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Energy-Efficient Resource Allocation for Device-to-Device Underlay Communication

Feiran Wang, Chen Xu, Lingyang Song, Zhu Han

arXiv:1412.2268v1cs.NI

TL;DR

D2D underlay sharing can improve resource use but requires coordination because it creates interference with cellular links. The paper formulates joint channel and power allocation as an iterative combinatorial auction and reports better performance than greedy and fixed-power algorithms, with increased system energy efficiency relative to a pure cellular system.

  • Problem

    D2D users sharing cellular resources can interfere with cellular communication, so channel and power allocation must be coordinated while accounting for energy efficiency and limited UE battery capacity.

    Source: §I · p. 1

  • Method

    The paper models joint channel and power allocation as a combinatorial auction with D2D pairs bidding for channel packages and jointly played channel-allocation and power-control levels.

    Source: §I · p. 2

  • Results

    The proposed algorithm outperforms the greedy heuristic and fixed-power algorithm in expected data, lifetime, and data rate; with six D2D pairs, its relative sum-rate gap over greedy is about 10%.

    Source: B. Performance of Different Algorithms · p. 8, §VI · p. 9

  • Takeaways & Limitations

    The simulations indicate that D2D underlaying cellular networks can increase system energy efficiency compared with a pure cellular system using the proposed allocation algorithm.

    Source: §VI · p. 9

Abstract

from arXiv · show

Device-to-device (D2D) communication underlaying cellular networks is expected to bring significant benefits for utilizing resources, improving user throughput and extending battery life of user equipments. However, the allocation of radio and power resources to D2D communication needs elaborate coordination, as D2D communication can cause interference to cellular communication. In this paper, we study joint channel and power allocation to improve the energy efficiency of user equipments. To solve the problem efficiently, we introduce an iterative combinatorial auction algorithm, where the D2D users are considered as bidders that compete for channel resources, and the cellular network is treated as the auctioneer. We also analyze important properties of D2D underlay communication, and present numerical simulations to verify the proposed algorithm.

I. INTRODUCTION

D2D underlay reuse can raise spectrum use, but it also creates interference that requires coordination. The paper formulates joint channel and power allocation as a combinatorial auction and models energy efficiency through expected data over battery lifetime.

I. INTRODUCTION

  • D2D sharing of cellular resources creates interference, motivating coordinated allocation; prior work often focused on a single D2D link or one D2D pair per channel.The paper instead allows multiple D2D pairs to share a channel.Source: §I · p. 1
  • The combinatorial-auction formulation represents channel sharing as packages of D2D pairs whose allocation value depends on their combined performance.D2D pairs act as bidders, and the cellular network allocates channels through iterative bidding.Source: §I · p. 2
  • The objective is expected data transmitted during battery lifetime, using Peukert’s law to capture nonlinear battery effects rather than relying only on rate over power.The paper describes this as a more practical energy-efficiency indicator for handheld UEs.Source: §I · p. 2, §II · p. 3
  • The proposed allocation uses jointly played channel-allocation and power-control levels, with power control modeled as a non-cooperative game among co-channel UEs.The auction iterates until an equilibrium state; the paper investigates equilibrium existence, uniqueness, and convergence.Source: §I · p. 2

II. SYSTEM MODEL

  • The system model assumes a single cell with K cellular UEs on K orthogonal channels, while D2D pairs may reuse those channels and only intra-cell interference is considered.The eNB is assumed to have perfect channel state information, and the analysis focuses on the uplink because downlink eNB interference can make D2D service quality difficult to guarantee.Source: §II · pp. 2–3

III. COMBINATORIAL RESOURCE AUCTION

The paper formulates joint D2D channel and power allocation as a two-level combinatorial auction game. Channel allocation and power control are played jointly to improve user energy efficiency.

III. COMBINATORIAL RESOURCE AUCTION

  • The proposed game jointly plays channel allocation and power control to maximize user energy efficiency.The two levels correspond to channel allocation and power control.Source: §III · p. 3
  • D2D pairs act as bidders, while the eNB sells channels to packages of pairs and maximizes the sum of channel users’ utilities.Multiple D2D pairs may share one channel, forming combinatorial bidders.Source: §III · p. 3
  • On each channel, co-channel UEs compete through power control to maximize their individual utilities until an equilibrium is reached.Source: §III · p. 3

A. Channel Allocation Level

The channel-allocation level groups D2D pairs into packages and allocates channels through an iterative auction. For each package, co-channel UEs play a power-control game using best responses.

