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On the Feasibility of Sharing Spectrum Licenses in mmWave Cellular Systems

Abhishek K. Gupta, Jeffrey G. Andrews, Robert W. Heath Jr

arXiv:1512.01290v2cs.ITmath.IT

TL;DR

The paper asks whether mmWave cellular operators can share spectrum licenses, motivated by the possibility of reducing license costs. It models multi-operator networks and derives SINR and rate distributions, concluding that sharing can increase per-user rates and remains feasible with co-located base stations.

  • Problem

    The paper considers whether mmWave operators can share spectrum licenses, with license-cost reduction among the stated potential benefits.

    Source: §I · p. 2

  • Method

    The authors model a multi-operator mmWave system and derive SINR and per-user rate distributions.

    Source: §VII · p. 28

  • Results

    License sharing increases per-user rates, and narrow beams play a key role in its feasibility.

    Source: §VII · p. 28

  • Takeaways & Limitations

    The authors conclude that operators can share licenses economically without increasing overhead, including in a co-located deployment.

    Source: §VII · p. 28

Abstract

from arXiv · show

The highly directional and adaptive antennas used in mmWave communication open up the possibility of uncoordinated sharing of spectrum licenses between commercial cellular operators. There are several advantages to sharing including a reduction in license costs and an increase in spectrum utilization. In this paper, we establish the theoretical feasibility of spectrum license sharing among mmWave cellular operators. We consider a heterogeneous multi-operator system containing multiple independent cellular networks, each owned by an operator. We then compute the SINR and rate distribution for downlink mobile users of each network. Using the analysis, we compare systems with fully shared licenses and exclusive licenses for different access rules and explore the trade-offs between system performance and spectrum cost. We show that sharing spectrum licenses increases the per-user rate when antennas have narrow beams and is also favored when there is a low density of users. We also consider a multi-operator system where BSs of all the networks are co-located to show that the simultaneous sharing of spectrum and infrastructure is also feasible. We show that all networks can share licenses with less bandwidth and still achieve the same per-user median rate as if they each had an exclusive license to spectrum with more bandwidth.

I. INTRODUCTION

The paper addresses whether mmWave cellular operators can share spectrum licenses, a question left open by prior work that largely assumed a single operator. It motivates sharing through mmWave’s directional links and lower interference to neighboring base stations, while noting the potential to use spectrum more fully and reduce license costs.

I. INTRODUCTION

  • Less interference to neighboring BSs and highly directional mmWave links motivate license sharing, which could let operators use the full spectrum and reduce license costs.Source: §I · p. 2

A. Background and Related Work

B. Contributions

The paper models heterogeneous mmWave operator networks and derives SINR and rate coverage to assess uncoordinated license sharing. It reports higher per-user rates with sharing, greater favorability as communication becomes more directional, and feasibility when operators’ base stations are co-located.

B. Contributions

  • The framework derives SINR and rate coverage for typical users in a multi-operator mmWave system to assess uncoordinated license sharing.Source: B. Contributions · p. 4
  • The model introduces access groups, whose users can connect to member operators’ base stations, and sharing groups, whose members can use one another’s spectrum.Source: B. Contributions · p. 4
  • License sharing achieves higher per-user rates, is more favorable with narrower antenna beams, and can reduce license costs.Source: B. Contributions · p. 5
  • The paper also finds spectrum sharing feasible when all operators’ base stations are co-located, supporting simultaneous sharing of spectrum and infrastructure.Source: B. Contributions · p. 5

II. SYSTEM MODEL

  • For tractability, the model assumes independent operators and also studies fully co-located base stations; real deployments are framed between these extremes.Source: §II · pp. 5–6, B. Contributions · p. 5

A. Channel Model

The channel model separates links into LOS and NLOS classes and uses distance-dependent blockage and path loss. The analysis assumes Rayleigh fading, steerable base-station antennas, and single-stream operation; the reported sharing trends persist with shadowing and a more general fading model.

