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Spectrum Sharing for Device-to-Device Communication in Cellular Networks

Xingqin Lin, Jeffrey G. Andrews, Amitava Ghosh

arXiv:1305.4219v5cs.IT

TL;DR

The paper asks how D2D users should share cellular spectrum and choose between direct and cellular communication. It develops a tractable PPP-based hybrid model and unified analytical framework for overlay and underlay optimization. The results identify distinct rate and coverage tradeoffs, including reduced underlay spectrum access when relaxed mode selection admits more D2D links.

  • Problem

    The paper addresses how D2D users should access spectrum and how potential D2D pairs should select direct versus cellular communication.

  • Method

    The paper uses a tractable hybrid network model with PPP-modeled mobile positions and a unified analytical approach for overlay and underlay D2D spectrum sharing.

  • Results

    Overlay and underlay improve overall mean rate versus pure cellular operation, while underlay coverage reveals a tradeoff between D2D spectrum access and the mode-selection threshold.

  • Takeaways & Limitations

    When a relaxed mode-selection threshold allows more D2D links, underlay should make less spectrum available to D2D to limit interference.

Abstract

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This paper addresses two fundamental and interrelated issues in device-to-device (D2D) enhanced cellular networks. The first issue is how D2D users should access spectrum, and we consider two choices: overlay (orthogonal spectrum between D2D and cellular UEs) and underlay (non-orthogonal). The second issue is how D2D users should choose between communicating directly or via the base station, a choice that depends on distance between the potential D2D transmitter and receiver. We propose a tractable hybrid network model where the positions of mobiles are modeled by random spatial Poisson point process, with which we present a general analytical approach that allows a unified performance evaluation for these questions. Then, we derive analytical rate expressions and apply them to optimize the two D2D spectrum sharing scenarios under a weighted proportional fair utility function. We find that as the proportion of potential D2D mobiles increases, the optimal spectrum partition in the overlay is almost invariant (when D2D mode selection threshold is large) while the optimal spectrum access factor in the underlay decreases. Further, from a coverage perspective, we reveal a tradeoff between the spectrum access factor and the D2D mode selection threshold in the underlay: as more D2D links are allowed (due to a more relaxed mode selection threshold), the network should actually make less spectrum available to them to limit their interference.

I. INTRODUCTION

The paper studies how D2D users should share cellular spectrum and select direct versus cellular communication modes. It develops a tractable PPP-based hybrid model and unified analysis to optimize overlay and underlay designs and derive system-level insights.

  • Motivation: D2D networking enables direct communication between cellular mobiles, supporting proximity services, public safety, local data transfer, and data flooding.Potential benefits include spectral efficiency, cellular coverage, energy efficiency, and reduced backhaul demand.
  • Research questions: Spectrum access and D2D mode selection are coupled design problems because potential D2D pairs may use either direct or conventional cellular communication.The mode-selection threshold is defined as the transmitter–receiver distance below which D2D communication occurs.
  • Approach: The paper develops a tractable baseline model and unified analytical framework using stochastic geometry and Poisson point processes for D2D-enabled cellular networks.The model captures random user positions, mode selection, transmit-power control, and orthogonal cellular scheduling.
  • Design insights: Overlay and underlay both improve overall mean rate relative to pure cellular operation, but underlay cellular rates do not improve or may slightly degrade because D2D interference offsets offloading gains.In overlay, cellular rates improve through D2D offloading, while D2D mobiles can achieve much higher rates than regular cellular mobiles in both scenarios.
  • Design insights: Underlay coverage exhibits a tradeoff: relaxing the mode-selection threshold allows more D2D links, so less spectrum should be made available to D2D to limit interference.The paper jointly studies spectrum sharing and mode selection in overlay and underlay settings.
  • Scope and extensions: The analysis assumes a traditional macrocell architecture and random underlay spectrum access, leaving heterogeneous networks and more advanced scheduling as extensions.The paper identifies multi-antenna methods, group communication, broadcasting, and efficient D2D scheduling as future directions.

