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Relay Selection in Wireless Powered Cooperative Networks with Energy Storage
Ioannis Krikidis
TL;DR
Relay selection in wireless-powered cooperative networks must account for spatially random relays with energy storage. This paper analyzes selection schemes using a two-state battery model and derives outage performance. It finds that storage leads to high-SNR outage floors whose levels depend on battery steady state, and extends the schemes to a multi-access-point setting with interference.
Problem
Relay selection for wireless-powered cooperative networks with spatially random, battery-equipped relays is an underexplored setting, although spatial randomness matters because RF harvesting depends on path loss.
Source: §I · p. 2Method
The paper models battery charging and discharging as a two-state Markov chain and analyzes relay-selection schemes with differing information requirements, including a multi-access-point extension.
Source: §I · p. 2, C. Battery model · p. 3Results
At high SNR, the schemes have outage floors dependent on the battery’s steady-state distribution, and incorporating battery status lowers the floor relative to schemes that ignore it.
Source: §I · p. 2, §VI · p. 12Takeaways & Limitations
Energy storage significantly affects relay-selection performance, while accounting for battery status can improve outage performance within the studied schemes.
Source: §I · p. 2, §VI · p. 12
Abstract
from arXiv · showhide
This paper deals with the problem of relay selection in wireless powered cooperative networks, where spatially random relays are equipped with energy storage devices e.g., batteries. In contrast to conventional techniques and in order to reduce complexity, the relay nodes can either harvest energy from the source signal (in case of uncharged battery) or attempt to decode and forward it (in case of charged battery). Several relay selection schemes that correspond to different state information requirements and implementation complexities are proposed. The charging/discharging behavior of the battery is modeled as a two-state Markov chain and analytical expressions for the steady-state distribution and the outage probability performance are derived for each relay selection scheme. We prove that energy storage significantly affects the performance of the system and results in a zeroth diversity gain at high signal-to-noise ratios; the convergence floors depend on the steady-state distribution of the battery and are derived in closed-form by using appropriate approximations. The proposed relay selection schemes are generalized to a large-scale network with multiple access points (APs), where relays assist the closest AP and suffer from multi-user interference.
I. INTRODUCTION
The paper studies relay selection in wireless-powered cooperative networks with spatially random, battery-equipped relays, motivated by the limits of recharging dense IoT deployments. It models relay locations and battery operation to analyze selection schemes with different information and complexity requirements.
I. INTRODUCTION
- The paper identifies spatially random relays with energy storage as an underexplored relay-selection setting, extending earlier battery and multi-relay studies that did not model spatial randomness.The work also notes that spatial randomness matters because RF harvesting depends strongly on path loss.Source: §I · p. 2
- The proposed schemes adapt relay selection to battery-equipped nodes that harvest from the source when empty and decode or forward when charged.The schemes differ in channel-state-information requirements and implementation complexity, and their outage performance is analyzed.Source: §I · p. 2
A. Topology
- The single-cell model places relays in a disc according to a homogeneous Poisson point process, with the access point at its origin and no direct access-point-to-destination link.The access point is backlogged, transmits at fixed power, and supplies the relays’ harvested energy.Source: §II · p. 2, A. Topology · p. 2
B. Cooperative protocol
- Communication uses two half-duplex time slots: the access point broadcasts first, then a successfully decoding selected relay forwards to the destination.The relay transmits at the source rate.Source: B. Cooperative protocol · pp. 2–3
C. Battery model
- Each relay’s storage has charged and empty states: charged relays can participate in relaying, while empty relays harvest, and one device cannot charge and discharge simultaneously.The battery’s charging and discharging are modeled as a two-state Markov chain; the analysis also describes an extension to a multi-state battery.Source: C. Battery model · p. 3
D. Channel model
The channel and outage model supports analysis of the random relay selection scheme, which needs no relay-location or battery-status feedback. Its outage probability has a high-SNR floor tied to the battery’s steady-state distribution.
