# Exploiting the Capture Effect to Enhance RACH Performance in Cellular-Based M2M Communications

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## Abstract

**:**

## 1. Introduction

- We formulated analysis models of the RA procedure considering the capture effect. Previous studies [4,5,6,12,13,14] adopted the collision model to analyze the RA procedure and assumed that the RA performance degradation due to the collisions of the preambles (Msg1) could not be prevented. However, we provide an RA analysis model that considers the capture effect. Therefore, we consider RA performance improvements due to the capture effect of the physical layer, even if the collision occurs. We provide an RA performance analysis model, in terms of the RA throughput, the connection failure probability, and the average energy consumption of the devices.
- Exploiting the capture effect to improve the RA performances, we propose the Msg3 PR scheme. This scheme causes a difference in the received power of messages at the eNB, so that the capture effect occurs frequently. In addition, it is easy to apply because the proposed scheme adopts the power ramping scheme that has already been used in the cellular system. Moreover, by applying this new technique, a device that has performed many retransmissions would have a higher RA success probability; thus, the connection failure probability could be reduced.
- In the simulation, we demonstrate the accuracy of proposed analysis and the advantages of the Msg3 PR scheme. In addition, the effects of various network parameters on the performance of the technology are demonstrated. Moreover, we discuss the beneficial points of the proposed scheme when used with other RA-related schemes.

## 2. System Model

#### 2.1. Random Access Procedure

- Msg1. Preamble transmissionThe RA procedure is initiated by the transmission of a preamble that is randomly chosen from preamble set V at a predetermined RA slot. As a result, there are three cases: singleton preamble, collided preambleand empty preamble. Singleton preamble is chosen by exactly one device, the collided preamble preamble is chosen by multiple devices, and the empty preamble is chosen by none of the devices. An eNB can only detect whether a specific preamble is transmitted, but cannot determine whether it is a collided preamble or a singleton preamble [17,18]. Devices that send Msg1 set the random-access-response (RAR) window.
- Msg2. RARWhen the eNB detects a preamble transmission, it sends an Msg2 for the corresponding preambles through the physical-downlink control channel (PDCCH). This Msg2 contains the radio-network temporary identifier (RA-RNTI), the timing-advance (TA) information, and the uplink grant. The RA-RNTI identifies the corresponding preamble, the TA information is used to adjust the synchronization of the corresponding device, and the uplink grant is used to schedule the transmission of Msg3. Because the eNB cannot distinguish between singleton and collided preambles, it sends Msg2 for either preamble. Therefore, multiple devices that select the same preamble during Msg1 transmission receive the same Msg2, which only indicates the corresponding preamble. If a device does not receive an Msg2 within the RAR window, it realizes that the current RA has failed.
- Msg3. RRC-connection requestAfter sending Msg1, the device observes the PDCCH for the RAR window. If it finds the corresponding Msg2, it sends the Msg3, containing its identifier, by using a physical-uplink shared channel (PUSCH) informed by the uplink grant in the Msg2. Devices that send Msg3 set the contention–resolution time. Devices that choose the same preamble (i.e., collided preamble) also send an Msg3 containing their own identifier by using the same uplink grant, and, therefore, an Msg3 collision can occur.
- Msg4. RRC-connection setupThe eNB transmits the Msg4 using the PDCCH to inform the device that an RRC connection has been set up. Because the Msg4 contains the device identifier received from successfully received Msg3, an RA collision can be resolved if a specific Msg3 is decoded by capture effect.

