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Uplink Capacity and Interference Avoidance for Two-Tier Femtocell Networks

Vikram Chandrasekhar, Jeffrey G. Andrews

arXiv:cs/0702132v9cs.NIcs.IT

TL;DR

Shared-spectrum two-tier DS-CDMA networks need uplink capacity analysis because cross-tier interference can cause unacceptable outage. The paper models outage and operating contours under random deployments, then evaluates time hopping, antenna sectoring, exclusion regions, and tier-selection handoff. Under worst-case corner-femtocell interference, time hopping with sectorized antennas provides about 7x higher femtocell density than a split-spectrum baseline, while exclusion and tier-selection policies provide modest additional gains.

  • Problem

    The paper asks how to characterize two-tier uplink capacity and cross-tier interference, and how hotspot density, power ratios, femtocell size, and avoidance mechanisms affect outage and capacity.

  • Method

    The paper develops an uplink outage and capacity analysis for shared-spectrum DS-CDMA using random spatial deployment models, power control, and interference avoidance with time hopping and sectorized antennas.

  • Results

    About 7x higher femtocell density is achieved with time-hopped CDMA and sectorized antennas than with split-spectrum two-tier networks using omnidirectional femtocell antennas under worst-case corner-femtocell interference.

  • Takeaways & Limitations

    Time hopping and antenna sectoring offer the largest reported capacity gains, while femtocell exclusion and tier-selection-based handoff provide modest operating-contour improvements.

Abstract

from arXiv · show

Two-tier femtocell networks-- comprising a conventional macrocellular network plus embedded femtocell hotspots-- offer an economically viable solution to achieving high cellular user capacity and improved coverage. With universal frequency reuse and DS-CDMA transmission however, the ensuing cross-tier cochannel interference (CCI) causes unacceptable outage probability. This paper develops an uplink capacity analysis and interference avoidance strategy in such a two-tier CDMA network. We evaluate a network-wide area spectral efficiency metric called the \emph{operating contour (OC)} defined as the feasible combinations of the average number of active macrocell users and femtocell base stations (BS) per cell-site that satisfy a target outage constraint. The capacity analysis provides an accurate characterization of the uplink outage probability, accounting for power control, path-loss and shadowing effects. Considering worst case CCI at a corner femtocell, results reveal that interference avoidance through a time-hopped CDMA physical layer and sectorized antennas allows about a 7x higher femtocell density, relative to a split spectrum two-tier network with omnidirectional femtocell antennas. A femtocell exclusion region and a tier selection based handoff policy offers modest improvements in the OCs. These results provide guidelines for the design of robust shared spectrum two-tier networks.

I. INTRODUCTION

The paper studies shared-spectrum two-tier femtocell networks, where cross-tier interference complicates uplink capacity. It asks how capacity and interference avoidance change with hotspot density, power ratios, femtocell size, antenna sectoring, time hopping, exclusion regions, and handoff policies.

  • Two-tier femtocells embed small-range access points within macrocells to improve cellular capacity and serve high-density stationary or low-mobility users.Examples include residential access points and urban hotspot data access points.
  • Shared spectrum is attractive because spectrum is scarce and flexible deployment may favor spectrum sharing over splitting tiers.
  • The analysis asks for two-tier uplink capacity with randomly scattered hotspots and randomly distributed active users per femtocell.
  • The paper examines cross-tier interference statistics and the effects of femtocell hotspot density, macrocell-femtocell power ratio, and femtocell size.
  • Interference avoidance using antenna sectoring and time hopping is evaluated alongside femtocell exclusion regions and tier-selection handoff policies.The stated goal is to assess their capacity benefits in shared-spectrum CDMA networks.

A. Related work

Prior work analyzed two-tier capacity under simplified microcell layouts, average interference, or split-spectrum designs. This paper addresses more variable hotspot placement and contrasts shared-spectrum interference avoidance with those approaches.

  • Earlier physical-layer studies focused on a single microcell or regularly spaced microcells because those configurations were analytically tractable.
  • Regularized microcell locations limit applicability because realistic deployments have inherent variability in microcell placement.
  • Related two-tier capacity work derived operating contours for different tier-selection schemes with arbitrarily placed microcells, then extended the framework to multiple microcells and macrocells.
  • Other studies examined antenna tilt, power-ratio control, and regular hexagonal tiers, with some concluding that spectrum splitting was more practical because shared spectrum increased outage probability.
  • Network-level research considered user behavior, load balancing, pricing, and optimization for multitier wireless infrastructures.