D. Channel model
- The channel model uses Rayleigh block fading, path loss proportional to 1/(1 + d^α), and additive white Gaussian noise; outage means the destination cannot support the target spectral efficiency.The analysis derives closed-form outage and diversity expressions for the selection schemes.Source: D. Channel model · p. 4, §III · p. 4
A. Random relay selection
- Random relay selection requires no battery-status or relay-location feedback, but selecting an empty-battery relay leaves it inactive and causes an outage.An outage can also arise from no relays being present, decoding failure, or destination-link failure.Source: A. Random relay selection · p. 4
- For random relay selection, a relay is fully discharged after selection regardless of decoding success, while an empty relay harvests from the received source signal.The probability of charging decreases as battery capacity Ψ increases, and the spectral efficiency does not affect battery state under these assumptions.Source: A. Random relay selection · p. 4
- At high SNR, random relay selection has an outage floor that depends on the battery’s steady-state distribution.The stated asymptotic analysis assumes a constant battery-to-source power ratio; its simplified expression is also described as holding for any destination distance.Source: A. Random relay selection · pp. 4–5
B. Relay selection based on the closest distance
Closest-distance selection uses relay-location information but does not account for battery status or instantaneous fading. Its battery steady state matches random selection, and its high-SNR outage floor is the same, though it converges faster.
B. Relay selection based on the closest distance
- Closest-distance selection requires prior relay-location knowledge and selects the relay nearest the access point, without using battery status or instantaneous fading.The paper describes low-rate feedback or GPS as possible means of obtaining relay locations.Source: B. Relay selection based on the… · p. 5
- The closest-distance and random-selection schemes have equivalent battery steady-state distributions because both select one relay without considering battery status and discharge it after selection.The analysis states that each relay has approximately the same selection probability under the two schemes.Source: B. Relay selection based on the… · p. 5
- The paper gives an exact outage-probability expression for closest-distance selection.Its steady-state charged probability is also derived.Source: B. Relay selection based on the… · p. 5
- Closest-distance selection and random selection converge to the same high-SNR outage floor, but closest-distance selection reaches that floor faster.The cited asymptotic comparison assumes α = 2, a constant battery-to-source power ratio, and ρ << d0.Source: B. Relay selection based on the… · p. 5
C. Random relay selection with battery information
Random relay selection with battery information restricts selection to charged relays and requires one-bit battery-status feedback. Its outage analysis includes both relay-link failures and the possibility that no charged relay is available.
C. Random relay selection with battery information
- RRSB randomly selects among charged relays and requires one-bit battery-status feedback at the beginning of each broadcast phase.The charged relays form a thinned Poisson point process in the analysis.Source: C. Random relay selection with battery… · pp. 5–6
- The RRSB steady-state charged probability is derived from the battery transitions, with the selected charged relay’s discharge probability tied to its selection probability.The paper notes that its approximation yields a simple closed-form steady-state expression and is more efficient when λπρ² is large.Source: C. Random relay selection with battery… · pp. 5–6
- RRSB outage can occur when no charged relay is present or when either hop of the relay transmission is in outage.The paper provides an outage-probability expression for the scheme.Source: C. Random relay selection with battery… · p. 6
- At high SNR, the RRSB outage probability is dominated by the event that no relay in the disc is fully charged.Under the stated constant-ratio limit, the relaying-link success probability tends to one.Source: C. Random relay selection with battery… · p. 6
D. Relay selection based on the closest distance with battery information
The RCSB scheme selects the closest charged relay and derives its steady-state battery probability and outage behavior. Distributed beamforming uses all charged relays, but incurs higher coordination complexity and has a high-SNR outage floor tied to the probability that no relay can participate.
