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Cognitive and Energy Harvesting-Based D2D Communication in Cellular Networks: Stochastic Geometry Modeling and Analysis

Ahmed Hamdi Sakr, Ekram Hossain

arXiv:1405.2013v2cs.NImath.PR

TL;DR

The paper studies cognitive D2D communication powered by RF energy harvested from ambient cellular interference and sharing an uplink or downlink cellular channel. Using stochastic geometry, it analyzes RSA and PSA access policies and finds improved D2D outage performance with cognitive access while cellular performance remains nearly unchanged under PSA versus RSA.

  • Problem

    The paper addresses how to combine spectrum-efficient cognitive D2D communication with RF energy harvesting from ambient interference in cellular networks.

  • Method

    It develops a stochastic-geometry framework for energy-harvesting D2D communication with channel inversion, spectrum sensing, and RSA or PSA cellular access.

  • Results

    Cognitive channel access improves D2D outage probability under the same SINR outage requirements for both RSA and PSA.

  • Takeaways & Limitations

    Carefully tuned network parameters can support acceptable D2D quality of service without significantly affecting cellular communication performance.

Abstract

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While cognitive radio enables spectrum-efficient wireless communication, radio frequency (RF) energy harvesting from ambient interference is an enabler for energy-efficient wireless communication. In this paper, we model and analyze cognitive and energy harvesting-based D2D communication in cellular networks. The cognitive D2D transmitters harvest energy from ambient interference and use one of the channels allocated to cellular users (in uplink or downlink), which is referred to as the D2D channel, to communicate with the corresponding receivers. We investigate two spectrum access policies for cellular communication in the uplink or downlink, namely, random spectrum access (RSA) policy and prioritized spectrum access (PSA) policy. In RSA, any of the available channels including the channel used by the D2D transmitters can be selected randomly for cellular communication, while in PSA the D2D channel is used only when all of the other channels are occupied. A D2D transmitter can communicate successfully with its receiver only when it harvests enough energy to perform channel inversion toward the receiver, the D2D channel is free, and the $\mathsf{SINR}$ at the receiver is above the required threshold; otherwise, an outage occurs for the D2D communication. We use tools from stochastic geometry to evaluate the performance of the proposed communication system model with general path-loss exponent in terms of outage probability for D2D and cellular users. We show that energy harvesting can be a reliable alternative to power cognitive D2D transmitters while achieving acceptable performance. Under the same $\mathsf{SINR}$ outage requirements as for the non-cognitive case, cognitive channel access improves the outage probability for D2D users for both the spectrum access policies.

I. INTRODUCTION

The paper combines cognitive D2D spectrum sharing with RF energy harvesting from ambient cellular interference. It develops a stochastic-geometry framework covering access policies, channel direction, outage, and network-parameter trade-offs.

  • Motivation and model: The model powers cognitive D2D transmitters solely with RF energy harvested from concurrent cellular interference.D2D transmitters sense a predefined nonexclusive channel before opportunistic access.
  • Contributions: Stochastic geometry yields closed-form expressions for harvested-energy, channel-availability, SINR-outage, and overall-outage probabilities under general path-loss exponents.The framework analyzes both D2D and cellular users while varying sensing thresholds, node densities, channel counts, and receiver sensitivity.
  • Contributions: The study compares random spectrum access (RSA) and prioritized spectrum access (PSA) for cellular transmissions.It also considers D2D operation on either downlink or uplink cellular channels.
  • Main findings: Uplink channels are preferable for D2D in dense cellular networks, whereas downlink channels perform better for cellular networks with low BS density.The paper derives a BS-density threshold for selecting uplink over downlink channels for D2D.
  • Main findings: For identical network parameters and SINR outage requirements, PSA provides superior overall D2D outage performance while cellular-user performance is almost unchanged.Multiple channels are used with cognition to protect cellular transmissions.

C. Energy Harvesting Model

D2D transmitters harvest RF power from concurrent downlink and uplink cellular transmissions, then use a harvest-then-transmit strategy. Spectrum sensing protects the shared D2D channel through a threshold-defined protection region.

