# Resource Allocation for Machine-Type Communication of Energy-Harvesting Devices in Wi-Fi HaLow Networks

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## Abstract

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## 1. Introduction

## 2. Problem Statement

#### 2.1. Channel Access Method

#### 2.2. Scenario

## 3. Related Papers

## 4. Mathematical Model

#### 4.1. Periodic RAW

#### 4.2. RAW Slot

- empty if none of the STAs transmits a frame;
- successful if only one STA accesses the channel, and the frame transmission is not affected by the noise;
- unsuccessful if only one STA accesses the channel, but the frame is damaged by the noise;
- collision if more than one STAs access the channel.

- the chosen STA transmits its frame successfully, or
- it runs out of energy, or
- its retry counter reaches $RL$, or
- the RAW slot is terminated.

- With probability ${\Pi}_{out}\left({\eta}_{t}\right)$, the process transits to the absorbing state ${\eta}_{t+1}=\ast $.
- With probability ${\Pi}_{e,k}\left({\eta}_{t}\right)$, the slot is empty and k other STAs run out of energy. Thus, the process transits to ${\eta}_{t+1}=(n-k,f,r)$.
- With probability ${\Pi}_{s,k}^{-}\left({\eta}_{t}\right)$, the slot is successful, the chosen STA does not try to transmit, and $k-1$ other STAs run out of energy; the process transits to ${\eta}_{t+1}=(n-k,f+1,r)$.
- With probability ${\Pi}_{f,k}^{-}\left({\eta}_{t}\right)$, the slot is unsuccessful, the chosen STA does not try to transmit, and k other STAs run out of energy. The process transits to ${\eta}_{t+1}=(n-k,f+1,r)$.
- With probability ${\Pi}_{c,k}^{-}\left({\eta}_{t}\right)$, the slot is collision, the chosen STA does not try to transmit, and k other STAs run out of energy. The process transits to ${\eta}_{t+1}=(n-k,f+1,r)$.
- With probability ${\Pi}_{f,k}^{+}\left({\eta}_{t}\right)$, the chosen STA tries to transmit a frame, the slot is unsuccessful, and k other STAs run out of energy. The process transits to ${\eta}_{t+1}=(n-k,f+1,r+1)$.
- With probability ${\Pi}_{c,k}^{+}\left({\eta}_{t}\right)$, the slot is collision, the chosen STA tries to transmit a frame, and k other STAs run out of energy. The process transits to ${\eta}_{t+1}=(n-k,f+1,r+1)$.

#### 4.2.1. The Probability of Chosen STA Transmitting a Frame

- $Pr(t,r)$ is the probability of the considered process not to transit to the absorbing state and the chosen STA making r transmission attempts by the moment t.
- $Pr(A,t,r)$ is the probability of the considered process by the moment t not to transit to the absorbing state, the chosen STA making r transmission attempts and an event $A\in \left(\right)open="\{"\; close="\}">TX,C,S$ occurring:
- –
- $TX$ means that the STA makes a transmission attempt.
- –
- C means that the STA makes a transmission attempt that leads to collision.
- –
- S means that the STA makes a transmission attempt that does not lead to collision.

#### 4.2.2. The Probability of Other STA Transmitting a Frame

#### 4.2.3. Additional Values

- ${\pi}_{k}\left({\eta}_{t}\right)$ is the probability of k other STAs transmitting in slot t,
- ${\pi}_{e}\left({\eta}_{t}\right)$ is the probability of none of the STAs transmitting in slot t,
- ${\pi}_{s}^{+}\left({\eta}_{t}\right)$ is the probability of only the chosen STA transmitting in slot t,
- ${\pi}_{s}^{-}\left({\eta}_{t}\right)$ is the probability of one other STA transmitting in slot t,
- ${\pi}_{c}^{+}\left({\eta}_{t}\right)$ is the probability of the chosen STA and at least one other STA transmitting in slot t,
- ${\pi}_{c}^{-}\left({\eta}_{t}\right)$ is the probability of the chosen STA not transmitting in slot t, but at least two other STAs transmitting in this slot.

