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Large-Scale MIMO versus Network MIMO for Multicell Interference Mitigation

Kianoush Hosseini, Wei Yu, Raviraj S. Adve

arXiv:1407.5747v1cs.ITmath.IT

TL;DR

Intercell interference is a key concern in dense cellular networks, and prior comparisons of LS-MIMO and network MIMO covered only special cases. This paper analyzes their channel and interference distributions using stochastic ordering and finds stronger user performance under LS-MIMO.

  • Problem

    Intercell interference limits dense cellular networks, while prior LS-MIMO versus network-MIMO performance comparisons covered only special cases.

    Source: §I · p. 1, B. Main Contributions · p. 2

  • Method

    The paper compares the architectures by analyzing signal and interference power distributions and applying stochastic-ordering tools to their SINR performance.

    Source: B. Main Contributions · p. 2, §IV · p. 5

  • Results

    LS-MIMO statistically provides stronger signal and SINR performance than network MIMO, with gains in coverage probability, ergodic rate, and expected weighted sum rate.

    Source: B. Main Contributions · p. 2, C. SINR Stochastic Ordering · p. 7

  • Takeaways & Limitations

    Given the likely lower cost of adding antennas than establishing backhaul data sharing and joint transmission, LS-MIMO could be a preferred practical route to multicell interference mitigation.

    Source: §I · p. 1

Abstract

from arXiv · show

This paper compares two important downlink multicell interference mitigation techniques, namely, large-scale (LS) multiple-input multiple-output (MIMO) and network MIMO. We consider a cooperative wireless cellular system operating in time-division duplex (TDD) mode, wherein each cooperating cluster includes $B$ base-stations (BSs), each equipped with multiple antennas and scheduling $K$ single-antenna users. In an LS-MIMO system, each BS employs $BM$ antennas not only to serve its scheduled users, but also to null out interference caused to the other users within the cooperating cluster using zero-forcing (ZF) beamforming. In a network MIMO system, each BS is equipped with only $M$ antennas, but interference cancellation is realized by data and channel state information exchange over the backhaul links and joint downlink transmission using ZF beamforming. Both systems are able to completely eliminate intra-cluster interference and to provide the same number of spatial degrees of freedom per user. Assuming the uplink-downlink channel reciprocity provided by TDD, both systems are subject to identical channel acquisition overhead during the uplink pilot transmission stage. Further, the available sum power at each cluster is fixed and assumed to be equally distributed across the downlink beams in both systems. Building upon the channel distribution functions and using tools from stochastic ordering, this paper shows, however, that from a performance point of view, users experience better quality of service, averaged over small-scale fading, under an LS-MIMO system than a network MIMO system. Numerical simulations for a multicell network reveal that this conclusion also holds true with regularized ZF beamforming scheme. Hence, given the likely lower cost of adding excess number of antennas at each BS, LS-MIMO could be the preferred route toward interference mitigation in cellular networks.

I. INTRODUCTION

Dense cellular deployments make intercell interference a key concern, and this paper compares LS-MIMO with network MIMO. It finds stronger performance under LS-MIMO despite the systems’ shared spatial degrees of freedom, CSI overhead, and cluster power.

I. INTRODUCTION

  • Dense deployments make intercell interference a key limiting factor, motivating multicell coordination to reduce interference and meet QoS requirements.The paper identifies systematic performance comparison as lacking.Source: §I · p. 1

A. Related Work

  • Unlike asymptotic massive MIMO, this comparison fixes a finite number of BS antennas and cooperating clusters.The related-work discussion notes the physical dimensions and analog front-end costs associated with very large antenna counts.Source: A. Related Work · pp. 1–2

B. Main Contributions

  • Earlier performance comparisons were limited to special cases; this study keeps cell sites fixed while allowing antenna counts and backhaul requirements to vary.The comparison is framed for a TDD multicell network with cooperating clusters.Source: B. Main Contributions · p. 2, A. Related Work · p. 2
  • Both architectures provide the same spatial DoF, CSI acquisition overhead, and cluster power, but LS-MIMO uses excess local antennas while network MIMO jointly shares CSI and data.LS-MIMO uses local interference nulling; network MIMO enables joint downlink transmission through backhaul sharing.Source: §I · p. 1, B. Main Contributions · p. 2
  • LS-MIMO provides stronger signal and SINR performance, improving coverage probability, ergodic rate, and expected weighted sum rate over network MIMO.Numerical results also show the conclusion holds with regularized ZF beamforming.Source: B. Main Contributions · p. 2

C. Paper Organization

The paper outlines its sections and notation, illustrates the two architectures in a two-BS example, and specifies the multicell system model and its simplifying assumptions.

