PaperlayerView exact revision on arXiv

Source-linked AI summary

Information and Energy Cooperation in Cognitive Radio Networks

Gan Zheng, Zuleita Ho, Eduard A. Jorswieck, Bjorn Ottersten

arXiv:1403.5648v1cs.IT

TL;DR

Existing cognitive radio cooperation is often limited to information exchange, leaving energy-constrained secondary transmitters unable to assist despite favorable channels. This paper studies joint information and energy cooperation through ideal, power-splitting, and time-splitting schemes, finding substantial gains and usually larger rate regions for power splitting when transfer efficiency is sufficiently high.

  • Problem

    Existing cooperation often operates only at the information level, so an energy-constrained secondary transmitter may be unable to relay even with good channel quality to the primary receiver.

  • Method

    The paper studies ideal cooperation plus practical power-splitting and time-splitting information-and-energy transfer protocols, deriving optimal and low-complexity solutions.

  • Results

    The proposed energy-cooperation schemes provide substantial performance gains, and power splitting usually supports a larger rate region than time splitting when energy-transfer efficiency is sufficiently high.

  • Takeaways & Limitations

    Providing energy alongside spectrum access creates stronger incentives for primary-secondary cooperation and improves overall spectrum utilization.

Abstract

from arXiv · show

Cooperation between the primary and secondary systems can improve the spectrum efficiency in cognitive radio networks. The key idea is that the secondary system helps to boost the primary system's performance by relaying and in return the primary system provides more opportunities for the secondary system to access the spectrum. In contrast to most of existing works that only consider information cooperation, this paper studies joint information and energy cooperation between the two systems, i.e., the primary transmitter sends information for relaying and feeds the secondary system with energy as well. This is particularly useful when the secondary transmitter has good channel quality to the primary receiver but is energy constrained. We propose and study three schemes that enable this cooperation. Firstly, we assume there exists an ideal backhaul between the two systems for information and energy transfer. We then consider two wireless information and energy transfer schemes from the primary transmitter to the secondary transmitter using power splitting and time splitting energy harvesting techniques, respectively. For each scheme, the optimal and zero-forcing solutions are derived. Simulation results demonstrate promising performance gain for both systems due to the additional energy cooperation. It is also revealed that the power splitting scheme can achieve larger rate region than the time splitting scheme when the efficiency of the energy transfer is sufficiently large.

I. INTRODUCTION

The paper extends cooperative cognitive radio networks from information-only cooperation to joint information and energy cooperation, addressing cases where the secondary transmitter can assist the primary receiver but lacks energy. It proposes ideal, power-splitting, and time-splitting schemes, with optimization and low-complexity solutions for beamforming and energy transfer.

  • Motivation: Existing cooperative cognitive radio networks let the secondary transmitter relay primary traffic in exchange for spectrum access, improving outcomes for both systems.Unlike interweave access and underlay schemes, cooperation focuses on end performance and need not restrict the secondary transmitter to low power.
  • Motivation: Most existing work assumes information-only cooperation, leaving cooperation infeasible when the secondary transmitter has a useful primary-receiver channel but insufficient energy.The paper addresses this limitation by adding energy transfer from the primary transmitter to the secondary transmitter.
  • Contribution: The paper proposes two-level cooperation: the primary transmitter sends information for relaying and energy that powers secondary relaying and secondary-user transmission.The secondary transmitter is modeled with multiple antennas and optimized beamforming subject to primary-rate and secondary-power constraints.
  • Contribution: Three schemes are studied: ideal cooperation, power splitting, and time splitting for joint information and energy transfer.The wireless schemes divide received resources between information decoding and energy harvesting, while the ideal scheme assumes non-causal information and shared transmit power.
  • Contribution: The study derives optimal algorithms and zero-forcing solutions for each scheme to characterize achievable primary-secondary rate regions and parameter effects.The system includes a multi-antenna secondary transmitter, harvested energy from the primary transmitter, and equal total energy across schemes for fairness.

III. IDEAL PRIMARY-COGNITIVE COOPERATION

The ideal cooperation scheme gives the secondary transmitter non-causal primary information and transferred energy through reliable backhauling, enabling joint primary relaying and secondary transmission. Its optimization is characterized through feasibility conditions, convex reformulation, and a lower-dimensional nonconvex search.

