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Secure and Green SWIPT in Distributed Antenna Networks with Limited Backhaul Capacity

Derrick Wing Kwan Ng, Robert Schober

arXiv:1410.3065v2cs.IT

TL;DR

The paper addresses secure information and renewable-energy transfer in distributed antenna SWIPT networks with limited backhaul and imperfect energy-receiver CSI. It formulates resource allocation as a non-convex problem, develops generalized Bender’s decomposition and a lower-complexity alternative, and reports globally optimal or close-to-optimal solutions with lower transmit power than co-located antennas.

  • Problem

    The paper asks how to minimize transmit power for secure SWIPT when backhaul capacity, renewable-energy sharing, imperfect ER CSI, and QoS requirements constrain distributed antenna networks.

  • Method

    The authors reformulate the mixed problem with binary selection and use generalized Bender’s decomposition for global optimization, plus d.c. programming for a lower-complexity locally optimal scheme.

  • Results

    The GBD-based algorithm obtains a global optimum, while the suboptimal algorithm achieves close-to-optimal performance; distributed SWIPT with renewable sharing requires less transmit power than co-located antennas.

  • Takeaways & Limitations

    Distributed antennas combined with renewable energy sharing are shown to reduce transmit-power requirements for secure SWIPT relative to centralized co-located-antenna systems.

Abstract

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This paper studies the resource allocation algorithm design for secure information and renewable green energy transfer to mobile receivers in distributed antenna communication systems. In particular, distributed remote radio heads (RRHs/antennas) are connected to a central processor (CP) via capacity-limited backhaul links to facilitate joint transmission. The RRHs and the CP are equipped with renewable energy harvesters and share their energies via a lossy micropower grid for improving the efficiency in conveying information and green energy to mobile receivers via radio frequency (RF) signals. The considered resource allocation algorithm design is formulated as a mixed non-convex and combinatorial optimization problem taking into account the limited backhaul capacity and the quality of service requirements for simultaneous wireless information and power transfer (SWIPT). We aim at minimizing the total network transmit power when only imperfect channel state information of the wireless energy harvesting receivers, which have to be powered by the wireless network, is available at the CP. In light of the intractability of the problem, we reformulate it as an optimization problem with binary selection, which facilitates the design of an iterative resource allocation algorithm to solve the problem optimally using the generalized Bender's decomposition (GBD). Furthermore, a suboptimal algorithm is proposed to strike a balance between computational complexity and system performance. Simulation results illustrate that the proposed GBD based algorithm obtains the global optimal solution and the suboptimal algorithm achieves a close-to-optimal performance. Besides, the distributed antenna network for SWIPT with renewable energy sharing is shown to require a lower transmit power compared to a traditional system with multiple co-located antennas.

I. INTRODUCTION

The paper motivates distributed antenna networks for secure SWIPT with renewable energy sharing, while addressing limited backhaul and receiver energy constraints through resource allocation.

  • Energy transfer: Wireless power transfer enables one-to-many RF charging and simultaneous wireless information and power transfer for energy-constrained mobile receivers.Unlike solar and wind sources, RF charging does not depend on receiver location or climate conditions in the same way.
  • System motivation: Distributed antenna systems use a central processor for baseband processing and remote radio heads for RF operations, connected through backhaul links.Their spatial distribution reduces transmitter–receiver distance and provides spatial diversity against path loss and shadowing.
  • System motivation: Limited backhaul capacity can make full cooperation infeasible because the central processor cannot send every user’s data to every remote radio head.Partial cooperation reduces backhaul load by sending each information stream only to selected remote radio heads.
  • Problem formulation: The paper formulates resource allocation as a non-convex problem minimizing total network transmit power under limited backhaul, renewable energy sharing, imperfect ER CSI, and secure SWIPT QoS.The proposed framework targets both secure communication and efficient wireless power transfer.
  • Algorithm design: A generalized Bender’s decomposition algorithm is proposed for optimal resource allocation, alongside a d.c.-programming scheme that provides a locally optimal solution with lower complexity.The d.c.-based method is intended as a computationally simpler alternative to the optimal iterative algorithm.

