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CoMP Meets Smart Grid: A New Communication and Energy Cooperation Paradigm

Jie Xu, Rui Zhang

arXiv:1303.2870v4cs.ITmath.IT

TL;DR

Renewable generation varies across BSs, making it challenging to coordinate supply with demand. The paper jointly optimizes CoMP transmission and aggregator-mediated energy sharing; simulations report higher sum-rate than suboptimal designs without both forms of cooperation.

  • Problem

    BSs' intermittent, geographically uneven renewable generation creates a coordination challenge in matching energy supply to demand.

    Source: §I · p. 1

  • Method

    The paper jointly optimizes BS transmit powers and energy transfers through an aggregator, accounting for transfer efficiency.

    Source: §I · p. 1, A. Energy Cooperation Model · p. 4

  • Results

    With β = 1, joint communication and energy cooperation achieves the highest sum-rate; with β = 0.9, its sum-rate is close to β = 1 and exceeds the three other suboptimal schemes.

    Source: §V · p. 10

  • Takeaways & Limitations

    The simulations report that joint cooperation substantially improves downlink throughput, while energy cooperation enables efficient use of harvested energy that might otherwise be wasted.

    Source: §I · p. 2, §V · p. 11

    The analysis assumes perfect communication and energy information sharing; the authors identify errors and backhaul limits as practical concerns for future robust designs.

    Source: §VI · p. 11

Abstract

from arXiv · show

In this paper, we pursue a unified study on smart grid and coordinated multi-point (CoMP) enabled wireless communication by investigating a new joint communication and energy cooperation approach. We consider a practical CoMP system with clustered multiple-antenna base stations (BSs) cooperatively communicating with multiple single-antenna mobile terminals (MTs), where each BS is equipped with local renewable energy generators to supply power and also a smart meter to enable two-way energy flow with the grid. We propose a new energy cooperation paradigm, where a group of BSs dynamically share their renewable energy for more efficient operation via locally injecting/drawing power to/from an aggregator with a zero effective sum-energy exchanged. Under this new energy cooperation model, we consider the downlink transmission in one CoMP cluster with cooperative zero-forcing (ZF) based precoding at the BSs. We maximize the weighted sum-rate for all MTs by jointly optimizing the transmit power allocations at cooperative BSs and their exchanged energy amounts subject to a new type of power constraints featuring energy cooperation among BSs with practical loss ratios. Our new setup with BSs' energy cooperation generalizes the conventional CoMP transmit optimization under BSs' sum-power or individual-power constraints. Finally, we validate our results by simulations under various practical setups, and show that the proposed joint communication and energy cooperation scheme substantially improves the downlink throughput of CoMP systems powered by smart grid and renewable energy, as compared to other suboptimal designs without communication and/or energy cooperation.

I. INTRODUCTION

The paper combines clustered CoMP communication with aggregator-mediated sharing of renewable energy among BSs. It models the system and energy constraints, then jointly optimizes transmission and energy exchange.

I. INTRODUCTION

  • The proposed aggregator-mediated energy cooperation uses existing grid infrastructure to share renewable energy among BSs, with group injections balanced by withdrawals.The paper contrasts this approach with dedicated power lines and assumes aggregator fees are sufficiently low to ignore.Source: §I · pp. 1–2
  • The design jointly optimizes BS transmit powers and transferred energy to maximize MT weighted sum-rate under practical energy-transfer losses.The formulation generalizes CoMP optimization under sum-power or individual-power constraints; with energy cooperation, the optimum uses all BSs' available power.Source: §I · p. 2

II. SYSTEM MODEL AND PROBLEM FORMULATION

  • The model focuses on one cluster of N multi-antenna BSs serving K single-antenna MTs with narrow-band ZF precoding, requiring K ≤ MN.Perfect sharing of communication and energy information provides an upper bound; harvesting rates and channels are treated as constant within each communication slot.Source: §II · p. 3

A. Energy Cooperation Model

  • Each BS uses locally harvested and transferred energy, while the model counts transmit power but omits other BS power consumption.The authors state that non-transmission power can be incorporated by offsetting harvested energy, subject to sufficient local generation or backup supply.Source: A. Energy Cooperation Model · p. 3
  • Energy transfers use a linear loss model: the receiving BS gets β_ij e_ij, where β_ij is the transfer efficiency and the aggregator's net exchange is balanced.The model also considers β_ij = 0 for no transfer and β_ij = 1 for lossless transfer.Source: A. Energy Cooperation Model · pp. 3–4

B. Downlink Cooperative ZF Transmission

The downlink model treats the cooperating BS cluster as a multi-antenna broadcast channel and uses cooperative ZF precoding. This precoding removes intra-cluster user interference, while power allocation is designed separately.

