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Resource Management for Device-to-Device Underlay Communication

Chen Xu, Lingyang Song, Zhu Han

arXiv:1311.1018v1cs.GTcs.NI

TL;DR

D2D underlay communication reuses cellular spectrum for direct links, but co-channel interference makes resource coordination important. This book studies power control, resource allocation, and game-theoretic approaches; its simulations report beneficial effects on system performance.

  • Problem

    D2D spectrum sharing can improve spectral efficiency but also causes cellular interference, making coordination important.

    Source: §1.1 · p. 3

  • Method

    The book studies physical-layer power control and beamforming alongside auction- and game-theoretic approaches to resource allocation, scheduling, and battery-lifetime optimization.

    Source: §1.4 · pp. 15–16

  • Results

    The simulations show that the proposed resource-management methods have beneficial effects on system performance.

    Source: Summary · p. 78

  • Takeaways & Limitations

    The book's studied methods address interference and resource management across D2D underlay settings, including multiple D2D pairs sharing cellular resources.

    Source: §1.4 · p. 15, Summary · p. 78

    The cited power-control scheme limits cellular interference but does not account for D2D-link quality.

    Source: §2.1.1 · p. 18

Abstract

from arXiv · show

Device-to-Device (D2D) communication is a technology component for LTE-A. The existing researches allow D2D as an underlay to the cellular network to increase the spectral efficiency. In this book, D2D communication underlaying cellular networks is studied. Some physical-layer techniques and cross-layer optimization methods on resource management and interference avoidance are proposed and discussed. WINNER II channel models is applied to be the signal and interference model and simulation results show that the performance of D2D link is closely related to the distance between D2D transmitter and receiver and that between interference source and the receiver. Besides, by power control, D2D SINR degrades, which will naturally contribute to low interference to cellular communication. A simple mode selection method of D2D communication is introduced. Based on path-loss (PL) mode selection criterion, D2D gives better performance than traditional cellular system. When D2D pair is farther away from the BS, a better results can be obtained. Game theory, which offers a wide variety of analytical tools to study the complex interactions of players and predict their choices, can be used for power and radio resource management in D2D communication. A reverse iterative combinatorial auction is formulated as a mechanism to allocate the spectrum resources for D2D communications with multiple user pairs sharing the same channel. In addition, a game theoretic approach is developed to implement joint scheduling, power control and channel allocation for D2D communication. Finally, joint power and spectrum resource allocation method is studied under consideration of battery lifetime, which is an important application of D2D communication on increasing user's energy efficiency. The simulation results show that all these methods have beneficial effects on improving the system performance.

Introduction

D2D reuses cellular spectrum for direct links, improving spectral utilization while creating co-channel interference that requires coordination. The section introduces a single-cell signal model and examines how user locations and power control affect D2D and cellular SINR.

1.1 Overview of Device-to-Device Communication

  • D2D reuses cellular resources through direct UE-to-UE links under BS control, but co-channel interference makes efficient coordination necessary.The section frames the book's work around physical-layer interference avoidance, resource allocation, joint scheduling and allocation, and battery-lifetime-aware optimization.Source: §1.1 · pp. 3–4

1.2 Signal and Interference Model

  • The signal model considers one cellular UE and one D2D pair sharing resources in a single cell, with the D2D receiver uniformly located within distance L of its transmitter.The user locations are updated in each simulation loop; propagation uses WINNER II models for indoor D2D and urban macrocellular links.Source: §1.2 · p. 5
  • In downlink sharing without power control, D2D SINR improves as the pair moves farther from the BS, while cellular UE SINR is less location-sensitive and remains higher.The BS is the D2D interference source in downlink, so D2D position directly affects interference strength.Source: §1.2 · p. 7
  • Cellular UE SINR depends on both D2D-pair and cellular-user positions, and the section models these links with WINNER II path loss and open-loop fractional power control.The power-control equation caps transmit power at Pmax and includes P0, resource-block count M, path loss L, and compensation factor α.Source: §1.2 · pp. 5, 7, 10
  • In uplink sharing without power control, D2D SINR is nearly unchanged with BS distance, while BS SINR improves as the D2D pair moves farther away.D2D interference at the BS depends on pair position; D2D SINR is reported as better than BS SINR in this setup.Source: §1.2 · p. 10
  • Power control reduces D2D SINR by about 30 dB while increasing cellular or BS SINR and narrowing the D2D SINR distribution.The stated mechanism is reduced D2D transmit power, which lowers interference to cellular users and the BS; path-loss compensation concentrates the distribution.Source: §1.2 · pp. 10–11