B. Contributions

The paper combines stochastic-geometry outage analysis with interference-avoidance mechanisms for randomly located users and femtocells. It reports larger gains from time hopping and antenna sectoring than from exclusion and tier-selection policies.

  • Random user and hotspot locations are modeled with a stochastic geometry framework to reflect opportunistic deployments across cell sites.The paper argues that embracing spatial randomness provides more accurate and plausible capacity insights.
  • Macrocell users and femtocell base stations are modeled as randomly distributed.
  • The outage analysis accounts for cellular geometry, cross-tier interference, and shadowing, using Poisson shot-noise and void-probability properties to model outage events explicitly.The analysis uses Poisson-Gaussian and alpha-stable models for relevant interference statistics.
  • Interference avoidance with universal frequency reuse can provide higher user capacity than splitting spectrum across tiers, including equitable tier loading with an order-wise difference in received-power ratios.
  • A femtocell exclusion region combined with tier-selection-based handoff yields modest operating-contour improvements, while time hopping and antenna sectoring offer the largest gains for small femtocells.

II. SYSTEM MODEL

The system model uses a hexagonal macrocell overlaid with randomly distributed femtocell base stations and Poisson-distributed active femtocell users. Both tiers use DS-CDMA with power control, sectorized reception, and simplified channel assumptions.

  • The reference macrocell is the interior of a hexagonal region, with tier 1 users communicating with the central base station.
  • Tier 1 users and tier 2 femtocell base stations form homogeneous spatial Poisson point processes with intensities λc and λf.
  • Each femtocell contains a Poisson-distributed population of active users with mean Uf within a circular radius Rf much smaller than the macrocell radius Rc.
  • The mean users and femtocell base stations per cell site are Nc = λc · |H| and Nf = λf · |H|, respectively.
  • Users employ DS-CDMA with processing gain G, while uplink power control compensates for propagation loss and log-normal shadowing.
  • The analysis ignores power-control errors and short-term fading, and assumes sectorized reception at macrocell and femtocell base stations.Femtocell sectoring is motivated by nearby cellular-user interference on the femtocell uplink.

A. TH-CDMA and Antenna sectoring

TH-CDMA and sectorized reception reduce the effective interfering field through temporal and spatial thinning. Sectorization is especially motivated by strong nearby cellular interference on the femtocell uplink.

  • TH-CDMA: TH-CDMA divides transmissions into Nhop hopping slots, thinning intra- and cross-tier interference by a factor of Nhop.Users select one slot and remain silent during the other Nhop −1 slots.
  • Antenna sectoring: Sectorized antennas are assumed at both macrocell and femtocell base stations, with sector width 2π/Nsec and alignment angle θ.The paper proposes directed femtocell antennas to mitigate nearby cellular-user interference.
  • Combined thinning: With Nhop slots and Nsec directed antennas, mapped interfering-point-process intensities become ηc = λc/(NhopNsec) and ηf = λf(1 −e−Uf)/(NhopNsec).The lemma formalizes combined temporal and spatial thinning at a given antenna sector.
  • Definitions: A sector region Hsec denotes the portion of the cell region H covered by a base-station antenna sector.For an omnidirectional femtocell at the macrocell corner, Hsec = H.
  • Definitions: The heterogeneous interferer processes seen by an antenna sector are represented by ˆΩc and ˆΩf, with equivalent homogeneous processes Φc and Φf over R2.Πc and Πf denote the restrictions of ˆΩc and ˆΩf to H.

B. Channel Model and Interference

The channel and interference model combines path loss, log-normal shadowing, uplink power control, and intra- and cross-tier interference. Small-femtocell assumptions support tractable point-process approximations while corner locations produce stronger macrocell interference.

  • Channel model: Path loss and log-normal shadowing are modeled separately for outdoor and indoor femtocell transmission, with exponents α and β and shadowing deviation σdB.Uplink power control sets transmit power according to attenuation toward the serving base station.
  • Interference components: Interference is grouped into macrocell, femtocell, cross-tier, and intra-tier components at the respective receiving base stations.Figure 2 distinguishes interference generated by Tier 1 and Tier 2 users.
  • Model assumptions: For small femtocells, other femtocells are approximated as point sources, while interfering users in a random femtocell are modeled at maximum power for tractability and worst-case analysis.The approximation uses gc(|Xi + Yj|) ≈ gc(|Xi|) and gf(|Yj|) ≈ gf(Rf).
  • Femtocell interference: Neighboring femtocell interference is modeled as a Poisson shot-noise process, while simultaneous users within a femtocell create intra-tier interference.The intra-tier term is conditioned on the femtocell containing U ≥ 1 active users.
  • Macrocell interference: Macrocell interference at a femtocell is lower bounded using Tier 1 interferers inside the reference macrocell.A corner femtocell experiences significantly higher macrocell interference than an interior femtocell, so the distribution is nonstationary.

