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Downlink and Uplink Cell Association with Traditional Macrocells and Millimeter Wave Small Cells

Hisham Elshaer, Mandar N. Kulkarni, Federico Boccardi, Jeffrey G. Andrews, Mischa Dohler

arXiv:1601.05281v1cs.IT

TL;DR

mmWave coverage is constrained by poor building penetration, motivating analysis of sub-6GHz–mmWave heterogeneous networks. The paper develops a framework for decoupled uplink and downlink association, derives SINR and rate coverage, and finds distinct decoupling trends alongside high feasible small-cell bias values.

  • Problem

    Universal mmWave coverage is unrealistic because mmWave signals have very poor penetration into buildings.

  • Method

    The paper proposes an analytical framework for decoupled uplink and downlink cell association in sub-6GHz–mmWave heterogeneous networks, deriving SINR and rate coverage.

  • Results

    The rate-based and SINR-based approaches exhibit different decoupling trends, with devices tending to connect uplink to sub-6GHz macrocells in the rate-based approach.

  • Takeaways & Limitations

    High small-cell bias values are possible in mmWave, with implications for modulation and coding schemes in future networks.

Abstract

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Millimeter wave (mmWave) links will offer high capacity but are poor at penetrating into or diffracting around solid objects. Thus, we consider a hybrid cellular network with traditional sub 6 GHz macrocells coexisting with denser mmWave small cells, where a mobile user can connect to either opportunistically. We develop a general analytical model to characterize and derive the uplink and downlink cell association in view of the SINR and rate coverage probabilities in such a mixed deployment. We offer extensive validation of these analytical results (which rely on several simplifying assumptions) with simulation results. Using the analytical results, different decoupled uplink and downlink cell association strategies are investigated and their superiority is shown compared to the traditional coupled approach. Finally, small cell biasing in mmWave is studied, and we show that unprecedented biasing values are desirable due to the wide bandwidth.

I. INTRODUCTION

The paper studies a hybrid network combining universally covering sub-6GHz macrocells with opportunistic mmWave small cells, focusing on independent uplink and downlink association. It develops analytical coverage and association results, validates them by simulation, and derives deployment insights on decoupling, beamforming, and biasing.

  • Motivation: mmWave offers high capacity but has poor penetration and diffraction, motivating coexistence with sub-6GHz macrocells for broader coverage.Sub-6GHz base stations provide universal coverage and control signaling when mmWave connections are unavailable.
  • Research gap: The paper addresses the lack of a complete analytical study of downlink-uplink decoupling in mixed sub-6GHz and mmWave networks.Users may independently connect to either base-station type in the uplink and downlink.
  • Contributions: The authors derive cell-association probabilities using maximum biased received power and maximum achievable rate criteria for both links.The two strategies are compared to characterize how their decoupling trends differ.
  • System design insights: High mmWave small-cell bias values are possible because of abundant bandwidth, but they require robust low-modulation-and-coding operation at very low SINR.The study also derives how biasing changes uplink and downlink SINR and rate coverage.
  • System design insights: Decoupled access gains are more pronounced in less dense urban environments, while beamforming gain dramatically increases association probability to mmWave small cells.These findings connect association decisions to deployment density and antenna alignment.

II. SYSTEM MODEL

The system model represents a two-tier heterogeneous network with sub-6GHz macrocells and mmWave small cells, using stochastic spatial models and link-specific propagation assumptions. It permits independent uplink and downlink association while modeling directional antennas, blockage, interference, and cell load.

