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Beam-searching and Transmission Scheduling in Millimeter Wave Communications

Hossein Shokri-Ghadikolaei, Lazaros Gkatzikis, Carlo Fischione

arXiv:1501.02516v1cs.ITcs.PF

TL;DR

MmW standards lose potential throughput to beam-searching deafness and single-link scheduling. The paper formulates joint beamwidth and power-control optimization, then develops interference-based approximations for practical concurrent scheduling. The overestimation approach improves throughput by 100% over existing standards, while the analysis indicates extremely narrow beams are generally not optimal.

  • Problem

    MmW communications face beam misalignment requiring time-consuming beam-searching and standards that schedule only one link per time slot.

    Source: §I · p. 1, A. Related Work · p. 1

  • Method

    The paper formulates joint beamwidth selection and power allocation, then develops standard-compliant scheduling approaches based on interference underestimation and overestimation.

    Source: §I · p. 1, B. Multiple Links Scenario · p. 4, §V · p. 6

  • Results

    100% throughput enhancement is achieved by the conservative overestimation approach compared with existing standards.

    Source: §IV · p. 6, §V · p. 6

  • Takeaways & Limitations

    Extremely narrow beams are generally not optimal, and useful operating choices concern directionality level and the number of concurrent transmissions.

    Source: §V · p. 6, Appendix B · p. 7

Abstract

from arXiv · show

Millimeter wave (mmW) wireless networks are capable to support multi-gigabit data rates, by using directional communications with narrow beams. However, existing mmW communications standards are hindered by two problems: deafness and single link scheduling. The deafness problem, that is, a misalignment between transmitter and receiver beams, demands a time consuming beam-searching operation, which leads to an alignment-throughput tradeoff. Moreover, the existing mmW standards schedule a single link in each time slot and hence do not fully exploit the potential of mmW communications, where directional communications allow multiple concurrent transmissions. These two problems are addressed in this paper, where a joint beamwidth selection and power allocation problem is formulated by an optimization problem for short range mmW networks with the objective of maximizing effective network throughput. This optimization problem allows establishing the fundamental alignment-throughput tradeoff, however it is computationally complex and requires exact knowledge of network topology, which may not be available in practice. Therefore, two standard-compliant approximation solution algorithms are developed, which rely on underestimation and overestimation of interference. The first one exploits directionality to maximize the reuse of available spectrum and thereby increases the network throughput, while imposing almost no computational complexity. The second one is a more conservative approach that protects all active links from harmful interference, yet enhances the network throughput by 100% compared to the existing standards. Extensive performance analysis provides useful insights on the directionality level and the number of concurrent transmissions that should be pursued. Interestingly, extremely narrow beams are in general not optimal.

I. INTRODUCTION

The paper targets two mmW limitations—beam-searching deafness and single-link scheduling—by jointly addressing beamwidth selection and concurrent transmission scheduling to improve effective throughput.

  • MmW offers multi-gigabit rates over short distances through directionality and large bandwidth, but also experiences high attenuation.Source: §I · p. 1
  • Existing standards assign each time slot to one transmitter-receiver pair, leaving directional spectrum-reuse potential underused.Source: §I · p. 1
  • Narrower beams increase directivity and transmission rate but require more searching, while wider beams reduce search time at the expense of rate.Source: §I · p. 1
  • Deafness occurs when transmitter and receiver main beams are misaligned, requiring exhaustive beam-searching that introduces alignment overhead.Source: A. Related Work · pp. 1–2
  • The paper provides an optimization framework and standard-compliant protocols for beamwidth selection, scheduling, and interference management.Source: B. Our Contribution · p. 2

II. SYSTEM MODEL AND PROBLEM FORMULATION

The system model represents each slot through alignment and data transmission, then models beam-dependent gains, interference, and normalized throughput to expose the alignment-rate tradeoff.

II. SYSTEM MODEL AND PROBLEM FORMULATION

  • Each time slot contains alignment followed by data transmission, with exhaustive refined-beam search performed within previously aligned sectors.Source: §II · p. 2

A. Modelling Alignment Overhead

B. Modelling Effective Transmission Rate

C. Maximizing Network Throughput

The paper formulates joint beamwidth, power, and scheduling optimization to maximize network throughput, but the problem is generally non-convex and depends on topology information that may be unavailable.

III. JOINT BEAMWIDTH SELECTION AND TRANSMISSION SCHEDULING

The paper addresses the non-convex joint optimization by first analyzing the single-link case and then reducing concurrent-transmission scheduling to multiple parallel single-link instances.

  • The optimization is generally non-convex, so the paper first studies the single-link case to derive useful tradeoff insights.Source: §III · p. 3
  • The general concurrent-transmission problem can be reduced to multiple parallel single-link instances.Source: §III · p. 4

A. Single Link Scenario

For a single link, maximum transmit power is optimal, while beamwidth selection balances directivity gains against alignment overhead; extremely narrow or wide beams are not generally optimal.

