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Initial Beam Association in Millimeter Wave Cellular Systems: Analysis and Design Insights

Ahmed Alkhateeb, Young-Han Nam, Md Saifur Rahman, Jianzhong Zhang, Robert W. Heath Jr

arXiv:1602.06598v1cs.ITmath.IT

TL;DR

Out-of-cell interference can disrupt initial beam training and reduce mmWave network performance. The paper models beam association and uses stochastic geometry to analyze an effective reliable rate that accounts for training overhead. It reports that this rate is maximized when average cell radius is on the order of the LOS range.

  • Problem

    Out-of-cell interference can cause beam-training misalignment, motivating evaluation of its effect on reliable mmWave network performance.

    Source: §I · p. 2

  • Method

    The paper defines an effective reliable rate that accounts for association overhead and a minimum SINR threshold, then derives it using stochastic geometry for two pilot-reuse cases.

    Source: §VI · p. 26

  • Results

    The effective rate of a mmWave cellular network is maximized when average cell radius is on the order of the LOS range.

    Source: §VI · p. 27

  • Takeaways & Limitations

    For the analyzed setting, network density should place the average cell radius around the LOS range to maximize effective rate.

    Source: §VI · p. 27

    The analysis assumes a specified forward-to-backward power ratio γ for LOS interference.

    Source: §V · p. 19

Abstract

from arXiv · show

Enabling the high data rates of millimeter wave (mmWave) cellular systems requires deploying large antenna arrays at both the basestations and mobile users. The beamforming weights of these large arrays need to be tuned to guarantee sufficient beamforming gains. Prior work on coverage and rate of mmWave cellular networks focused mainly on the case when basestations and mobile users beamfomring vectors are perfectly designed for maximum beamforming gains. Designing beamforming/combining vectors, though, requires training which may impact both the SINR coverage and rate of mmWave cellular systems. This paper characterizes and evaluates the performance of mmWave cellular networks while accounting for the beam training/association overhead. First, a model for the initial beam association is developed based on beam sweeping and downlink control pilot reuse. To incorporate the impact of beam training into system performance, a new metric, called the effective reliable rate, is defined and adopted. Using stochastic geometry, the effective reliable rate of mmWave cellular networks is derived for two special cases: with near-orthogonal control pilots and with full pilot reuse. Analytical and simulation results provide insights into the answers of three important questions: (i) What is the impact of beam association on mmWave network performance? (ii) Should orthogonal or reused control pilots be employed in the initial beam association phase? (iii) Should exhaustive or hierarchical search be adopted for the beam training phase? The results show that unless the employed beams are very wide or the system coherence block length is very small, exhaustive search with full pilot reuse is nearly as good as perfect beam alignment.

I. INTRODUCTION

Large mmWave antenna arrays require beam training, but prior network analyses often assumed perfect beam alignment and did not account for interference during training. This paper models initial beam association and evaluates its overhead alongside reliable network performance.

I. INTRODUCTION

  • The paper evaluates cellular-network performance with beam training because out-of-cell interference can cause misalignment and reduce network performance.Beam training selects codebook-based beamforming and combining vectors without explicit channel estimation.Source: §I · p. 2

A. Prior Work

  • Earlier network-performance analyses assumed perfect alignment, while link-level beam-training work omitted out-of-cell interference and its effect on network performance.Small pointing-error models may also fail to represent training errors that send beams in a different direction, rather than slightly away from the optimum.Source: A. Prior Work · pp. 2–3

B. Contribution

  • The paper models initial association as beam sweeping with downlink control-pilot reuse, followed by data transmission using the selected beam pair.The model accounts for the initial association overhead.Source: B. Contribution · p. 3
  • The effective reliable rate captures beam-training resources, its SINR penalty, and the minimum SINR required for reliable transmission.The paper derives the metric for full pilot reuse and near-orthogonal control pilots using stochastic geometry.Source: B. Contribution · p. 3
  • The contribution frames design questions around association impact, pilot reuse, and exhaustive versus hierarchical search.The analysis and simulations are used to provide insights into these choices.Source: B. Contribution · pp. 3–4
  • With properly designed initial association, mmWave networks can perform nearly as well as with perfect beam alignment.Full pilot reuse can provide better effective rates unless beams are very wide; hierarchical search can have an advantage only when the coherence block is very small.Source: B. Contribution · p. 4

II. SYSTEM MODEL

The system model combines a spatial network and blockage model with cell association and a single-path channel representation. It assumes a two-dimensional setting and identifies extension to 3D channels and beamforming as future work.