B. Spectrum Sharing

The paper models overlay as orthogonal spectrum partitioning and underlay as shared spectrum access. These choices are analyzed with PPP-based approximations that account for cellular scheduling and D2D interference.

  • Overlay: The uplink spectrum is divided into orthogonal portions in overlay, with fraction η assigned to D2D and fraction 1 − η assigned to cellular communication.η is the overlay spectrum partition factor.
  • Underlay: In underlay, each D2D transmitter independently accesses βB of B subchannels through frequency hopping.β ∈[0, 1] measures D2D spectrum-access aggressiveness.
  • Cellular scheduling: Cellular uplink analysis approximates the hexagonal coverage region by an equal-area disk and models cellular interferers outside it as a PPP with density λb.The typical cellular transmitter is uniformly distributed within the disk, while only one uplink transmitter per macrocell is active at a time.
  • Overlay: The overlay interpretation extends naturally to time-frequency resources, where η represents the proportion of OFDMA resource blocks assigned to D2D.The remaining resource blocks are used by cellular users.
  • D2D scheduling: D2D-mode users form a PPP and use spatial Aloha, transmitting independently in each time slot with probability κ.Each user is silent with probability 1−κ, providing a baseline for comparing more sophisticated scheduling schemes.

D. Performance Metrics

The paper evaluates cellular and potential-D2D rates using stochastic-geometry SINR analysis and ergodic link spectral efficiency. Potential-D2D performance combines cellular-mode and direct-D2D-mode rates according to distance-based mode selection.

  • Mode selection: Potential D2D UEs use cellular mode with probability P(D ≥µ) and D2D mode with probability P(D < µ).The threshold µ determines the distance-based mode-selection split.
  • Rate metrics: The average rate of potential D2D UEs is Td = P(D ≥µ) · Tc + P(D < µ) · ˆTd.The two terms correspond to cellular mode and D2D mode, respectively.
  • SINR analysis: The received-signal model includes the desired link, heterogeneous interfering links, and additive white Gaussian noise, yielding an SINR-based performance analysis.The typical and interfering links are characterized by transmit power, link length, fading, and signals.
  • Analytical foundation: Under channel inversion and Rayleigh fading, the desired normalized signal power is exponential, enabling rate expressions based on the interference Laplace transform.Channel inversion compensates for large-scale pathloss but not small-scale fading.
  • Spectral efficiency: Ergodic link spectral efficiency R combines physical-layer modulation and coding with medium-access protocols and accounts for the time and/or frequency resources accessed by a link.In overlay, a D2D link with Aloha probability κ effectively accesses κη time-frequency resources.

B. Transmit Power Analysis

The paper analyzes cellular and D2D transmit powers and derives how the D2D mode-selection threshold affects average potential-D2D transmit power. D2D achieves substantially lower transmit power than cellular links at the same SNR target.

  • The analysis derives average transmit powers for cellular UEs, potential D2D UEs, and potential D2D UEs operating in D2D mode.These power distributions are later used in rate-performance analysis.
  • E[P_c] and E[P_d] increase with pathloss exponent α and are inversely proportional to the square root of BS density.
  • The power-minimizing mode-selection threshold is independent of the D2D-distance distribution and inversely proportional to the square root of BS density.It depends only on the average cellular transmit power.
  • The optimal threshold increases with pathloss exponent α, making D2D transmission more favorable for saving transmit power.
  • The typical UE power constraint of 23 dBm is respected even at SNR_m=10 dB.
  • 15 dB lower transmit power is available to D2D transmitters than cellular transmitters for the same SNR_m target.With the same power budget, D2D links can achieve about 15 dB higher SNR_m.

IV. ANALYSIS OF OVERLAY IN-BAND D2D

This section derives SINR distributions and spectral efficiencies for overlay in-band D2D, then validates the analytical SINR distributions against simulation. It also characterizes sparse and dense network behavior.