1.3 Mode Selection

The section compares cellular, forced-D2D, and path-loss (PL) mode selection, finding that PL selection performs best at intermediate D2D distances while direct-link performance degrades as pair distance grows.

1.3 Mode Selection

  • PL D2D selects direct mode when either device-to-BS path loss exceeds the path loss between the communicating devices.The alternatives are cellular mode for all devices or forced D2D mode for all communicating devices.Source: §1.3 · p. 11
  • At maximum pair distance L=35 m, PL mode is best; at L=45 m, FORCE mode has the worst capacity distribution, while CEL and PL modes are similar.At L=5 m, FORCE and PL criterion give the same capacity distribution; at L=15 m, PL mode gives higher capacity than FORCE mode.Source: §1.3 · pp. 11, 14
  • A threshold in pair distance can guide whether to use D2D; choosing the better cellular or direct channel condition can obtain optimal performance.The section presents PL mode as a way to address this distance-dependent mode-selection problem.Source: §1.3 · p. 14

1.4 Introduction to Game Theory in D2D Communication

The section applies game theory to D2D resource management, including spectrum auctions, joint scheduling and allocation, and battery-lifetime optimization. It describes mechanisms for these settings and reports favorable system-sum-rate and battery-lifetime outcomes.

Game-theoretic foundations

  • Game theory models interdependent rational players choosing actions to maximize utility; a Nash equilibrium is a strategy profile where no player can gain by deviating unilaterally.The section motivates these tools as a way to study resource scheduling and interference avoidance in D2D communication.Source: §1.4 · pp. 14–15

Spectrum resource allocation

  • Combinatorial auctions let bidders express preferences over resource packages, and the section applies this approach to optimize system capacity for D2D links reusing cellular bands.Iterative combinatorial auctions submit multiple bids over rounds while the auctioneer computes provisional allocations and ask prices.Source: §1.4 · p. 15
  • A reverse iterative combinatorial auction allocates spectrum among D2D links sharing resources; its algorithm achieves good system sum rate and high system efficiency with lower complexity than exhaustive search.The mechanism also investigates cheat-proofness, convergence, and price monotonicity.Source: §1.4 · pp. 15–16

Joint scheduling and resource allocation

  • For joint scheduling, power control, and channel allocation, cellular UEs lead Stackelberg pairs, D2D UEs follow, and pairs are scheduled by utility priority.Leaders charge channel-use fees; the approach analyzes optimal leader prices and follower powers and derives a Stackelberg equilibrium.Source: §1.4 · p. 16

Battery lifetime

  • A resource-allocation game maximizes D2D UEs’ battery lifetime subject to a rate constraint, using transmission and circuit energy and Peukert’s law.Because selfish resource use can reduce cellular communication quality, the approach adds pricing penalties; simulations show good battery-lifetime performance.Source: §1.4 · p. 16

Physical-layer Techniques

The chapter addresses D2D underlay resource management and interference avoidance through physical-layer techniques. It introduces power control and joint beamforming and power control as approaches to managing interference and throughput.

Physical-layer Techniques

  • The chapter investigates D2D-underlay physical-layer techniques for resource management and interference avoidance, including power control and joint beamforming with power control.The joint mechanism is intended to avoid interference between cellular and D2D links while maximizing system throughput.Source: Physical-layer Techniques · p. 17

2.1 Power Control

The section proposes distributed threshold-based power control for uplink D2D resource sharing, balancing D2D-link feasibility with cellular-interference limits. The scheme calculates power at the D2D transmitter and reports power savings and favorable throughput trade-offs.

