Source-linked AI summary
Wireless Information Transfer with Opportunistic Energy Harvesting
Liang Liu, Rui Zhang, Kee-Chaing Chua
TL;DR
The paper addresses unresolved trade-offs in wireless information and power transfer for energy-constrained networks. It derives receiver mode-switching rules and finds that large received signals should be directed to energy harvesting rather than information decoding.
Problem
Trade-offs in emerging wireless networks with simultaneous information and power transfer remain unknown.
Method
The paper derives an optimal receiver mode-switching rule to characterize information-transfer and harvested-energy trade-offs.
Results
Large received signals should be switched to energy harvesting rather than information decoding.
Takeaways & Limitations
The derived rule supports selecting receiver modes to achieve different trade-offs between information transfer and energy harvesting.
Takeaways & Limitations
The analysis assumes that interference lies within the same band as the transmitted signal.
Abstract
from arXiv · showhide
Energy harvesting is a promising solution to prolong the operation of energy-constrained wireless networks. In particular, scavenging energy from ambient radio signals, namely wireless energy harvesting (WEH), has recently drawn significant attention. In this paper, we consider a point-to-point wireless link over the narrowband flat-fading channel subject to time-varying co-channel interference. It is assumed that the receiver has no fixed power supplies and thus needs to replenish energy opportunistically via WEH from the unintended interference and/or the intended signal sent by the transmitter. We further assume a single-antenna receiver that can only decode information or harvest energy at any time due to the practical circuit limitation. Therefore, it is important to investigate when the receiver should switch between the two modes of information decoding (ID) and energy harvesting (EH), based on the instantaneous channel and interference condition. In this paper, we derive the optimal mode switching rule at the receiver to achieve various trade-offs between wireless information transfer and energy harvesting. Specifically, we determine the minimum transmission outage probability for delay-limited information transfer and the maximum ergodic capacity for no-delay-limited information transfer versus the maximum average energy harvested at the receiver, which are characterized by the boundary of so-called "outage-energy" region and "rate-energy" region, respectively. Moreover, for the case when the channel state information (CSI) is known at the transmitter, we investigate the joint optimization of transmit power control, information and energy transfer scheduling, and the receiver's mode switching. Our results provide useful guidelines for the efficient design of emerging wireless communication systems powered by opportunistic WEH.
I. INTRODUCTION
The paper studies opportunistic wireless energy harvesting at a receiver that must switch between information decoding and energy harvesting under varying channels and interference. It derives switching and resource-allocation policies characterizing information–energy trade-offs, with and without transmitter CSI.
- Energy harvesting from ambient radio signals is proposed as a way to prolong energy-constrained wireless-network operation.
- Practical circuit limitations motivate time switching because the receiver cannot simultaneously decode information and harvest energy from the same signal.
- The receiver opportunistically switches between ID and EH using instantaneous channel gain and interference power, exploiting their dynamics and different power sensitivities.
- The paper derives optimal switching rules that characterize outage-energy and rate-energy boundaries through outage probability or ergodic capacity versus average harvested energy.
- With CSI at the transmitter, the paper jointly optimizes transmit power control, information and energy scheduling, and receiver mode switching.
- A key allocation property is that high-power received signals should generally be assigned to EH rather than ID, consistent with the energy receiver’s poorer sensitivity.
- The paper treats interference as a potential WEH source, while noting that its fundamental role in simultaneous information-and-power transfer remains unknown.
II. SYSTEM MODEL
The system is a point-to-point single-antenna flat-fading link with time-varying co-channel interference and block-based transmissions. Receiver mode selection depends on instantaneous channel and interference conditions, while transmitter CSI enables scheduling and power control.
- The model consists of one single-antenna transmitter–receiver pair communicating over a flat-fading channel with aggregate co-channel interference.
- Channel gain and interference power are modeled as jointly distributed random variables and are constant within sufficiently short transmission blocks.
- The receiver perfectly knows the instantaneous channel gain and interference power, while additive noise is circularly symmetric complex Gaussian with variance σ2.
- CSI Unknown at Tx: Without CSIT, the transmitter continuously sends information with constant power P, and the receiver selects ID or EH from the instantaneous channel and interference.
- CSI Known at Tx: With CSIT, the transmitter schedules information, energy, or no transmission and the receiver correspondingly switches between ID and EH.
