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Power Efficient Resource Allocation for Full-Duplex Radio Distributed Antenna Networks

Derrick Wing Kwan Ng, Yongpeng Wu, Robert Schober

arXiv:1502.02134v1cs.ITmath.IT

TL;DR

Resource allocation in distributed full-duplex networks must account for antenna circuit power and uplink/downlink QoS. The paper proposes optimal and polynomial-time suboptimal algorithms; simulations report convergence to the optimum and close-to-optimal suboptimal performance.

  • Problem

    Resource allocation for distributed antenna networks must account for base-station antenna circuit power while meeting uplink and downlink QoS requirements.

    Source: §I · p. 4

  • Method

    The paper develops a generalized Bender’s decomposition algorithm for an optimal solution and a polynomial-time suboptimal algorithm based on difference-of-convex programming.

    Source: §I · p. 4

  • Results

    The optimal algorithm converges to the optimal solution in less than 350 iterations, while the suboptimal algorithm converges to a local optimal value in less than 20 iterations.

    Source: A. Convergence and Computational… · p. 21

  • Takeaways & Limitations

    The suboptimal algorithm approaches optimal performance in a small number of iterations, balancing computational complexity and optimality.

    Source: §I · p. 4, §VI · p. 25

Abstract

from arXiv · show

In this paper, we study the resource allocation algorithm design for distributed antenna multiuser networks with full-duplex (FD) radio base stations (BSs) which enable simultaneous uplink and downlink communications. The considered resource allocation algorithm design is formulated as an optimization problem taking into account the antenna circuit power consumption of the BSs and the quality of service (QoS) requirements of both uplink and downlink users. We minimize the total network power consumption by jointly optimizing the downlink beamformer, the uplink transmit power, and the antenna selection. To overcome the intractability of the resulting problem, we reformulate it as an optimization problem with decoupled binary selection variables and non-convex constraints. The reformulated problem facilitates the design of an iterative resource allocation algorithm which obtains an optimal solution based on the generalized Bender's decomposition (GBD) and serves as a benchmark scheme. Furthermore, to strike a balance between computational complexity and system performance, a suboptimal algorithm with polynomial time complexity is proposed. Simulation results illustrate that the proposed GBD based iterative algorithm converges to the global optimal solution and the suboptimal algorithm achieves a close-to-optimal performance. Our results also demonstrate the trade-off between power efficiency and the number of active transmit antennas when the circuit power consumption is taken into account. In particular, activating an exceedingly large number of antennas may not be a power efficient solution for reducing the total system power consumption. In addition, our results reveal that FD systems facilitate significant power savings compared to traditional half-duplex systems, despite the non-negligible self-interference.

I. INTRODUCTION

The paper targets power-efficient resource allocation in distributed full-duplex networks, where antenna-circuit power, uplink/downlink QoS, and coupled transmission powers complicate design. It models a central processor coordinating full-duplex base stations and users, with residual self-interference represented in the channel model.

I. INTRODUCTION

  • Distributed antennas can mitigate path loss and shadowing, but their circuit power becomes non-negligible as antenna counts grow and is often omitted from power-efficient network design.The paper also identifies antenna switching as a potential source of additional savings when service loads vary.Source: §I · pp. 2–3
  • The paper jointly optimizes downlink beamforming, uplink transmit power, and antenna selection to minimize network power while meeting both uplink and downlink QoS requirements.Its proposed approaches include an optimal iterative algorithm and a polynomial-time suboptimal scheme.Source: §I · p. 4

A. Notation

  • The notation section defines matrix operations and sets, including Hermitian transpose, trace, rank, and positive semidefiniteness.It also specifies complex Gaussian notation and the gradient operator.Source: A. Notation · p. 4

B. System Model

  • The network has a central processor connected by backhaul to L full-duplex base stations, each with multiple antennas, and single-antenna half-duplex users scheduled for simultaneous uplink and downlink transmission.The central processor has full network channel-state information and coordinates resource allocation.Source: B. System Model · pp. 4–5

C. Channel Model

  • Residual self-interference after cancellation is modeled as a channel matrix between the base stations’ downlink transmit and uplink receive antennas.The model assumes frequency-flat fading, interpretable as one OFDM subcarrier.Source: C. Channel Model · pp. 5–6

D. Network Power Consumption Model

The network power model includes antenna circuit consumption alongside transmission-related power, while the problem formulation uses uplink and downlink achievable rates to represent QoS. Uplink decoding uses a linear receiver with maximum ratio combining.