  • Energy harvesting: The harvesting circuit collects RF power from all downlink and uplink channels, but excludes power from concurrent D2D transmissions.Downlink and uplink contributions are represented separately, with conversion efficiency 0 < a ≤ 1.
  • Energy harvesting: A transmitter may lack enough energy in one slot, so harvesting and DC conversion are activated under a time-slotted harvest-then-transmit strategy.Available harvesting power varies with transmitter location, channel gains, and network statistics.
  • Spectrum sensing: Before transmission, each D2D transmitter senses channel cd and uses it only when received neighboring cellular interference does not exceed threshold γ.The sensed transmitter is a BS for downlink operation or a cellular user for uplink operation.
  • Spectrum sensing: The protection region is random and depends on whether cd is a downlink or uplink channel; analysis approximates it by a disc with mean radius r̄P.Uplink protection-region radius also depends on random cellular-user transmit power.
  • Spectrum sensing: The D2D channel is unavailable when a cellular transmitter inside the protection region uses cd.Consequently, not every D2D transmitter can access the channel in a network realization.

E. Spectrum Access Model for Cellular Transmissions

The cellular network shares a common set of orthogonal channels with D2D transmissions, while RSA and PSA determine how cellular users occupy those channels. The analysis derives cellular and D2D access probabilities under these policies.

  • Access policies: RSA assigns any channel, including the D2D channel cd, independently and randomly with equal probability to cellular users.PSA instead reserves cd for cellular use until all other available channels are occupied.
  • Performance analysis: The framework evaluates D2D transmission probability and SINR outage for both D2D and cellular users.D2D transmission requires channel availability and sufficient harvested energy; outage analysis then quantifies SINR performance.
  • Modeling assumption: All BSs are assumed to adopt the same spectrum access policy, although PPP thinning can obtain intensities for BSs using different policies.This is the common-policy case analyzed in the paper.
  • Cellular access: A cellular user receives a connection only when a channel is available, with qf denoting the probability that its serving BS has a free channel.The number of channels used by a BS is min{Nu, |C|}.
  • Cellular access: The probability that a BS can serve cellular users increases with more channels or BSs and decreases with more cellular users.The result applies to both RSA and PSA.

1) Spectrum access probabilities for the RSA policy:

The access-probability analysis distinguishes RSA from PSA by tracking use of the shared D2D channel and the remaining channels. PSA reduces cellular use of cd but increases congestion on other channels.

  • RSA: RSA assigns each generic channel with the same probability because BSs select channels randomly and independently.The corresponding channel-use probability is obtained in Lemma 2.
  • PSA: Under PSA, cellular use of cd differs from use of other channels because cd is selected only after the remaining channels are occupied.The relevant probabilities are given in Lemma 3.
  • Policy comparison: Compared with RSA, PSA lowers the probability that cellular communication uses the D2D channel cd.This directly increases its availability for D2D access.
  • Policy comparison: PSA’s reduction in cd access comes at the expense of increased cellular congestion on channels in C \ {cd}.The non-D2D channel access probability therefore rises relative to RSA.

B. Transmission Probability for D2D Transmitters

D2D transmission requires both a free cognitive channel and sufficient harvested energy for channel inversion. The analysis characterizes these probabilities and shows that channel count has an optimal operating point.

  • Channel availability: The D2D channel is free when no cellular BS uses it within the transmitter’s protection region.Its probability pf depends on the channel-use probability qd, which differs under RSA and PSA.
  • Energy requirement: The required inversion power is determined by the receiver distance do and target received power ρd.The receiver is placed at the boundary of its allowed circle, yielding an upper bound on required transmit power and a lower bound on sufficient-energy probability.
  • Energy harvesting: For general path-loss exponent α, the sufficient-energy probability ps is expressed through κ1, κ2, and κ3, with κ3 = κ1 + κ2.The coefficients incorporate cellular channel-access probabilities and interference contributions.
  • Energy harvesting: When α = 4, ps admits a closed-form expression based on the complementary error function.The aggregate harvested-interference distribution becomes Lévy, allowing FPH(x) to be written using erfc.
  • Channel-count trade-off: An optimal number of channels maximizes both κ3 and ps, while adding very many channels does not necessarily improve ps.At large channel counts, ps becomes limited by the ratio of cellular-user and BS intensities.