  • The framework analyzes a typical D2D or cellular link using spatial averaging under a stationary Poisson model.
  • Overlay D2D interference forms a homogeneous PPP with density κλ_d because random Aloha access thins the D2D transmitter process.
  • Analytical CCDF and spectral-efficiency expressions are derived separately for D2D links and cellular uplinks.The cellular uplink expression involves an integration, unlike the closed-form D2D SINR CCDF.
  • In sparse networks, interference and noise have the same order impact on SINR coverage, whereas dense-network effects depend on the SINR target.Interference is more pronounced for low SINR targets in dense networks, while noise dominates for high targets.
  • Θ(θ_c) outage scaling characterizes sparse networks, while Θ(θ_c^α) scaling characterizes dense, interference-limited networks.
  • The analytical cellular uplink SINR distribution is compared with hexagonal-grid simulations, while the D2D analytical distribution closely matches Monte Carlo results.The D2D analysis requires no approximation; the cellular uplink analysis uses an approximate approach.

B. Optimizing Spectrum Partition

The paper optimizes overlay spectrum partition and mode selection using rate expressions and a weighted proportional-fair utility. The optimal partition becomes the D2D weight when potential D2D users are restricted to D2D mode.

  • The weighted proportional-fair utility is wc log T_c + wd log T_d, with wc,wd>0 and wc+wd=1.
  • For partition factor η, cellular rate is (1−η)R_c, while potential-D2D rate is (1−η)R_c in cellular mode and ηR_d in D2D mode.
  • As the mode-selection threshold μ increases, cellular average rate increases, while potential-D2D average rate first increases and then decreases.The D2D-rate decline is attributed to increased intratier interference.
  • When μ→∞, the optimal spectrum partition η⋆ converges to wd.In the plotted case, η⋆=0.4=wd independently of q, the proportion of potential D2D UEs.
  • The optimal partition for fixed μ can be combined with numerical optimization over μ to obtain the joint design choice (μ⋆,η⋆(μ⋆)).

V. ANALYSIS OF UNDERLAY IN-BAND D2D

Underlay in-band D2D is analyzed through PPP-based interference models and rate expressions for cellular and D2D links. The analysis shows that spectrum access increases D2D rates but intensifies interference, creating utility and coverage tradeoffs with mode selection.

  • Analytical Model: The effective D2D interferers form a thinned homogeneous PPP with density κβλd, alongside cellular interferers of density λb.Random frequency- and time-domain access produces the thinning factor κβ.
  • Link Spectral Efficiency: Increasing β decreases both D2D and cellular spectral efficiency because added D2D interferer density outweighs the reduced per-subchannel transmit power.Thus, maximizing link spectral efficiency favors narrower bandwidth with higher D2D power density, although this limits D2D throughput.
  • Optimizing Spectrum Access: Underlay interference offsets cellular offloading gains, so cellular rates remain nearly constant or slightly decrease as the mode selection threshold µ increases.Larger β raises potential-D2D rates but lowers cellular rates.
  • Optimizing Spectrum Access: The underlay utility optimization has a complicated dependence on β and is therefore solved numerically as a single-variable problem.The utility is evaluated against β for different proportions q of potential D2D UEs.
  • Coverage Constraints: Coverage imposes a β–µ tradeoff: increasing β spreads signal power across wider bandwidth, requiring fewer cochannel D2D transmissions and therefore a smaller µ.A smaller µ causes more potential D2D UEs to use cellular mode rather than D2D mode.
  • Coverage Constraints: Joint β–µ coverage constraints are not incorporated into the underlay spectrum-access optimization and are identified as future work.The paper states that both D2D and cellular outage requirements impose joint constraints.

VI. OVERLAY VS. UNDERLAY: A CASE STUDY

The case study compares overlay and underlay D2D spectrum sharing through average-rate performance, showing distinct resource and interference effects for cellular and potential D2D users. It also identifies extensions beyond the traditional macrocell setting.

