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On Linear Power Control Policies for Energy Harvesting Communications

Hafez M. Garmaroudi, Zikai Dou, Shengtian Yang, Jun Chen

TL;DR

Simulations show that under quasi-static fading, the maximin optimal linear policy performs comparable to the maximin optimal policy (the top-performing policy), while the capacity-agnostic multiplicative-factor optimal linear policy performs slightly worse; nevertheless, both novel policies significantly outperform the fixed-fraction policy in the low-to-medium signal-to-noise ratio (SNR) regime.

Abstract

This paper studies optimal linear power control for battery-limited energy harvesting communications. It provides a systematic analysis of linear power control policies, covering the greedy and fixed-fraction policies as special cases. Three optimality notions are introduced: the maximin optimal linear policy for a given battery capacity and mean-to-capacity ratio (MCR), and two capacity-agnostic policies that minimize the nominal additive gap and maximize the nominal multiplicative factor, respectively. Except the capacity-agnostic additive-gap optimal linear policy, which coincides with the fixed-fraction policy, the other two optimal linear policies are novel and constitute the main contributions of this paper. It is shown, among others, that the worst nominal multiplicative factor for both novel policies is approximately 0.6530, a substantial improvement over the fixed-fraction policy's value of 0.5. Simulations show that under quasi-static fading, the maximin optimal linear policy performs comparable to the maximin optimal policy (the top-performing policy), while the capacity-agnostic multiplicative-factor optimal linear policy performs slightly worse; nevertheless, both novel policies significantly outperform the fixed-fraction policy in the low-to-medium signal-to-noise ratio (SNR) regime. Moreover, this paper also investigates the optimality of the greedy policy for certain families of energy-arrival distributions, and establishes the tightest semi-universal bounds on the battery-capacity threshold for greedy optimality.

On Linear Power Control Policies for Energy Harvesting Communications

TL;DR

Simulations show that under quasi-static fading, the maximin optimal linear policy performs comparable to the maximin optimal policy (the top-performing policy), while the capacity-agnostic multiplicative-factor optimal linear policy performs slightly worse; nevertheless, both novel policies significantly outperform the fixed-fraction policy in the low-to-medium signal-to-noise ratio (SNR) regime.

Abstract

This paper studies optimal linear power control for battery-limited energy harvesting communications. It provides a systematic analysis of linear power control policies, covering the greedy and fixed-fraction policies as special cases. Three optimality notions are introduced: the maximin optimal linear policy for a given battery capacity and mean-to-capacity ratio (MCR), and two capacity-agnostic policies that minimize the nominal additive gap and maximize the nominal multiplicative factor, respectively. Except the capacity-agnostic additive-gap optimal linear policy, which coincides with the fixed-fraction policy, the other two optimal linear policies are novel and constitute the main contributions of this paper. It is shown, among others, that the worst nominal multiplicative factor for both novel policies is approximately 0.6530, a substantial improvement over the fixed-fraction policy's value of 0.5. Simulations show that under quasi-static fading, the maximin optimal linear policy performs comparable to the maximin optimal policy (the top-performing policy), while the capacity-agnostic multiplicative-factor optimal linear policy performs slightly worse; nevertheless, both novel policies significantly outperform the fixed-fraction policy in the low-to-medium signal-to-noise ratio (SNR) regime. Moreover, this paper also investigates the optimality of the greedy policy for certain families of energy-arrival distributions, and establishes the tightest semi-universal bounds on the battery-capacity threshold for greedy optimality.
Paper Structure (18 sections, 18 theorems, 119 equations, 2 figures, 5 tables)

This paper contains 18 sections, 18 theorems, 119 equations, 2 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Worst-Case Optimal Linear Policies
  4. Maximin Optimal Linear Policy for Fixed Battery Capacity and MCR
  5. Capacity-Agnostic Optimal Linear Policies for Fixed MCR
  6. From Quasi-Static Fading to Block Fading
  7. Simulation Results
  8. Performance Analysis
  9. Saddle-Point Structures of Maximin Optimal Linear Policies
  10. Optimality of Greedy Policy for Certain Families of Energy-Arrival Distributions
  11. Greedy Threshold Bounds for Given Possible-Value Interval and Mean
  12. Greedy Threshold Bounds for Given Least Possible Value and Clipped Mean
  13. Greedy Threshold Upper Bound for Given MCR
  14. Conclusion
  15. Proofs of Results in Section \ref{['subsec:saddle_point_structures']}
  16. ...and 3 more sections

Key Result

Proposition 3.1

If $c\leq p/(1-p)$, then $s_{\text{mol}}(c,p)=1$.

Figures (2)

  • Figure 1: Multiplicative-factor performance comparison for quasi-static fading and three energy-arrival distribution families with $\text{NMCR}=0.1$.
  • Figure 2: Multiplicative-factor performance comparison for Rayleigh block fading and three energy-arrival distribution families with $\text{NMCR}=0.1$.

Theorems & Definitions (23)

  • Remark 2.1
  • Proposition 3.1
  • Conjecture 4.1
  • Proposition 4.1
  • Conjecture 4.2
  • Theorem 4.2
  • Theorem 4.3
  • Conjecture 4.3
  • Lemma 4.4
  • Theorem 4.5
  • ...and 13 more