A. Channel Model

  • Each operator’s base stations are divided into LOS and NLOS tiers according to the typical user’s link type, with distance-dependent LOS probability and link-specific path loss.Source: A. Channel Model · p. 6

SUMMARY OF NOTATION

  • The analysis uses Rayleigh fading; the numerical results report that Nakagami fading adds no design insights and that including shadowing does not change observed trends.Source: SUMMARY OF NOTATION · p. 7
  • Base stations use steerable antennas, while user antenna gain is aggregated with base-station gain for analysis; treating the gains separately is left for future work.Source: SUMMARY OF NOTATION · p. 8
  • The model assumes single-stream operation; generalizing to massive MIMO or multi-stream MIMO with hybrid beamforming is future work.Source: SUMMARY OF NOTATION · p. 8

B. Access and License Sharing Model

The model distinguishes which operators’ base stations a user may access from which operators’ licenses it may share. It evaluates SINR coverage, defined as the probability that the associated base station’s SINR exceeds a threshold.

B. Access and License Sharing Model

III. SINR AND RATE COVERAGE PROBABILITY

  • SINR coverage probability is the probability that the associated base station’s SINR exceeds threshold T, equivalently the SINR CCDF.Source: §III · p. 10

A. Association Criterion and Probability

The association rule selects the accessible base station with the highest average received power. The section derives association probabilities and SINR coverage by accounting for the exclusion regions this rule creates across network and link-type tiers.

A. Association Criterion and Probability

  • A user associates with an accessible operator’s base station when no other accessible base station has higher average received power.The association event is split into comparisons against other base stations of the serving operator and against base stations of other accessible operators.Source: A. Association Criterion and Probability · p. 10
  • Average-power association creates tier-specific exclusion regions for interfering base stations, with no exclusion region for networks outside the accessible set.The exclusion regions constrain where base stations can be located and therefore affect aggregate interference.Source: A. Association Criterion and Probability · p. 11
  • The serving-distance density and probability of association with an operator are obtained by accounting for LOS and NLOS tiers and summing their contributions.The association probability is computed by summing across both link types.Source: A. Association Criterion and Probability · p. 11
  • SINR coverage is computed by integrating conditional SINR coverage over the serving-distance density and summing coverage across disjoint serving tiers.Conditional coverage uses the interference Laplace transform, and the two serving link types contribute to each operator’s coverage probability.Source: A. Association Criterion and Probability · pp. 11–12

B. Interference Characterization

The interference analysis combines contributions from independent network tiers and separates LOS from NLOS interference. It also shows that antenna beamwidth matters because aligned base stations dominate interference when their gain greatly exceeds sidelobe gain.

B. Interference Characterization

  • Interference from each independent network tier is combined through a product of its Laplace-transform terms, with LOS and NLOS contributions distinguished.The total interference is the sum across networks; each network’s transform accounts separately for LOS and NLOS base stations.Source: B. Interference Characterization · p. 12
  • Aligned base stations contribute substantially more interference than unaligned ones when main-lobe gain greatly exceeds sidelobe gain, making beamwidth important to sharing benefits.The aligned and unaligned terms are associated with gains G1 and G2, respectively.Source: B. Interference Characterization · p. 13
  • The theorem gives SINR coverage for a typical user using the interference transform and serving-distance density, while a simpler case is introduced because the general expressions resist direct insight.The general expression combines the coverage calculation with the network-access association weighting.Source: B. Interference Characterization · p. 13
  • Coverage decreases monotonically with operator count in the simplified interference-limited system with identical operators, closed access, shared licenses, and zero sidelobe gain.The corollary assumes equal LOS and NLOS pathloss exponents of 4.Source: B. Interference Characterization · p. 13

C. Rate Coverage

The section derives rate coverage from SINR coverage while accounting for the user load at the serving base station. Its simplified analysis finds that the sharing comparison depends on target rate and antenna beamwidth.