III. PER TIER OUTAGE PROBABILITY

The paper formulates per-tier outage probabilities from SIR thresholds and interference distributions, then uses them to derive feasible operating contours. Hopping and sectorization reduce interference, with protocol preference depending on femtocell loading and the transmission regime.

  • Outage and operating contours: Operating contours consist of feasible (Nf, Nc) combinations satisfying target outage constraints for macrocell and femtocell users.The outage event is an instantaneous despread narrowband SIR below threshold γ.
  • Interference distributions: For α = 4, cross-tier femtocell interference follows a Lévy-stable distribution with stability exponent 1/2.Theorem 1 provides the corresponding probability density and cumulative distribution functions.
  • Femtocell size: Increasing femtocell size Rf strictly increases outage probabilities from femtocell interference because the interference distribution parameter grows with Rf^β.Edge users in larger femtocells can generate excessive interference at nearby femtocell base stations.
  • Hopping protocols: For Nhop ≫ 1, joint hopping is preferable in CDMA because it reduces femtocell intensity by Nhop and produces a quadratic decrease in κf.Independent hopping instead reduces the number of interfering users per active femtocell sub-quadratically.
  • Hopping protocols: With Nhop = 2, joint hopping is clearly superior in heavily loaded femtocells, whereas lightly loaded femtocells show nearly identical joint and independent performance.For light loading, ηf ≃ ˜ηf ≈ λf Uf/(Nsec·Nhop).
  • Random-access regime: In the non-CDMA limit Nhop = G ≫ 1, independent hopping is preferable because joint hopping lets a single in-femtocell interferer cause outage.Independent slot assignment makes slot sharing between femtocell users unlikely.
  • Femtocell outage: The lower bound on cellular interference becomes tight enough to support accurate femtocell outage analysis using dominant cellular interferers.Increasing Nhop thins the macrocell interferer intensity and mitigates cross-tier interference.
  • Femtocell outage: Sectorized femtocell reception performs considerably better than an interior omnidirectional femtocell under worst-case corner macrocell interference.Theorems 1 and 3 are used to state the femtocell outage probability and derive capacity contours.

IV. FEMTOCELL EXCLUSION REGION AND TIER SELECTION

The paper evaluates femtocell exclusion regions and tier-selection handoff as additional interference-avoidance mechanisms. Exclusion can substantially reduce macrocell outage, while tier selection provides only marginal benefits for small femtocells.

  • Exclusion region: A femtocell exclusion region around the macrocell base station silences nearby femtocell transmissions likely to cause individual macrocell outages.The scheme targets strong neighboring femtocell interferers.
  • Exclusion region: An exclusion region reduces the femtocell population area from λf|H| to λf(|H|−|Rf,exc|).The resulting tier-2 network remains a heterogeneous spatial point process on H.
  • Exclusion-region results: Close agreement between analysis and simulation indicates that nearby dominant femtocell interferers primarily influence macrocell outage events.The exclusion-region results use theoretical lower bounds and empirically estimated probabilities.
  • Exclusion-region results: Even a small exclusion radius Rexc f significantly decreases macrocell outage probability.This can permit more simultaneous active femtocell transmissions while maintaining Pc out ≤ ǫ.
  • Tier selection: Tier selection hands off any Tier 1 user within radius Rf of a femtocell to that femtocell base station.The policy reduces the intensity of Tier 1 users within H after handoff.
  • Tier-selection results: Tier selection offers marginal benefits for small femtocells because they cover too little area to hand off significant numbers of cellular users.Small femtocell size nevertheless leads to lower uplink outage probability.
  • Operating contours: Operating contours with exclusion and tier selection are obtained by applying the corresponding lemmas to the macrocell and femtocell outage theorems.The femtocell interference term is approximated by a Poisson shot-noise process.

V. NUMERICAL RESULTS

The numerical results compare analytically derived and empirical operating contours for shared-spectrum two-tier networks under sectorization, time hopping, power-ratio choices, and additional tier-management policies. Interference avoidance substantially increases sustainable femtocell density, while exclusion and tier selection provide more limited gains.