#### 2.2. Power Capture Effect

#### 2.3. Uplink Power Control

## 3. Motivation and Proposed Scheme

## 4. Analysis Model

#### 4.1. System Model

**Definition**

**1.**

**Definition**

**2.**

**Definition**

**3.**

**Definition**

**4.**

#### 4.2. RA Throughput

#### 4.2.1. One-Shot RA Throughput Analysis

#### 4.2.2. Steady-State RA Throughput Analysis Model

#### 4.3. Connection Failure Probability

#### 4.4. Average Energy Consumption

#### 4.4.1. Energy Consumption Model

- The energy consumed during a failed RA event is equal to that consumed in the following steps: waiting for the first RA slots($({\tau}_{RA\_REP}/2){P}_{1}$), transmitting Msg1 (${P}_{3}$), waiting for the RAR window (${\tau}_{RAR}{P}_{1}$), wating for the Msg2 ($({W}_{RAR}/2){P}_{2}$), receiving the Msg2 (${\tau}_{msg2}{P}_{2}$), processing time for Msg3 (${T}_{proc}{P}_{2}$), transmitting Msg3 (${P}_{3}$), and expiring the contention-resolution timer (${W}_{con\_sol}{P}_{2}$).
- The energy consumed during a successful RA event is equal to that consumed during the following steps. From transmitting Msg1 to receiving Msg2, the power consumed by the successful RA follows that consumed by the failed RA procedure and equals $(({\tau}_{RA\_REP}/2){P}_{1}+{P}_{3}+{\tau}_{RAR}{P}_{1}+({W}_{RAR}/2){P}_{2}+{\tau}_{msg2}{P}_{2}+{T}_{proc}{P}_{2}+{P}_{3})$. In addition, the following steps are: for waiting Msg4 ($({W}_{con\_sol}/2){P}_{2}$), the power consumed when receiving Msg4 (${\tau}_{msg4}{P}_{2}$), processing time for acknowledgement (ACK) (${T}_{proc2}{P}_{2}$), and the power consumed by transmitting the ACK of Msg4 (${P}_{3}$).

#### 4.4.2. Average Energy Consumption

## 5. Simulation Results

#### 5.1. Performance of the Msg3 PR Scheme

- RA throughput(Anal.)—Equation (18).(Sim.)$$E\left[S\right|N]=\frac{Total\phantom{\rule{0.166667em}{0ex}}\#\phantom{\rule{0.166667em}{0ex}}ofRA\phantom{\rule{0.166667em}{0ex}}Success\phantom{\rule{0.166667em}{0ex}}Devices}{N\times SimNumber},$$
- Connection failure probability(Anal.)—Equation (25).(Sim.)$${\mathbb{P}}_{CF|N}=\frac{Total\phantom{\rule{0.166667em}{0ex}}\#\phantom{\rule{0.166667em}{0ex}}of\phantom{\rule{0.166667em}{0ex}}Connection\phantom{\rule{0.166667em}{0ex}}Failed\phantom{\rule{0.166667em}{0ex}}Devices}{Total\phantom{\rule{0.166667em}{0ex}}\#\phantom{\rule{0.166667em}{0ex}}of\phantom{\rule{0.166667em}{0ex}}RA\phantom{\rule{0.166667em}{0ex}}Completed\phantom{\rule{0.166667em}{0ex}}Devices},$$
- Average energy consumption(Anal.)—Equation (30).(Sim.)$$E\left[W\right|N]=\frac{Total\phantom{\rule{0.166667em}{0ex}}E.C\phantom{\rule{0.166667em}{0ex}}of\phantom{\rule{0.166667em}{0ex}}RA\phantom{\rule{0.166667em}{0ex}}Completed\phantom{\rule{0.166667em}{0ex}}Devices}{Total\phantom{\rule{0.166667em}{0ex}}\#\phantom{\rule{0.166667em}{0ex}}of\phantom{\rule{0.166667em}{0ex}}RA\phantom{\rule{0.166667em}{0ex}}Completed\phantom{\rule{0.166667em}{0ex}}Devices}.$$

#### 5.1.1. The Consequences of the Capture Effect and Its Properties

#### 5.1.2. The RA Throughput

#### 5.1.3. The Connection Failure Probability

#### 5.1.4. The Average Energy Consumption

#### 5.2. Coexistence with Other Schemes

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Markov chain model of the devices. State $<t,k>$ indicates that the devices with the trial number ${T}_{u}=t$ and ${Z}_{u}=k$. Note that state transitions occur when (

**a**) random acess (RA) failure, (

**b**) RA success, and (

**c**) connection failure occurs, respectively.

**Figure 4.**The power consumption model for (

**a**) single failed RA event (

**b**) single successful RA event.

**Figure 5.**RA success probability according to the location of the device with $N=60$. i.e., $\mathbb{P}\left({S}_{u}\right|N=60,{X}_{u}=x)$.

