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Spectrum Sharing Between Cellular and Mobile Ad Hoc Networks: Transmission-Capacity Trade-Off

Kaibin Huang, Vincent K. N. Lau, Yan Chen

arXiv:0808.2181v2cs.IT

TL;DR

Growing broadband demand motivates sharing underutilized cellular uplink spectrum between a cellular network and a MANET. The paper uses transmission-capacity analysis with stochastic geometry to compare overlay and underlay, with and without SIC. For small target outage probability, capacities obey a sharing-dependent linear trade-off; overlay is more efficient than underlay, and SIC increases both capacities by a threshold-dependent linear factor.

  • Problem

    The paper addresses how a cellular uplink and MANET should share spectrum while balancing their transmission capacities.

  • Method

    Using stochastic geometry, the paper analyzes transmission-capacity trade-offs for spectrum overlay and underlay with Poisson transmitters, with and without SIC.

  • Results

    For small target outage probability, the coexisting networks’ transmission capacities satisfy a sharing-method- and SIC-dependent linear equation, with overlay more efficient than underlay.

  • Takeaways & Limitations

    SIC increases both networks’ transmission capacities by a linear factor determined by the interference-power threshold for qualifying canceled interferers.

Abstract

from arXiv · show

Spectrum sharing between wireless networks improves the efficiency of spectrum usage, and thereby alleviates spectrum scarcity due to growing demands for wireless broadband access. To improve the usual underutilization of the cellular uplink spectrum, this paper studies spectrum sharing between a cellular uplink and a mobile ad hoc networks. These networks access either all frequency sub-channels or their disjoint sub-sets, called spectrum underlay and spectrum overlay, respectively. Given these spectrum sharing methods, the capacity trade-off between the coexisting networks is analyzed based on the transmission capacity of a network with Poisson distributed transmitters. This metric is defined as the maximum density of transmitters subject to an outage constraint for a given signal-to-interference ratio (SIR). Using tools from stochastic geometry, the transmission-capacity trade-off between the coexisting networks is analyzed, where both spectrum overlay and underlay as well as successive interference cancelation (SIC) are considered. In particular, for small target outage probability, the transmission capacities of the coexisting networks are proved to satisfy a linear equation, whose coefficients depend on the spectrum sharing method and whether SIC is applied. This linear equation shows that spectrum overlay is more efficient than spectrum underlay. Furthermore, this result also provides insight into the effects of different network parameters on transmission capacities, including link diversity gains, transmission distances, and the base station density. In particular, SIC is shown to increase transmission capacities of both coexisting networks by a linear factor, which depends on the interference-power threshold for qualifying canceled interferers.

I. INTRODUCTION

The paper studies capacity trade-offs when a cellular uplink and MANET share licensed uplink spectrum, addressing limited theoretical results for coexisting networks. It evaluates spectrum underlay and overlay using transmission capacity.

  • Licensed spectrum is often underutilized because cellular systems may allocate equal uplink and downlink bandwidth despite heavier downlink traffic.
  • The paper examines spectrum sharing between a cellular network and a mobile ad hoc network to improve uplink spectrum usage.
  • The central question is how sharing affects the capacity trade-off between the coexisting networks.
  • Transmission capacity measures feasible transmitter densities under outage-probability and target-SIR constraints, with weights depending on the sharing method.
  • The resulting trade-off analysis can help control coexisting-network sizes for optimizing uplink spectrum usage.
  • Spectrum overlay and underlay provide alternative sharing approaches, while prior work offers few theoretical results on their network-capacity trade-off.

B. Contributions and Organization

The paper models coexisting cellular and ad hoc networks and derives outage and transmission-capacity results for multiple spectrum-sharing settings. Its main conclusions compare overlay, underlay, network parameters, and SIC.

  • Network model: The analysis models base stations, cellular uplink users, and MANET transmitters with Poisson point processes of different densities.
  • Capacity trade-off: For small target outage probability, coexisting-network transmission capacities satisfy a linear equation whose coefficients depend on sharing method and SIC.
  • Capacity trade-off: Spectrum underlay has a capacity region no larger than spectrum overlay, but an appropriate transmission-power ratio can make the regions identical.
  • Parameter effects: Transmission capacities vary with base-station density, spatial-diversity gains, and the distance between an ad hoc transmitter and receiver.
  • Parameter effects: SIC increases both transmission capacities by a linear factor dependent on the interference-power threshold for qualifying canceled interferers.
  • Validation: Simulation results show tight outage bounds and agreement between asymptotic trade-off curves and non-asymptotic simulations.