2.1 Power Control

  • The section frames threshold-based power control as addressing both interference management and power saving for D2D underlay links.Uplink resource reuse offers D2D channel-rate and operability benefits, but requires limiting D2D-to-BS interference while saving power subject to reliable D2D performance.Source: §2.1 · p. 17, §2.1.1 · p. 17

2.1.1 Power Control Scheme

  • The BS notifies an interference-margin threshold and provides D2D-transmitter channel information; the transmitter calculates its own power and decides whether to transmit based on its allowed power and link status.The scheme is designed for uplink resource sharing and distributed scheduling, considering both cellular and D2D link performance.Source: §2.1.1 · p. 19

2.1.2 Threshold Based Power Calculation

  • The power calculation sets D2D power to satisfy a minimum D2D-receiver SINR while respecting the interference margin and a minimum SINR requirement at the BS.It uses estimated channel gains and accounts for the cellular-user-to-D2D-receiver path loss and channel gain.Source: §2.1.2 · pp. 20–21
  • The scheme saves about 35% power versus fixed 23 dBm and performs statistically better in energy efficiency than fixed power, similarly to centralized control in patent.The cited figures show power savings and energy-efficiency distributions under statistical channel estimation.Source: §2.1.2 · p. 22, Figure 2.5 · p. 23, Figure 2.6 · p. 23
  • With power control, D2D throughput is below fixed maximum 23 dBm but above centralized power control; sum throughput remains appreciable as excessive cellular interference is avoided.The comparison is reported for statistical channel estimation.Source: §2.1.2 · pp. 22, 25, Figure 2.7 · p. 24, Figure 2.8 · p. 24

2.2 Beamforming

The BS jointly beamforms and controls D2D transmit power to manage interference while maximizing system sum rate subject to cellular and D2D SINR thresholds. Simulations report better overall throughput than separate or absent controls, with gains depending on D2D-pair count and cellular radius.

2.2.2 Beamforming Matrix and Power Calculation

  • Joint beamforming and power control improves whole-system performance; beamforming benefits D2D throughput by constraining BS interference, while power control benefits cellular throughput by limiting D2D interference.The comparison includes joint control, beamforming only, power control only, and neither control.Source: §2.2.2 · p. 30, Figure 2.14 · p. 31, Figure 2.15 · p. 31
  • With different numbers of D2D pairs, the proposed scheme gives the optimal system throughput performance.Figure 2.17 plots system throughput against the number of D2D pairs.Source: §2.2.2 · p. 30, Figure 2.17 · p. 32
  • At small cellular radii, beamforming effectively prevents BS-to-D2D interference and the performance gain is obvious; as radius increases, cellular received power falls and power control becomes more important.Figure 2.18 compares system throughput across cellular radii.Source: §2.2.2 · p. 30, Figure 2.18 · p. 33
  • Power control does not strongly degrade D2D throughput because it keeps D2D SINR above threshold; the proposed scheme’s gap is more apparent at small cellular radii, where reducing D2D power benefits system throughput but D2D fading becomes obvious.The reported comparison focuses on the top two throughput lines in Figure 2.19.Source: §2.2.2 · pp. 30, 34, Figure 2.19 · p. 33

2.2.1 Joint Beamforming and Power Control Scheme

  • For one cell with one cellular user and one D2D pair, the BS uses their downlink CSI to beamform against excessive BS interference and calculates D2D power to maximize sum rate subject to both links’ SINR thresholds.The BS sets the thresholds, which can be tuned to meet performance requirements; the scheme is centralized and adapts to D2D link quality.Source: §2.2.1 · pp. 26–27, §2.2.2 · pp. 27, 29, 34

Radio Resource Management

The section proposes a reverse iterative combinatorial auction to allocate cellular downlink spectrum resources among D2D pairs sharing channels. The scheme is described as cheat-proof, finite-convergent, and lower in complexity than traditional combinatorial allocation, with simulations showing good system sum-rate performance.