A. Network Model

  • Base stations are modeled as an outdoor homogeneous Poisson point process, with outdoor users distributed independently in a stationary point process.Performance is evaluated for a typical user at the origin.Source: A. Network Model · p. 4

SYSTEM MODEL PARAMETERS

  • Buildings act as propagation blockages, and each link is classified as LOS or NLOS according to a distance-dependent LOS probability.The model uses p(r) = e^-r/μ, where μ depends on building geometry and density.Source: A. Network Model · p. 4, SYSTEM MODEL PARAMETERS · p. 5
  • The typical user associates with the base station having the smallest path loss, with cell association occurring on a longer timescale than beam association.The model assumes the user knows the serving base-station ID before beam association.Source: SYSTEM MODEL PARAMETERS · p. 5

B. Channel Model

  • The channel model uses a single path per base station, representing a typical LOS channel or an approximation of NLOS with one scattering cluster.The analysis assumes a 2D plane; extending it to 3D channels with azimuth and elevation angles and 3D beamforming is future work.Source: B. Channel Model · p. 6

C. Antenna Model and Beamforming Gains

The paper models directional arrays with sectored beam patterns and codebooks, then uses beam training to select vectors for data transmission. Its analysis simplifies antenna patterns while reporting that the main performance trends also hold for uniform arrays of reasonable sizes.

C. Antenna Model and Beamforming Gains

  • The model represents beamforming gains with sectored patterns, using main- and side-lobe gains and a main-lobe beamwidth for each array.The BS codebook contains non-overlapping main lobes covering the angular range; the MS side lobes are neglected.Source: C. Antenna Model and Beamforming Gains · pp. 6–7
  • Random BS array orientations set the reference direction for departure angles, while the MS has a codebook of combining vectors.The BS beam patterns are assumed non-overlapping and designed to cover the full angular range.Source: C. Antenna Model and Beamforming Gains · p. 7
  • The analysis neglects MS side lobes for tractability, and simulations report similar main performance trends for uniform arrays of reasonable sizes.The adopted sectored pattern approximates actual array patterns.Source: C. Antenna Model and Beamforming Gains · pp. 6–7

III. INITIAL BEAM TRAINING AND ASSOCIATION MODEL

  • Beam training is adopted to establish the initial link without explicit channel estimation; more enhanced channel-estimation methods may follow.The paper describes beam sweeping to find beamforming and combining vectors, then uses the resulting pair to transmit data.Source: §III · p. 8
  • Each coherence block is divided into initial beam association and data transmission, with training selecting vectors for the subsequent data phase.The model does not exploit prior beamforming-vector knowledge from earlier coherence blocks or assume that training must be repeated in every practical system.Source: §III · p. 8

A. Beam Sweeping

The model sweeps BS and MS codebook pairs, uses reused downlink control pilots to distinguish co-pilot from orthogonal-pilot interference, and selects the pair with maximum control-level SNR for data transmission.

