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Optimal Base Station Antenna Downtilt in Downlink Cellular Networks

Junnan Yang, Ming Ding, Guoqiang Mao, Zihuai Lin, De-gan Zhang, Tom Hao Luan

arXiv:1802.07479v1cs.NIcs.ITmath.IT

TL;DR

Prior studies found that ASE can approach zero as a downlink network densifies when BS and UE antenna heights differ. This paper derives analytical results for how antenna downtilt affects coverage and ASE, including expressions for an optimal downtilt at each BS density. With that downtilt, the ASE crash can be delayed by nearly one order of magnitude in BS density.

  • Problem

    In a fully loaded UDN with a nonzero BS–UE antenna-height difference, ASE can decrease toward zero as the network densifies.

    Source: §II · p. 4

  • Method

    The paper analytically studies how antenna pattern and downtilt affect downlink coverage probability and ASE, deriving expressions for optimal downtilt at a given BS density.

    Source: §I · pp. 2–3

  • Results

    Optimal antenna downtilt can delay the ASE crash by nearly one order of magnitude in BS density.

    Source: §VI · p. 24

  • Takeaways & Limitations

    The derived expressions and simulation results can help network operators choose BS downtilt to achieve optimal system throughput.

    Source: §I · p. 3

Abstract

from arXiv · show

From very recent studies, the area spectral efficiency (ASE) performance of downlink (DL) cellular networks will continuously decrease and finally to zero with the network densification in a fully loaded ultra-dense network (UDN) when the absolute height difference between a base station (BS) antenna and a user equipment (UE) antenna is larger than zero, which is referred as the ASE Crash. We revisit this issue by considering the impact of the BS antenna downtilt on the downlink network capacity. In general, there exists a height difference between a BS and a UE in practical networks. It is common to utilize antenna downtilt to adjust the direction of the vertical antenna pattern, and thus increase received signal power or reduce inter-cell interference power to improve network performance. This paper focuses on investigating the relationship between the base station antenna downtilt and the downlink network capacity in terms of the coverage probability and the ASE. The analytical results of the coverage probability and the ASE are derived, and we find that there exists an optimal antenna downtilt to achieve the maximal coverage probability for each base station density. Moreover, we derive numerically solvable expressions for the optimal antenna downtilt, which is a function of the base station density. Our theoretical and numerical results show that after applying the optimal antenna downtilt, the network performance can be improved significantly. Specifically, with the optimal antenna downtilt, the ASE crash can be delayed by nearly one order of magnitude in terms of the base station density.

I. INTRODUCTION

The paper examines whether BS antenna downtilt can improve downlink coverage and area spectral efficiency (ASE), including the ASE crash associated with nonzero BS–UE antenna-height differences. It develops analytical results for optimal downtilt and evaluates a 3D random cellular-network model.

I. INTRODUCTION

  • For each BS density, an optimal downtilt maximizes coverage probability by trading off received-signal gain against interference reduction.The paper also derives numerically solvable expressions for the optimal downtilt, with LoS, NLoS, and noise components contributing to it.Source: §I · p. 3
  • Optimal downtilt can delay the ASE crash by nearly one order of magnitude in base-station density.The authors report significant performance improvement and say operators can use the derived expressions and simulations to determine downtilt for optimal throughput.Source: §I · p. 3

II. RELATED WORK

  • Earlier downtilt studies mostly used simulations or field trials, while the paper targets a theoretical analysis of downlink coverage and ASE.Prior work reported capacity improvement in simulations and SIR increases of about 5–10 dB for selected UE locations.Source: §II · p. 4

A. Scenario Description

  • The model places BSs on a plane using a homogeneous Poisson point process and assumes constant BS–UE antenna-height difference.It represents LoS and NLoS propagation with a segmented path-loss model and includes a directional 3D antenna pattern with vertical downtilt.Source: A. Scenario Description · pp. 4–5, B. 3D Antenna Patterns · p. 7

C. User Association and Performance Metrics

The section adopts strongest-received-power user association and defines coverage probability using an SINR threshold. It also introduces ASE in terms of the SINR distribution.

C. User Association and Performance Metrics

IV. MAIN RESULTS

The section derives coverage probability for a 3D cellular network and examines how antenna downtilt changes received signal strength and interference. The effects vary with BS density.

A. The Coverage Probability

  • Theorem 1 and related lemmas provide coverage-probability results under the path-loss model and strongest-received-power association.Computing the coverage probability requires three folds of integrals, including LoS and NLoS interference transmission.Source: A. The Coverage Probability · pp. 8–11
  • At λB = 10^3 BSs/km2, r = 15.8 m, and θoptimal = 36°, the signal-strength ratio with versus without downtilt is 6.2529.The ratio characterizes the received-signal effect of antenna downtilt.Source: B. The impact of antenna downtilt on… · p. 11
  • At low BS density, downtilt increases both signal and interference power, with the signal increase outweighing the interference increase; at extremely high density, it also reduces inter-cell interference.The comparison is between the full downtilt model and a case with downtilt applied to the received signal but not interference.Source: B. The impact of antenna downtilt on… · pp. 12–13

C. The Optimal Antenna Downtilt

For each BS density, the analysis identifies an antenna downtilt that maximizes coverage probability. The optimal angle balances signal strength against interference, with the dominant factors changing as density increases.