  • Maximum transmission power is optimal for a single link because it increases SNR without increasing alignment overhead.Source: A. Single Link Scenario · p. 4
  • The single-link optimization can be reduced from three variables, and the coordinator can find optimal beamwidths using gradient descent.Source: A. Single Link Scenario · p. 4
  • Narrower beams increase directivity and data rate, but also increase alignment time and reduce time available for data transmission.Source: A. Single Link Scenario · p. 4
  • The optimal beamwidth is the unique solution of the throughput derivative condition for the considered parameter region.Source: A. Single Link Scenario · p. 4
  • Extremely narrow beams are not always optimal because their alignment overhead can be large, while wide beams lose directivity gain.Source: A. Single Link Scenario · p. 4

B. Multiple Links Scenario

For multiple links, the paper develops interference-agnostic and interference-aware scheduling approaches that exploit concurrent transmissions while addressing unknown or harmful interference.

IV. NUMERICAL RESULTS

Simulations examine how beamwidth and concurrent-transmission scheduling affect effective throughput in short-range mmW networks. They show an alignment-throughput balance and substantial gains from activating multiple links.

Simulation setup

  • The simulations use 60 GHz devices in a 10×10 m2 area, 2.5 mW maximum power, 90° sector beams, and 100 random topologies.Throughput is measured in bits per time slot per hertz.Source: §IV · p. 5

Alignment-throughput tradeoff

  • The single-link optimum balances beam-searching overhead against the directivity benefit of narrower beams.Narrow beams incur more searching overhead, while wider beams reduce directivity gain.Source: §IV · p. 5
  • Lower pilot overhead enables more beam-searching iterations within the same time budget, making narrower beams more beneficial.The effect follows from the increased time available for alignment and transmission.Source: §IV · p. 5

Concurrent transmissions

  • With 10 links, Oracle, interference under-estimation, and over-estimation achieve 525%, 401%, and 177% performance enhancement, respectively.The comparison uses Single Link Activation as the baseline.Source: §IV · p. 6
  • The under-estimation approach is close to optimal for small local networks with narrow beams, whereas dense networks can invalidate its low-interference assumption.The passage characterizes local networks as typically having fewer than 20 links.Source: §IV · p. 6

V. CONCLUSION

The conclusion frames mmW throughput gains as dependent on jointly addressing beam alignment and concurrent-transmission scheduling. It proposes low-complexity, standard-compliant interference approximations for short-range networks and identifies cellular extension as future work.

Contributions

  • The paper formulates joint beamwidth selection and power control, but exact solution requires network topology and is not efficiently solvable.This motivates approximation algorithms based on interference overestimation and underestimation.Source: §V · p. 6
  • The over-estimation approach protects active links from harmful interference and doubles network throughput compared with existing standards.Its overprotection reduces the attainable performance gain.Source: §V · p. 6
  • The under-estimation approach neglects interference and provides near-optimal performance with light computational complexity in moderately large mmW networks.Its validity is tied to the stated network regime.Source: §V · p. 6

Scope and future work

  • The proposed standard-compliant algorithms target short-range mmW scenarios, while extending them to cellular mmW networks remains future work.Cellular settings introduce hybrid digital-analog beamforming and additional challenges.Source: §V · p. 6

APPENDIX A

Appendix A derives a reduced throughput representation by showing that, under the paper’s parameter assumptions, interference terms can be neglected or summarized through beamwidth-dependent quantities.

Reduction

  • The proof reduces beamwidth dependence to a single decision variable representing the relevant transmission and reception beamwidth product.The alignment procedure is described through this variable.Source: Appendix A · p. 6

Approximation

  • Under optimal transmission power, the throughput can be characterized by the beamwidth variable when the dominant signal term greatly exceeds the secondary term.The secondary term is neglected when S1 ≫ S2.Source: Appendix A · pp. 6–7
  • For the parameter region of interest, the secondary term is negligible compared with the dominant term.This supports the throughput approximation used in the appendix.Source: Appendix A · pp. 6–7

Multiple links

  • In multiple-link scenarios, interference between non-deaf links is characterized through products of their beamwidth-dependent quantities.Deaf links can contribute negligible interference when at least one directional gain is sufficiently small.Source: Appendix A · p. 7

APPENDIX B

Appendix B establishes that throughput has at most one interior extremum and that, under the stated parameter conditions, this extremum is a maximum rather than a boundary solution.

Uniqueness of the extremum

  • The derivative of throughput has at most one root because its defining equation equates a strictly decreasing function with a strictly increasing function.Therefore, the throughput has at most one extremum.Source: Appendix B · p. 7

Maximum condition

  • The appendix proves the extremum is a maximum by showing that the derivative is positive at the feasible-set beginning and negative at its end.The resulting optimum lies inside the feasible set rather than at a boundary.Source: Appendix B · p. 7

Boundary behavior

  • Near the maximum beamwidth, the remaining transmission time approaches 1 − Tp/T because the slot duration is much longer than a pilot transmission.Neglecting alignment overhead there makes throughput strictly decrease with beamwidth.Source: Appendix B · p. 7
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