Source-linked AI summary
Two-hop Communication with Energy Harvesting
Deniz Gunduz, Bertrand Devillers
TL;DR
The paper addresses how to optimize two-hop communication when source and relay nodes harvest energy over time. It derives offline transmission policies using known energy-arrival profiles, obtaining an optimal full-duplex scheme and a special-case half-duplex solution. The half-duplex result is restricted to a single energy packet at the source, while the full-duplex policy combines source Max-Bit transmission with relay forwarding.
Problem
The paper asks how to maximize data delivery in two-hop networks whose source and relay operate with energy harvested over time.
Method
The paper develops offline transmission algorithms using known energy-arrival profiles, including Max-Bit source transmission and relay forwarding under energy and bit causality.
Results
The paper identifies an optimal full-duplex transmission scheme and characterizes an optimal half-duplex schedule when the source has a single energy packet.
Takeaways & Limitations
For full-duplex relaying, maximizing source bits by the deadline and then forwarding feasible bits at the relay yields the maximum destination throughput.
Takeaways & Limitations
The half-duplex result is limited to a single source energy packet, while general half-duplex scheduling is characterized as complicated.
Abstract
from arXiv · showhide
Communication nodes with the ability to harvest energy from the environment have the potential to operate beyond the timeframe limited by the finite capacity of their batteries; and accordingly, to extend the overall network lifetime. However, the optimization of the communication system in the presence of energy harvesting devices requires a new paradigm in terms of power allocation since the energy becomes available over time. In this paper, we consider the problem of two-hop relaying in the presence of energy harvesting nodes. We identify the optimal offline transmission scheme for energy harvesting source and relay when the relay operates in the full-duplex mode. In the case of a half-duplex relay, we provide the optimal transmission scheme when the source has a single energy packet.
I. INTRODUCTION
Energy harvesting enables wireless nodes to operate beyond battery-limited lifetimes, but energy availability over time makes optimal network operation distinct from conventional battery-limited optimization. This paper studies offline two-hop transmission with energy-harvesting source and relay nodes.
- Energy harvesting can enable self-sustaining wireless nodes whose operation is not limited by battery lifetime.
- Optimal operation depends on the energy-harvesting profile while satisfying energy-neutral operation.Energy used by time t cannot exceed energy harvested by that time.
- Prior work studies transmission-time minimization, deadline-constrained data maximization, battery limitations, and broader harvesting and battery models.
- This paper focuses on a two-hop network with energy-harvesting source and relay nodes using offline knowledge of energy arrivals.
II. SYSTEM MODEL
The system is a two-hop source–relay–destination network in which source and relay energy arrivals are known offline and transmission powers must satisfy energy and bit causality. Both nodes adapt power and rates over AWGN links.
- The network consists of an energy-harvesting source, relay, and destination operating over a period T.Source and relay energy packets arrive at known instants with known amounts.
- The model assumes unlimited battery sizes and accounts only for energy used in transmission, not relay receive energy.
- Source and relay can adapt transmission power and rates instantaneously over AWGN source-to-relay and relay-to-destination channels.
- Feasible power allocations must obey nonnegative power, energy-causality, and relay bit-causality constraints.Relay-transmitted bits can only follow their arrival from the source.
- The objective is to maximize the number of bits delivered to the destination by deadline T using the Max-Bit single-hop policy as a reference.
III. FULL-DUPLEX RELAY
For a full-duplex relay, the optimal offline policy first maximizes the source’s transmitted bits under its energy arrivals, then has the relay forward as many available bits as its own energy permits.
- The full-duplex optimization selects source and relay power allocations subject to the feasible-power set.
- The source’s energy profile determines its bit-arrival profile at the relay, which then forwards feasible bits under energy and bit causality.
- The optimal source policy maximizes total bits sent to the relay by T and is given by the Max-Bit algorithm.
- The Max-Bit source policy produces a piecewise-linear, non-decreasing transmission profile that increases only at energy-arrival instants.
- The relay uses the resulting continuous bit-arrival profile and its energy arrivals to transmit at the highest power allowed by both profiles.
- The complete solution applies Max-Bit at the source and then an adapted point-to-point algorithm at the relay to maximize delivered bits by the deadline.The relay problem differs because data arrive continuously and the objective is deadline-constrained bit maximization.
IV. HALF-DUPLEX RELAY
For a half-duplex relay, the paper optimizes both transmission scheduling and power allocation. With a single source energy packet, the optimal schedule is solved numerically by balancing source transmission against relay forwarding.
- Half-duplex scheduling: Half-duplex operation requires nonoverlapping source and relay transmissions, so scheduling must be optimized alongside power allocation.The feasibility condition is P_s(t) · P_r(t) = 0 for all t ∈ [0,T].
- Power allocation: The source should not generally maximize its own delivered bits, because the relay’s feasible forwarding schedule can make a lower source rate globally better.An example shows B1 < B2 because the rate function is strictly concave, despite the second source schedule transmitting fewer bits to the relay.
- Single-packet source case: For a single source energy packet, the source uses all energy over 0 < t < T, then the relay forwards the received bits during T−t.The relay uses the optimal point-to-point transmission schedule in the remaining interval.
- Half-duplex scheduling: The source transmits first over one connected interval, followed by relay forwarding during the remaining time.This two-portion structure follows from shifting source transmission earlier and relay transmission later.
- Numerical solution: The optimal source duration t* is found numerically by equating source-transmitted and relay-forwarded bits, using interval bracketing and bisection.The relay’s maximum forwarding curve is evaluated at candidate breakpoints before bisection refines t*.
- Numerical solution: The relay’s optimal power profile is determined by its energy-arrival curve, with candidate source durations falling across intervals defined by relay energy arrivals.For the sample profile, increasing source energy decreases t* and moves it among different relay-arrival intervals.
V. CONCLUSIONS AND FUTURE WORK
The paper formulates offline two-hop communication with energy-harvesting source and relay nodes. It gives an optimal full-duplex scheme and a low-complexity numerical solution for the half-duplex case with one source energy packet, while leaving relay buffer limitations for future study.
- Contributions: The paper studies offline transmission schemes for a two-hop network whose source and relay harvest energy from the environment.The energy-arrival profiles are assumed known when optimizing transmission.
- Contributions: The full-duplex relay case has an optimal transmission scheme, whereas the general half-duplex scheduling problem is more complicated.The half-duplex analysis therefore focuses on a restricted source-energy setting.
- Contributions: For a single source energy packet, the paper characterizes optimal source and relay transmissions and provides a low-complexity numerical algorithm for the optimal schedule.This is the paper’s stated half-duplex result.
- Future work: Relay battery or data-buffer limitations remain an extension because overflow can invalidate the two-portion schedule used in the half-duplex analysis.Future scheduling must account for energy or data accumulated while the source transmits.