C. Paper Organization

  • Section II gives an illustrative comparison, Sections III–VI cover models, distributions, stochastic ordering, and numerical results, and Section VII concludes.The paper also defines its mathematical notation.Source: C. Paper Organization · p. 3

D. Notation

  • The notation defines Γ(k, θ) as the Gamma distribution with shape k and scale θ.It also specifies conventions for matrices, vectors, probabilities, and expectations.Source: D. Notation · p. 3

II. AN ILLUSTRATIVE EXAMPLE

  • The two-BS example contrasts co-located LS-MIMO antennas with a farther network-MIMO transmitter: the latter has weaker expected signal power, while interference powers match in distribution.The figure depicts the two architectures side by side.Source: §II · p. 3, Figure 1 · p. 3

III. SYSTEM MODEL

  • The model uses fixed cooperating clusters, Rayleigh fading with distance-based path loss, ZF, an orthogonal-beam approximation, equal cluster power, and round-robin scheduling.The clusters transmit concurrently over shared spectrum.Source: §III · pp. 3–4

A. Received Signal Model in an LS-MIMO System

In LS-MIMO, each BS uses its channel knowledge to design ZF beams for scheduled users while suppressing interference to other users in the cluster; equal-power beams contribute to each user’s received signal and SINR.

A. Received Signal Model in an LS-MIMO System

  • With CSI for cluster users, the BS designs ZF beams to serve its scheduled users while suppressing interference to the others.The channel matrix covers the users in the cluster, and the beam for user i is selected from the ZF beamforming matrix.Source: A. Received Signal Model in an LS-MIMO… · p. 4
  • Each beam is normalized to ensure equal power assignment.The beam associated with user i is denoted by w_ibl.Source: A. Received Signal Model in an LS-MIMO… · p. 4
  • The user’s received signal comprises its intended transmission, inter-cluster interference, and receiver noise; the model then gives its SINR.The information signal has unit average power and the noise has variance σ^2.Source: A. Received Signal Model in an LS-MIMO… · p. 4

B. Received Signal Model in a Network MIMO System

In network MIMO, cooperating BSs jointly use cluster CSI to design ZF beams for users. The model normalizes beams and expresses each user’s received signal and SINR using the joint transmission, inter-cluster interference, and noise.

B. Received Signal Model in a Network MIMO System

IV. SIGNAL AND INTERFERENCE POWER DISTRIBUTIONS

The section derives tractable LS-MIMO signal and single-beam interference power distributions from ZF beam geometry and isotropic channels.

IV. SIGNAL AND INTERFERENCE POWER DISTRIBUTIONS

  • For isotropic channels, ZF makes the signal and interference power distributions tractable in terms of Gamma random variables.The isotropic condition holds for LS-MIMO channel vectors.Source: §IV · p. 5

A. Distributions of the Signal and Interference Powers in an LS-MIMO System

  • In LS-MIMO, channel vectors are isotropic BM-dimensional vectors whose powers sum BM independent exponential terms.This channel structure supports tractable signal and interference power distributions under ZF.Source: A. Distributions of the Signal and… · p. 5, §IV · p. 5
  • Under ZF, each user's signal channel is projected onto a BM−Kc+1-dimensional beamforming space.The signal power is characterized as the power of an isotropic BM-dimensional vector projected into that space.Source: A. Distributions of the Signal and… · p. 5
  • Each out-of-cluster interfering beam occupies a one-dimensional space, so received interference is the channel power projected onto that beam.The section states the resulting single-beam interference power distribution in Lemma 2.Source: A. Distributions of the Signal and… · p. 5

B. Distributions of the Signal and Interference Powers in a Network MIMO System

Because network MIMO channel vectors include differing path-loss components, the section approximates their powers with Gamma distributions to obtain tractable signal and interference power models.