A. Beam Sweeping

  • The BS and MS sweep possible beamforming/combining pairs, and the MS selects the pair maximizing a decision metric for data transmission.The search covers the codebook vectors, with the resulting pair used in the data phase.Source: A. Beam Sweeping · p. 9, C. Beam Pair Decision Criterion · p. 11
  • The beam-sweeping analysis relies on single-path channels and zero MS side lobes for independence, while simulations indicate its main insights apply more generally.Beam-association phases are assumed time-aligned across BSs, with synchronous transmission; the text notes this timing requirement can be relaxed in some cases.Source: A. Beam Sweeping · pp. 9–10

B. Downlink Control Pilot Reuse

  • Pilot reuse is modeled by assigning each BS the serving BS's pilot with independent probability δc, partitioning interferers into co-pilot and orthogonal-pilot groups.The model assumes random reuse for analytical tractability; orthogonal pilots for all interfering BSs may require many pilots and be difficult in practice.Source: B. Downlink Control Pilot Reuse · p. 10

C. Beam Pair Decision Criterion

  • The MS chooses the beam pair with maximum control-level SNR, treating co-pilot signals as desired power and cancelling interference from orthogonal-pilot BSs.The selected beamforming and combining patterns are then used during data transmission.Source: C. Beam Pair Decision Criterion · p. 11

IV. COVERAGE AND EFFECTIVE RATE

The paper evaluates beam association through SINR coverage and an effective achievable rate that accounts for training resources, SINR penalties, and a minimum-SINR requirement. Because control-level SNR and data SINR are correlated, it analyzes near-orthogonal and full pilot-reuse cases.

A. Performance Metrics

  • Beam association affects performance through both resources spent training and possible SINR loss from beam misalignment.The metrics account for the fact that practical systems may not transmit reliably below a minimum SINR threshold.Source: A. Performance Metrics · p. 12
  • SINR coverage is the probability that data-transmission SINR exceeds a threshold, and is decomposed by optimal and sub-optimal beam-pair events.The sub-optimal event maximizes MS beamforming gain while still having non-zero SINR coverage.Source: A. Performance Metrics · p. 12
  • The effective achievable rate captures training-resource overhead, beam-association SINR penalties, and the minimum SINR constraint.The metric weights achievable rate by the fraction of resources available for data transmission and considers SINR thresholds supported by the modulation and coding scheme.Source: A. Performance Metrics · pp. 12–13
  • Correlated control-level SNR and data SINR make coverage difficult to characterize for arbitrary pilot reuse, so the analysis treats two extreme reuse cases.The cases are very small pilot reuse and full reuse; the paper uses them to draw conclusions about beam association and broader settings.Source: A. Performance Metrics · p. 13

B. Performance with Near-Orthogonal Pilots

The analysis treats near-orthogonal pilots and full pilot reuse as extreme cases for beam association. Near-orthogonal pilots make optimal beam selection likely but can impose substantial training overhead, while full-reuse coverage bounds are reported as tight against simulations.

B. Performance with Near-Orthogonal Pilots

  • With negligible co-pilot interference, beam association yields maximum BS and MS gains with high probability, making the optimal beam-pair probability approximately one.The near-orthogonal approximation omits co-pilot interference from the control-level SNR.Source: B. Performance with Near-Orthogonal… · p. 14
  • Near-orthogonal pilots make the SINR penalty negligible, but the required orthogonal pilots can create large training overhead and low resource efficiency.The paper defines the negligible-interference case using a minimum pilot reuse factor.Source: B. Performance with Near-Orthogonal… · p. 14

C. Performance with Full Pilot Reuse

  • Under full pilot reuse, the MS cannot distinguish serving-BS and other-BS pilot signals, so non-negligible beam-alignment errors can affect SINR coverage.The paper derives upper and lower bounds on SINR coverage for this setting.Source: C. Performance with Full Pilot Reuse · pp. 15–16
  • Simulations show that the derived full-reuse SINR-coverage bounds are tight across the illustrated MS beamwidths and serve as good approximations.Figure 3 compares the bounds with simulation results for MS beamwidths of 180° and 45°.Source: Figure 3 · p. 17, C. Performance with Full Pilot Reuse · p. 18

V. DISCUSSION: INITIAL BEAM ASSOCIATION IMPACT AND DESIGN INSIGHTS

The section evaluates how initial beam training and association affect mmWave cellular performance, then considers network density, beamwidth, pilot reuse, and search strategy. Its simulation model uses a sectored antenna pattern with gain scaling designed to satisfy power conservation, continuity, and appropriate beamwidth scaling.