IV. ANALYSIS OF SINR OUTAGE PROBABILITY

The paper derives D2D SINR outage under energy, channel-access, and interference conditions, then identifies when uplink spectrum is more beneficial than downlink spectrum.

  • Outage definition: D2D outage occurs when the receiver SINR falls below the threshold τ.The overall outage additionally includes insufficient harvested energy and an unavailable D2D channel.
  • Interference model: The typical D2D receiver experiences cellular interference on the shared channel and interference from other active D2D transmitters.Only D2D transmitters with sufficient energy and channel access contribute to the D2D interference process.
  • Model limitation: Active D2D transmitters form a point-hole process because they cannot lie within distance rp of cellular transmitters using the D2D channel.The analysis notes that this process is difficult to treat because its probability generating functional is unknown.
  • D2D outage result: The D2D SINR outage probability is given by OD = 1 − exp[−K1].The expression applies to either downlink or uplink use of the D2D channel, with K1 capturing the modeled interference effects.
  • Uplink versus downlink: Beyond a reference BS density, using an uplink channel is more beneficial than using a downlink channel for cognitive D2D communication.Increasing BS density then raises θ for downlink and reduces K1 for uplink, producing higher pf and lower SINR outage for uplink use.

B. Outage Probability for a Cellular User

Cellular-user outage is analyzed by modeling association, channel-specific access, and interference for downlink and uplink transmissions under RSA and PSA.

  • Cellular association: Each cellular user associates with its closest BS, ensuring the serving BS is closer than any interferer.This association supports the SINR analysis for a typical cellular user or macro BS.
  • Interference model: The cellular SINR model distinguishes channels other than cd from the shared D2D channel through qc and qd.Interfering BS or user processes use intensity qcλB on ordinary channels and qdλB on cd.
  • Outage result: The cellular SINR outage probability on channel c is derived for an interference-limited network with α = β.The channel-specific result uses access probabilities obtained for both RSA and PSA.
  • Average outage: Average cellular outage is obtained by averaging channel-specific outage over the probability that a user is served on each channel.The overall calculation also incorporates the probability qf that a BS has at least one free channel for its associated users.

V. NUMERICAL RESULTS AND DISCUSSIONS

Numerical evaluations compare four combinations of channel direction and access policy, validate the stochastic-geometry assumptions, and reveal trade-offs between harvesting, channel access, and outage-related performance.

  • Evaluation design: The evaluation compares Downlink-RSA, Downlink-PSA, Uplink-RSA, and Uplink-PSA using ps, pf, D2D transmission probability, cellular qf, and cellular SINR outage.Monte Carlo simulations validate the PPP assumptions used to derive the analytical expressions.
  • Evaluation design: Under the stated baseline, λB = 1 BS/km2, λU = 10λB users/km2, λD = 20 users/km2, |C| = 10 channels, α = 4, and β = 3.The numerical setup uses 37 dBm macro-BS transmit power and −104 dBm thermal noise power unless otherwise stated.
  • BS-density effects: Increasing λB decreases pf for downlink cd but leaves pf constant for uplink cd.For downlink, the protection-region effect dominates; for uplink, θ and qd are independent of λB.
  • BS-density effects: Increasing λB raises ps because more concurrent cellular transmissions provide harvestable ambient interference.Thus, BS density balances the probability of harvesting sufficient energy against finding the D2D channel free.
  • Policy and channel comparisons: For downlink, D2D transmission probability first increases and then decreases with λB, whereas uplink performance follows the increasing-then-saturating harvesting trend.PSA outperforms RSA for every λB shown, and uplink use is more beneficial than downlink use.