D. Relay selection based on the closest distance with battery information
- RCSB selects the closest charged relay, and its battery charging/discharging behavior follows the RRSB scheme.The supplied passages state that steady-state and outage expressions are given, but do not show their values.Source: D. Relay selection based on the… · p. 6
E. Distributed beamforming
- Distributed beamforming selects all charged relays that decode successfully and coherently transmit as a virtual antenna array.The protocol requires CRC checks, time synchronization, signaling among relays, and channel-state information at the relays.Source: E. Distributed beamforming · p. 7
- The DB scheme fully discharges each charged relay at the end of the relaying slot, making its steady-state battery distribution independent of network density.Every charged selected relay is discharged, whether or not it decoded successfully.Source: E. Distributed beamforming · p. 7
- At high SNR, DB outage equals the probability that the set of charged, successfully decoding relays is empty, which is exponential in ηDB.The outage expression quickly converges, requiring fewer than 10 terms.Source: E. Distributed beamforming · p. 7
- DB requires continuous feedback for coherent combining, whereas the asymptotic comparison favors single-relay selection because it keeps more relays charged.The passage attributes this comparison to the outage floor depending on η1 and being independent of the channel.Source: E. Distributed beamforming · pp. 7–8
- At high SNR, the proposed relay-selection schemes have an ordering under the stated constant-ratio and λπρ² >> 0 conditions.The supplied passage does not include the ordering itself.Source: E. Distributed beamforming · p. 7
IV. GENERALIZATION TO MULTI-CELL SCENARIOS
The paper extends relay selection to a multi-cell network with randomly located access points and relays, where relay decoding is affected by multi-user interference. The model uses Voronoi-cell assignments and orthogonal relay channels.
IV. GENERALIZATION TO MULTI-CELL SCENARIOS
- In the multi-cell model, APs form a PPP with density µ and relays form a PPP with density λ; each relay connects to its closest AP, and relays in each Voronoi cell assist that AP.The analysis studies a typical cell with the AP at the origin and approximates each Voronoi cell by a disc of radius ρ = 1/4√µ.Source: §IV · p. 8
- Each AP has a destination at distance ρ, no direct AP-to-destination link is available, and communication uses decode-and-forward relays.The destination placement is described as a worst-case scenario.Source: §IV · p. 8
- Relay transmissions use orthogonal channels, so destinations are free from multi-user interference, while interference affects relay decoding.External AP energy harvesting is treated separately in the single-cell RRS scheme discussion.Source: §IV · p. 8
A. RRS scheme
In the multi-cell setting, interference affects the first hop, while closest-relay selection has a lower high-SNR outage floor than random selection. The section extends both policies and gives their outage analyses.
A. RRS scheme
- For RRS, multi-user interference affects relay decoding on the first hop and raises the outage floor relative to the single-cell case.The high-SNR relay decoding success probability is denoted Q1(0,ρ).Source: A. RRS scheme · p. 8
B. RCS scheme
- RCS applies closest-relay selection within each cell; like RRS, interference affects only the broadcast phase, leaving the battery steady-state probability equivalent to the single-cell case.Source: B. RCS scheme · pp. 8–9
- In the multi-cell case, the closest-relay RCS scheme has a lower high-SNR outage floor than RRS because closest-relay selection protects the source signal against interference.Source: B. RCS scheme · p. 9
C. RRSB/RCSB schemes
The RRSB and RCSB policies extend to the multi-cell case by applying the corresponding selection policy within each Voronoi cell. This extension leaves battery steady-state distributions unchanged and affects relay decoding probability.
C. RRSB/RCSB schemes
- RRSB and RCSB extend to multi-cell networks by applying each policy in every Voronoi cell.The extension does not modify battery steady-state distributions; it affects decoding probability at relay nodes.Source: C. RRSB/RCSB schemes · p. 9
- The RRSB and RCSB schemes are stated to converge asymptotically to an outage expression.The supplied passage does not include the expression.Source: C. RRSB/RCSB schemes · p. 9
V. NUMERICAL RESULTS
Battery-aware selection schemes achieve lower high-SNR outage floors than schemes that ignore battery state, while the distributed beamforming scheme performs best at low and moderate SNRs. The results also show how system parameters affect outage and validate the analytical approximations.