Radio Resource Management

  • A reverse iterative combinatorial auction allocates cellular downlink spectrum resources to D2D pairs sharing channels, targeting improved system sum rate.Spectrum resources are bidders and D2D-pair packages are auctioned as goods in each round.Source: Radio Resource Management · p. 35
  • The auction uses resource-unit valuations and a non-monotonic descending-price algorithm whose utility accounts for D2D channel gain and system costs.The section explains the price-update non-monotonicity and reports lower complexity than traditional combinatorial allocation.Source: Radio Resource Management · p. 35
  • The proposed auction is described as cheat-proof and finite-convergent, and simulations show good system sum-rate performance.Source: Radio Resource Management · p. 35

3.1 Basics of Model and Auction Mechanism

This section models downlink resource sharing among multiple cellular users and D2D pairs, where shared spectrum creates interference in both directions. It defines channel-rate-based valuations and bidder utilities to formulate spectrum allocation as an auction problem.

3.1 Basics of Model and Auction Mechanism

  • The model allows cellular resource blocks to be shared by multiple D2D pairs, with interference from the BS to D2D receivers and from D2D transmitters to cellular receivers.D2D users feed CSI to the BS, which sends control signals for power control and resource allocation.Source: §3.1 · pp. 37–38
  • The model uses Rayleigh fading and free-space path loss, and defines cellular and D2D rates from their SINRs under received interference and noise.The sum-rate objective aggregates cellular and D2D channel rates.Source: §3.1 · pp. 38–39
  • Resource-block valuations target channel rate and account for interference: assigning a cellular resource to a D2D package has positive gain when D2D signal contribution exceeds its interference contribution.Source: §3.1 · pp. 39–40
  • A bidder’s utility is its package valuation minus its pay price, which represents costs such as control-signal transmission and information feedback.The model uses linear anonymous item prices.Source: §3.1 · pp. 40–41
  • The allocation assigns packages to bidders without overlapping packages, and XOR bidding allows multiple bids but at most one winning bid per bidder.Source: §3.1 · p. 41

3.2 Resource Allocation Algorithm Based on Reverse Iterative Combinatorial Auction

The section formulates D2D spectrum allocation as a reverse iterative combinatorial auction in which cellular spectrum units bid for D2D-pair packages. Its price updates respond to excess supply or demand, while allocation constraints limit each bidder to one package and each item to one sale.

3.2 Resource Allocation Algorithm Based on Reverse Iterative Combinatorial Auction

  • The reverse iterative combinatorial auction assigns cellular spectrum units to packages of D2D pairs, seeking an allocation that maximizes overall gain.An efficient allocation is defined as one maximizing overall gain.Source: §3.2 · p. 42
  • The integer linear program maximizes overall gain while allowing at most one package per bidder and preventing any item from being sold more than once.The auctioneer selects winners from submitted bids because the winner-determination problem is NP-hard.Source: §3.2 · p. 43
  • Allocating efficiency benchmarks auctions as the final allocation’s overall gain divided by that of an efficient allocation.Source: §3.2 · p. 43
  • Linear ask prices decrease for oversupplied items and increase for temporarily overdemanded items; bidders bid at current prices when package utility is nonnegative.The algorithm ends when all D2D links are auctioned or every channel has won a package.Source: §3.2 · pp. 44–45

3.3 Analysis of the Auction-Based Resource Allocation Algorithm

The reverse iterative combinatorial auction is analyzed for truthful bidding, finite convergence, price behavior, computational complexity, and signaling overhead. Its price step affects convergence speed, while the proposed allocation can reduce complexity relative to exhaustive search.

Cheat-Proof

  • The reverse I-CA is cheat-proof: each cellular bidder’s best strategy is to report its true demand in every auction round.The proof considers the utility effects of bidding for packages and concludes that deception causes a utility loss.Source: §3.3 · pp. 46–47

Convergence

  • The algorithm converges in finitely many iterations because a finite set of packages is eventually allocated through the bidding process.A bidder waits until its utility is nonnegative to bid; contested packages are allocated through an ascending-price process.Source: §3.3 · p. 47
  • A larger price step Δ speeds convergence, while a smaller Δ slows it; fine-tuning δ has the same effect but less impact.Source: §3.3 · p. 47

Price Monotonicity

  • Raising an item’s price during the descending-price auction may be needed to reflect competition and can improve allocation efficiency.When bids conflict, fine tuning prompts bidders to reassess utility until one winner remains; the ascending-price process maximizes auctioneer revenue in that situation.Source: §3.3 · pp. 47–48