**Figure 10.**Average energy consumption of devices that completed the RA procedure (${N}_{max}=8$, $V=20$).

**Figure 11.**Cumulative distribution function (CDF) of RA results when optimal acess class barring (ACB) is used.

Notation | Description |
---|---|

$\mathcal{N}/N$ | a set of devices participate RA/the size of $\mathcal{N}$ |

${M}_{v}$ | the number of devices that select preamble v among terminals excluding device u |

${V}_{u}$ | a preamble selected by device u |

${T}_{u}$ | the RA trial number of device u |

${R}_{u}$ | the ramping number of device u |

${S}_{u}$ | the event that device u succeeds in the RA procedure |

${P}_{u}\left({{P}_{u}}^{rx}\right)$ | transmission (received) power of (from) device u |

${K}_{max}\left(x\right)$ | the maximum ramping number of a device located at a distance x from eNB |

$PRS$ | Power ramping step |

${X}_{u}$ | distance from eNB to device u |

${Z}_{u}$ | the zone where device u belongs |

${N}_{T=t}^{k}\left({N}_{R=r}^{k}\right)$ | a set of devices located within $zone\phantom{\rule{0.277778em}{0ex}}k$ with trial number t (with ramping number r) |

${\overline{\delta}}_{F,k}\left(t\right)\left(\right)open="("\; close=")">{\overline{\delta}}_{S,k}\left(t\right)$ | the average energy consumption of device located within $zone\phantom{\rule{0.277778em}{0ex}}k$ with the trial number t, having |

single failed (successful) RA events, | |

${w}_{S}(t,k)\left(\right)open="("\; close=")">{w}_{F}\left(k\right)$ | the energy consumption of the device that succeeded (failed) in the connection |

W | the energy consumption of device which is completed the RA procedure |

Notation | Definition | Values |
---|---|---|

Parameters Relative to RA Procedure | ||

V | the number of preambles | 20, 40, 60 |

${N}_{max}$ | maximum number of RA trial | 4, 8, 12 |

${X}^{cell}$ | radius of single cell | 1500 m |

${X}_{u}$ | The distribution of devices | uniform |

Parameters Relative to Power Model | ||

$PIRTP$ | Preamble initial receive target power | −104 dBm |

${\mathcal{P}}_{Cmax}$ | Maximum transmit power | 23 dBm |

$PRS$ | Power ramping step | 1, 2, 3, 4 dB |

$delta$ | offset value | 0 dBm |

${PL}_{0}$ | reference path-olss | 127 dBm |

${x}_{0}$ | reference point distance | 1500 m |

$\alpha $ | path-loss exponent | 2 |

Parameters Relative to Energy Consumption Model [10] | ||

${\tau}_{RA\_REP}$ | periodicity of RACH | 5 ms |

${\tau}_{RAR}$ | processing delay | 2 ms |

${W}_{RAR}$ | RAR window size | 5 ms |

${\tau}_{msg2},{\tau}_{msg4}$ | requiring time for receiving Msg2/Msg4 | 1 ms |

${W}_{con\_sol}$ | size of Contention-resolution timer | 48 ms |

${\mathcal{P}}_{1}$ | power consumption when the device is waiting | −37 dBm |

${\mathcal{P}}_{2}$ | power consumption when the device is receiving | −22 dBm |

Power ramping step (PRS) $\backslash {\mathit{R}}_{\mathit{u}}$ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|

1 dB | 4.9 | 4.9 | 4.9 | 9.8 | 13.3 | 15.8 | 20.0 | 28.4 |

2 dB | 4.9 | 4.9 | 12.0 | 21.3 | 36.6 | 59.1 | 81.8 | 95.7 |

3 dB | 4.9 | 14.0 | 26.3 | 50.6 | 81.2 | 97.6 | 99.9 | 99.9 |

4 dB | 4.9 | 15.3 | 45.0 | 82.7 | 98.9 | 99.9 | 99.9 | 99.9 |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Kim, J.; Lee, J.
Exploiting the Capture Effect to Enhance RACH Performance in Cellular-Based M2M Communications. *Sensors* **2017**, *17*, 2169.
https://doi.org/10.3390/s17102169

**AMA Style**

Kim J, Lee J.
Exploiting the Capture Effect to Enhance RACH Performance in Cellular-Based M2M Communications. *Sensors*. 2017; 17(10):2169.
https://doi.org/10.3390/s17102169

**Chicago/Turabian Style**

Kim, Jonghun, and Jaiyong Lee.
2017. "Exploiting the Capture Effect to Enhance RACH Performance in Cellular-Based M2M Communications" *Sensors* 17, no. 10: 2169.
https://doi.org/10.3390/s17102169