B. Distributions of the Signal and Interference Powers in a Network MIMO System

  • Network MIMO channel vectors are not i.i.d. because their components have different path-loss strengths.This prevents direct use of the isotropic-channel characterization applied to LS-MIMO.Source: B. Distributions of the Signal and… · p. 5
  • A sum of independent, non-identically distributed Gamma variables is approximated by a Gamma variable matching its first and second-order statistics.This second-order matching yields tractable approximations for the channel strengths.Source: B. Distributions of the Signal and… · p. 5
  • Approximation 2 treats intended and interfering channel vectors as isotropic, assigning each spatial dimension a fractional shape contribution of k_il/BM or k_ij/BM.The approximation defines the respective vector scales as θ_il and θ_ij.Source: B. Distributions of the Signal and… · p. 6
  • With these approximations, the section states Gamma-distribution models for single-beam signal and interference powers in network MIMO.Their parameters are tied to k_il, θ_il, k_ij, and θ_ij.Source: B. Distributions of the Signal and… · p. 6
  • The resulting power distributions provide the basis for the subsequent stochastic ordering comparison of LS-MIMO and network MIMO.The paper uses these distributions to compare performance metrics.Source: B. Distributions of the Signal and… · p. 6

V. ORDERING RESULT AND PERFORMANCE EVALUATION

At a fixed user location, the analysis orders signal power statistically across the two systems and finds that LS-MIMO generally provides stronger signal power.

V. ORDERING RESULT AND PERFORMANCE EVALUATION

  • The comparison holds for an identical base-station deployment and separates signal-power and aggregate-interference statistics at fixed user locations before combining them to order SINR.The analysis uses stochastic orders to connect those statistical comparisons.Source: §V · p. 6

A. Stochastic Ordering of the Signal Powers

  • Under Approximations 1 and 2, each user's LS-MIMO signal power first-order stochastically dominates that user's network MIMO signal power.This comparison is made for corresponding systems with BM antennas per LS-MIMO base station and M per network MIMO base station.Source: A. Stochastic Ordering of the Signal… · p. 6
  • The signal-power theorem relies on approximations for the network MIMO distribution, whose accuracy is checked through numerical simulations.The stated ordering is therefore conditional on Approximations 1 and 2.Source: A. Stochastic Ordering of the Signal… · p. 6
  • The signal-power ordering is similar when a user is equidistant from its serving network MIMO base stations; otherwise, LS-MIMO has statistically stronger signal power.The paper attributes the network MIMO signal penalty to receiving intended signals from multiple scattered base stations.Source: A. Stochastic Ordering of the Signal… · p. 6

B. Distribution of the Aggregate Interference Powers

Across the evaluated performance measures, LS-MIMO has the stronger stochastic performance: its users have higher SINR and utility, while the systems' aggregate interference distributions match.

B. Distribution of the Aggregate Interference Powers

  • Aggregate interference power has the same distribution under both systems at each user location.The analysis attributes this equivalence to the same number of interfering beams from the same base-station locations and uniformly distributed transmission directions.Source: B. Distribution of the Aggregate… · pp. 6–7
  • The interference equivalence relies on approximating network MIMO channels as isotropic, treating beam sets as orthogonal, and matching Gamma distributions.The result also assumes equal power allocation across downlink ZF beams.Source: B. Distribution of the Aggregate… · p. 7

C. SINR Stochastic Ordering

  • Under Approximations 1 and 2, each user's LS-MIMO SINR first-order stochastically dominates the corresponding network MIMO SINR.Consequently, LS-MIMO has higher coverage probability for every choice of QoS threshold.Source: C. SINR Stochastic Ordering · p. 7

D. Performance Evaluation

  • Averaged over small-scale fading, LS-MIMO users achieve better utility, including higher ergodic rate and expected weighted sum rate than network MIMO users.The utility result assumes a non-decreasing utility function of SINR; the rate result uses log2(1 + SINR).Source: D. Performance Evaluation · pp. 7–8

VI. NUMERICAL VALIDATION

Across the numerical comparisons, LS-MIMO provides stronger signal power and downlink-rate performance than network MIMO; the advantage also holds with RZF. The approximate theoretical inter-cluster interference distributions are indistinguishable.