  • Network deployment: Macrocells, small cells, and user equipments are modeled as independent homogeneous Poisson point processes in R2.The two base-station tiers have densities λm and λs, while users have density λu.
  • Network deployment: The model overlays sub-6GHz macrocells with mmWave small cells and analyzes a typical user at the origin.The serving base station is designated as the tagged base station.
  • Propagation assumptions: mmWave links use a distance-dependent LOS blockage model, directional sectorized base-station antennas, and Rayleigh small-scale fading.A link within distance μ is LOS with probability ω; serving links are aligned while interfering beams are randomly oriented.
  • Traffic and load: The analysis ignores shadowing and assumes full uplink and downlink queues with resources equally shared among users.The model uses average serving-cell loads Nm and Ns for rate calculations.
  • Signal model: Sub-6GHz links use SINR, whereas mmWave links use SNR because the two tiers occupy orthogonal bands and mmWave interference is assumed negligible.The noise-limited mmWave assumption is stated to hold even at high small-cell densities.

III. CELL ASSOCIATION

The cell-association analysis considers four uplink/downlink tier-selection cases under decoupled association. It constructs pathloss point processes and derives association probabilities by maximizing either biased received power or achievable rate.

  • Association cases: Four cases describe whether the typical user associates with a macrocell or small cell in the downlink and uplink.The cases use KDL and KUL to denote the downlink and uplink association tiers.
  • Association cases: The probabilities of complementary association cases sum to one, linking macrocell and small-cell selection in each direction.The sums are stated separately for the corresponding downlink and uplink case pairs.
  • Association strategies: The derivation compares two association strategies: maximizing biased downlink/uplink received power and maximizing downlink/uplink rate.Their outcomes are compared later to assess differing decoupling trends.
  • Pathloss analysis: For each tier, pathlosses are mapped into independent Poisson point processes with tier-specific intensity measures.The resulting pathloss distributions are expressed through their complementary cumulative distribution functions and probability density functions.

A. Maximum biased received power association

The paper develops maximum biased received-power and maximum-rate association criteria for uplink and downlink selection. The rate-based derivation uses simplifying approximations to obtain tractable probabilities, and the resulting trends are validated against simulation.

  • Maximum biased received power association: Max-BRP selects uplink and downlink serving cells using the maximum biased received powers for the respective links.The paper defines association probabilities for macrocell and mmWave small-cell selection under this criterion.
  • Association probabilities: The analysis derives uplink and downlink association probabilities for both Max-BRP and maximum achievable-rate association.Closed-form expressions are available for a special pathloss-exponent case.
  • Coverage approximation: The model approximates sub-6GHz SINR by SIR and mmWave SINR by SNR to simplify the coverage and association expressions.The resulting coverage expressions use exponential fading and neglect noise in the sub-6GHz case.
  • Maximum achievable-rate association: The Max-Rate derivation neglects the load term by setting Nm and Ns to 1 because the association variable appears on both sides of the rate condition.The authors explicitly characterize this approximation as suboptimal but tractable.
  • Validation: The derived rate-based association probability matches simulation results well, supporting the assumptions used for the approximation.The validation is reported for the assumptions concerning uplink interferers and exclusion regions.

IV. SINR AND RATE DISTRIBUTIONS: DOWNLINK AND UPLINK

The paper derives SINR and rate coverage distributions for downlink and uplink operation in the mixed sub-6GHz/mmWave deployment, while leaving Max-Rate SINR and rate derivations for future work.

  • SINR and rate coverage distributions are derived for downlink and uplink in both mmWave and sub-6GHz tiers.These distributions support analysis of how association strategies affect whole-system SINR and rate.
  • Max-BRP association is analyzed for SINR and rate coverage, whereas corresponding Max-Rate derivations are left for future work because they are complicated.
  • Biasing is used in the SINR and rate coverage results to validate trends produced by the Max-Rate association strategy.

A. SINR coverage

The analysis derives uplink and downlink SINR and rate coverage under simplifying propagation, interference, load, and power-control assumptions for the two-tier network.