D. Channel State Information

The system models imperfect ER channel knowledge explicitly while using joint beamforming, artificial noise, and selective RRH participation to support secure transmission under backhaul constraints.

  • Channel state information: Desired IR channels are assumed perfectly known during transmission, whereas ER channels may be outdated because ERs do not interact with RRHs during information transmission.The ER uncertainty is represented deterministically rather than through a stochastic model.
  • Channel state information: Each uncertain ER channel is modeled as an estimate plus an unknown error within an ellipsoidal uncertainty region.The uncertainty radius depends on channel coherence time, while the region orientation depends on the channel estimation method.
  • Signal model: Joint beamformers combine the per-RRH beamforming vectors used by distributed RRHs to serve each information receiver.Each information stream is transmitted simultaneously to its intended receiver through a dedicated beamforming vector.
  • Signal model: Artificial noise is generated locally at the RRHs and optimized to degrade ER channels while minimally affecting IRs, without consuming backhaul capacity.Because artificial noise is unknown to both receiver types, its covariance must be carefully designed.
  • Backhaul model: Selective RRH participation lowers backhaul use by setting an RRH’s beamforming vector for an IR to zero when that RRH does not transmit the IR’s data.Backhaul consumption counts the information receivers whose data is delivered to each RRH.

F. RRH Power Supply Model

The model supplies CP and RRH operation through a controlled micropower grid that shares renewable energy while accounting for lossy delivery and RF-based information, security, and energy transfer.

  • F. RRH Power Supply Model: The CP transfers energy to RRHs through a dedicated micropower grid, while RRH harvesters add renewable energy that can also be shared.The grid is controlled by the CP and supports RRH power consumption.
  • F. RRH Power Supply Model: The system models power loss from all L + 1 energy sources when delivering energy to the L RRHs.The loss depends on the micropower-grid B-coefficient matrix and its fixed topology and loads.
  • F. RRH Power Supply Model: Each energy source can adjust the energy injected into the micropower grid up to its available generated energy.The CP power generator is treated as the (L + 1)-th energy source.
  • F. RRH Power Supply Model: The model treats renewable energy availability as constant over each resource-allocation interval because harvesting changes more slowly than channel conditions.For the stated small-cell setting, energy propagation delay is negligible relative to channel coherence time.
  • F. RRH Power Supply Model: RF signals jointly support information decoding, energy harvesting, and security constraints in the SWIPT system.Information signals serve both information and energy transfer, while artificial noise also supplies energy to ERs.
  • F. RRH Power Supply Model: Harvested RF energy is converted to stored electrical energy with common efficiency 0 < µ ≤ 1, while thermal noise and multicell interference contributions are neglected.The same efficiency is assumed for all ERs.
  • F. RRH Power Supply Model: The framework can accommodate single-user detection at potential eavesdroppers without changing the resource-allocation algorithm structure.The paper’s baseline security analysis instead uses a worst-case interference-cancellation assumption.

B. Optimization Problem Formulation

The formulation minimizes total network transmit power subject to secure communication, energy-transfer, backhaul, power-supply, and positive-semidefinite covariance constraints under imperfect CSI.