#### 4.2.4. The Probability of the Process to Transit to the Absorbing State

- If the STA cannot transmit the frame by the end of the RAW, i.e., ${T}_{raw}-{T}_{real}(t,f)<\tau $, the process transits to the absorbing state, i.e., ${\Pi}_{out}=1$.
- Otherwise, two situations are possible:
- –
- if $r\ne RL-1$, the process transits to the absorbing state if the frame transmission is successful, or if the chosen STA runs out of energy:$$\begin{array}{cc}\hfill {\Pi}_{out}& =Pr(Q<{q}_{e}){\pi}_{e}+Pr(Q<{q}_{ts})p{\pi}_{s}^{+}\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& +Pr(Q<{q}_{tf}){\pi}_{c}^{+}+Pr(Q<{q}_{rs}){\pi}_{s}^{-}\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& +Pr(Q<{q}_{rf}){\pi}_{c}^{-}+(1-p){\pi}_{s}^{+}.\hfill \end{array}$$
- –
- if $r=RL-1$, the process transits to the absorbing state on any transmission attempt, or if the chosen STA runs out of energy:$${\Pi}_{out}=Pr(Q<{q}_{e}){\pi}_{e}+Pr(Q<{q}_{rs}){\pi}_{s}^{-}+Pr(Q<{q}_{rf}){\pi}_{c}^{-}+{\pi}_{s}^{+}+{\pi}_{c}^{+}.$$

#### 4.2.5. The Probability of the Slot Being Empty

#### 4.2.6. The Probability of the Slot Being Successful and the Chosen STA Not Trying to Transmit

#### 4.2.7. The Probability of the Slot Being Unsuccessful and the Chosen STA Not Trying to Transmit

#### 4.2.8. The Probability of the Slot Being Collision and the Chosen STA Not Trying to Transmit

#### 4.2.9. The Probability of the Chosen STA Trying to Transmit and the Slot Being Unsuccessful

#### 4.2.10. The Probability of the Chosen STA Trying to Transmit and the Slot Being Collision

#### 4.3. The Probability of the Chosen STA Transmitting Its Frame Successfully

## 5. Numerical Results

#### 5.1. RAW Slot

#### 5.2. Periodic RAW

## 6. Conclusions

- We have developed a model of data transmission in the RAW slot when STAs transmit single packets, the STAs have limited amounts of energy, and their transmissions can be disrupted by random noise. The model allows us to calculate the probability that the data are delivered with a given RAW configuration.
- We have shown that it is important to consider the amount of STAs’ energy in order to properly configure the RAW parameters, while the usage of models that do not consider the STA energy consumption may violate the requirements on the reliability of communications.
- We have shown how to use the developed model to optimize the RAW slot duration in order to provide the required probability of data delivery and to minimize the amount of consumed channel resources.
- We have shown that the channel resource consumption can change drastically depending on the reliability requirements: changing the required probability by 1% can increase the consumption by almost 100%, so the RAW parameters optimization shall take into account the requirements of particular applications.

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

ACK | Acknowledgement Frame |

AIFS | Arbitration Inter-Frame Space |

AP | Access Point |

CSMA/CA | Carrier Sense Multiple Access with Collision Avoidance |

EDCA | Enhanced Distributed Channel Access |

IoT | Internet of Things |

RAW | Restricted Access Window |

SIFS | Short Inter-Frame Space |

STA | Station |

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**Figure 4.**The dependency of the probability of successful frame transmission on the RAW slot duration for various p, $\langle Q\rangle $, and N.

**Figure 5.**The dependency of the cycle duration on the number of groups for different data generation probability ${p}_{in}$.

**Figure 6.**The dependency of the probability of successful frame transmission on the RAW duration for small numbers of STAs.

Symbol | Meaning |
---|---|

${N}_{0}$ | Total number of STAs in the network |

G | Number of STA groups |

${N}_{1},{N}_{2}$ | Number of STAs in big and small groups |

${G}_{1},{G}_{2}$ | Number of big and small groups |

T | RAW period |

${D}_{max}$ | Maximal transmission delay |

${p}_{in}$ | Probability of an STA having data to transmit in its RAW slot |

${T}_{raw}$ | RAW slot duration |

${S}_{raw}(n,{T}_{raw})$ | Probability of the STA making a successful transmission in a RAW slot to which n STAs are assigned |

${S}_{total}$ | Probability of the STA making a successful transmission during a RAW period |

$\sigma $ | Empty slot duration |

$\tau $ | Non-empty slot duration |

${D}_{dat}$ | Data frame duration |

${D}_{ack}$ | Ack frame duration |

t | Model time measured in virtual slots from the beginning of the considered RAW slot |