A. Channel Allocation Level

  • Each channel’s package comprises a subset of D2D pairs, and the auction maximizes combined utility subject to allocation constraints.The constraints prevent a D2D pair from appearing in multiple packages and ensure each pair receives one channel.Source: A. Channel Allocation Level · pp. 3–4
  • The multi-round auction assigns channels by highest utility-gain bids, then adjusts packages by moving pairs when doing so increases utility.Each D2D pair can be adjusted only once.Source: A. Channel Allocation Level · p. 4

B. Power Control Level

  • For each bidder-package evaluation, co-channel UEs choose transmit powers to maximize their own utilities, using best responses to other players’ powers.Each player’s power is bounded by its maximum transmit power.Source: B. Power Control Level · p. 4
  • The power-control game has an equilibrium and has a unique equilibrium under the stated condition; iterative best responses are used to find it.The iteration updates powers until the changes are below a tolerance.Source: B. Power Control Level · p. 4

C. Overall mechanism

The overall mechanism nests iterative power control within channel allocation. Its analysis covers convergence, finite termination, computational complexity, signaling, and system-performance factors.

C. Overall mechanism

  • The overall algorithm runs the power-control game at each channel-allocation step to calculate powers and utilities.The same iterative power-control method is used when packages are adjusted.Source: C. Overall mechanism · p. 4, §IV · p. 5

IV. ANALYSIS OF THE CA ALGORITHM

  • The analysis considers algorithm complexity and signaling overhead, as well as how UE count and maximum D2D distance affect system performance.Source: §IV · p. 4

A. Convergence and Computational Complexity

  • The power-control iteration converges linearly to the unique Nash equilibrium.The proof uses an increasing power sequence bounded by the maximum transmit power.Source: A. Convergence and Computational… · p. 5
  • The channel-and-power allocation algorithm terminates in finite time because package utility is nondecreasing during adjustments over finitely many combinations.Source: A. Convergence and Computational… · p. 5
  • O(KD^2) is the proposed algorithm’s complexity, compared with O(KD) for the greedy heuristic, which the paper says performs worse.The proposed algorithm has higher complexity but much better performance than the greedy heuristic.Source: A. Convergence and Computational… · p. 5

B. Signaling Overhead

The scheme uses existing UE-to-eNB CSI without additional signaling overhead, but needs additional D2D-related CSI. Iterations run at the eNB, and adapting to large-scale channel variations is left for future work.

B. Signaling Overhead

  • UE-to-eNB CSI requires no additional signaling overhead compared with proportional fairness and maximum carrier-to-interference schemes.Source: B. Signaling Overhead · p. 5
  • The scheme additionally requires CSI between D2D and cellular UEs and between the UEs in each D2D pair, estimated from detection signals and reported to the eNB.Source: B. Signaling Overhead · p. 5
  • The iterations run at the eNB without network signaling until control-signal forwarding; channel adaptation for large-scale variation is future work.The paper focuses on near-optimal solutions.Source: B. Signaling Overhead · p. 6

C. Number of UEs

Adding D2D pairs while the number of cellular UEs stays fixed lowers cellular-UE utilities. D2D-pair average performance remains nearly unchanged as pair count grows, while adding channels improves it.

C. Number of UEs

  • With cellular-UE count fixed, cellular-UE utilities decrease as the number of D2D pairs grows.The section attributes this to the interference from the additional D2D pair.Source: C. Number of UEs · p. 6
  • A new D2D pair entering a channel makes every UE on that channel worse off.The proof treats the entrant's interference as increased noise and shows equilibrium utility decreases with noise.Source: C. Number of UEs · p. 6
  • D2D-pair average performance stays nearly the same as pair count grows, but improves when the number of channels increases.A departing D2D pair also leaves the remaining players in its package better off.Source: C. Number of UEs · p. 6

D. Maximum D2D Communication Distance

The maximum D2D communication distance affects the power needed to maintain a direct link. The paper also notes that cumulative-utility penalties can incorporate fairness, while its focus is energy efficiency.

D. Maximum D2D Communication Distance

  • Larger distance between D2D UEs increases optimal transmit power to overcome signal attenuation.The paper links the distance threshold to direct-link decisions and notes that greater transmit power can cause more interference to cellular communication.Source: D. Maximum D2D Communication Distance · p. 6

E. Fairness

  • A cumulative-utility penalty can be added to the utility function to address D2D-user fairness; this paper focuses on energy efficiency.The penalty approach was proposed in and can be incorporated into the algorithm.Source: E. Fairness · p. 6

V. SIMULATION RESULTS

The simulations show that the proposed algorithm improves system sum rate over the greedy heuristic, while D2D users outperform cellular users on per-UE measures. More channels improve expected data for both user types, and the power-control algorithm converges in six iterations in the illustrated realization.