  • B. Optimization Problem Formulation: The objective minimizes total network transmit power while guaranteeing communication and power-transfer QoS for fixed maximum backhaul capacities.The optimization is posed for a given time slot.
  • B. Optimization Problem Formulation: The required SINR at each IR exceeds the tolerable ER SINR, guaranteeing a nonnegative secrecy rate under the adopted constraints.The formulation uses Γreqk ≫ Γtol > 0 and Rseck = [log2(1+Γreqk)−log2(1+Γtol)]+ ≥ 0.
  • B. Optimization Problem Formulation: Each backhaul link carries IR k’s required secrecy rate, so individual-link capacity consumption is constrained rather than only total network backhaul usage.This distinguishes the formulation from prior formulations based on aggregate backhaul capacity.
  • B. Optimization Problem Formulation: The algorithm design assumes feasibility, with MAC-layer scheduling identified as a way to improve the probability that the optimization problem is feasible.This is an operational assumption rather than a guarantee of feasibility.
  • B. Optimization Problem Formulation: The power-grid constraint compares total network consumption with maximum available grid power after line losses.The available power is represented by 1^T eS − (eS)^T B eS ≥ 0.
  • B. Optimization Problem Formulation: CP and RRH circuit powers, amplifier inefficiency, and source-supply limits are included in the power-consumption constraints.RRH transmit-power allowances additionally limit out-of-cell interference.
  • B. Optimization Problem Formulation: The formulation enforces minimum ER power transfer and nonnegative energy supplies, while requiring V to be a valid positive-semidefinite Hermitian covariance matrix.The ER guarantee assumes ERs use all received power for energy harvesting.
  • B. Optimization Problem Formulation: The baseline assumes surplus RRH renewable energy is transferred to the external grid rather than stored locally.Dynamic harvesting with RRH energy storage is described as an extensible alternative.

IV. RESOURCE ALLOCATION ALGORITHM DESIGN

The paper addresses the non-convex resource-allocation problem by binary reformulation, then combines an optimal GBD-based algorithm with a lower-complexity d.c.-programming alternative.

  • IV. RESOURCE ALLOCATION ALGORITHM DESIGN: The non-convex optimization is reformulated with binary selection variables to enable resource-allocation algorithm design.The reformulation introduces Wk = wkwHk and auxiliary variables sl,k.
  • IV. RESOURCE ALLOCATION ALGORITHM DESIGN: Binary variables indicate whether IR k’s data is conveyed to RRH l and therefore whether that backhaul link consumes the required rate.Constraints C10 and C11 force sl,k = 1 when Tr(WkRl) > 0.

B. Iterative Resource Allocation Algorithm

The iterative GBD procedure alternates continuous primal optimization and binary master optimization, using SDP relaxation, dual information, and feasibility cuts until convergence.

  • B. Iterative Resource Allocation Algorithm: For fixed binary selections, the primal problem optimizes {Wk, V, eS} and supplies an upper bound on the reformulated problem’s optimum.The master problem then uses the resulting information to update binary decisions.
  • B. Iterative Resource Allocation Algorithm: For fixed continuous variables, the master problem is a MILP whose solution supplies a lower bound, and primal-master iterations continue until convergence.This establishes the bounding mechanism used by GBD.
  • B. Iterative Resource Allocation Algorithm: The primal step converts infinitely many imperfect-CSI constraints into finite constraints before solving the relaxed optimization problem.Constraints C2 and C7 are specifically transformed for tractable resource allocation.
  • B. Iterative Resource Allocation Algorithm: Removing Rank(Wk) ≤ 1 produces a convex SDP that can be solved efficiently by standard convex-programming solvers.The reformulation retains auxiliary variables δ and ν for the transformed constraints.
  • B. Iterative Resource Allocation Algorithm: Strong duality holds for the relaxed SDP under Slater’s condition, enabling an equivalent dual formulation and recovery of primal-dual solutions.The dual variables are collected in Φ and passed to the master problem.
  • B. Iterative Resource Allocation Algorithm: Theorem 1 establishes that the SDP relaxation is tight enough to construct rank-one beamforming matrices without changing the objective value.The construction applies when an optimal relaxed beamforming matrix has rank greater than one.
  • B. Iterative Resource Allocation Algorithm: When the primal problem is infeasible for a binary assignment, an l1-minimization problem measures aggregated constraint violations and generates a feasibility cut.The cut separates the infeasible assignment from the master problem’s search space.

2) Solution of the master problem in the i-th iteration:

The master problem uses optimality and feasibility cuts generated from prior primal iterations to progressively restrict the search for the global solution. Each iteration can be formulated as a standard MILP and solved with numerical MILP solvers.