V. NUMERICAL RESULTS
- RRSB/RCSB achieve the lowest high-SNR outage floors, while DB outperforms them at low and moderate power, at the cost of channel-state information.RRS and RCS converge to the same higher floor; the theoretical expressions match simulations for RRS, RCS, RRSB, and RCSB, while the DB approximation is tight for d0 = 2ρ.Source: §V · p. 9, Figure 4 · p. 10
- Increasing d0 raises outage through path loss, while DB is more robust; Ψ trades harvesting ease against relay transmit power and the probability of being charged.Small Ψ lowers the harvesting threshold but may leave insufficient relaying power; high Ψ reduces the probability that relays become charged.Source: §V · pp. 9–10, Figure 5 · p. 10
- Changing spectral efficiency r0 affects convergence rate, not the outage floor, which depends on the battery’s steady-state distribution.Higher r0 slows convergence.Source: Figure 6 · p. 10, §V · p. 10
- Increasing relay-disc radius ρ lowers high-SNR outage floors but worsens outage at low and moderate SNRs when d0 = ρ increases the longest-hop distance.The high-SNR improvement is associated with more participating relays and lower probabilities of selecting an uncharged relay or having no charged relay in the disc.Source: §V · pp. 10–11, Figure 7 · p. 11
- The proposed approximation efficiently estimates the RRSB/RCSB steady-state battery distribution and supports closed-form expressions that are accurate when λπρ2 >> 0.Figure 8 compares the exact distribution from simulation against the approximation across system settings.Source: Figure 8 · p. 11, §V · p. 11
- RRSB outperforms batteryless RRS at low and moderate SNRs, with a larger gain as conversion efficiency ζ falls or disc radius increases.At high SNR, RRSB has an outage floor, whereas batteryless RRS provides diversity gain one; the latter assumes perfect relay channel knowledge and dynamic-PS circuitry.Source: Figure 9 · p. 11, §V · pp. 11–12
- In the multi-cell setting, battery-aware RRSB/RCSB achieve lower outage floors; unlike the single-cell case, their floors differ because relay decoding probabilities differ.The theoretical results match the simulations; increasing AP density reduces Voronoi-cell radii.Source: Figure 10 · p. 11, §V · p. 12
VI. CONCLUSION
- The two-state Markov-chain analysis yields closed-form outage performance, and battery storage produces high-SNR outage floors whose levels depend on the battery’s steady-state distribution.The conclusion identifies battery-state awareness as a substantial performance improvement and DB as a low/moderate-SNR option requiring CSI.Source: §VI · p. 12
APPENDIX
The appendix proofs derive the relay-count and channel-probability expressions used to establish the steady-state battery distribution and outage results for RRS and RCS.
A. Proof of Proposition 1
- The CDF of u_i, derived using unit-variance exponential fading and the uniform relay-location density 1/(πρ²) in disk D, expresses the probability an empty battery fully charges during broadcast.Source: A. Proof of Proposition 1 · p. 12
B. Proof of Theorem 1
- The RRS outage proof combines the Poisson relay count with source-decoding and relaying-link success probabilities to establish the outage expression.The relaying-link distance is obtained using the cosine law.Source: B. Proof of Theorem 1 · pp. 12–13
C. Proof of Theorem 2
- The RCS outage proof combines the nearest-relay distance distribution with probabilities of decoding at the selected relay and at the destination.These expressions are substituted into the general outage formula to establish Theorem 2.Source: C. Proof of Theorem 2 · p. 13
D. Proof of Remark 2
These proofs simplify the RCS asymptotic expression under a small-relay-region condition and derive the DB outage expression from the active-relay process.
D. Proof of Remark 2
- For ρ << d0, the relay-destination distance is approximated by d0, simplifying the relaying-link expression used to prove Remark 2.The proof uses the small-x approximation 1 − exp(−x) ≈ x as x → 0.Source: D. Proof of Remark 2 · p. 13
E. Proof of Theorem 5
- In DB, charged relays able to decode form a thinned PPP, and the outage expression follows from the Poisson number of participating relays and their summed fading gains.The proof assumes ρ << d0 so relay-destination distances are approximated by d0; the resulting sum has a Gamma CDF with shape K.Source: E. Proof of Theorem 5 · pp. 13–14
F. Proof of Remark 3
The appendix simplifies the DB high-SNR expression and derives multi-cell RRS decoding probabilities by averaging over relay distance and interference.
F. Proof of Remark 3
- At high SNR, z0 → 0, and the DB outage expression is simplified using small-argument approximations for the incomplete Gamma and Bessel functions.The derivation also uses a series representation for the modified Bessel function.Source: F. Proof of Remark 3 · p. 14
G. Proof of Theorem 6
- For multi-cell RRS, relay decoding probability is conditioned on AP-relay distance and incorporates interference through its Laplace transform before averaging over distance.The proof combines the resulting decoding probability with the single-cell analysis to establish Theorem 6.Source: G. Proof of Theorem 6 · pp. 14–15