers are optimized in the uplink, compared with MK variables for cell-free and MN variables for user-centric downlink power control.This makes uplink power optimization much smaller in dimension.
  • Sum-rate maximization: Sum-rate maximization can be handled as a special case of global energy-efficiency maximization.The paper presents this as an alternative objective using the same general approach.
  • Sum-rate maximization: With perfect CSI and zero-forcing precoding, the sum-rate function is concave and can be globally maximized with polynomial complexity using standard convex programming.Zero forcing removes multi-user interference in this setting.
  • Channel model: The channel matrices used in the optimization are generated under a clustered millimeter-wave channel model with cluster and ray parameters.The model defines Ncl as the number of clusters and Nray as the number of rays per cluster.

NAP NMS

The section specifies the millimeter-wave channel and simulation setup for comparing beamforming and power-control schemes. Channels can be correlated for closely spaced devices through shared scatterers, while the reported evaluations use defined carrier, bandwidth, deployment, and averaging parameters.

  • Channel correlation: Figure 2 selects scatterers inside an ellipse around each AP-MS pair, producing correlated channels for nearby users while treating the MS3 channel as statistically independent in the example.The ellipse construction links channel correlation to device proximity.
  • Beamforming comparisons: Figures 3 and 4 compare fully-digital and hybrid beamforming versus maximum transmit power for N=1 and N=3, using M = 80, K = 6, and NAP × NMS = 16 × 8.Figure 3 reports global energy efficiency, while Figure 4 reports average achievable rate per user.
  • Channel model: The line-of-sight channel component depends on a random phase, a binary LOS indicator, and transmitter-receiver distance.The LOS probability is specified for the UMi scenario.
  • Channel correlation: Nearby AP-MS channels are correlated by generating all channels from the same set of random clusters and scatterers.The model uses three rays per cluster in the considered area.
  • Simulation setup: The simulations use f0 = 73 GHz, B = 200 MHz, a 250×250 sqm UMi Open Square area, and 25,000 randomly deployed clusters.The cluster density is 0.4 cluster/sqm.
  • Simulation setup: The reported numerical values are averaged over 1000 independent channel scenarios and random user and access-point locations.The optimization uses a relative-tolerance convergence criterion.
  • Power-control evaluation: The optimized power-control results are compared with uniform power allocation, with ePc,m = 1 W for each AP and ePc,k = 0.3 W for each mobile station.The optimization results use dashed curves and uniform allocation uses solid curves of the same color.

B. Numerical results

The numerical results evaluate energy efficiency and achievable rates under fully digital and hybrid beamforming, perfect and imperfect CSI, and user-centric association with N=1 or N=3. Power optimization generally improves performance, while practical incomplete-CSI hybrid schemes favor serving one user per AP in the considered dense deployments.

  • Power control: The proposed power optimization method generally outperforms uniform power allocation for global energy efficiency and downlink average rate.With imperfect CSI, the optimized curve can underperform because optimization uses estimated channels while evaluation uses the true channel coefficients.
  • Power control: In perfect CSI with fully digital beamforming and N=1, uniform and optimal power allocation achieve the same performance for rate maximization.This occurs because rate increases with total available power and one served user makes uniform allocation coincide with the rate-maximizing strategy.
  • Energy efficiency: Global energy efficiency differs from rate because it is not monotonically increasing with maximum transmit power, leaving a gap between uniform and optimized allocation even for N=1.The corresponding rate behavior does not show this gap in the perfect-CSI, fully digital, N=1 case.
  • User-centric association: For imperfect CSI and hybrid beamforming, N=1 provides much better rate-per-user performance than N=3 for most users.The paper attributes this to nearby APs dedicating their resources to one user rather than sharing them among multiple users.
  • Overall findings: The study concludes that power allocation increases energy efficiency and average rate-per-user, whereas hybrid beamforming causes considerable performance degradation.The conclusion covers the considered cell-free and user-centric millimeter-wave architectures and channel-estimation settings.

APPENDIX: SUCCESSIVE LOWER-BOUND MAXIMIZATION

Successive lower-bound maximization combines alternating optimization with sequential convex programming to solve difficult non-convex subproblems through cyclic block updates and tractable approximations. Under stated conditions, it monotonically improves the objective and converges to first-order optimal points.

  • Alternating optimization: The method partitions variables into blocks and cyclically optimizes one block while keeping the others fixed.This follows the alternating-optimization structure and decomposes the problem into block subproblems.
  • Alternating optimization: If each block subproblem is globally solved under the stated uniqueness and product-set conditions, alternating maximization monotonically improves the objective and reaches a first-order optimal point.The result depends on global solution of each subproblem and the conditions specified in the appendix.
  • Sequential optimization: Sequential optimization replaces a difficult maximization problem with a sequence of easier approximate problems using surrogate objectives and constraints.The approximation sequence is required to satisfy three properties for each iteration.
  • Convergence guarantees: The solutions of the approximate problems produce a monotonically increasing convergent objective sequence, and every convergent solution sequence reaches a first-order optimal point.The guarantee holds subject to constraint qualifications and the properties of the lower-bound approximations.
  • Requirements: The technique requires lower bounds that satisfy all three required properties while still yielding an appropriate approximation of the original objective.Constructing such lower bounds is necessary before applying the method.
Loading 1903.11365v1…