${\eta}_{t}=(n,f,r)$ | State of the Markov process in virtual slot t that describes the transmission within a RAW slot, here n is the number of still active STAs, f is the number of elapsed non-empty slots, and r is the retry counter of the considered STA |

$RL$ | Retry limit |

${T}_{real}(t,f)$ | Real (not virtual) time which corresponds to t virtual slots out of which f are non-empty |

Q | Amount of energy which the STA has at the beginning of the RAW slot |

k | Number of STAs that run out of energy during a virtual slot |

${\Pi}_{out}$ | Probability that the process transits to the absorbing state |

${\Pi}_{e,k}$ | Probability of an empty slot |

${\Pi}_{s,k}^{+},{\Pi}_{s,k}^{-}$ | Probability of a slot with successful transmission made by the considered STA (+) and by an other STA (-) |

${\Pi}_{f,k}^{+},{\Pi}_{f,k}^{-}$ | Probability of a slot with unsuccessful transmission made by the considered STA (+) and by an other STA (-) |

${\Pi}_{c,k}^{+},{\Pi}_{c,k}^{-}$ | Probability of a collision slot involving (+) and not involving (-) the considered STA |

${\pi}_{k}\left({\eta}_{t}\right)$ | Probability of k other STAs transmitting in slot t, |

${\pi}_{e}\left({\eta}_{t}\right)$ | Probability of none of the STAs transmitting in slot t, |

${\pi}_{s}^{+}\left({\eta}_{t}\right)$ | Probability of only the chosen STA transmitting in slot t, |

${\pi}_{s}^{-}\left({\eta}_{t}\right)$ | Probability of one other STA transmitting in slot t, |

${\pi}_{c}^{+}\left({\eta}_{t}\right)$ | Probability of the chosen STA and at least one other STA transmitting in slot t |

${\pi}_{c}^{-}\left({\eta}_{t}\right)$ | Probability of the chosen STA not transmitting in slot t, but a collision to happen |

V | Consumed voltage |

${I}_{LS},{I}_{RX},{I}_{TX}$ | Current consumed by the STA for channel listening, receiving and transmitting |

${q}_{e}$ | Energy consumed by the STA during an empty slot |

${q}_{rf}$ | Energy consumed by the STA during a non-empty slot, in which it does not transmit |

${q}_{rs}$ | Energy consumed by the STA during a successful slot, in which it does not transmit |

${q}_{tf}$ | Energy consumed by the STA during a non-empty slot, in which it transmits |

${q}_{ts}$ | Energy consumed by the STA during a successful slot, in which it transmits |

Parameter | Value | Parameter | Value | Parameter | Value |
---|---|---|---|---|---|

$\sigma $ | 52 μs | $\tau $ | 2196 μs | ${q}_{e}$ | 3 μJ |

${D}_{Ack}$ | 240 μs | V | $1.1$ V | ${q}_{rf}$ | 202 μJ |

${D}_{dat}$ | 1480 μs | ${I}_{LS}$ | 50 mA | ${q}_{rs}$ | 215 μJ |

$SIFS$ | 160 μs | ${I}_{TX}$ | 280 mA | ${q}_{tf}$ | 495 μJ |

$AIFS$ | 316 μs | ${I}_{RX}$ | 100 mA | ${q}_{ts}$ | 508 μJ |

$C{W}_{0}$ | 16 | $RL$ | 7 |

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**MDPI and ACS Style**

Bankov, D.; Khorov, E.; Lyakhov, A.; Famaey, J.
Resource Allocation for Machine-Type Communication of Energy-Harvesting Devices in Wi-Fi HaLow Networks. *Sensors* **2020**, *20*, 2449.
https://doi.org/10.3390/s20092449

**AMA Style**

Bankov D, Khorov E, Lyakhov A, Famaey J.
Resource Allocation for Machine-Type Communication of Energy-Harvesting Devices in Wi-Fi HaLow Networks. *Sensors*. 2020; 20(9):2449.
https://doi.org/10.3390/s20092449

**Chicago/Turabian Style**

Bankov, Dmitry, Evgeny Khorov, Andrey Lyakhov, and Jeroen Famaey.
2020. "Resource Allocation for Machine-Type Communication of Energy-Harvesting Devices in Wi-Fi HaLow Networks" *Sensors* 20, no. 9: 2449.
https://doi.org/10.3390/s20092449