B. Channel and Modulation

The system uses frequency-hopping over OFDM sub-channels and compares disjoint-subset overlay with full-band underlay. SIC reduces interference, while the analysis adopts simplifying assumptions about sub-channel assignments.

  • B. Channel and Modulation: The uplink spectrum is divided into M frequency-flat sub-channels using OFDM, and transmitters hop randomly over assigned sub-channels.
  • C. Spectrum Sharing Methods: Spectrum overlay assigns disjoint sub-channel subsets to the two networks, whereas underlay lets both networks use all M sub-channels.
  • C. Spectrum Sharing Methods: Overlay requires initialization to communicate available sub-channels and allowable ad hoc-node density, while underlay has less initialization overhead.
  • Model assumptions: The analysis assumes identical sub-channel sets across cells; otherwise, per-channel users form non-homogeneous PPPs and the case is deferred.
  • SIC: SIC is applied at base stations and ad hoc receivers to reduce interference and increase transmission capacities.
  • SIC: A targeted interferer qualifies for cancellation when its interference power exceeds the received signal power multiplied by κ; larger κ means fewer cancellations.

D. Transmission Capacity

The paper defines transmission capacities through SIR outage constraints and analyzes them using outage-probability bounds for Poisson interferer processes.

  • Capacity definition: Transmission capacity is defined from the maximum transmitter density satisfying a specified SIR outage constraint.The cellular and ad hoc capacities use densities λ_ε and ˜λ_ε whose outage probabilities equal ε.
  • Capacity definition: Reliable decoding requires SIR at least θ, with outage probabilities for both networks constrained by ε.The supported information rate is log2(1+θ) under Gaussian signaling.
  • Analytical approach: The analysis treats spectrum overlay and underlay with and without SIC, using outage probabilities as the analytical basis.The outage analysis adopts an existing approach for Poisson fields of interferers.
  • Analytical approach: Power-law shot noise lacks a closed-form CCDF, so the analysis derives upper and lower bounds on outage probabilities.These bounds are developed by separating strong interferers from weak-interferer aggregate interference.
  • Analytical approach: For spectrum overlay, the typical sub-channel’s transmitter and interferer processes are modeled as homogeneous Poisson point processes.The Marking Theorem and Slivnyak’s Theorem support the sub-channel process characterization.

B. Outage Probabilities: Spectrum Underlay

For spectrum underlay, outage probabilities are coupled through mutual interference between the cellular and ad hoc networks and depend on the transmission-power ratio.

  • Underlay outage analysis: Underlay SIRs and outage probabilities are bounded using the same Poisson-process framework applied to the coexisting networks.The cellular interferers can be grouped into a homogeneous marked PPP with transmission-power marks.
  • Underlay coupling: Underlay outage probability for each network depends on the transmitter densities of both networks because of mutual interference.This network coupling can produce smaller transmission capacities than spectrum overlay.
  • Underlay coupling: Underlay outage probabilities also depend on the transmission-power ratio η.The effect of η is characterized in the capacity analysis.
  • Distance distribution: The inner-cell user distance distribution required for outage bounds is governed primarily by the base-station density λ_b.The analysis assumes cell-edge outage probabilities are no smaller than inner-cell outage probabilities.

C. Outage Probabilities: Spectrum Sharing with SIC

With SIC, the outage expressions are modified by a factor representing cancellation benefits, while asymptotic capacity trade-offs characterize sharing efficiency and parameter effects.

  • SIC outage analysis: SIC modifies the no-SIC outage bounds by multiplying the corresponding expressions by a factor χ.The factor satisfies χ<1 and represents reduced outage relative to χ=1 without SIC.
  • SIC outage analysis: Decreasing the SIC factor κ reduces χ and therefore reduces outage probabilities.Here κ determines the interference-power threshold for qualifying canceled interferers.
  • Asymptotic capacity trade-off: For ε→0, the coexisting networks’ transmission capacities satisfy a linear trade-off equation.The slope at which ˜C increases as C decreases is −µ/˜µ and depends on network parameters.
  • Asymptotic capacity trade-off: For ε→0, spectrum overlay has a capacity region at least as large as spectrum underlay, with equality only for a specified transmission-power ratio.Underlay’s efficiency can be compensated by choosing η so both networks are outage limited.
  • Parameter effects: Transmission capacities vary systematically with base-station density, ad hoc link distance, outage probability, sub-channel count, and SIC-related ϕ.Both capacities increase linearly with ε and M and inversely with ϕ.
  • Parameter effects: Spatial diversity multiplies capacity by factors bounded by diversity-dependent powers under overlay and underlay.Under underlay, the relevant bounds depend on whether the cellular network is outage limited.