D. Network Power Consumption Model

  • The power model combines a static network term with dynamic terms, including active/idle antenna consumption and power-amplifier consumption.An antenna is active when serving at least one user, and active-mode signal-processing power exceeds idle-mode power.Source: D. Network Power Consumption Model · p. 7

III. PROBLEM FORMULATION

  • The paper first introduces QoS metrics for the considered FD radio communication network, then formulates resource-allocation algorithm design as a non-convex optimization problem.Source: §III · p. 7

A. Achievable Data Rate

  • Uplink data rate is evaluated using a linear receive beamformer, with maximum ratio combining adopted for decoding.The paper states that zero-forcing and MMSE beamforming are not considered because they do not facilitate efficient resource-allocation design in this network.Source: A. Achievable Data Rate · p. 8

B. Optimization Problem Formulation

The optimization minimizes total network power subject to simultaneous uplink and downlink QoS and antenna-selection constraints. Its mixed binary and non-convex structure motivates iterative optimal and polynomial-time suboptimal solution approaches.

B. Optimization Problem Formulation

  • The objective is to minimize total network power while meeting QoS requirements for uplink and downlink users simultaneously.The required receive SINRs define successful decoding targets for both link directions.Source: B. Optimization Problem Formulation · p. 9
  • Per-antenna downlink radiated-power limits and uplink transmit-power bounds accompany the QoS constraints.The formulation also constrains antenna-state variables to be binary.Source: B. Optimization Problem Formulation · p. 9
  • The design optimizes antenna states as well as uplink and downlink transmit powers to reduce network power.Adaptive switching is expected to help when QoS requirements are not stringent or user counts are low.Source: B. Optimization Problem Formulation · p. 9

IV. RESOURCE ALLOCATION ALGORITHM DESIGN

  • The problem is mixed non-convex and combinatorial because binary antenna-selection variables are coupled with beamforming and uplink-power variables, while a downlink constraint is non-convex.These features make the original optimization difficult to solve directly.Source: §IV · p. 9
  • The optimal approach reformulates the problem and applies generalized Bender’s decomposition to obtain a global optimum.The reformulation retains non-convex constraints while separating the binary selection variables.Source: §IV · pp. 9–10
  • A polynomial-time suboptimal resource-allocation algorithm is also proposed using difference-of-convex programming.It finds a local optimal solution to the considered optimization problem.Source: §IV · p. 10

C2: P U

The reformulation introduces auxiliary variables to represent products involving binary antenna-selection variables. A big-M formulation makes the affected constraint affine in new variables, while the remaining non-convexities are handled separately.

C2: P U

  • Auxiliary continuous variables q_m,n represent products of binary antenna-selection variables and are binary-valued when the selection variables are binary.Constraints C8–C10 enforce this relationship.Source: C2: P U · p. 10
  • Even after introducing q_m,n, constraint C2 remains non-convex because it contains products of q_m,n with uplink power variables.These products obstruct computationally efficient resource allocation.Source: C2: P U · p. 10

C13: ˜P U

  • The big-M formulation replaces products involving q_m,n and uplink powers or downlink beamforming with auxiliary variables, making the reformulated C2 constraint affine.The original and reformulated constraints are equivalent when the stated binary and big-M constraints hold.Source: C13: ˜P U · p. 11
  • Uplink-downlink duality cannot be applied because the transmit powers are coupled in constraints C1 and C2 and each transceiver’s powers are constrained.Source: C13: ˜P U · pp. 11–12

B. Optimal Iterative Resource Allocation Algorithm

The optimal iterative algorithm uses generalized Bender’s decomposition (GBD) to handle binary antenna-selection variables by alternating a continuous primal problem with a mixed-integer master problem. An SDP relaxation and feasibility cuts support the iteration toward an optimal solution.

