# On the Throughput Region of Wireless Random Access Protocols with Multi-Packet Reception Using Multi-Objective Optimization

## Abstract

**:**

## 1. Introduction

#### 1.1. Open Issues and Paper Contributions

#### 1.2. Organization

## 2. System Model and Assumptions

#### 2.1. Scenario Description and Epoch-Slot Definition

#### 2.2. Throughput and Throughput Region

#### 2.3. N-Reception Model

## 3. Multi-Objective Optimization

#### 3.1. Case $N=J-1$

#### 3.2. Symmetrical Case N-Reception Model

#### 3.3. General Case N-Reception Model

## 4. Generalized MPR Conditional Probabilistic Reception Model

#### Symmetrical Case

## 5. Results

## 6. Conclusions

## Funding

## Conflicts of Interest

## Appendix A. Derivation of the Coefficients C_{l} in (6) of the Throughput Expansion Function in (5)

## Appendix B. Derivation of the Expression in (11) of the Elements of the Jacobian Determinant Matrix for the N-Reception Model Considering $\mathit{N}\mathbf{=}\mathit{J}\mathbf{-}\mathit{1}$

## Appendix C. Derivation of the Optimum Transmission Probabilities in (12) for the N-Reception Model Considering $\mathit{N}\mathbf{=}\mathit{J}\mathbf{-}\mathit{1}$

## References

- Chen, Y.; Cheng, L.; Wang, L. Prioritized resource reservation for reducing random access delay in 5G URLLC. In Proceedings of the IEEE 28th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC), Montreal, QC, Canada, 8–13 October 2017; pp. 1–5. [Google Scholar]
- Hussain, S.; Khan, U.A.; Anjum, M.R.; Hayat, M.A. Reconfigurable antenna parameters with the change in the position of switches. Electron. Devices
**2016**, 5, 34–44. [Google Scholar] - Meloni, A.; Murroni, M. Random access in DVB-RCS2: Design and dynamic control for congestion avoidance. IEEE Trans. Broadcast.
**2014**, 60, 16–28. [Google Scholar] [CrossRef] - Casini, E.; de Gaudenzi, R.; Herrero, O.D. Contention resolution diversity slotted ALOHA (CRDSA): An enhanced random access schemefor satellite access packet networks. IEEE Trans. Wirel. Commun.
**2007**, 6, 1408–1419. [Google Scholar] [CrossRef] - Tong, L.; Naware, V.; Venkitasubramaniam, P. Signal processing in random access. IEEE Signal Process. Mag.
**2004**, 21, 29–39. [Google Scholar] [CrossRef] - Zorzi, M.; Rao, R. Capture and retransmission control in mobile radio. IEEE J. Sel. Areas Commun.
**1994**, 12, 1289–1298. [Google Scholar] [CrossRef][Green Version] - Yu, Y.; Cai, X.; Giannakis, G.B. On the stability of slotted ALOHA with capture. IEEE Trans. Wirel. Commun.
**2006**, 5, 257–261. [Google Scholar] [CrossRef] - Ghez, S.; Verdu, S.; Schwartz, S. Stability properties of slotted Aloha with multipacket reception capability. IEEE Trans. Autom. Control
**1988**, 33, 640–649. [Google Scholar] [CrossRef] - Ghez, S.; Verdu, S.; Schwartz, S. Optimal decentralized control in the random access multipacket channel. IEEE Trans. Autom. Control
**1989**, 34, 1153–1163. [Google Scholar] [CrossRef] - Zhao, Q.; Tong, L. A dynamic queue protocol for multiaccess wireless networks with multipacket reception. IEEE Trans. Wirel. Commun.
**2004**, 3, 2221–2231. [Google Scholar] [CrossRef] - Zhao, Q.; Tong, L. A multiqueue service room MAC protocol for wireless networks with multipacket reception. IEEE Trans. Netw.
**2003**, 11, 125–137. [Google Scholar] [CrossRef][Green Version] - Naware, V.; Mergen, G.; Tong, L. Stability and delay of finite-user slotted ALOHA with multipacket reception. IEEE Trans. Inf. Theory
**2005**, 51, 2636–2656. [Google Scholar] [CrossRef] - Luo, J.; Ephremides, A. On the throughput, capacity, and stability regions of random multiple access. IEEE Trans. Inf. Theory
**2006**, 52, 2593–2607. [Google Scholar] - Ngo, M.H.; Krishnamurty, V. Game theoretic cross-layer transmission policies in multipacket reception wireless networks. IEEE Trans. Signal Process.
**2007**, 55, 1911–1926. [Google Scholar] [CrossRef] - Ngo, M.H.; Krishnamurthy, V.; Tong, L. Optimal channel-aware ALOHA protocol for random access in WLANs with multipacket reception and decentralized channel state information. IEEE Trans. Signal Process.
**2008**, 56, 2575–2588. [Google Scholar] [CrossRef] - Adireddy, S.; Tong, L. Exploiting decentralized channel state information for random access. IEEE Trans. Inf. Theory
**2005**, 51, 537–561. [Google Scholar] [CrossRef] - Samano-Robles, R.; Gameiro, A. Multi-Objective and Financial Portfolio Optimization of p-Persistent Carrier Sense Multiple Access Protocols with Multi-Packet Reception. Chapter Commun. Comput. Inf. Sci. Optim. Nat. Sci.
**2015**, 499, 68–94. [Google Scholar] - Samano-Robles, R.; McLernon, D.C.; Ghogho, M. A random access protocol incorporating multi-packet reception, retransmission diversity and successive interference cancellation. In Proceedings of the 8th International Workshop on Multiple Access Communications (MACOM2015), Helsinki, Finland, 3–4 September 2015. [Google Scholar]
- Liva, G. Graph-based analysis and optimization of contention resolution diversity slotted ALOHA. IEEE Trans. Commun.
**2011**, 59, 477–487. [Google Scholar] [CrossRef] - Rao, R.R.; Ephremides, A. On the stability of interacting queues in a multiple-access system. IEEE Trans. Inf. Theory
**1988**, 4, 918–930. [Google Scholar] [CrossRef] - Boyd, S.; Vandenberghe, L. Convex Optimization; Cambridge University Press: Cambridge, UK, 2004. [Google Scholar]
- Tong, Y.; Dai, L. Maximum sum rate of slotted Aloha with successive interference cancellation. IEEE Trans. Commun.
**2018**, 16, 5385–5400. [Google Scholar] [CrossRef] - Samano-Robles, R.; Ghogho, M.; McLernon, D.C. Wireless Networks with retransmission diversity and carrier sense multiple access. IEEE Trans. Signal Process.
**2009**, 57, 3722–3726. [Google Scholar] [CrossRef]