V. SIMULATION AND NUMERICAL RESULTS

Simulations evaluate the outage bounds and asymptotic capacity trade-offs, finding close agreement in sparse-transmitter regimes and larger overlay capacity regions.

  • Outage bounds: Outage probabilities converge to their lower bounds as transmitter densities decrease, while upper and lower bounds differ by roughly constant multiplicative factors.This behavior is observed across the evaluated cases.
  • Outage bounds: SIC reduces outage probabilities by approximately a factor of 0.54, close to the analytical factor χ.SIC also loosens the bounds at relatively large transmitter densities by reducing strong interferers.
  • Capacity trade-offs: Simulated capacity regions for spectrum overlay are larger than those for spectrum underlay.Without SIC, asymptotic curves closely match simulations; with SIC, simulations remain close to asymptotic upper bounds.
  • Capacity trade-offs: For spectrum overlay with SIC, simulation results are practically identical to the asymptotic upper bounds.The simulations use target outage probability ε=10^-2 for the trade-off comparison.
  • Capacity trade-offs: The asymptotic results characterize transmission capacities beyond the asymptotically small-outage regime.The paper compares the asymptotic results with non-asymptotic simulations.

VI. CONCLUSION

The paper derives transmission-capacity trade-offs for coexisting cellular and ad hoc networks across spectrum-sharing methods, with asymptotic linear relations and parameter-based capacity gains.

  • The transmission-capacity trade-off is analyzed for spectrum overlay and underlay, with and without successive interference cancellation (SIC).
  • For small target outage probability, the coexisting networks’ transmission capacities satisfy a linear equation with method- and SIC-dependent coefficients.
  • The trade-off supports adapting ad hoc node density to cellular uplink traffic dynamics while maintaining outage constraints for both networks.
  • Transmission capacities can increase by decreasing ad hoc link distances and increasing base-station density or link diversity gains.
  • SIC increases transmission capacities by a linear factor determined by the interference-power threshold for qualifying canceled interferers.
  • Simulations show tight outage-probability bounds and validate the asymptotic linear capacity trade-off in the non-asymptotic regime.

APPENDIX

The appendix develops stochastic-geometry calculations for combined Poisson processes, marked interferers, and SIC-related interference statistics.

  • The combined cellular and ad hoc transmitter processes are modeled using the superposition property of Poisson processes.
  • The appendix defines disks and their areas to calculate the probability that a typical point belongs to one of the component processes.
  • Fading factors are incorporated as additional marks in the point process.
  • Combining the derived interference statistics with the preceding analytical procedure yields the desired results.

C. Proof for Lemma 3

The proof characterizes user-to-base-station distance and extends outage-probability bounds to SIC by partitioning interferers according to their cancellability.

  • The largest disk contained in a typical base station’s Voronoi cell is used to derive the distance distribution for an inner-cell user.
  • The CDF of the disk radius is related to the event that another base station lies within twice that radius.
  • Differentiating the resulting relation gives the desired distance-distribution result.
  • With SIC, interferers are partitioned into strong and weak processes using an interference-power threshold.
  • The outage bounds are extended to SIC by replacing exponential terms with expressions involving the expected number of canceled strong interferers.

E. Proof for Theorem 1

The theorem proof obtains asymptotic capacity trade-offs by expanding outage bounds as target outage probability vanishes, including the SIC case.

  • As the target outage probability approaches zero, the cellular and ad hoc transmitter densities also approach zero, enabling asymptotic expansion.
  • Combining the asymptotic expressions produces the capacity trade-off function for spectrum sharing.
  • The capacities are constrained by outage requirements for both coexisting networks before combining the resulting asymptotic relations.
  • For overlay with SIC, canceling the strongest interferers trims the upper tail of the power shot-noise distribution, complicating its series expansion.
  • The overlay-SIC result follows by combining the stated equations, while underlay-SIC results use a similar procedure.
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