C. The Optimal Antenna Downtilt

  • For each BS density, an optimal antenna downtilt maximizes coverage probability, balancing reduced interference against lower signal power for cell-edge UEs.The paper uses a Gaussian approximation of antenna gain to make the derivation tractable and obtains a numerically solvable condition for the optimal angle.Source: C. The Optimal Antenna Downtilt · pp. 13–14
  • In sparse networks, NLoS signal and noise terms are the main determinants of the optimal downtilt.The signal is mostly NLoS and noise is dominant in this regime.Source: C. The Optimal Antenna Downtilt · p. 15
  • At intermediate densities, the transition of signals and some interference links from NLoS to LoS makes all terms relevant to the optimal downtilt.Source: C. The Optimal Antenna Downtilt · p. 15
  • At sufficiently high density, LoS links dominate and noise is small, so the LoS term chiefly determines the optimal downtilt.Source: C. The Optimal Antenna Downtilt · p. 15

D. The Area Spectral Efficiency

The section defines ASE in bps/Hz/km2 and relates its calculation to the SINR distribution at a typical UE.

D. The Area Spectral Efficiency

V. SIMULATION AND DISCUSSION

The simulations validate the coverage-probability analysis and show that the best antenna downtilt depends on BS density. The optimum balances stronger received signal against reduced inter-cell interference.

V. SIMULATION AND DISCUSSION

A. Validation of Theorem 1 on the Coverage Probability

  • For each BS density, one antenna downtilt maximizes coverage probability, reflecting a tradeoff between signal power and inter-cell interference.Larger downtilt reduces interference but can decrease signal power for cell-edge UEs; smaller downtilt has the opposite effects.Source: A. Validation of Theorem 1 on the… · pp. 16–17
  • Antenna downtilt significantly impacts coverage probability, and the optimal downtilt increases as BS density increases from nearly zero degrees to 90 degrees.Figure 2 plots coverage probability against antenna downtilt with γ = 0 dB.Source: A. Validation of Theorem 1 on the… · p. 17, Figure 2 · p. 17

B. Validation of Theorem 6 on the Optimal Antenna Downtilt

The simulations validate the optimal-downtilt analysis and show that its value rises with BS density. The signal and interference effects vary as links transition between NLoS and LoS.

B. Validation of Theorem 6 on the Optimal Antenna Downtilt

  • The optimal antenna downtilt increases as BS density increases and approaches 90° around 10^6 BSs/km2; at γ = 0 dB, Theorem 6’s analytical results match simulations very well.With all links treated as LoS, optimal downtilt results are almost the same as those from the proposed model.Source: B. Validation of Theorem 6 on the… · pp. 18–19
  • As signals and dominant interference transition from NLoS to LoS, the optimal downtilt’s role shifts from strengthening the signal toward reducing interference.At sparse densities, the NLoS and noise terms determine the optimum; during the transition, both LoS/NLoS and noise terms matter.Source: B. Validation of Theorem 6 on the… · pp. 18–19

C. The Gain of Signal Strength Using Antenna Downtilt

  • At sparse densities, adjusting downtilt yields a received-signal gain of around 6.5; during the NLoS-to-LoS transition, that gain decreases as interference reduction becomes the main benefit.Once all links are LoS, the received-signal gain increases with density to obtain the best coverage probability.Source: C. The Gain of Signal Strength Using… · pp. 19–20

D. The Reduction of Interference Using Antenna Downtilt

E. Network Performance with the Optimal Network-Wide Antenna Downtilt

Network-wide optimal downtilt improves coverage probability and delays the ASE crash by nearly one order of magnitude in BS density. BS-specific empirical downtilt leaves the ASE trend unchanged.

1) The coverage probability with the Optimal Network-Wide Antenna Downtilt:

  • Coverage probability reaches zero at 3 × 10^4 BSs/km2 with optimal downtilt, versus around 3 × 10^3 BSs/km2 in previous work.Optimal downtilt gives better coverage probability than no downtilt, while leaving the pattern of rising and then falling coverage unchanged.Source: 1) The coverage probability with the… · p. 21, Figure 6 · p. 21

2) The ASE with the Optimal Network-Wide Antenna Downtilt:

F. Network Performance with the Empirical BS-Specific Antenna Downtilt

VI. CONCLUSION

  • The paper derives analytical results for coverage probability, ASE, and optimal downtilt, which increases as BS density grows.The conclusion reports that optimal downtilt can improve ASE and delay the crash by nearly one order of magnitude in BS density.Source: §VI · p. 24

APPENDIX A:PROOF OF THEOREM 1

The proof organizes the coverage-probability calculation by link-distance range and LoS/NLoS status.

APPENDIX A:PROOF OF THEOREM 1

  • The proof splits link distances into [0, d1] and [d1, ∞); the first range can contain LoS and NLoS links, while the second contains only NLoS links.For the first range, it separately identifies the NLoS signal case within 0 < r ≤ y1, where y1 corresponds to r2 = d1.Source: Appendix A · pp. 24, 26, 27
  • The displayed denominator includes LoS interference, NLoS interference, and receiver noise.The proof states that these path-range cases complete the derivation.Source: Appendix A · p. 28

APPENDIX B:PROOF OF THEOREM 6

The proof differentiates coverage probability with respect to antenna downtilt while holding base-station density and threshold constant. It separates the non-signal terms into noise and interference components, then uses the zero-derivative condition to establish Theorem 6.

APPENDIX B:PROOF OF THEOREM 6

  • The proof sets the derivative of coverage probability with respect to antenna downtilt to zero while holding base-station density and threshold constant.This is the condition used to derive the optimal downtilt.Source: Appendix B · p. 28
  • The non-signal terms are divided into noise, LoS interference, and two NLoS interference components split at distance d1.The split distinguishes interference base stations with distance u < d1 from those with u > d1.Source: Appendix B · p. 28
  • After plugging Eq. (46) and Eq. (47) into Eq. (44), the proof considers all three parts and concludes Theorem 6, completing the proof.Source: Appendix B · p. 29
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