V. DISCUSSION: INITIAL BEAM ASSOCIATION IMPACT AND DESIGN INSIGHTS

  • The evaluation examines beam-association impact, network density and beamwidth, control-pilot reuse, and exhaustive versus hierarchical beam search.The section aims to identify when hierarchical search can be beneficial and when it may not be needed.Source: §V · p. 18
  • The model targets power conservation (total transmitted power is constant, not a function of beamwidth), continuity (at ΘBS = 1, recover the omnidirectional pattern with GBS = 2π), and appropriate scaling of main- and side-lobe gains.Source: §V · p. 19

A. Impact of Beam Association on Millimeter Wave Cellular Performance

Beam association changes the effective reliable rate, with its impact depending on network density, beamwidth, and coherence block length. Full pilot reuse performs well with narrow beams, while near-orthogonal pilots can approach perfect alignment with wider beams and lower training overhead.

A. Impact of Beam Association on Millimeter Wave Cellular Performance

  • With perfect beam alignment, the effective reliable rate is optimized at an average cell radius of about 30 m, corresponding to BS density λ ≈ 350 BS/km2.Near-orthogonal control pilots favor larger, sparser networks, especially at low coherence block lengths; full pilot reuse achieves much better performance.Source: A. Impact of Beam Association on… · pp. 19–20
  • For a larger LOS range, the optimal cell radius with perfect alignment shifts toward sparser networks because more links are LOS in dense networks.The resulting interference and noise-limited regimes also shift toward sparser networks.Source: A. Impact of Beam Association on… · p. 20
  • Near-orthogonal-pilot beam association yields better effective rates than full pilot reuse and performs very close to perfect beam alignment; the difference between association models is relatively small.Source: A. Impact of Beam Association on… · p. 21
  • The cell radius maximizing effective reliable rate can be close to the LOS range when a suitable beam-association strategy is adopted.The selected radius depends on parameters including BS and mobile-user beamwidths.Source: A. Impact of Beam Association on… · p. 21
  • With perfect alignment, BS beams narrower than 2° can give high effective reliable rates, but near-orthogonal association favors wider beams because very narrow beams require more training.Full pilot reuse performs better than near-orthogonal pilots and approaches perfect alignment in the plotted cases.Source: A. Impact of Beam Association on… · p. 22, Figure 6 · p. 22

B. Orthogonal or Reused Pilots?

The better pilot-reuse choice depends on beamwidth and the balance between training misalignment and out-of-cell interference. Full reuse is recommended except when data beams are very wide, where smaller reuse factors can perform better.

B. Orthogonal or Reused Pilots?

  • Small pilot reuse factors yield better performance when both BS and MS beams are 180° wide.The comparison varies pilot reuse factor at a 50 m average cell radius and a 70k-symbol coherence block.Source: B. Orthogonal or Reused Pilots? · p. 23
  • Maximum effective rates occur mainly at full reuse or very small reuse factors; smaller reuse can alleviate beam-alignment error that increases with wide beams.The results also show that out-of-cell interference affects which reuse choice performs better.Source: B. Orthogonal or Reused Pilots? · pp. 23–24
  • Full pilot reuse is recommended unless data-transmission beams are very wide.The two compared association models—near-orthogonal pilots and full reuse—perform better in different scenarios.Source: B. Orthogonal or Reused Pilots? · pp. 23–24

C. Exhaustive or Hierarchical Search?

Hierarchical search first selects wide control beams and then refines them into narrow data beams, reducing training overhead relative to exhaustive search. Its rate advantage depends on coherence block length: it helps when blocks are relatively small, while exhaustive search is similar or better when blocks are long enough.

