Throughput Maximization for the Gaussian Relay Channel with Energy Harvesting Constraints (1109.0724v2)

Abstract: This paper considers the use of energy harvesters, instead of conventional time-invariant energy sources, in wireless cooperative communication. For the purpose of exposition, we study the classic three-node Gaussian relay channel with decode-and-forward (DF) relaying, in which the source and relay nodes transmit with power drawn from energy-harvesting (EH) sources. Assuming a deterministic EH model under which the energy arrival time and the harvested amount are known prior to transmission, the throughput maximization problem over a finite horizon of $N$ transmission blocks is investigated. In particular, two types of data traffic with different delay constraints are considered: delay-constrained (DC) traffic (for which only one-block decoding delay is allowed at the destination) and no-delay-constrained (NDC) traffic (for which arbitrary decoding delay up to $N$ blocks is allowed). For the DC case, we show that the joint source and relay power allocation over time is necessary to achieve the maximum throughput, and propose an efficient algorithm to compute the optimal power profiles. For the NDC case, although the throughput maximization problem is non-convex, we prove the optimality of a separation principle for the source and relay power allocation problems, based upon which a two-stage power allocation algorithm is developed to obtain the optimal source and relay power profiles separately. Furthermore, we compare the DC and NDC cases, and obtain the sufficient and necessary conditions under which the NDC case performs strictly better than the DC case. It is shown that NDC transmission is able to exploit a new form of diversity arising from the independent source and relay energy availability over time in cooperative communication, termed "energy diversity", even with time-invariant channels.

• The paper introduces algorithms that jointly optimize source and relay power allocation using KKT conditions to maximize throughput for delay-constrained traffic.
• It proposes a separation principle for no-delay traffic that efficiently decomposes the non-convex energy harvesting scheduling problem.
• The study highlights the concept of energy diversity, showing that exploiting stochastic energy arrivals can yield significant throughput gains.

Throughput Maximization for the Gaussian Relay Channel with Energy Harvesting Constraints

The paper of throughput maximization in wireless networks with energy harvesting (EH) constraints presents an intersection of major challenges in communication theory, optimization, and resource management. The paper by Huang, Zhang, and Cui investigates these challenges in the context of the Gaussian relay channel, particularly considering both the source and relay nodes powered by EH sources rather than traditional time-invariant energy sources. This context is driven by applications in wireless sensor networks (WSNs), where recharging or replacing batteries is impractical.

The primary focus is on a three-node system with a source, a relay, and a destination, wherein the relay employs decode-and-forward (DF) relaying. Two types of data traffic are evaluated: delay-constrained (DC) traffic, where immediate decoding is required, and no-delay-constrained (NDC) traffic, which allows for arbitrary decoding delays. The research explores maximizing throughput over a finite time horizon, with $N$ transmission blocks, under deterministic EH models where energy arrival times and quantities are known a priori.

Main Contributions

1. Throughput Maximization Algorithms: The authors allege that joint source and relay power allocation is essential for maximizing throughput in the DC case. An efficient algorithm utilizing Karush-Kuhn-Tucker (KKT) conditions is proposed, demonstrating the monotonic non-decreasing nature of optimal power allocations over time blocks. For the NDC case, the paper advances a separation principle—argued to be optimal—that partitions the problem into two solvable stages, optimizing the source and relay power profiles separately. This separation effectively handles the intrinsic non-convexity associated with EH constraints.
2. Energy Diversity: The concept of "energy diversity" is introduced, which arises independently from time-variant channels due to the stochastic nature of energy arrival at the source and relay nodes. This diversity is shown to be exploitable under NDC conditions, with potential throughput gains over the DC counterpart. The paper provides necessary and sufficient conditions for NDC to outpace DC in throughput performance.
3. Optimal Power Profiles: For both cases (DC and NDC), the power allocation strategies developed are shown to be non-decreasing, offering practical insights into energy-efficient scheduling in EH scenarios.

Implications and Future Directions

The implications of this work are multifaceted, touching upon both theoretical and practical aspects of EH communication systems. The algorithms devised for power allocation can serve as benchmarks for further improvements in energy-efficient protocol design, especially in resource-constrained environments like WSNs. The concept of energy diversity might stimulate further exploration into how temporal energy constraints can be leveraged as a form of diversity similar to channel diversity.

Future research could consider extending these results to random EH models, which consider stochastic energy arrivals that are not known a priori, posing additional challenges for optimal resource scheduling. Moreover, the research can be broadened to include scenarios with finite energy storage limits and explore other relay strategies such as amplify-and-forward (AF) or compress-and-forward (CF), potentially yielding broader insights applicable to a wider range of cooperative communication systems.

This paper sets a technical baseline for understanding and optimizing relay channels under energy harvesting constraints, and its findings could substantially influence the design of next-generation, sustainable wireless communication networks.