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On the Transfer of Information and Energy in Multi-User Systems
Ali Mohammad Fouladgar, Osvaldo Simeone
TL;DR
Wireless systems must jointly transfer information and energy despite conflicting design constraints. Using information-theoretic analysis of multiple-access and multi-hop channels, the paper characterizes achievable regions and capacity, showing that energy requirements call for additional coordination. Examples further show that a harvesting relay's strategy should change with second-hop quality.
Problem
Prior work mainly addressed single-transmitter systems, leaving joint information-and-energy transfer in baseline multi-user channels less explored despite conflicting design constraints.
Method
The paper uses information-theoretic analysis to characterize the rate-energy region of a multiple-access channel and the capacity-energy function of a multi-hop channel with a harvesting relay.
Results
Energy constraints generally require additional coordination: multiple-access encoders may need time-sharing, while a harvesting relay's optimal first-hop strategy depends on second-hop SNR.
Takeaways & Limitations
Joint information-and-energy requirements significantly affect communication-strategy design in multi-user wireless networks.
Abstract
from arXiv · showhide
The problem of joint transfer of information and energy for wireless links has been recently investigated in light of emerging applications such as RFID and body area networks. Specifically, recent work has shown that the additional requirements of providing sufficient energy to the receiver significantly affects the design of the optimal communication strategy. In contrast to most previous works, this letter focuses on baseline multi-user systems, namely multiple access and multi-hop channels, and demonstrates that energy transfer constraints call for additional coordination among distributed nodes of a wireless network. The analysis is carried out using information theoretic tools, and specific examples are worked out to illustrate the main conclusions.
I. INTRODUCTION
Energy and information impose conflicting wireless-design constraints, motivating analysis beyond prior single-transmitter settings. This letter studies multiple access and multi-hop channels and shows that energy requirements increase the need for coordination among distributed nodes.
- Energy and information generally impose conflicting constraints because signal power depends on average squared value, whereas information depends on signal variations and entropy rate.
- Prior work primarily studied point-to-point, parallel point-to-point, or multi-antenna broadcast systems with minimum received-energy constraints.
- The letter extends the setting to multiple-access and multi-hop channels, providing baseline multi-user scenarios with multiple transmitters.
- For the multiple-access channel, the paper characterizes achievable rate-energy trade-offs and gives an example showing enhanced coordination between encoders is needed to satisfy energy-transfer requirements.
- For the multi-hop channel, the paper derives a capacity characterization and examines communication-strategy issues caused by a relay harvesting energy for its second-hop transmission.
II. MULTIPLE ACCESS CHANNEL WITH RECEIVED ENERGY CONSTRAINT
The DM-MAC framework augments independent-message communication with input-cost and received-energy requirements. Achievability is defined through reliable decoding and an average received-energy constraint that holds with high probability.
- The DM-MAC has two encoders sending independent messages to a decoder over finite input and output alphabets, while requiring sufficient received energy.
- A code comprises two message sets, two encoders assigning codewords to messages, input cost constraints, and a decoder estimating both messages.
- The average probability of error is defined as the probability that the decoded message pair differs from the transmitted pair.
- A rate-energy triple is achievable when a sequence of codes satisfies the coding requirements, including received energy of at least B with high probability as blocklength grows.
- The capacity-energy region is the closure of all achievable rate-energy triples under the two encoder cost constraints.
A. Capacity-Energy Region
The DM-MAC capacity-energy region characterizes achievable rate pairs together with a minimum received-energy requirement. Its formulation uses coordinated time-sharing among encoder codebooks, and the proof adds an energy-outage error event to standard MAC analysis.
- The capacity-energy region is the union of rate-energy triples satisfying the theorem’s rate inequalities under encoder cost constraints.
- The rate bounds are R1 ≤ I(X1; Y |X2, Q) and R2 ≤ I(X2; Y |X1, Q).
- The auxiliary variable Q enables time-sharing between encoder codebooks and requires the encoders to coordinate their switching sequence.
- Achievability and converse follow standard DM-MAC arguments, with achievability adding an error event for failure of the received-energy condition.
B. Example
The Gaussian MAC example shows that received-energy constraints can make coordinated time-sharing necessary. Information-maximizing Gaussian inputs suffice below the unconstrained received-power level, while higher energy requirements use a second, energy-only signaling mode.
- For B ≤ 2P + 1, the maximum sum-rate remains 2 log2(1 + 2P), and time-sharing is not needed.
- The information mode uses Gaussian inputs, whereas the energy mode has both encoders transmit equal constant signals for coherent combining.
- The energy-only signaling choice maximizes energy transfer through coherent combining but carries no information.
- The time-sharing strategy is optimized over P ′, P ′′, and λ subject to input-cost and received-energy constraints.
- When B > 2P + 1, time-sharing is necessary to achieve optimal performance in the example.
III. MULTI-HOP CHANNEL WITH A HARVESTING RELAY
The multi-hop model studies a three-node discrete memoryless channel where a relay assists communication and harvests energy from the encoder’s received signal. Codes include an encoder, a causal relay encoder, input-cost constraints, and an energy-harvesting requirement.
- The DM-MHC consists of two separate point-to-point channels connecting an encoder, an energy-harvesting relay, and a decoder.
- A code contains a message set and an encoder mapping each message to a codeword subject to an input-cost constraint.
- The relay encoder selects each transmission symbol from the past received sequence, so its inputs are constrained by the harvesting condition.
- Achievability requires vanishing decoding error while respecting the encoder and relay cost constraints, and the capacity-energy function is the supremum of achievable rates.
A. Capacity-Energy Function
The paper characterizes the capacity-energy function of the DM-MHC with a harvesting relay. Achievability uses decode-and-forward, with an additional vanishing-probability error event to ensure the relay-harvesting condition.
- Theorem 2 characterizes the capacity-energy function Ce(P1, P2) for a DM-MHC with a harvesting relay.
- Achievability follows through decode-and-forward coding.
- The proof adds an error event for violation of the relay-energy condition, whose probability vanishes as n →∞ by the weak law of large numbers.
B. Example
The multi-hop example compares capacity and the optimizing input probability as second-hop SNR changes. Harvesting energy is favored at low SNR, whereas information transfer is favored at sufficiently high SNR.
- Figure 4 plots capacity-energy Ce(P1, P2) against second-hop SNR and optimum probability p for P1 = 4, P2 = 0.
- With no harvested energy, capacity is min {2, 1/2 log2(1+P2)}, achieved by uniform X1 and Gaussian X2 ∼N(0, P2).
- The harvesting-relay example uses p = Pr[X1 = 2] = Pr[X1 = −2], with 1/2 −p assigned to X1 = 1 and X1 = −1.
- At small second-hop SNR, p = 0.5 maximizes energy transfer; at sufficiently large SNR, p = 0.25 maximizes information transfer.
- The encoder must adjust its first-hop transmission strategy according to the quality of the second link.
IV. CONCLUSIONS
The conclusions report that energy and information requirements materially affect multi-terminal wireless-network design. They also identify practical coding strategies for achieving desired energy-information trade-offs as future work.
- The two baseline multi-user scenarios show significant design consequences when wireless networks must support both energy and information flow.
- The paper connects these conclusions with related results for a two-way communication model.
- Designing practical coding strategies that achieve a desired trade-off between energy and information transfer remains an open direction.
- The converse arguments use bounds on received energy and a uniformly random time index to derive single-letter constraints.
- The proof observes that the two terms in the minimum depend separately on the input marginals, enabling optimization over those marginals.