  • SINR coverage is defined as the average fraction of UEs whose SINR exceeds a target threshold at a given time.
  • Because mmWave networks are usually noise limited, mmWave coverage uses SNR while sub-6GHz coverage uses SINR.The coverage probabilities are expressed as Pm = P(SINR > τ) and Ps = P(SNR > τ), respectively.
  • The absence of interference between mmWave and sub-6GHz base stations permits separate derivation of their SINR/SNR coverage.
  • The main coverage expression assumes maximum uplink transmit power without power control for simplicity and fairness.Fractional pathloss compensation adds an integral and makes the macrocell coverage expression complex, so the paper uses the no-power-control expression.
  • Theorem 1 gives typical uplink and downlink SINR coverage under the Max-BRP association criterion.The theorem’s expressions use quantities derived or defined earlier in Section III.
  • Rate coverage derivation requires tier loads, approximated as in Section III-B and validated against simulation results in Fig. 5(b).

V. PERFORMANCE EVALUATION AND TRENDS

Monte Carlo simulations validate the analytical association results and examine decoupled access, antenna gain, propagation parameters, and Max-Rate behavior in the hybrid network.

  • The analysis is validated through Monte Carlo simulations using randomly deployed UEs and base stations under the stated propagation and blockage model.
  • Association probability: More than 20% of UEs have decoupled access when the Scell-to-Mcell density ratio is 40, corresponding to a 20% decoupling gain.
  • Association probability: Scell beamforming gain dramatically improves Scell association probability and should therefore be considered during association.
  • Association probability: Higher Scell antenna gain lowers decoupling gain because downlink coverage expands faster than uplink coverage across LOS and NLOS regions.The reported mechanism follows from the different pathloss exponents in LOS and NLOS areas.
  • Association probability: A higher LOS-ball radius increases decoupling gain, while larger differences between NLOS or macrocell and LOS pathloss exponents decrease it.The paper identifies decoupling as more relevant in low-density urban environments with lower pathloss exponents and larger LOS balls.
  • Max-Rate association probability validation and trends: Max-Rate association closely matches simulation and produces more mmWave Scell offloading than Max-BRP because of mmWave’s wider bandwidth.
  • Max-Rate association probability validation and trends: Max-Rate decoupling favors Scells in downlink and Mcells in uplink, reversing the Max-BRP association pattern.The more limited uplink range allows Scells to serve more UEs in downlink than uplink, especially for farther UEs.
  • Max-Rate association probability validation and trends: The Max-Rate downlink association increase over Max-BRP is more than 40% higher than the corresponding uplink increase.

B. SINR and rate coverage results

The analysis closely matches simulation for SINR and rate distributions and supports examining mmWave noise-limited behavior and small-cell biasing. Large rate-optimal biases arise because mmWave bandwidth can offset very low SINR.

  • SINR and rate coverage analysis validation: Analysis expressions for SINR and rate distributions match simulation results closely at zero bias.This validation supports using the analysis to derive further system insights.
  • SINR and rate coverage analysis validation: A flat rate-threshold region between 10^7 and 10^9 b/s separates sub-6GHz UEs from mmWave UEs with very good channels.The separation reflects the substantial rate difference created by mmWave bandwidth in the mixed deployment.
  • SINR ≈ SNR validation: At λs = 30/km2, mmWave SINR and SNR nearly overlap, while at λs = 200/km2 their difference remains very small.These results support approximating mmWave SINR by SNR because interference has minimal coverage impact in the considered densities.
  • Scell biasing effect on SINR and rate trends: 5th-percentile SINR rises slightly before declining beyond 5 dB bias, whereas 5th-percentile rate peaks at 30 dB for UL and 35 dB for DL.The initial SINR increase is attributed to negligible mmWave interference, while the rate peaks reflect the much higher mmWave bandwidth.
  • Scell biasing effect on SINR and rate trends: The corresponding SINR at these rate-optimal biases is around -30 dB, yet the large bandwidth supports high rate and biases over 100x typical sub-6GHz values.The results motivate robust modulation and coding for operation at very low SINR.
  • Scell biasing effect on SINR and rate trends: UL 5th-percentile rate peaks at a lower bias than DL rate, consistent with UL association toward Mcells and DL association toward Scells.The same trend appears in the Max-Rate association results.
  • Impact on infrastructure density: The rate-optimal biases remain 30 dB for UL and 35 dB for DL across Scell densities because mmWave operation is noise limited.Marginal interference effects explain the invariance with density.