  • Numerical validation: Theoretical and empirical operating contours closely agree for macrocell and interior-femtocell cases, supporting the accuracy of the capacity analysis.The comparisons use Nhop = 1 and Nsec = 3.
  • Power-ratio effects: Increasing P_f^r decreases the largest sustainable Nf for a given Nc but increases the largest sustainable Nc for a given Nf.The two outage constraints therefore impose opposing capacity trade-offs across the tiers.
  • Interference avoidance: Greater than 2.5x improvement in Nf is obtained with P_f^r = 10 and Nhop = 4, while an interior femtocell accommodates up to Nc = 45 tier-1 users.These operating contours apply to both corner and interior femtocell comparisons against the split-spectrum baseline.
  • Tier-management policies: Exclusion regions and tier selection increase Nf by up to 10 femtocells, or 50 users, for Nc < 30, but do not increase the maximum Nc.Their gains are concentrated at low-to-moderate Nc because tier selection mainly curbs tier-1 interference when Nf is large.
  • Scope boundary: The study does not directly compare randomly placed users and hotspots with a two-tier network having a given configuration.The authors defer that comparison because of space limitations and cite prior work for related results without interference avoidance.

VI. CONCLUSION

The paper presents uplink capacity analysis and interference avoidance for shared-spectrum two-tier DS-CDMA networks. Time-hopped CDMA with sectorized receive antennas outperforms the split-spectrum baseline, while exclusion regions and tier-selection handoff provide conservative OC improvements.

  • The analysis derives exact macrocell outage probabilities and tight lower bounds on femtocell outage probabilities.These results account for the shared-spectrum two-tier DS-CDMA setting.
  • Time-hopped CDMA coupled with sectorized receive antennas consistently outperforms split-spectrum operation with omnidirectional femtocell antennas.
  • 7x improvement in femtocell density is shown in network operating contours under worst-case corner-femtocell interference.
  • A femtocell exclusion region and tier-selection-based handoff offer conservative improvements in the operating contours.

APPENDIX A

The appendix models hopping-slot and active-femtocell selection as independent thinning of Poisson fields, then maps the resulting processes to homogeneous spatial Poisson point processes. This reduction yields a one-dimensional Poisson representation whose interference distribution is Levy-stable.

  • Hopping-slot selection independently Bernoulli-thins macrocell users and femtocell BSs with probability 1/Nhop.
  • Active-femtocell selection contributes a thinning factor 1 − e^-Uf for femtocells containing at least one active user.The active-user population per femtocell is modeled as Poisson with mean Uf.
  • Independent marking combines hopping-slot and active-femtocell selection, producing a femtocell process with intensity λf/Nhop (1 − e^-Uf).
  • The Mapping theorem converts the heterogeneous thinned processes over an antenna sector into homogeneous processes over R^2.The sector width is determined by Nsec.
  • Femtocell interference is represented as a Poisson sum over the mapped process and then transformed from the plane to a one-dimensional Poisson process.The one-dimensional process has intensity πηf.
  • The resulting interference follows a Levy-stable distribution with stability exponent δ = 2/α; for α = 4, δ = 0.5.

APPENDIX C

The appendix derives macrocell outage from independent interference components and bounds femtocell outage using dominant interferer sets and Poisson void probabilities. It also models exclusion-region handoff through spatial thinning, while noting a correlation limitation in the thinning approximation.

  • Macrocell interference components Ic,in, Ic,out, and Ic,f are modeled as mutually independent random variables.
  • Macrocell outage is computed from the probability that cumulative interference remains below the SIR threshold ρc.The cumulative distribution is obtained through a three-fold convolution.
  • For a fixed number of in-cell interferers, outage is avoided when residual out-of-cell and femtocell interference is below the remaining threshold.
  • Femtocell cellular interference is lower bounded by considering dominant macrocell interferers capable of individually causing outage.The lower bound follows from the probability that the dominant-interferer set is nonempty.
  • A corner femtocell with an omnidirectional antenna receives cellular interference from three surrounding cellsites.
  • Femtocell-user interference and cellular interference are combined using their mutual independence, with a first-order approximation in the low-outage regime.
  • Outside the femtocell exclusion region, the analysis splits femtocell interferers into dominant and non-dominant sets and uses Poisson void probabilities for a lower bound.
  • The handoff analysis assumes independent Bernoulli thinning of macrocell users, although closely spaced users have correlated handoff events.
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