VI. NUMERICAL VALIDATION

  • The simulations use wrap-around square-lattice clusters, equal spatial degrees of freedom per user, and a path-loss plus Rayleigh-fading channel model.Each BS schedules K = 5 users in the described downlink-rate comparisons.Source: §VI · p. 8

1) Signal power stochastic dominance

  • At both tested user locations, LS-MIMO signal-power CCDFs dominate network MIMO, with the gap increasing nearer one cooperating BS.The locations are (15m, 15m), almost equidistant from the cooperating BSs, and (235m, 235m), closer to one BS.Source: §VI · p. 8, Figure 3 · p. 9, Figure 4 · p. 9

2) Interference power distribution

  • The approximate theoretical CDFs of aggregate inter-cluster interference are indistinguishable, and numerical CDFs differ from them only slightly.The numerical curves do not match the approximate distributions perfectly because of assumptions noted in the paper.Source: §VI · p. 8, Figure 5 · p. 9

3) Downlink rates with round-robin scheduling

  • Almost 55% rate improvement for 10th-percentile users under LS-MIMO, holding across different numbers of transmit antennas.The comparison uses round-robin scheduling.Source: Figure 6 · p. 9, §VI · p. 9

4) Performance evaluation with RZF

  • With RZF, LS-MIMO outperforms comparable network MIMO, while RZF provides considerable gains in both systems.The RZF comparison uses ζ = 9 and round-robin scheduling with K = 5 users per BS.Source: §VI · p. 9, Figure 7 · p. 10

VII. CONCLUDING REMARKS

The paper compares LS-MIMO and network MIMO under matched power, spatial degrees of freedom, and CSI-acquisition overhead. It attributes LS-MIMO’s advantage to stronger intended signals and concludes that it could be the preferred practical approach, including with RZF.

VII. CONCLUDING REMARKS

  • Network MIMO’s delivery from multiple scattered BSs incurs a signal-power penalty when serving-BS channel strengths differ; aggregate inter-cluster interference is identically distributed across the systems.The paper combines these findings using stochastic orders to show LS-MIMO’s performance improvement across a wide range of utility functions.Source: §VII · p. 10
  • The analytical comparison uses ZF, while numerical results show the LS-MIMO conclusion also holds with RZF.The paper notes that adding antennas at each BS is likely less costly than data-sharing backhaul and joint transmission across BSs.Source: §VII · p. 10

APPENDIX A PROOF OF THEOREM 1

The proof shows that LS-MIMO users’ signal power first-order stochastically dominates that of network MIMO, while the two systems’ aggregate interference powers are identically distributed.

APPENDIX A PROOF OF THEOREM 1

  • LS-MIMO signal power first-order stochastically dominates network MIMO signal power because its Gamma distribution has larger shape and scale parameters.The proof compares the signal-power distributions for a user served by its closest BS.Source: Appendix A · p. 10

APPENDIX B PROOF OF THEOREM 2

  • Aggregate interference power at a user is identically distributed under LS-MIMO and network MIMO.The proof assumes orthogonal ZF beams and derives the interference distributions for each system before comparing them.Source: Appendix B · p. 11

APPENDIX C PROOF OF THEOREM 3

The proof evaluates each user’s achievable SINR under both systems, using a common interference distribution and an inequality from Theorem 1. The supplied passage ends before stating the resulting comparison.

APPENDIX C PROOF OF THEOREM 3

  • The proof evaluates user i’s achievable SINR in both systems using the expressions in equations (2) and (4).The comparison relies on Theorem 2 for the aggregate interference terms.Source: Appendix C · p. 11
  • The two interference random variables are described as having a common distribution.This common distribution is used in the SINR comparison.Source: Appendix C · p. 11
  • The proof applies an inequality from Theorem 1 for every choice of γ0 before stating an implication.The supplied passage does not include the implication’s conclusion.Source: Appendix C · p. 11

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