C. Exhaustive or Hierarchical Search?

  • Hierarchical search uses wide control beams to find a beam pair, then refines that pair into narrow beams for data transmission.Its main advantage over exhaustive search is smaller training overhead.Source: C. Exhaustive or Hierarchical Search? · pp. 24–25
  • Wide beams in the control search can increase training misalignment errors; small pilot reuse factors may alleviate this at the cost of changing hierarchical-search overhead.Exhaustive search with narrow beams normally experiences small misalignment errors with full pilot reuse.Source: C. Exhaustive or Hierarchical Search? · p. 25
  • Hierarchical search achieves better effective rates when the coherence block is relatively small; exhaustive search is similar or better when the block is large enough.The comparison optimizes pilot reuse factors for the plotted search strategies.Source: C. Exhaustive or Hierarchical Search? · p. 25

D. Evaluation with Uniform Arrays and Multi-Path Channels

The evaluation tests whether simplified channel and antenna assumptions preserve performance trends, then summarizes how beam association, pilot reuse, search strategy, and network density shape effective reliable rate.

D. Evaluation with Uniform Arrays and Multi-Path Channels

  • Across the three channel and antenna scenarios, performance trends are similar, with some scaling differences, supporting the analytical assumptions of single-path links and sectored antennas.The scenarios include single-path channels with sectored patterns, single-path channels with ULAs, and three-cluster channels with ULAs.Source: D. Evaluation with Uniform Arrays and… · pp. 25–26

VI. CONCLUSIONS

  • The effective reliable rate captures beam-association resource overhead, its SINR penalty, and the minimum-SINR requirement for reliable transmission.Using stochastic geometry, the paper analyzes near-orthogonal-pilot and full-pilot-reuse cases.Source: §VI · pp. 26–27
  • For narrow-beam networks, effective rate is maximized when average cell radius is on the order of the LOS range; at a fixed LOS range, optimal cell radius increases as beamwidth increases.Source: §VI · p. 27
  • Beam association trades training SINR penalty against resource overhead: narrow beams have a low penalty but relatively high overhead, while wide beams reverse that balance.Source: §VI · p. 27
  • Beam association can approach perfect-alignment performance when downlink control-pilot reuse is adjusted to key system parameters.The conclusions also report that full pilot reuse generally yields better effective reliable rates unless the employed beams are very wide.Source: §VI · p. 27
  • Full pilot reuse can normally yield better effective reliable rates, except when the employed beamforming or combining vectors are very wide.The conclusions recommend adjusting reuse based on key system parameters.Source: §VI · p. 27
  • Hierarchical search exceeds exhaustive search only for relatively small coherence blocks; with large blocks, exhaustive search performs better because it has lower beam-misalignment error probability.The abstract-level conclusion says exhaustive search with full pilot reuse is nearly as good as perfect beam alignment unless beams are very wide or coherence blocks very small.Source: §VI · p. 27
  • Future analysis could include winds and antenna impairments as additional sources of misalignment error and examine joint cell and beam association.Source: §VI · p. 27

APPENDIX A

Appendix A expresses SINR coverage as a mixture over beam-association outcomes, then bounds conditional coverage by serving-link type and evaluates interference contributions.

APPENDIX A

  • Overall SINR coverage is decomposed into the probabilities of exceeding the threshold conditioned on OBP and SBP, weighted by the probabilities of those outcomes.Source: Appendix A · p. 27, P TP · p. 27

P TP

  • For OBP, coverage is conditioned on whether the associated base station is LOS or NLOS, with association probabilities multiplying the corresponding conditional coverage terms.The LOS/NLOS association probabilities are stated to match those derived in [12, Section III-B].Source: P TP · pp. 27–28

PT GBSGMShL

  • The conditional LOS coverage derivation uses the serving-link gain and distance distributions together with the interference distribution and its Laplace transforms.Source: PT GBSGMShL · p. 28
  • Under full pilot reuse, SBP has probability zero under the zero-MS-sidelobe assumption while other base stations transmit data during the considered beam training.The resulting training procedure yields either the joint BS-MS beamforming gain or zero.Source: PT GBSGMShL · p. 29

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