B. Optimal Iterative Resource Allocation Algorithm

  • GBD alternates a continuous primal problem, which supplies an upper bound, with a mixed integer linear program (MILP) master problem, which supplies a lower bound.The problems are solved iteratively until their solutions converge.Source: B. Optimal Iterative Resource… · p. 12
  • For a fixed antenna-selection vector, the primal problem optimizes continuous variables, while the master problem handles the binary-only constraint.The master problem uses optimality and feasibility cuts to reduce the search region.Source: 1) Solution of the primal problem in… · p. 12, 2) Solution of the master problem in… · p. 15
  • Removing the downlink beamformer rank constraint yields a convex SDP; when its solution is rank one for every user, the relaxation preserves the original problem’s optimum.With statistically independent downlink channel vectors, the relaxed solution is rank one with probability one.Source: 1) Solution of the primal problem in… · pp. 12, 14
  • When the primal problem is infeasible for a selection, an l1-minimization problem measures constraint violations and supplies inputs for a feasibility cut.The violation-minimization problem is an SDP solvable by interior-point methods.Source: 1) Solution of the primal problem in… · pp. 14–15
  • The master problem becomes an MILP using the prior primal and violation-problem solutions, and its lower bound is monotonically non-decreasing across iterations.The cited passage states that standard MILP solvers can solve the master problem.Source: 2) Solution of the master problem in… · p. 16

3) Overall algorithm:

The algorithm repeatedly solves a primal problem for the current antenna selection and then updates the selection through a master problem. Feasible and infeasible primal outcomes provide different cuts, and the algorithm stops when its upper and lower bounds are sufficiently close.

3) Overall algorithm:

  • The algorithm initializes all binary antenna-selection variables to one and solves the primal problem using SDP relaxation in each iteration.For feasible selections, it records a resource-allocation policy and multiplier set for an optimality cut.Source: 3) Overall algorithm · pp. 16–17
  • For infeasible selections, the algorithm solves an l1-minimization problem and uses its policy and multipliers to generate an infeasibility cut.Only feasible primal solutions update the upper bound.Source: 3) Overall algorithm · p. 17
  • The algorithm solves the master MILP using accumulated feasible and infeasible solutions and stops when the upper–lower bound gap falls below a predefined threshold.When both problems can be solved each iteration, the algorithm is guaranteed to converge to the optimal solution.Source: 3) Overall algorithm · p. 17

C. Suboptimal Resource Allocation Algorithm Design

The suboptimal design replaces the nonpolynomial-time MILP master problem with a polynomial-time approach based on difference-of-convex optimization. It relaxes binary antenna selections to continuous values and penalizes nonbinary solutions.

C. Suboptimal Resource Allocation Algorithm Design

1) Problem reformulation via difference of convex functions programming:

  • The reformulation allows selection variables to range from zero to one and expresses the remaining binary-selection condition as a difference of convex functions.The feasible set is convex apart from this reverse-convex constraint.Source: 1) Problem reformulation via… · pp. 17–18
  • A large penalty factor penalizes selection values that are not zero or one, making the reformulated problem equivalent to the original in optimal policy and objective value.The problem is then in canonical difference-of-convex form, for which successive convex approximation yields a local optimum.Source: 1) Problem reformulation via… · p. 18

2) Suboptimal iterative algorithm:

The suboptimal iterative algorithm successively solves convex upper-bound problems and converges to a local optimum with polynomial time complexity. Simulations report faster convergence for the suboptimal method and lower computational complexity than brute force, particularly as antenna counts grow.