  • Ideal cooperation: The secondary transmitter non-causally knows the primary message, uses dirty paper coding, and superimposes its own signal without introducing primary interference at the secondary user.The primary transmitter and secondary transmitter cooperate through an ideal information and energy backhaul.
  • Ideal cooperation: Transferred energy ηβPp increases the secondary transmitter’s available power to Ps0 + ηβPp for serving both primary and secondary users.Here βPp is the transferred energy amount and η is the energy-transfer efficiency.
  • Problem formulation: The optimization maximizes the secondary-user rate subject to primary-user rate and secondary-transmitter power constraints.The formulation explicitly balances secondary performance against primary quality of service and available transmit power.
  • Feasibility: The problem is feasible only when the primary rate requirement does not exceed the derived feasibility bound; in some settings, no energy transfer is needed.No transfer may be needed when primary power is limited, secondary power is abundant, or transfer efficiency is too low.
  • Convex reformulation: The original optimization is recast as a convex second-order cone problem that can be solved efficiently.The reformulation is described as an SOCP.
  • Simplified characterization: At optimality, both the primary-rate and power constraints are active, yielding an equivalent nonconvex problem solved through a two-dimensional search.The active-constraint characterization provides a simplified structure despite the original problem’s convex reformulation.
  • Feasibility-region illustration: The feasibility-region illustration shows a conflict between the primary-rate and power constraints as beamforming power and transferred-energy parameters vary.Increasing beamforming power moves the relevant boundary upward while tightening the power constraint and shrinking the feasible blue region.

D. ZF Solution

The zero-forcing solution imposes no interference from the secondary transmitter to the primary user and provides a simple closed-form alternative. Its optimized channel-power point performs well in the illustrated example.

  • The zero-forcing design imposes a zero-interference constraint from the ST to the PU.
  • The optimization maximizes the secondary-channel gain subject to the power and cooperation constraints.
  • The feasible channel-power region reflects a conflict between the primary and secondary constraints as qp and β vary.
  • The optimal β depends on primary-channel strength, primary power, energy-transfer efficiency, and the ST–PU channel quality.
  • The ZF solution is simple and performs quite well in the illustrated channel-power comparison.

IV. POWER SPLITTING COOPERATION – SYSTEM MODEL AND OPTIMIZATION

The power-splitting protocol lets the secondary transmitter both amplify-forward the primary signal and harvest energy, then jointly optimizes splitting and beamforming under rate and power constraints.

  • System model: The ST listens to the PT through the channel g, then forwards the primary signal to the PU.
  • System model: Power splitting divides the received RF signal between AF forwarding and energy harvesting with power fractions ρ and 1 −ρ.
  • System model: Harvested energy increases the ST’s available transmit power by η(1 −ρ)(2Pp∥g∥2 + N0).
  • System model: The ST superimposes the relaying signal with its own data and transmits both using cognitive beamforming.
  • Optimization: The optimization jointly selects ρ, the cognitive beamformer ws, and the forwarding beamformer wp to maximize SU rate under PU-rate and ST-power constraints.

B. Feasibility Check

Feasibility is checked by maximizing the achievable PU rate over the power-splitting parameter. The resulting unique optimizer defines the maximum feasible PU rate, while lower target rates remain admissible.

  • Feasibility is assessed by finding the maximum PU rate, equivalently by optimizing over ρ.
  • The power-splitting problem has a unique closed-form optimizer ρ∗ corresponding to the maximum PU rate R∗P.
  • Any PU target rate smaller than R∗P can be used when solving the SU-rate optimization problem.

C. The Optimal Solution

The optimal power-splitting solution uses duality and one-dimensional optimization, while the closed-form ZF alternative provides a simpler benchmark. In the illustrated case, the optimal solution substantially outperforms ZF.

  • Optimal solution: For a feasible problem, the optimal solution is obtained by reducing the design to a one-dimensional optimization over ρ.
  • Optimal solution: Lemma 1 characterizes the optimal objective through a uniquely determined equation set involving dual variables λ1 and λ2.
  • Optimal solution: Given ρ, the dual variables identify the optimal cognitive and forwarding beamformers ws and wp.
  • ZF solution: The ZF alternative removes interference between primary and secondary transmissions and yields a closed-form design.
  • Parameter effects: The optimal splitting behavior changes with system parameters: stronger primary power or channels permit more energy transfer, whereas weak transfer efficiency or ST–PU channels favor information decoding.
  • Comparison: The optimal solution’s feasible ρ range contains the ZF range, and its SU rate is higher than double the ZF SU rate in the illustrated setting.

V. TIME SPLITTING COOPERATION – SYSTEM MODEL AND OPTIMIZATION

The time-splitting protocol reserves an initial phase for energy transfer, then uses two equal phases for primary relaying and secondary transmission. Its optimization maximizes the SU rate subject to PU-rate and ST-power constraints.

  • System model: The PT dedicates a fraction α of the frame to energy transfer, leaving two equal-duration phases for cooperation and transmission.The protocol requires 0 ≤ α ≤ 1.
  • System model: During Phase I, the PT transmits to the ST for energy harvesting and to the PU for information decoding.The harvested energy depends on the PT power and EH efficiency η.
  • System model: During Phase II, the PT sends the primary signal to the ST, which applies MRC before forwarding it with a beamforming vector.The ST receives signals at the PU and ST and processes the primary signal for forwarding.
  • System model: During Phase III, the ST superimposes the processed primary signal with its own data and transmits both toward the PU and SU.The PT remains idle in this phase.
  • Optimization: The optimization maximizes SU rate under PU-rate and ST-power constraints while imposing PT peak power Pmax.Given α and Pp1, the remaining optimization can be solved through a 2-D search over (α, Pp1).