V. SIMULATION RESULTS

  • The simulation evaluates a single circular cell during uplink, averaging results over 1,000 realizations with uniformly distributed UEs and D2D pairs close enough to meet the D2D distance requirement.The channel coefficients are independent complex Gaussian, and free-space propagation path loss is used.Source: §V · pp. 6–7

A. Convergence

  • In the illustrated realization, transmit power converges to equilibrium in six iterations with a 1 mW stopping parameter; a larger parameter speeds convergence but increases error.The example has one cellular UE and two D2D pairs sharing a channel.Source: A. Convergence · p. 7, Figure 2 · p. 7

B. Performance of Different Algorithms

  • With six D2D pairs, the proposed algorithm’s system sum-rate advantage over the greedy heuristic is about 10%; fixed-power CA has higher sum rate but consumes more power.The proposed algorithm and greedy heuristic consume about the same energy because they use the same power-control scheme.Source: Figure 3 · p. 7, Figure 4 · p. 7, B. Performance of Different Algorithms · p. 8
  • D2D UEs achieve about 150% more expected data, 100% higher average rates, and 25% longer battery lifetime than cellular UEs.As D2D pairs enter, per-D2D-UE performance nearly holds steady while cellular-UE performance degrades rapidly, attributed to interference from the new pairs.Source: Figure 5 · p. 7, B. Performance of Different Algorithms · p. 8, Figure 6 · p. 8
  • As channels increase, expected data rises for cellular and D2D UEs, with a more significant improvement for cellular UEs; continued increases are expected to have little further effect.The simulations fix four D2D pairs and set the number of cellular UEs equal to the number of channels.Source: B. Performance of Different Algorithms · p. 8, Figure 8 · p. 8

C. Performance with Different D2D Distances

The distance analysis shows that increasing the maximum D2D distance reduces expected data and battery lifetime, while limiting distance improves both at the cost of fewer UEs using D2D mode. The conclusion reports that the proposed algorithm outperforms the greedy heuristic and fixed-power algorithm on expected data, lifetime, and data rate.

C. Performance with Different D2D Distances

  • Expected data per D2D UE falls about 40% for each 0.1-cell-radius increase in the maximum D2D distance.Fig. 9 presents expected data per UE across maximum D2D distances.Source: C. Performance with Different D2D… · p. 8, Figure 9 · p. 9
  • At about 0.8 cell radius, D2D expected data matches cellular UEs under the proposed algorithm, compared with about 0.6 for the greedy heuristic.The analysis relates the decline to D2D pairs losing the benefit of proximity as their separation grows.Source: C. Performance with Different D2D… · p. 9
  • D2D UE battery lifetime shortens by 2.5 hours per 0.1-cell-radius increase, and falls below cellular UE lifetime beyond about 0.8 cell radius.The passage attributes the reduction to greater transmit power needed to maintain quality of service over longer distances.Source: C. Performance with Different D2D… · p. 9
  • Limiting maximum D2D distance improves battery lifetime and expected data, but reduces the number of UEs able to use D2D mode.The maximum distance should be designed to balance these effects and generally should allow D2D performance to exceed cellular performance.Source: C. Performance with Different D2D… · p. 9

VI. CONCLUSION

  • The proposed algorithm outperforms the greedy heuristic and fixed-power algorithm on expected data, lifetime, and data rate, and improves system energy efficiency over pure cellular operation.The conclusion also reports that the number of D2D pairs and maximum D2D distance negatively affect individual UE performance.Source: §VI · p. 9

APPENDIX A PROOF OF BEST RESPONSE

The proof derives each player's best response by locating a unique stationary point of its utility and accounting for the feasible power bound.

APPENDIX A PROOF OF BEST RESPONSE

  • For fixed other-player powers, the best response is the smaller of the unique positive root of f_i and the maximum feasible power.The proof uses the derivative of utility with respect to p_i and shows that f_i decreases from a positive value to negative values, yielding the unique root.Source: Appendix A · p. 9

APPENDIX B PROOF OF EXISTENCE OF NASH EQUILIBRIUM

The existence proof establishes that each player's feasible power set is compact and convex and that utility is continuous and quasi-concave in that player's power.

APPENDIX B PROOF OF EXISTENCE OF NASH EQUILIBRIUM

  • A Nash equilibrium exists because each player's power set is nonempty, compact, and convex, while utility is continuous and quasi-concave in own power.The proof checks quasi-concavity by considering whether the feasible powers lie below, above, or across the utility's peak.Source: Appendix B · p. 10

APPENDIX C PROOF OF UNIQUENESS OF NASH EQUILIBRIUM

The uniqueness proof uses a standard best-response function and analyzes how each player's optimal power changes with interference and channel quality.

APPENDIX C PROOF OF UNIQUENESS OF NASH EQUILIBRIUM

  • The uniqueness argument invokes the standard-function condition that scaling powers by μ > 1 yields μb(p) > b(μp).The proof reduces this condition to showing f′_i(μp̃_i) < 0 and gives p_0p̃_i + (I_i − σ²)/g_ii > 0 as a sufficient condition.Source: Appendix C · p. 10
  • The best response increases with other players' transmit powers and decreases with better channel quality.The proof derives these monotonicities for the unconstrained optimum and applies the maximum-power cap to obtain the best response.Source: Appendix C · p. 10
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