Complexity

  • For sufficiently large m and n, the proposed reverse I-CA has lower stated complexity than exhaustive allocation; limiting each channel to one D2D pair reduces it further.The comparison is O(nm) versus O(n(2^m−1)+p0(d)/Δ), with the reduced scheme stated as O(n·m+p0(d)/Δ).Source: §3.3 · p. 48

Overhead

  • The scheme requires global CSI at the base station, but no additional signaling overhead beyond existing schedulers that also use global CSI.The required CSI is more complicated because it must account for D2D–cellular interference; this chapter does not simplify the scheme because it targets a nearest-optimal solution.Source: §3.3 · pp. 48–49

3.4 Performance Results and Discussions

Simulations using WINNER II channel models compare the proposed reverse I-CA with exhaustive, reduced, and random allocation. The auction outperforms random allocation and maintains high efficiency across user and resource settings, though its approximate optimization leaves a gap to exhaustive search.

System Sum Rate

  • System sum rate increases with both the number of D2D pairs and the number of resource units.More resource units increase the chance of assigning D2D links resources with less interference, a pattern the authors liken to multiuser diversity.Source: §3.4 · p. 49
  • The proposed reverse I-CA is much superior to random allocation, while exhaustive allocation yields the highest sum rate and only a small advantage over R-I-CA as resource units increase.With 8 resource units, reduced R-I-CA approximates R-I-CA; with 2 units, restricting each channel to one D2D pair can cause substantial capacity loss when pairs outnumber resources.Source: §3.4 · p. 50, Figure 3.2 · p. 50, Figure 3.3 · p. 51

System Efficiency

  • The proposed algorithm’s efficiency is high and stable across user and resource settings, with its lowest η around 0.7.η is defined as the proposed sum rate divided by the exhaustive-optimal sum rate; the lower value occurs when both resource units and D2D pairs are few.Source: §3.4 · pp. 50, 52, Figure 3.5 · p. 52
  • Efficiency remains above 0.9 at the reported other points, reflecting a small gap to exhaustive search that the authors attribute to approximate optimization.The descending-price rule selects the highest current bid, maximizing current overall gain, but the algorithm follows a local or approximate-global-optimum principle.Source: §3.4 · p. 52

Price Monotonicity

  • In the illustrated non-monotonic auction, D2D pair 2’s unit price rises during bidding and it is the last pair sold.The fine-tuning step δ is much smaller than the descending step Δ, making the price increase difficult to see.Source: §3.4 · p. 52, Figure 3.6 · p. 53

Cross-layer Optimization

Cross-layer optimization addresses coordination for D2D underlay communication, where shared resources can create interference. The chapter considers joint scheduling and spectrum allocation, as well as auction-based power and channel allocation that accounts for battery lifetime.

Cross-layer Optimization

4.1 Time-Domain Scheduling

This section develops a Stackelberg-game scheme for jointly scheduling D2D pairs and allocating resources, with cellular UEs as leaders and D2D UEs as followers. Simulations report good throughput for both UE types, fair D2D service, and improved system throughput.

4.1.1 Model Assumptions

  • The model fixes cellular channels and pairs, with K D2D pairs selected each TTI to share the K cellular channels; the analysis focuses on uplink because downlink eNB interference impairs D2D service.The considered setting has D > K D2D pairs.Source: §4.1.1 · pp. 55–56

4.1.2 Stackelberg Game

  • Cellular UEs lead by setting a channel price, while D2D UEs follow by choosing transmit power to maximize their payoff; the analyzed game has a unique equilibrium.The price is a coordination fee, and the equilibrium is stable against unilateral deviations.Source: §4.1.2 · pp. 57, 60