C. System design implications

The results support mmWave-specific association and deployment choices: directional beamforming and decoupled access improve association and performance, while rate favors UL Mcells and DL Scells. Aggressive mmWave biasing can raise rate but requires operation at very low SINR.

  • System design implications: Accounting for Scell beamforming gain dramatically improves mmWave Scell association probability, making directional beams important during association.The conclusion explicitly identifies beamforming gain as an association-phase design requirement.
  • System design implications: Decoupled access remains relevant for both maximum-received-power and rate associations, with UL and DL decoupling in different directions.DUDe is identified as key for optimal performance under both criteria.
  • System design implications: Decoupled access is more relevant in less dense urban environments characterized by smaller path-loss exponents and a larger LOS-ball radius.These environmental features correspond to higher decoupling gains.
  • System design implications: Aggressive mmWave Scell biasing can benefit rate but forces UEs to operate at very low SINR.Robust modulation and coding are needed to harvest mmWave rate benefits in these regimes.
  • System design implications: Rate favors UL association with sub-6GHz Mcells and DL association with mmWave Scells.The paper connects this reversed UL/DL association pattern with allocating UL on Mcells and DL on Scells.

VI. CONCLUSIONS

The paper develops an analytical framework for decoupled uplink and downlink association in hybrid sub-6GHz/mmWave networks, comparing maximum biased received power with maximum achievable rate. It derives SINR and rate coverage, finds distinct decoupling trends under rate-based association, and identifies high mmWave small-cell biasing as feasible but demanding robust low-modulation operation.

  • The paper proposes a detailed analytical framework for cell association in sub-6GHz/mmWave heterogeneous networks with decoupled uplink and downlink association.
  • Maximum biased received power and maximum achievable rate association are analyzed to highlight their main differences.
  • Rate-based association produces a different decoupling trend, with devices tending to connect in the uplink to sub-6GHz macrocells.
  • SINR and rate coverage probabilities are derived, with special emphasis on small-cell biasing.
  • High small-cell bias values are possible because of mmWave's wide bandwidth, but supporting them requires robust low-modulation schemes.
  • Future extensions include uplink power control, indoor users, mobility, cell load in rate-based association, sub-6GHz small cells, and multiple decoupled base-station connections.

APPENDIX A

Appendix A derives propagation-process intensities and association-related distributions for mmWave and sub-6GHz links, then establishes the conditions used for maximum-rate association and coverage expressions.

  • The mmWave propagation process accounts for distance-dependent path-loss exponents that differ between LOS and NLOS links under blockage.
  • For sub-6GHz macrocells, the propagation process uses a path-loss model without blockage.
  • Maximum-rate association derivations require differentiability and finite-integral conditions before the resulting density expression can be written.
  • The appendix derives the downlink association probability to a sub-6GHz macrocell using SIR coverage and the mmWave downlink SNR density.
  • Leibniz's rule is used to exchange differentiation and integration when simplifying the SNR-density expression.
  • The proof concludes the derived coverage expression and states that the uplink macrocell result follows similarly.

APPENDIX C

Appendix C derives downlink SINR and SNR coverage expressions for macrocell and mmWave small-cell association, using association conditions, independence, interference transforms, and an analogous uplink substitution.

  • The downlink macrocell SINR coverage derivation starts from the macrocell association condition L_min,s > a_DL L_min,m.
  • Independence of the macrocell and small-cell point processes supports the factorization used in the coverage derivation.
  • The macrocell coverage expression incorporates the Laplace transform of interference and the propagation-process intensity.
  • The mmWave small-cell downlink association condition is L_min,m > L_min,s, which is used to derive its SNR coverage.
  • The uplink macrocell coverage is obtained by replacing downlink transmit power and bias parameters with their uplink counterparts.
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