B. Downlink Cooperative ZF Transmission

  • The cluster's N BSs form a K-user MISO broadcast channel with MN transmit antennas, and the model assumes K ≤ MN.The channel to each MT is formed by concatenating that MT's channel vectors from all BSs.Source: B. Downlink Cooperative ZF Transmission · p. 4
  • The transmitted signal for each MT is formed from its information signal and cluster-wide precoding vector, with receiver noise modeled as zero-mean AWGN.The noise may include interference from BSs outside the cluster; suitable frequency assignments can minimize inter-cluster interference.Source: B. Downlink Cooperative ZF Transmission · p. 4
  • Given the ZF precoders, the BS power constraints are rewritten in terms of the MT power allocations.These constraints are the power constraints under the energy-cooperation model.Source: B. Downlink Cooperative ZF Transmission · pp. 4–5
  • Cooperative ZF precoding makes the inter-user interference within the cluster zero.The paper separately designs ZF precoding and power allocation, while noting that the results can extend to joint design or other precoders.Source: B. Downlink Cooperative ZF Transmission · p. 5

C. Problem Formulation

The formulation jointly chooses transmit powers and inter-BS energy transfers to maximize weighted sum-rate. With practical transfer losses, the feasible power region lies between no sharing and ideal sharing.

C. Problem Formulation

  • The objective jointly optimizes MT transmit powers and inter-BS energy transfers to maximize weighted sum-rate, with larger MT weights expressing higher transmission priority.The formulation notes that weights can be designed to ensure rate fairness.Source: C. Problem Formulation · p. 5
  • No energy transfer reduces the problem to conventional MISO-BC weighted sum-rate maximization with per-BS power constraints.With ideal lossless sharing, the per-BS constraints combine into a single sum-power constraint.Source: C. Problem Formulation · p. 5
  • With practical energy-transfer losses, the feasible power region is larger than with no sharing but smaller than with ideal sharing.The two-cell figure illustrates this ordering; the paper states the corresponding multi-cell relationship as a conjecture in this discussion.Source: C. Problem Formulation · pp. 5–6
  • For two BSs with practical sharing, the feasible-region boundary needs only one transfer direction per pair to attain it.The discussion extends this boundary property to the general multi-cell case and connects it to the increasing weighted sum-rate objective.Source: C. Problem Formulation · p. 5

III. OPTIMAL SOLUTION

The paper solves the joint power-and-energy problem through its convex dual. It recovers optimal transmit powers first, then finds a feasible optimal energy-transfer plan.

III. OPTIMAL SOLUTION

  • Convexity and strong duality allow the authors to solve the primal problem equivalently through its dual.The dual search minimizes a function of the BS power-constraint multipliers.Source: §III · p. 6
  • For fixed multipliers, the Lagrangian separates into per-user power and per-pair energy-transfer subproblems.The method restricts consideration to multipliers satisfying the stated nonnegativity and pairwise inequalities so the dual function is bounded.Source: §III · p. 6
  • A subgradient-based method such as the ellipsoid method can minimize the convex, potentially nondifferentiable dual function.The paper gives subgradients in terms of harvested energy and optimal transmit power.Source: §III · p. 6
  • After finding the optimal multipliers, the corresponding per-user powers are recovered as the optimal transmit allocation.The optimal energy transfers need not be unique for those powers; any transfers satisfying the linear constraints are optimal.Source: §III · pp. 6–7
  • A linear feasibility program finds a valid energy-transfer plan, and the overall algorithm is run at a central unit with cluster CSI and energy information.The paper identifies the feasibility program as a simple LP.Source: §III · p. 7

A. Practical Implementation of Energy Cooperation

In the practical-loss case, optimal power allocations determine each BS’s net energy exchange with the aggregator. This avoids computing and signaling the individual pairwise transfers.