  • The master problem in iteration i uses solutions from the primal problems at feasible and infeasible prior iterations.The feasible and infeasible iteration sets are denoted by F and I, respectively.
  • Optimality and feasibility cuts form hyperplanes from prior iterations that reduce the search region for the global optimal solution.The cuts are functions of the binary selection variables in the outer minimization problem.
  • The inner minimization problems recover the corresponding primal solutions from each prior iteration.This relationship is stated in Proposition 1 for both optimality and feasibility cuts.
  • Substituting the cut expressions converts the master problem into a standard MILP solvable by Mosek or Gurobi.Its objective value is monotonically non-decreasing because each iteration adds a constraint to the master problem.

3) Overall algorithm:

The generalized Bender’s decomposition algorithm repeatedly solves the primal problem for binary selections and updates the master problem with information from feasible or infeasible iterations. It converges to the global optimum in finitely many iterations under the stated solvability conditions, but has non-polynomial complexity.

  • The algorithm initializes the iteration limit, a small stopping constant, the iteration index, and random binary selection values.It then repeatedly solves the primal problem for the current binary-variable assignment.
  • Feasible primal iterations produce an intermediate resource allocation policy, Lagrange multipliers, and an objective value for the master problem.Infeasible iterations instead contribute feasibility information to the decomposition process.
  • Finite-iteration convergence to the global optimal solution is guaranteed when the master and primal problems are solved in every iteration.The stopping criterion compares the relevant bounds against the predefined threshold κ.
  • The optimal algorithm has non-polynomial computational complexity because each iteration requires solving an MILP master problem.

C. Suboptimal Resource Allocation Algorithm Design

The suboptimal design replaces direct binary handling with a continuous relaxation and penalty-based difference-of-convex formulation. Successive convex approximation yields a polynomial-time algorithm that converges locally while retaining rank-one transmit solutions.

  • 1) Problem reformulation via difference of convex functions programming: The binary constraint is the major obstacle in solving the reformulated optimization problem.It is replaced by a continuous variable constrained between zero and one together with a difference-of-convex condition.
  • 1) Problem reformulation via difference of convex functions programming: A large penalty factor φ penalizes selection variables that differ from 0 or 1, producing a convex feasible set for the reformulated problem.The resulting formulation is treated as difference-of-convex programming.
  • 2) Iterative suboptimal algorithm: Successive convex approximation linearizes the differentiable convex function and repeatedly solves a convex upper-bound problem.The procedure continues until convergence or the maximum iteration count is reached.
  • 2) Iterative suboptimal algorithm: The suboptimal algorithm converges to a locally optimal solution with polynomial-time computational complexity.The iterative procedure generates a sequence of feasible solutions while tightening the upper bound.
  • 2) Iterative suboptimal algorithm: Rank(W_k) = 1 is guaranteed despite the adopted semidefinite-programming relaxation.The optimal algorithm instead achieves optimal system performance but has non-polynomial complexity.
  • 2) Iterative suboptimal algorithm: The suboptimal algorithm’s complexity is polynomial in K, M, L, N_TL, and its iteration count T_Iter for a given solver accuracy Δ > 0.The complexity can be further reduced using a tailor-made interior-point method and is described as desirable for real-time implementation.

V. RESULTS

The simulations evaluate the proposed algorithms in a two-tier distributed antenna network with cooperative and non-cooperative RRHs, renewable-energy profiles, imperfect ER CSI, and comparisons against cooperative and co-located antenna systems.

