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Wireless Powered Communications: Performance Analysis and Optimization

Caijun Zhong, Xiaoming Chen, Zhaoyang Zhang, George Karagiannidis

arXiv:1510.01812v2cs.ITmath.IT

TL;DR

Energy-constrained wireless devices need power, and the paper examines throughput when a dedicated power beacon supplies it. It analyzes time-split harvesting and transmission, then finds that antennas can improve throughput while interference may help or harm depending on conditions.

  • Problem

    The paper examines average throughput when an energy-constrained source relies on a dedicated power beacon to communicate with a destination.

    Source: §II · p. 2

  • Method

    It analyzes time-split harvest-then-transmit communication using a multi-antenna power beacon and Nakagami-m fading for the beacon-to-source link.

    Source: §II · p. 2

  • Results

    More PB antennas improve throughput, while interference can raise throughput at low transmit power but cause losses at high transmit power.

    Source: §VI · pp. 7, 9

  • Takeaways & Limitations

    The optimal time split does not depend on instantaneous channel state information, providing a low-complexity way to enhance throughput.

    Source: §VII · p. 10

Abstract

from arXiv · show

This paper investigates the average throughput of a wireless powered communications system, where an energy constrained source, powered by a dedicated power beacon (PB), communicates with a destination. It is assumed that the PB is capable of performing channel estimation, digital beamforming, and spectrum sensing as a communication device. Considering a time splitting approach, the source first harvests energy from the PB equipped with multiple antennas, and then transmits information to the destination. Assuming Nakagami-m fading channels, analytical expressions for the average throughput are derived for two different transmission modes, namely, delay tolerant and delay intolerant. In addition, closed-form solutions for the optimal time split, which maximize the average throughput are obtained in some special cases, i.e., high transmit power regime and large number of antennas. Finally, the impact of co-channel interference is studied. Numerical and simulation results have shown that increasing the number of transmit antennas at the PB is an effective tool to improve the average throughput and the interference can be potentially exploited to enhance the average throughput, since it can be utilized as an extra source of energy. Also, the impact of fading severity level of the energy transfer link on the average throughput is not significant, especially if the number of PB antennas is large. Finally, it is observed that the source position has a great impact on the average throughput.

I. INTRODUCTION

The introduction motivates dedicated power beacons for wireless-powered links and outlines a time-splitting, point-to-point system. It proposes throughput analysis for two transmission modes and studies how interference, antennas, fading, and source position affect performance.

I. INTRODUCTION

  • The introduction motivates energy harvesting because finite batteries require recharging, while natural sources such as solar and wind provide intermittent, random energy.The paper notes that this instability may be unsuitable for services with stringent QoS requirements.Source: §I · p. 1

A. Literature

  • Earlier SWIPT work often colocates energy and information sources; short energy-harvesting range motivates dedicated PBs, whose deployment is described as less costly.The paper frames its point-to-point analysis as a small-scale counterpart to the network-scale study in.Source: A. Literature · pp. 1–2, B. Motivation and Contributions · p. 2

B. Motivation and Contributions

  • The paper derives exact average-throughput expressions for both modes without interference, plus an interference-case integral expression and throughput bounds.High-power and large-antenna approximations support closed-form optimal time splits in special cases.Source: B. Motivation and Contributions · p. 2
  • More PB antennas improve throughput; interference can help or hurt, fading severity matters little with many antennas, and source position strongly affects throughput.Without interference, throughput is symmetric in source position, worst at the midpoint and best near either endpoint; with interference, the optimum depends on source transmit and interference power.Source: B. Motivation and Contributions · p. 2

C. Structure and notations

  • The paper is organized around system modeling, mathematical preliminaries, noise-only and interference-plus-noise analyses, numerical results, and a conclusion.Its notation section defines vector and scalar conventions and lists special functions used in the analysis.Source: C. Structure and notations · p. 2

II. SYSTEM MODEL

  • The model uses a multi-antenna PB to power a single-antenna source, which harvests energy before transmitting to a single-antenna destination.The PB is assumed capable of channel estimation, digital beamforming, and spectrum sensing; Nakagami-m fading models the PB-to-source link.Source: §II · p. 2, A. Noise Limited Scenario · p. 3

B. Interference plus Noise Scenario

This section models a single dominant co-channel interferer in both the energy-harvesting and information-transmission phases. It also presents optimization preliminaries used in the analysis.