A. Practical Implementation of Energy Cooperation

  • For this practical-loss case, the authors derive each BS’s net power draw from or injection into the aggregator.This is the implementation quantity used in place of specifying every pairwise transfer.Source: A. Practical Implementation of Energy… · p. 7
  • When energy cooperation is feasible with 0 < βij < 1, the optimal solution has each BS power constraint met with equality.Thus, the total available energy at the BSs is used to maximize weighted sum-rate.Source: A. Practical Implementation of Energy… · p. 7
  • Once optimal transmit powers are known, each BS’s net aggregator exchange follows from its transmit-power requirement relative to its harvested energy.A deficit is drawn from the aggregator; a surplus is injected.Source: A. Practical Implementation of Energy… · p. 7
  • The BSs need only their optimal transmit powers to implement energy cooperation, so the central unit can skip the LP for individual transfers.This reduces central computation complexity and backhaul signaling overhead.Source: A. Practical Implementation of Energy… · p. 7

B. Energy Exchange Behavior of BSs

With practical transfer losses, optimal exchange has a one-way direction at each BS: it sends energy or receives it, but does not do both simultaneously.

B. Energy Exchange Behavior of BSs

  • The section examines optimal pairwise transfer amounts to provide insight into energy exchange, although exact amounts are unnecessary for implementation.The practical implementation can use each BS’s net aggregator exchange instead.Source: B. Energy Exchange Behavior of BSs · p. 7
  • Each BS either transfers energy to other BSs in its cluster or receives energy from them, but not both at once.The paper attributes this to the unnecessary energy loss from simultaneous receiving and transferring.Source: B. Energy Exchange Behavior of BSs · p. 7
  • The one-way exchange rule affirms the earlier conjecture drawn from the feasible-power-region discussion.The paper points back to its two-cell figure discussion.Source: B. Energy Exchange Behavior of BSs · p. 7

C. Comparison to No Energy Cooperation

Without energy sharing, a BS with abundant harvested energy may leave power unused while throughput is limited by BSs with less energy. Energy cooperation uses the BSs’ total available energy for weighted sum-rate maximization, despite transfer losses.

C. Comparison to No Energy Cooperation

  • With communication and energy cooperation, total energy across BSs is used to maximize weighted sum-rate, unlike conventional CoMP where abundant local energy may be wasted.Energy transfer incurs losses, but the authors identify a resulting energy-cooperation gain over conventional CoMP.Source: C. Comparison to No Energy Cooperation · p. 8

IV. SUBOPTIMAL SOLUTIONS

  • The comparison benchmarks the proposed joint scheme against suboptimal designs using only energy cooperation, only communication cooperation, or neither.These alternatives provide performance benchmarks for the proposed joint approach.Source: §IV · p. 8

A. No Energy Cooperation, Communication Cooperation Only

The no-energy-cooperation design sets inter-BS energy transfers to zero, while energy-only cooperation uses local ZF transmission and orthogonal bands. The latter can be optimized with less information overhead than joint communication and energy cooperation.

A. No Energy Cooperation, Communication Cooperation Only

  • With no energy cooperation, inter-BS transfers are disabled and Algorithm 1 solves the weighted sum-rate problem.An energy-storage device could preserve unused energy for later use, but increases cellular-system operating cost.Source: A. No Energy Cooperation,… · p. 8

B. No Communication Cooperation, Energy Cooperation Only

  • With energy cooperation only, each BS serves its associated MTs independently using ZF over orthogonal bands, while BSs may still share energy.The MT-BS association is assumed given; the caption identifies a two-cell sum-rate comparison with E1 + E2 = 30.Source: B. No Communication Cooperation,… · p. 8, Figure 4 · p. 9
  • The energy-only optimization is a special case of the joint problem and can use Algorithm 1 with locally computed channel parameters.It requires considerably less complexity and overhead than the joint problem, which requires transmit messages and CSI from all BSs.Source: B. No Communication Cooperation,… · pp. 8–9

C. No Cooperation

Simulations compare cooperation schemes in two- and three-cell settings, including a practical renewable-energy setup. Joint communication and energy cooperation outperforms the suboptimal alternatives, while the relative gains of energy and communication cooperation vary with energy availability and harvesting patterns.