  • The simulated cooperative cluster contains L = 3 RRHs, K = 5 IRs, and M = 2 ERs in a heavily loaded first-tier area.The cooperative RRHs are separated by 150 meters, and multicell interference from a second tier is included.
  • RRH 4–RRH 12 are non-cooperative second-tier RRHs that serve only IRs, while the cooperative RRHs jointly serve the first-tier receivers.The second tier is used to capture multicell interference in the simulation topology.
  • The comparisons include full first-tier cooperation, full cooperation without energy cooperation, and a co-located antenna system with the same total number of transmit antennas.The co-located baseline assumes unlimited backhaul and energy supply.
  • The simulations use Γ_tol = 0 dB for ERs and normalized maximum ER channel-estimation error σ²_∥g_m∥² = 0.05 under an Euclidean-sphere uncertainty region.
  • Renewable-energy harvesting data are averaged over 15-minute intervals, giving 96 samples per 24 hours for wind and solar profiles.The profile data were obtained in Belgium on August 01, 2014.
  • The five IRs require minimum SINRs of [6, 9, 12, 15, 18] dB, respectively, and their aggregated secrecy rate is 15.5818 bit/s/Hz.

A. Convergence of the Proposed Iterative Algorithms

The proposed optimal algorithm reaches the global optimum in fewer than 80 iterations, while the suboptimal algorithm reaches a locally optimal value in fewer than 10. Increasing backhaul capacity and antenna count reduces transmit power, and distributed antennas outperform co-located antennas in the reported comparisons.

  • Convergence of the Proposed Iterative Algorithms: The optimal algorithm reaches the global solution after fewer than 80 iterations, while the suboptimal algorithm converges locally after fewer than 10 iterations.For K = 5 IRs and L = 3 cooperative RRHs, brute-force global optimization would require solving 2^15 SDPs.
  • Average Total Transmit Power: Increasing backhaul capacity per link from 10 to 15 bits/s/Hz decreases the transmit power of both proposed schemes.The reported explanation is that greater capacity enables more effective transmission.
  • Average Total Transmit Power: Transmit power decreases gradually as the total number of transmit antennas increases, because additional cooperation degrees of freedom improve resource allocation.The performance gap between the proposed optimal algorithm and fully cooperative transmission is expected to narrow with increasing antenna count.
  • Average Total Transmit Power: Fully cooperative transmission with energy cooperation has lower average transmit power but consumes exceedingly high backhaul capacity.The proposed suboptimal algorithm achieves excellent system performance with only 10 iterations.
  • Average Total Transmit Power: The co-located antenna scheme requires higher transmit power because it lacks network-type spatial diversity against path loss.The comparison is made against the two proposed distributed-antenna schemes.
  • Average Total Transmit Power: With imperfect CSI, average transmit power increases as normalized channel estimation error grows, except under perfect CSI.Greater uncertainty requires more artificial-noise power and additional information-signal power to neutralize interference at desired receivers.

C. Average Total Harvested Power

Harvested RF power decreases with more transmit antennas because additional beamforming degrees of freedom improve allocation efficiency and reduce leakage toward energy receivers. The proposed schemes support secure communication and efficient power transfer despite imperfect energy-receiver CSI, while distributed renewable-energy-sharing systems offer potential power savings over co-located antennas.

  • Average Total Harvested Power: Total harvested RF power from the proposed schemes decreases monotonically as the number of transmit antennas increases.The additional antenna degrees of freedom improve resource-allocation efficiency.
  • Average Total Harvested Power: More antennas allow beamforming to steer more accurately toward information receivers, reducing information-signal power allocation and leakage to energy receivers.This explains the lower harvested power observed for fully cooperative transmission with energy cooperation.
  • Average Total Harvested Power: Larger normalized CSI error variance requires more transmit power, producing higher RF energy levels available for harvesting.The additional power is needed to satisfy power-transfer and communication-secrecy QoS requirements.
  • Average Total Harvested Power: The proposed schemes guarantee each information receiver’s required secrecy rate despite imperfect energy-receiver CSI.The stated secrecy rate is Rseck = log2(1 + Γreqk) − log2(1 + Γtol).
  • Average Total Harvested Power: Distributed antenna SWIPT with renewable-energy sharing shows potential power savings compared with centralized systems using co-located antennas.This conclusion is reported as a simulation result of the proposed resource-allocation framework.
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