2) Suboptimal iterative algorithm:

  • The suboptimal algorithm converges to a local optimal solution with polynomial time computational complexity.For a given solution accuracy, the paper gives an interior-point complexity expression in terms of the total number of transmit antennas, NTL.Source: 2) Suboptimal iterative algorithm · p. 19

V. SIMULATION RESULTS

  • The reported simulations assume 50 dB of self-interference cancellation at FD base stations and 30 dBm circuit power consumption per antenna.The default network has 60 antennas across three FD base stations.Source: §V · p. 20
  • Figure 2 shows convergence of the proposed iterative algorithms.Source: Figure 2 · p. 21

A. Convergence and Computational Complexity of the Proposed Iterative Algorithms

The optimal algorithm reaches its solution in fewer than 350 iterations, while the suboptimal algorithm converges locally in fewer than 20. The proposed algorithms reduce power relative to baseline systems, though antenna-circuit costs make activating every antenna potentially inefficient.

A. Convergence and Computational Complexity of the Proposed Iterative Algorithms

  • With KU = 2 uplink users, the proposed optimal algorithm converges in fewer than 350 iterations, where upper and lower bounds meet; the suboptimal algorithm reaches a local optimal value in fewer than 20.Source: A. Convergence and Computational… · p. 21
  • The suboptimal algorithm has significantly lower computational complexity than brute force, especially as the number of antennas grows.The comparison uses 20 iterations and solution accuracy ǫ = 0.1; in the worst case, the optimal algorithm may have brute-force complexity, though this seldom occurs in practice.Source: A. Convergence and Computational… · p. 21

B. Average Total System Power Consumption

  • The proposed algorithms provide significant power savings over baseline architectures, while the suboptimal algorithm performs practically the same as the optimal one in the considered scenario.The comparisons include baselines that activate all available antennas and half-duplex systems.Source: B. Average Total System Power… · p. 22
  • When system load is relatively small, an extra antenna’s circuit power can outweigh its transmission-power reduction, so activating all antennas may increase total power.As downlink SINR requirements rise, the proposed algorithms activate more antennas, and their gap from baseline system 1 diminishes.Source: B. Average Total System Power… · p. 22
  • Half-duplex baselines require substantially more power at stringent downlink SINRs, while distributed antennas provide spatial diversity that supports savings over centralized antenna systems.The paper attributes the half-duplex power burden to compensating for spectral-efficiency loss and the distributed-antenna savings to shorter transmitter–receiver distances.Source: B. Average Total System Power… · p. 23
  • Average total system power increases as the number of downlink users grows, and both proposed algorithms outperform all baseline schemes.More users impose additional QoS constraints and reduce the feasible solution set.Source: B. Average Total System Power… · p. 23

C. Average Number of Activated Antennas

The simulations show that antenna activation balances circuit power against transmit-power savings, while the conclusion reports that dynamic antenna switching can substantially reduce power and the suboptimal algorithm approaches optimal performance.

C. Average Number of Activated Antennas

  • More stringent downlink SINR requirements lead to more activated antennas, whose added spatial degrees of freedom can reduce downlink transmit power and, in turn, self-interference and uplink transmit power.Source: C. Average Number of Activated Antennas · p. 24
  • With more downlink users, the schemes activate more antennas; the added spatial degrees of freedom help reduce power because increased co-channel interference cannot be suppressed simply by raising every user's transmit power.Source: C. Average Number of Activated Antennas · p. 24
  • When active-antenna circuit power is high, the BSs become more conservative about antenna activation; they favor more antennas when circuit power is low or downlink SINR demands are high.Source: C. Average Number of Activated Antennas · p. 25

VI. CONCLUSIONS

  • The suboptimal algorithm approaches optimal performance in a small number of iterations, while dynamically switching off antennas yields substantial power savings; excess active antennas may be inefficient when QoS is not stringent.Source: §VI · p. 25

APPENDIX

The appendix proves structural properties of the relaxed optimization problem and relates solutions of its master problem to those of the original formulation.

A. Proof of Theorem 1

B. Proof of Proposition 1

  • The constructed Θ(t) also solves the master-problem minimization for the t-th constraint, and the same approach establishes the stated solution equivalence for problems (23) and (26).Source: B. Proof of Proposition 1 · p. 27

C. Proof of Theorem 2

The proof of Theorem 2 uses Lagrangian duality and a case analysis to establish the stated result.

C. Proof of Theorem 2

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