C. No Cooperation

  • With neither communication nor energy cooperation, inter-BS energy transfers are zero and Algorithm 1 still solves the weighted sum-rate problem.Source: C. No Cooperation · p. 9

V. SIMULATION RESULTS

  • Joint communication and energy cooperation with β = 1 always achieves the highest sum-rate, and β = 0.9 stays close while outperforming the three suboptimal schemes; energy-only cooperation leads below E = 6 dB, but communication-only leads above it.The comparison covers low- and high-SNR regimes; β = 0.9 represents imperfect energy transfer.Source: Figure 5 · p. 9, Figure 6 · p. 9, §V · p. 10
  • Energy cooperation is most beneficial at night, when solar-dependent BS 3 has very low harvesting; its gain is smaller when daytime harvesting is more evenly distributed.Energy-only cooperation also improves on no cooperation under uneven harvesting.Source: §V · p. 11
  • In the practical three-cell setup, joint cooperation with β = 1 or β = 0.9 considerably outperforms the three suboptimal schemes at all tested values of average harvested energy.The setup uses real aggregated Belgian solar and wind generation over four days.Source: §V · pp. 10–11

VI. CONCLUDING REMARKS

The paper proposes aggregator-assisted energy cooperation and jointly optimizes energy transfers and CoMP transmission. Simulations indicate potential sum-rate gains, especially when harvested energy is unevenly distributed among base stations.

VI. CONCLUDING REMARKS

  • Simulations show potential sum-rate gains from jointly exploiting communication and energy cooperation in cellular networks.The weighted sum-rate problem uses downlink CoMP with ZF precoding and is solved for optimal transmit power allocation and energy transfer.Source: §VI · p. 11
  • The proposed approach optimizes energy transfer among cooperating base stations alongside CoMP transmit power allocation.It formulates weighted sum-rate maximization for downlink CoMP with ZF precoding and develops an efficient solution using convex optimization.Source: §VI · p. 11
  • Energy cooperation is most beneficial under a practical transfer-efficiency value when harvested energy is unevenly distributed among base stations.Source: §VI · p. 11
  • The study assumes perfectly obtained and shared communication and energy information, leaving estimation, measurement, and backhaul imperfections for robust-design study.Source: §VI · p. 11
  • The study fixes one cell cluster and user association, excludes grid energy purchases, and considers independent communication-scheduling slots rather than storage over time.The discussion identifies joint user-association or cell-clustering design, external energy trading, and integrating storage across different timescales as future problems.Source: §VI · pp. 11–12

APPENDIX A PROOF OF LEMMA 3.1

The appendix establishes conditions under which the objective is bounded and uses those conditions to prove positivity of the optimal parameters.

APPENDIX A PROOF OF LEMMA 3.1

  • If all μ_i are zero, the objective is unbounded as p_k grows; boundedness therefore requires that the μ_i are not all zero.Source: Appendix A · p. 12
  • Boundedness also requires β_ijμ_j − μ_i ≤ 0 for every distinct pair i, j; otherwise the objective grows without bound as e_ij increases.Source: Appendix A · p. 12

APPENDIX B PROOF OF PROPOSITION 3.1

  • The proof of Proposition 3.1 uses Lemma 3.1’s conditions to rule out a nonpositive optimal μ_i, concluding that every μ_i* is positive.Source: Appendix B · p. 12

APPENDIX C PROOF OF PROPOSITION 3.2

The proof of Proposition 3.2 rules out an optimal solution in which a base station both receives and sends energy, by constructing a feasible solution with a higher objective value.

APPENDIX C PROOF OF PROPOSITION 3.2

  • For a given base station i, the argument considers simultaneous positive transfers in and out of i and assumes counterpart stations j and k, each different from i, without establishing that j and k differ.Source: Appendix C · p. 12
  • The proof constructs a replacement set of energy transfers while retaining transmit powers, then uses feasibility and a larger objective to contradict optimality.Source: Appendix C · p. 12
  • An optimal solution cannot have a base station both receiving and sending energy, since a constructed feasible solution would achieve a larger objective value.Source: Appendix C · p. 12
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