B. Interference plus Noise Scenario

  • One dominant interferer contributes energy at the source during harvesting and interference at the destination during transmission; its power remains constant over block T.The model notes that the analysis could extend to multiple independent, non-identically distributed interferers.Source: B. Interference plus Noise Scenario · p. 3

III. PRELIMINARIES

  • The preliminaries include optimization lemmas; their proofs establish concavity for functions whose maximizers are sought.One lemma identifies an optimum using the Lambert W function.Source: §III · p. 4
  • A preliminary lemma expresses an optimal x using the Lambert W function.The lemmas are introduced as results invoked later in the analysis.Source: §III · p. 4

IV. NOISE LIMITED SCENARIO

The section focuses on achievable average throughput in a noise-limited wireless-powered communication network.

IV. NOISE LIMITED SCENARIO

  • The stated focus is achievable average throughput in the noise-limited wireless-powered communication network.Source: §IV · p. 4

A. Delay intolerant transmission

For delay-intolerant transmission, the source sends at a fixed rate and fading can cause outage, so average throughput depends on the outage probability. The section characterizes throughput and the optimal time split, including high-power and large-antenna cases.

A. Delay intolerant transmission

  • The average throughput is characterized for fixed-rate delay-intolerant transmission, where fading can cause outage.The throughput expression uses the outage probability.Source: A. Delay intolerant transmission · p. 4
  • The outage analysis uses the Gamma-distributed channel gain and derives a simpler product-channel CDF by averaging over one channel gain.The alternative avoids the multiple summations of an existing CDF expression.Source: A. Delay intolerant transmission · pp. 4–5
  • In the high-transmit-power regime, the optimal time split has a closed-form solution and decreases with transmit power, antenna count, and Nakagami-m fading parameter.A larger fading parameter corresponds to less severe fading and requires less harvesting time.Source: A. Delay intolerant transmission · p. 5
  • The optimal time split generally increases with transmission rate, and its exact value can be found numerically when a closed form is unavailable.The paper describes one-dimensional search as an efficient option.Source: A. Delay intolerant transmission · p. 5
  • As the number of antennas grows large, the optimal time split also has a closed-form solution and decreases with transmit power and antenna count.The large-antenna analysis approximates outage using the law of large numbers.Source: A. Delay intolerant transmission · p. 5

B. Delay tolerant transmission

For delay-tolerant transmission, throughput is based on ergodic capacity because long codewords experience channel realizations over time. The section gives throughput expressions and bounds, while noting that the exact optimal time split is difficult to express in closed form.

B. Delay tolerant transmission

  • Delay-tolerant throughput uses ergodic capacity because sufficiently long codewords experience channel realizations over time.The source's constant rate is bounded by ergodic capacity.Source: B. Delay tolerant transmission · p. 5
  • The average throughput is expressed using a Meijer G-function, and the exact optimal time split is difficult to obtain in closed form.The throughput derivation uses the channel-product distribution and a Meijer G representation of the logarithm.Source: B. Delay tolerant transmission · pp. 5–6
  • A simple lower bound is provided for delay-tolerant throughput, with a high-SNR approximation also derived.The lower-bound derivation uses convexity of log(1 + exp(x)).Source: B. Delay tolerant transmission · p. 6

V. INTERFERENCE PLUS NOISE SCENARIO

The interference-plus-noise analysis presents analytical average-throughput expressions for both transmission modes.

V. INTERFERENCE PLUS NOISE SCENARIO

  • For the interference-plus-noise scenario, the paper presents analytical average-throughput expressions for both transmission modes.Source: §V · p. 6

A. Delay intolerant transmission

For delay-intolerant transmission with interference plus noise, the section gives an exact integral throughput expression and an upper bound. The optimal time split is generally challenging to express in closed form and can be found by numerical search.

A. Delay intolerant transmission

B. Delay tolerant transmission

The section presents throughput analysis for delay-tolerant transmission and simulations of how antennas, time allocation, fading, interference, and source position affect system performance. Interference can help when its harvested energy outweighs its harm to information transmission, with the balance depending on operating conditions.