- CSI Known at Tx: With CSIT, transmit power p(ν) is optimized under either an average constraint Eν[p(ν)] ≤ Pavg or a peak constraint p(ν) ≤ Ppeak.
III. INFORMATION TRANSFER AND ENERGY HARVESTING TRADE-OFFS IN FADING CHANNELS
The paper formulates information-transfer and energy-harvesting trade-offs through outage-energy and rate-energy regions, with and without CSIT. These regions characterize achievable non-outage probability or ergodic capacity against average harvested energy under receiver-mode and, with CSIT, transmit-power decisions.
- Without CSIT, constant transmit power is used for information transfer, whereas CSIT enables truncated channel inversion or water-filling power allocation.
- The region boundaries are obtained by optimizing receiver mode switching, and with CSIT also transmit power, for each target average harvested energy.
- The outage-energy region pairs achievable non-outage probability with average harvested energy for delay-limited information transmission.
- The rate-energy region pairs achievable ergodic capacity with average harvested energy for information transmission without delay limits.
- CSIT improves both achievable outage-energy and rate-energy trade-offs.
- Each region has extreme points representing maximum information performance with minimum harvested energy and minimum information performance with maximum harvested energy.
- The optimization problems are generally nonconvex, but time-sharing yields strong duality, enabling Lagrange-duality solutions for the optimal trade-offs.
IV. OUTAGE-ENERGY TRADE-OFF
The outage-energy trade-off section studies receiver mode switching, with or without transmit power control, to balance delay-limited outage performance against average harvested energy.
- The analysis minimizes outage probability while maximizing average harvested energy for both cases without and with CSIT.
A. The Case Without CSIT: Optimal Receiver Mode Switching
Without CSIT, the receiver selects information decoding or energy harvesting separately for each fading state to characterize the outage-energy boundary. The optimal rule favors harvesting in states with sufficiently large signal-plus-interference power.
- The optimization decomposes into independent fading-state subproblems that compare the Lagrangian values of information decoding and energy harvesting.
- For a target harvested energy, the receiver partitions the nonnegative (h, I) plane into optimal ID and EH regions.
- Meeting harvested-energy targets above the minimum requires sacrificing outage performance by assigning some non-outage states to EH mode.
- The ID/EH boundary is λ* hP + λ* I = 1, so states with hP + I > 1 are assigned to EH mode.
- Increasing the harvested-energy target raises λ*, shifts the boundary downward, and shrinks the ID region.
- The boundary reaches (δmin = 0, Qmax) when the ID region becomes empty.
- When interference is absent, outage states are assigned to EH because they cannot support ID, but their poor channel gains contribute little harvested energy.
B. The Case With CSIT: Joint Information/Energy Scheduling, Power Control, and Receiver Mode Switching
With CSIT, the paper jointly optimizes transmit power, information/energy scheduling, and receiver mode switching. Under I(ν) = 0 and h1 ≥ h2, the best channels support EH while poor channels may be silenced.
- The CSIT optimization jointly selects transmit power, information or energy transfer, and receiver ID/EH mode for each fading state.
- ID-mode power allocation uses truncated channel inversion subject to the peak-power constraint.
- The optimal EH-mode power allocation is governed by channel threshold h2 and uses Ppeak when h ≥ h2.
- The transmitter has three modes: information transfer with channel inversion, energy transfer with peak power, and silence with no transmission.
- For h1 ≥ h2, the mode regions are characterized using the largest root h3 of a quadratic involving λ*, β*, Ppeak, r0, and σ2.
- The best channels are allocated to EH rather than ID, while poor channel conditions cause the transmitter to shut down and save power.
V. RATE-ENERGY TRADE-OFF
This section investigates resource allocation for rate-energy trade-offs, comparing cases with and without transmitter channel-state information (CSIT).
- The schemes jointly characterize information and energy transfer allocation across the two CSIT settings.
- The analysis derives optimal schemes balancing maximum ergodic capacity against maximum average harvested energy with and without CSIT.
- The corresponding optimization problems are formulated as Problems (P3) and (P4).
A. The Case Without CSIT: Optimal Receiver Mode Switching
Without CSIT, the paper derives receiver switching regions for rate-energy trade-offs by allocating fading states between information decoding and energy harvesting.
- Optimal receiver mode switching: The optimal ID region is characterized using a dual variable for a given harvested-energy target, with the remaining nonnegative (h, I) plane assigned to EH.
- Optimal receiver mode switching: Meeting a harvested-energy constraint requires sacrificing ergodic capacity by allocating some fading states to EH mode.