C. Outage Probability for D2D users

The section evaluates D2D SINR and overall outage across spectrum-sensing thresholds, channel counts, receiver sensitivity, channel type, and access policy. PSA generally improves D2D performance, while receiver sensitivity creates a trade-off between transmission probability and SINR.

  • Decreasing γ improves D2D SINR outage, while PSA provides better coverage than RSA for both downlink and uplink D2D channels.At γ = −60 dBm, PSA reduces outage from 43% to 17% for downlink and from 55% to 24% for uplink.
  • At γ = −60 dBm, D2D SINR outage falls from 43% to 17% for downlink and from 55% to 24% for uplink under PSA.PSA reduces cellular access to the D2D channel, lowering active interferers and improving SINR.
  • Increasing |C| improves D2D SINR outage for both policies and channel types, with PSA reaching outage below 0.3 using 11 uplink channels versus at least 25 for RSA.
  • D2D overall outage is minimized at an optimal receiver sensitivity ρd because lower sensitivity worsens SINR while higher sensitivity reduces transmission probability ps.The SINR outage dominates below the optimum, whereas ps dominates above it.
  • For cellular users, PSA has a negligible effect compared with RSA, while uplink channels outperform downlink channels in dense cellular networks and downlink channels perform better at low BS density.

APPENDIX A PROOF OF ACCESS PROBABILITIES

The appendix derives cellular channel-access probabilities for RSA and PSA by conditioning on the number of users served by a base station. PSA excludes the D2D channel until all alternative channels are occupied.

  • The access probabilities are derived by conditioning on the number Nu of users served by a generic base station and then averaging over Nu.
  • Under RSA, each channel is selected with the same probability when cellular communication chooses among available channels.
  • Under PSA, base stations randomly use channels other than cd, reserving cd until no alternative channel remains.The D2D channel is used only when the associated-user count exceeds |C| − 1.
  • For a downlink D2D transmitter, base stations using cd are modeled by thinning the base-station PPP to intensity λ′B = qdλB.The number of such base stations in the protection region is Poisson distributed.

APPENDIX C PROOF OF LEMMA 5

The appendix derives the Laplace transform and cumulative distribution of aggregate harvested interference for downlink and uplink cellular channels. It uses PPP-based modeling, fading assumptions, and inverse Laplace transformation.

  • The aggregate interference at a D2D transmitter is characterized through its Laplace transform.
  • The downlink interference transform uses Rayleigh-fading independence, exponential moments, and the probability generating functional of a PPP.
  • The uplink analysis models transmitting cellular users through a point process whose intensity accounts for each base station receiving at most |CU| transmissions.
  • The uplink cellular-user point process is not a PPP, and this modeling assumption is validated by simulations in Section V.
  • The harvested-power transform is LPH(s) = exp[−κ3s^(2/α)] with κ3 = κ1 + κ2, and its cumulative distribution is obtained by inverse Laplace transformation.The derivation uses the Bromwich inversion theorem with a modified contour.

APPENDIX D PROOF OF THEOREM 1

The appendix derives the D2D SINR outage probability by combining the complementary-cdf expression with Laplace transforms of cellular and D2D interference. It then applies analogous interference analysis and serving-distance distributions to obtain cellular outage probabilities.

  • The complementary cdf of SINR_D is obtained using exponential channel fading and Laplace transforms of cellular and D2D interference.The transforms are evaluated at τρ_d.
  • Spectrum sensing creates a protection radius around the intended D2D receiver for the nearest interfering macro BS or cellular user.For simplicity, the analysis centers this region at the D2D transmitter and assumes d_o << r̄_P.
  • The cellular-interference transform uses the BS transmit power for downlink channels and cellular-user transmit power for uplink channels.
  • Combining the derived interference terms yields the SINR outage probability O_D of a typical D2D receiver.
  • Cellular outage analysis accounts for unprotected D2D interferers, serving-BS exclusion in downlink, and the Rayleigh distribution of user-to-serving-BS distance.The resulting outage probability follows using the corresponding interference transforms and distance distribution.
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