C. Rate Coverage

  • The load is random because cell areas and user counts vary, and prior work, supports approximating it by its mean without compromising result accuracy.The rate is interpreted as data bits received per second per user.Source: C. Rate Coverage · p. 14
  • Rate coverage is derived from SINR coverage across accessible networks, with per-user rate depending on serving-link SINR and the resources allocated per user.The model uses the mean serving-base-station load; round-robin and proportional-fair schedulers are cited as giving approximately an equal resource fraction per user on average.Source: C. Rate Coverage · pp. 14–15
  • For small normalized target rates, rate coverage decreases as operator count rises, while for large normalized target rates it increases, favoring sharing in the latter regime.The normalized target is ρ′ = ρN_u/B̄.Source: C. Rate Coverage · p. 15
  • With two operators and θb = π, sharing becomes more beneficial than exclusivity above ρ′ = 3.3, corresponding to Rc = 0.20.The text interprets this switch as only 20% of users benefiting at that threshold, which is not favorable from the operator’s perspective.Source: C. Rate Coverage · p. 15
  • With θb = 10°, the sharing crossover occurs at Rc = 0.83, and antenna directionality changes the minimum rate-coverage level at which sharing becomes more beneficial.At the crossover, the text says 83% of users benefit from sharing, making it favorable from the operator’s perspective.Source: C. Rate Coverage · p. 15

IV. PERFORMANCE COMPARISON

The comparison defines four systems by their access rules, license-sharing arrangements, and whether base stations are co-located. Open access with shared licenses serves as an upper bound, while the co-located case examines sharing spectrum and infrastructure together.

IV. PERFORMANCE COMPARISON

  • System 1 is the closed-access, exclusive-license baseline: users connect only to their own operator and each operator uses only its own spectrum.The system serves as the baseline for evaluating sharing benefits.Source: §IV · p. 16
  • System 2 combines open access with full license sharing and is treated as an upper bound rather than a practical system.Users can connect to any network, but this arrangement requires full coordination, shared control channels, and technology sharing.Source: §IV · p. 16
  • When all networks are identical, System 2 is equivalent to one network with aggregate base-station and user densities because users see the combined network under open access.The equivalence is conditional on identical network parameters.Source: §IV · p. 16
  • System 3 keeps closed access while sharing the full spectrum, without requiring transmission coordination, shared control channels, infrastructure, or backhaul.Users remain attached to their own service provider, making this system close to a practical implementation.Source: §IV · p. 17
  • System 4 combines closed access and full license sharing with all operators’ base stations co-located, modeling one site process and common LOS/NLOS status at each site.The model uses a single PPP for base-station locations and treats the co-located base stations as all LOS or all NLOS to a typical user.Source: §IV · p. 18

V. PARTIAL LOADING OF THE NETWORK

The section relaxes the always-loaded assumption by modeling how user association determines BS activity and interference. It then adapts coverage analysis to partial loading, where inactive BSs reduce interference and may favor license sharing.

V. PARTIAL LOADING OF THE NETWORK

  • Inactive BSs reduce interference in partially loaded networks, which should favor license sharing.The assumption that every BS is occupied can break down in very dense networks.Source: §V · p. 19
  • The closed-access user count per BS is approximated by a distribution, and the load approximation is reported to closely match simulations.The user-count approximation is attributed to.Source: §V · p. 19
  • The associated-user density for network m sums contributions from networks whose users can connect to its BSs, then relates that density to BS density.Each contribution is the user density multiplied by that network’s association probability; η_m is the associated-user-to-BS-density ratio.Source: §V · p. 19
  • For Systems 1, 2, and 3, BSs are independently thinned with probability 1−κ_m(0), and coverage uses the resulting BS density.The probability that a BS is off is κ_m(0), the probability that it has no associated user.Source: §V · pp. 19–20
  • For System 4, partial-load interference is characterized by its Laplace transform and used to obtain coverage probability.The coverage expression uses the transform in (29) and f_s(x) in (23).Source: §V · p. 20

VI. NUMERICAL RESULTS

The numerical results examine how license-sharing benefits and SINR and rate trade-offs vary with beamwidth, loading, co-location, interference, bandwidth, sharing-group size, and operator density. They also test model robustness and compare sharing trends at 28 GHz and 73 GHz.