- Optimal receiver mode switching: Fading states with the largest h values are allocated to information decoding under the no-CSIT rate-energy trade-off.
- Optimal receiver mode switching: Although good channels favor ID, EH becomes preferable above a channel threshold because its Lagrangian value grows linearly with h while ID grows logarithmically.
- Optimal receiver mode switching: As the dual variable λ∗ increases, the optimal ID region shrinks.
- The Case With CSIT: With CSIT, transmitter scheduling adds information-transfer, energy-transfer, and silent modes, while poor channels can trigger transmission shutdown.
VI. CONSIDERATION OF RECEIVER ENERGY CONSUMPTION
This section incorporates receiver energy consumption into the outage-energy analysis and examines how it changes optimal switching regions and trade-offs.
- Receiver energy consumption model: The receiver consumes constant power PI in ID mode, while EH-mode consumption is assumed negligible because practical energy receivers are mostly passive.
- Scope: The receiver-energy-consumption extension studies only the outage-energy trade-off without CSIT because of space limitations.
- Modified outage-energy problem: Net harvested energy subtracts the constant consumption Q0 and the expected ID-mode consumption from harvested energy.
- Optimal switching regions: Considering receiver consumption requires allocating more fading states to EH mode to achieve the same net harvested energy.
- Outage-energy trade-off: Receiver power consumption degrades the outage-energy trade-off, although Qmax remains unchanged when all fading states are assigned to EH.
VII. NUMERICAL RESULTS
The numerical results compare three suboptimal receiver switching rules with optimal schemes for outage-energy and rate-energy trade-offs. Interference-based switching stays close to optimal, while periodic and SINR-based switching can degrade substantially under certain conditions.
- Interference-based switching performs similarly to optimal switching across average transmit powers in the delay-limited, no-CSIT comparison.
- Periodic switching incurs about 10%−20% higher outage probability than optimal switching.
- For large P, optimal switching assigns some high-hP + I fading states to EH, whereas SINR-based switching tends to assign low-h states.
- The mismatch causes SINR-based switching to harvest less incremental energy per EH state and require more EH states, producing high outage probability at large P.
- With CSIT and no-delay-limited transmission, interference-based switching remains close to optimal, while the other rules are notably worse; SINR-based switching can underperform periodic switching above 8 dB SNR.
VIII. CONCLUDING REMARKS
The paper develops receiver mode switching and, with transmitter CSI, joint power-control and scheduling policies for opportunistic wireless energy harvesting. Its central result is that allocating the best direct-channel fading states to power transfer achieves the optimal trade-offs, while several heuristic rules reduce receiver complexity.
- The paper frames interference as a potential energy source and identifies joint information-power balancing in interference channels as a problem for further investigation.
- The study considers a point-to-point flat-fading link with time-varying interference and optimizes outage probability or ergodic capacity against harvested energy.
- With transmitter CSI, the paper jointly optimizes information and energy scheduling, transmit power control, and receiver ID/EH switching.
- The optimal strategy allocates fading states with the best direct-channel gains to power transfer rather than information transfer.
- Three heuristic switching rules are proposed to reduce receiver complexity and are compared against optimal performance.
- The analysis assumes same-band interference and a single-user setup, leaving wide-band interference and multi-user extensions unresolved.
APPENDIX
The appendix characterizes vertex points and optimal policies on the outage-energy and rate-energy region boundaries with and without CSIT. These boundary points correspond to allocating all states to EH, or selecting states and transmit powers to optimize information performance while meeting energy constraints.
- The appendix characterizes boundary vertex points for the outage-energy and rate-energy regions with and without CSIT.
- O-E region without CSIT: In the outage-energy region without CSIT, Qmax is achieved when EH is active in all fading states, yielding zero non-outage probability.
- O-E region without CSIT: Qmin is the harvested energy when maximum non-outage probability is achieved, and it is nonzero because outage states remain available for energy harvesting.
- O-E region with CSIT: With CSIT in the outage-energy region, peak power is assigned to states with the largest direct-channel gains to maximize signal-harvested energy.
- R-E region with CSIT: For the rate-energy region with CSIT, Qmax again uses EH in all states, while maximum rate uses water-filling power allocation under average and peak constraints.
- R-E region with CSIT: The minimum harvested energy in the rate-energy setting is generally nonzero because the receiver can harvest interference when the information-decoding condition is not met.