B. Delay tolerant transmission

VI. NUMERICAL AND SIMULATION RESULTS

  • More PB antennas improve throughput, but their benefit diminishes at sufficiently high transmit power as performance becomes limited by the fixed transmission rate.For delay-intolerant transmission with Rc = 1, the maximum throughput is 0.5 at τ = 0.5 and 0.6 at τ = 0.4.Source: §VI · p. 7
  • For delay-tolerant transmission, larger τ is preferred at low transmit power, while smaller τ is preferred at high power.Low power calls for more harvesting time to maintain low outage probability; high power requires less harvesting time.Source: §VI · pp. 7–8
  • The high-power approximation for optimal τ tightens with transmit power or antenna count, while the large-N approximation performs extremely well even at N = 2 regardless of transmit power.The section examines these approximations against the optimal time split.Source: §VI · pp. 8–9
  • Increasing Nakagami-m fading severity raises throughput when N = 1, but has marginal impact when N = 10 because channel hardening mitigates fading.Source: §VI · p. 9
  • Strong interference can raise throughput at low transmit power but cause significant loss at high power, reflecting its competing energy-supply and signal-corruption effects.Whether interference helps also depends on path-loss exponent, interference distance, and interference power.Source: §VI · p. 9
  • Without interference, throughput is symmetric in the PB-to-source and source-to-destination distances and is worst at the midpoint; with interference, the optimal source location depends on transmit and interference power.Source: §VI · p. 9
  • As interferer-to-source distance increases, throughput falls; a larger path-loss exponent widens the distance range over which interference improves throughput, and the effect also depends on interference power.At α = 2, interference appears undesirable, whereas at α = 2.5 or 3 strong interference can improve throughput in the reported setting.Source: §VI · p. 10

VII. CONCLUSION

The paper derives average-throughput expressions for delay-intolerant and delay-tolerant transmission and examines throughput-maximizing time splits and co-channel interference. It concludes that interference's effect depends on the propagation environment and system setup, while several practical challenges remain for future study.

VII. CONCLUSION

  • Closed-form approximations for the throughput-maximizing time split are reported as very accurate and do not require instantaneous channel state information.The paper describes this as a low-complexity way to enhance system throughput.Source: §VII · p. 10
  • Whether co-channel interference helps or hurts average throughput depends on the path loss exponent, transmit power, network topology, and interference power.Source: §VII · p. 10
  • Minimum circuit activation energy, mobile energy storage, and multiuser communication are identified as topics for future study.The paper presents these as examples of theoretical and practical challenges in wireless powered communications.Source: §VII · p. 10

APPENDIX A PROOF OF LEMMA 2

The appendices establish the optimization properties behind the time-split results and derive an exact outage probability for Proposition 3. They use curvature arguments for the optimization lemmas and distributional calculations for the outage result.

APPENDIX A PROOF OF LEMMA 2

  • Lemma 2's proof establishes convexity below x⋆ and concavity above it, locating the maximum at x∗ in the concave regime.The proof also states that x⋆ < x∗.Source: Appendix A · p. 11

APPENDIX B PROOF OF LEMMA 3

  • Lemma 3's proof uses strict concavity to establish a unique maximizing x∗, obtained by solving an equation and expressed using the Lambert W function.Source: Appendix B · p. 11

APPENDIX C PROOF OF PROPOSITION 3

  • Proposition 3's proof derives the exact outage probability by characterizing the SINR through the distributions of U and V.It obtains U's CDF by conditioning and averaging, and uses the inverse Laplace transform for V's distribution.Source: Appendix C · p. 11

APPENDIX D PROOF OF PROPOSITION 4

The proof of Proposition 4 lower-bounds ergodic capacity using Jensen’s inequality. It evaluates expectations involving the logarithms of U and V to obtain the desired result.

APPENDIX D PROOF OF PROPOSITION 4

  • Jensen’s inequality is used to lower-bound ergodic capacity.Source: Appendix D · p. 12
  • The expectation of ln γI is evaluated through the expectations of ln U and ln V.Source: Appendix D · p. 12
  • The proof computes E{ln V} using the pdf of V and an integration formula, then combines the results to obtain the desired result.Source: Appendix D · p. 12

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