B. ZF Solution

The zero-forcing time-splitting solution reduces the remaining design to power allocation after fixing the time and first-phase PT power variables.

  • ZF Solution: The ZF solution is derived for time splitting using the same zero-forcing principle applied to the cooperation design.The ZF constraint is imposed on the beamforming configuration.
  • ZF Solution: For fixed (α, Pp1), the power variables (qs, qp) are obtained directly, but the resulting objective lacks a closed-form solution.The optimal solution therefore uses a 2-D search over (α, Pp1).

VI. SIMULATION RESULTS

Simulations evaluate the proposed cooperation schemes under a multi-antenna wireless setting and show gains from energy cooperation for both systems. Power splitting generally outperforms time splitting when transfer efficiency is sufficiently high.

  • Simulation setup: The simulations use N = 4 ST transmit antennas, normalized noise, Pp = 20 dB, Pmax = 30 dB, and a PU requirement rp = 3 bps/Hz.The modeled setting includes short ST links and a weaker PT–PU link, with wireless sensor and WiFi–ZigBee scenarios as examples.
  • Rate regions: Energy cooperation greatly enlarges the PU-SU achievable rate region, with power splitting outperforming time splitting in the illustrated channel realization.The comparison uses Ps0 = 10 dB and energy-transfer efficiency η = 0.5; ideal cooperation provides an outer bound.
  • SU rate: Substantial SU-rate gains occur over information-only cooperation, especially at low to medium ST energy, even when η = 0.1.At high ST energy with η = 0.1, information-only cooperation approaches the practical energy-cooperation schemes.
  • PU outage: When η ≥ 0.5, power splitting and time splitting achieve PU outage probabilities below 20% and 35%, respectively.Without cooperation, outage exceeds 80% because of the weak primary channel; information-only cooperation helps mainly at high ST energy.
  • Conclusions: The paper studies ideal, power-splitting, and time-splitting information-and-energy cooperation schemes, deriving optimal and low-complexity solutions for each.It concludes that power splitting usually supports a larger rate region when energy-transfer efficiency is sufficiently high.

APPENDIX A PROOF OF PROPOSITION 1

The appendix derives the maximum PU rate and parameterizes the beamforming optimization by exploiting quadratic structure and constraint equalities.

  • PU-rate optimization: With zero SU rate and ws = 0, the maximum PU rate uses qp = Ps0 + βηPp, with β optimized from the resulting PU-rate expression.The optimum β is characterized by setting the derivative to zero and identifying a unique critical point.
  • Beamforming parameterization: The optimization objective is phase-adjusted because it depends on ws only through quadratic forms.This permits replacing the objective with its real part without changing the optimization.
  • Beamforming parameterization: The optimal direction of wp is determined by hsp and the phase of hp, leaving its power qp as the remaining variable.The appendix then reformulates the problem in terms of the beamforming power.
  • Beamforming parameterization: For the secondary beamformer, the PU-rate and ST-power constraints are active at equality, enabling a parameterization of ws.Substitution of this parameterization yields the compact optimization formulation.

APPENDIX D FEASIBILITY RANGE IN POWER-SPLITTING COOPERATION

The feasibility analysis defines auxiliary coefficients, derives an equation in ρ, and characterizes the optimal solution through its roots and coefficient signs.

  • The analysis introduces a1, b1, and c1 to rewrite the feasibility condition in a compact form.
  • Setting the derivative with respect to ρ to zero identifies the candidate optimal value ρ∗.
  • The resulting root analysis depends on the sign of A1 and distinguishes three possible cases for ρ∗.
  • When NC > η∥hsp∥2, the roots satisfy ρ1 > 0 and ρ2 < 0, yielding ρ∗ = min(ρ1, 1).
  • After obtaining ρ∗, the maximum achievable PU rate is compared with the PU rate requirement to test feasibility.

APPENDIX E FEASIBILITY RANGE OF ρ IN POWER SPLITTING

This appendix characterizes the feasible range of ρ for power-splitting cooperation by analyzing quadratic roots and comparing optimal and zero-forcing schemes.

  • A feasible solution requires the secondary transmitter to satisfy the PU rate requirement even without serving the SU.
  • The power-splitting feasibility analysis separates the cases of zero and nonzero A and examines the discriminant of the quadratic equation.
  • For a nonnegative discriminant, the feasible range is analyzed using the ordered real roots ρ̄min and ρ̄max.
  • A negative discriminant yields no feasible ρ.
  • The optimal solution has a larger feasibility region for ρ than the zero-forcing solution because C_zf > C.
Loading 1403.5648v1…