4.1.3 Joint Scheduling and Resource Allocation

  • At each TTI, the eNB schedules D2D pairs sequentially using a priority queue that reflects follower utility and cumulative utility from earlier TTIs.An additional cost based on cumulative utility lowers a previously selected pair’s priority; δ controls the fairness effect.Source: §4.1.3 · pp. 61–62
  • Increasing δ has little effect on cellular UE rates, while D2D rates tend to converge, improving fairness; an excessively large δ makes scheduling behave like Round Robin.When C = 10, D2D rate performance is reported as much better than cellular UE performance, and D2D UEs achieve similar or higher rates overall.Source: §4.1.3 · pp. 62, 66
  • Larger β leads D2D followers to choose higher transmit power, raising their rates while increasing interference and lowering cellular UE rates.The simulations also report that D2D UEs use much less transmit power than cellular UEs.Source: §4.1.3 · p. 66
  • The proposed algorithm achieves good throughput for cellular and D2D UEs, fairly serves D2D UEs, and improves system throughput.The scale factor β and fairness coefficient δ affect its performance.Source: §4.1.3 · p. 66

4.2 Energy Efficient Improvement

This section formulates D2D resource allocation around battery lifetime, analyzes a game, and adds pricing to address interference externalities through an auction algorithm. Simulations report longer D2D battery lifetime than cellular communication and auction performance close to centralized allocation, and much better than random allocation.

4.2.1 Model Assumptions and Battery lifetime

  • The game seeks to maximize total D2D battery lifetime subject to rate constraints, accounting for transmission and circuit energy and modeling lifetime with Peukert’s law.Circuit power is assumed constant across D2D UEs.Source: §4.2.1 · pp. 68–69

4.2.2 Resource Allocation Game

  • The resource-allocation game has a Nash equilibrium, and the paper states that a Pareto-optimal strategy must be a Nash equilibrium.The authors describe existence of the equilibrium as ensuring feasibility of the game.Source: §4.2.2 · pp. 70–71

4.2.3 Resource Auction Algorithm

  • Pricing addresses interference externalities in the resource-allocation game, and the auction iteratively awards channels while adjusting transmit powers to preserve rate constraints.Its costs increase when a pair reuses multiple channels or multiple pairs share a channel.Source: §4.2.3 · pp. 71–73
  • At a 6bps/Hz rate constraint, average D2D battery lifetime is approximately 63h, about seven times the approximately 9h cellular UE lifetime reported for an average rate of about 5.8bps/Hz.The comparison uses the paper’s stated cellular-rate and battery-lifetime values.Source: §4.2.3 · p. 73
  • Larger maximum D2D distances are associated with quickly declining battery lifetime and cellular rate.The paper notes that longer D2D distances require more transmit power and increase interference to the cellular network.Source: §4.2.3 · p. 76
  • The auction algorithm performs close to centralized allocation and much better than random allocation; D2D communication can greatly extend battery lifetime compared with traditional cellular communication.Centralized allocation maximizes overall lifetime, whereas random allocation assigns resources randomly.Source: §4.2.3 · pp. 73, 76

Summary

The book proposes physical-layer and cross-layer methods for D2D resource management and interference avoidance. Its simulations report beneficial system-performance effects, while identifying several problems for future work.

Summary

  • WINNER II simulations relate D2D-link performance to transmitter–receiver and interference-source–receiver distances; path-loss-based mode selection favors D2D over cellular, especially when the pair is farther from the BS.The summary also states that power control degrades D2D SINR, contributing to lower interference to cellular communication.Source: Summary · p. 77
  • A distributed threshold-based power-control scheme targets feasible D2D connections while limiting cellular SINR degradation, and joint beamforming and power control target system sum rate while protecting both link types.The BS performs beamforming and calculates D2D transmit power, checking cellular and D2D SINR thresholds.Source: Summary · p. 77
  • A reverse iterative combinatorial auction allocates spectrum for multiple D2D pairs sharing a channel, alongside game-theoretic joint scheduling, power control, and channel allocation.Source: Summary · pp. 77–78
  • Simulation results show that the proposed methods have beneficial effects on system performance.Source: Summary · p. 78
  • Joint power and spectrum allocation considers battery lifetime as an application for increasing UE energy efficiency.Source: Summary · p. 78
  • Future work remains on simplifying resource-allocation algorithms, multi-cell joint optimization, and multi-hop D2D transmission.Source: Summary · p. 78
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