Validation of analysis and SINR coverage trends

  • System 1 has higher SINR coverage than System 2 at high SINR, but lower coverage at low SINR; System 3 also suffers from nearby cross-network interference.System 2 has high coverage with open access, while closed access in System 3 can place another network’s BS closer to the user than the serving BS.Source: Figure 2 · p. 21, §VI · pp. 21–22
  • Co-located System 4 performs better than independent System 3 at low SINR thresholds, while System 3 performs better at high thresholds.Co-location prevents another operator’s BS from being closer than the serving BS, but places other operators’ BSs at the serving BS location.Source: Figure 2 · p. 21, §VI · p. 22

Sharing licenses achieves higher rate coverage

  • Systems 3 and 4 have, respectively, 25% and 32% higher median rates than System 1, attributed to extra bandwidth gained from spectrum license sharing.Source: §VI · p. 22

Validation of the model with realistic scenario

  • Similar rate-coverage trends persist with grid BS deployments and 3GPP antenna patterns, and with Nakagami fading instead of Rayleigh.The authors say these results support their deployment, shadowing, and Rayleigh-fading assumptions.Source: §VI · pp. 22–23, Figure 4 · p. 23, Figure 5 · p. 24

Impact of beamwidth on median rate

  • At about 25° beamwidth, the advantage shifts toward exclusive licenses; below that threshold, sharing becomes more beneficial, and typical mmWave beams are under 15°.The reported systems with shared licenses outperform System 1 at moderate and low antenna beamwidths.Source: §VI · pp. 23–24, Figure 6 · p. 24

Partial loading favors sharing

  • Under partial loading with user density 30/km2, System 3 has a 40% higher median rate than System 1, with reduced interference cited as the reason.Source: §VI · p. 24

Sharing reduces spectrum cost significantly

  • With 10° beamwidth antennas, each network needs only 75 MHz to match the exclusive-license median rate, saving 25% of license cost.The comparison is against exclusive licenses of 100 MHz per network and assumes linear pricing.Source: Figure 8 · p. 25, §VI · pp. 25–26

Optimal cardinality of sharing groups depends on the target rate

  • The final analysis examines how the optimal sharing-group size depends on target rate, with rate trading off increased available bandwidth against increased interference.Source: §VI · p. 26, Figure 9 · p. 26

Sharing-group cardinality

  • As sharing group |Qn| grows, the 75th-percentile rate rises, the 25th-percentile rate falls, and the median rate peaks at |Qn| = 3, so the optimal group size depends on target performance.Both available bandwidth and summed interference increase as more operators share licenses.Source: §VI · p. 26

Impact of asymmetry among operators

  • Both operators gain from license sharing only when their BS densities are similar (15 to 45/km2 here); sharing benefits the denser operator more as its density rises.Source: §VI · p. 26, Figure 10 · p. 27

Results for 73GHz band

  • At 73 GHz, license sharing achieves a slightly higher gain of 28% than the 25% at 28 GHz; rate-coverage trends are similar, due to reduced interference.The 73 GHz case uses 1 GHz bandwidth.Source: §VI · p. 27

VII. CONCLUSIONS

The paper models a two-level multi-operator mmWave system and derives SINR and per-user-rate distributions. It concludes that license sharing can improve per-user rate, with feasibility shaped by beamwidth and target rate.

  • The paper models a two-level multi-operator architecture and derives SINR and per-user-rate distributions.Source: §VII · p. 28
  • License sharing improves per-user rate, with narrow beams playing a key role in sharing feasibility.Source: §VII · p. 28
  • As network count increases, interference and bandwidth both increase, making optimal sharing-group cardinality dependent on target rate.Source: §VII · p. 28
  • Future work includes studying multi-antenna techniques such as multiplexing and hybrid beamforming.Source: §VII · p. 28
  • The authors also identify sharing backhaul and other infrastructure, especially with co-located base stations, as a further cost-reduction direction.Source: §VII · p. 28

APPENDIX A

The appendices derive interference Laplace transforms for the modeled systems, using point-process and fading properties. They extend the derivation to co-located base stations under partial loading.

APPENDIX A

  • For LOS interferers, the derivation excludes base stations inside the serving-distance radius and uses the PPP probability generating functional and exponential-fading MGF to obtain the interference Laplace transform.Source: Appendix A · p. 28
  • The appendix then integrates over angle using the defined function and notes that the NLOS interference transform follows similarly.Source: Appendix A · p. 29

APPENDIX B

  • The interference Laplace transform uses the PPP probability generating functional, independence, exponential-fading MGF, and discrete antenna-gain probabilities.Source: Appendix B · p. 29

PROOF OF THE LAPLACE TRANSFORM FOR CO-LOCATED BS UNDER PARTIAL LOADING

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