  • 16% D2D links produces a remarkable overall-rate increase in both overlay and underlay because D2D links achieve high rates.
  • Overlay potential-D2D rate increases almost linearly with η, whereas underlay potential-D2D rate increases diminishingly as β increases.Underlay growth diminishes because cellular and mutual D2D interference degrade received SINR.
  • Increasing η reduces cellular-UE rate through reduced spectrum, while increasing β reduces it through greater D2D interference.Cellular performance is relatively sensitive to η in overlay but robust to β in underlay.
  • As SNRm rises from −4 dB to 10 dB, cellular and overlay D2D rates increase linearly, while underlay D2D growth diminishes, especially above 4 dB.The underlay pattern indicates increasing transmit powers gradually make performance interference-limited.
  • Underlay D2D rates are mainly interference-limited, whereas overlay D2D rates are more resource-limited; cellular rates show the reverse sensitivity pattern across scenarios.
  • The framework jointly studies spectrum sharing and mode selection, and extends underlay analysis from rate performance to a coverage tradeoff.Future work includes heterogeneous networks, multiple antennas, group communication, scheduling, multi-hop, and cooperative D2D.

APPENDIX

The appendix derives link-length distributions and transmit-power behavior under the model’s geometric assumptions. It shows that average D2D transmit power is minimized at a specific mode-selection threshold.

  • The uplink approximation replaces a hexagonal macrocell coverage region with a ball of radius R and assumes uniform cellular-transmitter location.
  • The typical cellular-link length has PDF fLc(x) = 2πλbx · Ix∈[0, 1.
  • The typical D2D-link length distribution is conditioned on the D2D mode-selection threshold µ.
  • Average transmit power combines cellular-mode power and D2D-mode power according to the threshold-conditioned link distribution.
  • µ⋆ = (E[Pc])1/α minimizes average D2D transmit power because E[Pd] decreases before and increases after this stationary point.

C. Proof of Proposition 2

The proof derives cellular and D2D spectral-efficiency expressions from conditional SINR transforms under the Poisson hybrid-network model. These transforms account for cellular and D2D interference distributions.

  • The conditional Laplace transform uses Palm expectations, Slivnyak’s theorem, the PPP probability generating functional, and exponential fading.
  • The D2D interferer density is λd = qλ(1 −e−ξπµ2), and the resulting SINR analysis yields D2D spectral efficiency Rd = κE[log(1 + SINR)].
  • The D2D SINR complementary distribution is obtained from the conditional Laplace-transform analysis.
  • Cellular spectral efficiency is derived by averaging over the Poisson number of potential uplink transmitters and their link lengths.
  • The cellular interference transform is combined with the SINR expression to obtain cellular spectral efficiency and its SINR complementary distribution.

E. Proof of Corollary 2

The corollary proof analyzes uplink interference asymptotically in sparse and dense cellular networks. It uses different approximations according to the macrocell radius regime.

  • For sparse networks with small λb, the macrocell radius R is large and the analysis applies for r ∈ [R, ∞).
  • The sparse-network approximation uses 1 −e−y ≈y for small y, independent fading and link length, and E[Pc] = E[Lcα].
  • These sparse-network asymptotics yield the Laplace transform of uplink interference.
  • For dense networks with large λb, the macrocell radius R is small, requiring a separate asymptotic expression.
  • Combining the sparse and dense asymptotic results with Proposition 3 completes the corollary proof.

F. Proof of Proposition 4

The proof accounts for D2D power splitting across accessed subchannels and derives spectral-efficiency expressions using the visible D2D transmitter density. It similarly evaluates cellular-link spectral efficiency through the interference Laplace transform and relates these expressions to SINR coverage.

  • D2D spectral efficiency: D2D transmitters split their average power across βB accessed subchannels, reducing the per-subchannel average power by a factor of 1/βB.This adjustment is incorporated into the D2D spectral-efficiency derivation.
  • D2D spectral efficiency: The D2D transmitter density seen on each subchannel is λd = β·qλ(1−e^−ξπµ2).
  • D2D spectral efficiency: The D2D link spectral-efficiency expression follows after substituting the interference-related terms into equation (43), with its SINR CCDF obtained analogously to equation (35).
  • Cellular spectral efficiency: The cellular-link spectral efficiency Rc is derived by calculating the interference Laplace transform and substituting it into the corresponding integral expression.The proof identifies the Laplace-transform calculation as the key intermediate step.
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