**Figure 1.**Random access network with multi-packet reception capabilities (using a multiple-antenna receiver).

**Figure 2.**Throughput region of a multi-packet reception (MPR) system with two subsets of terminals: ${J}_{1}={J}_{2}=3$ using the N-reception model with different values of N.

**Figure 3.**Throughput region of a multi-packet reception (MPR) system with two subsets of terminals: ${J}_{1}=3$ and ${J}_{2}=1$ using the N-reception model with different values of N.

**Figure 4.**Throughput region of a multi-packet reception (MPR) system with two subsets of terminals: ${J}_{1}=30$ and ${J}_{2}=30$ using the N-reception model with different values of N.

**Figure 5.**Throughput region of a multi-packet reception (MPR) system with two subsets of terminals: ${J}_{1}={J}_{2}=3$ using the general reception model with different values of the reception parameter $\alpha $.

**Figure 6.**Throughput region of a multi-packet reception (MPR) system with two subsets of terminals: ${J}_{1}=3$ and ${J}_{2}=1$ using the general reception model with different values of the reception parameter $\alpha $.

Variable | Meaning |
---|---|

J | Total number of terminals in the network. |

N | Number of antennas at the receiver. |

${p}_{j}$ | Transmission probability of terminal j. |

${T}_{j}$ | Packet throughput of terminal j. |

$\mathcal{T}$ | Set of colliding terminals. |

${q}_{j|\mathcal{T}}$ | Probability of correct reception of terminal j |

given the set of colliding terminals $\mathcal{T}$. | |

${q}_{\mathcal{S}|\mathcal{T}}$ | Probability of correct reception of all terminals in $\mathcal{S}$ |

given the set of colliding terminals $\mathcal{T}$. | |

$\mathbf{T}$ | Vector of stacked throughput variables of all terminals. |

${\mathcal{C}}_{T}$ | Throughput region. |

$\mathbf{p}$ | Vector of stacked probability variables of all terminals. |

$\alpha $ | MPR reception exponent. |

${\mathcal{S}}_{l}$ | Set of terminals of size l: $|{\mathcal{S}}_{l}|=l$. |

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**MDPI and ACS Style**

Sámano-Robles, R. On the Throughput Region of Wireless Random Access Protocols with Multi-Packet Reception Using Multi-Objective Optimization. *Technologies* **2018**, *6*, 117.
https://doi.org/10.3390/technologies6040117

**AMA Style**

Sámano-Robles R. On the Throughput Region of Wireless Random Access Protocols with Multi-Packet Reception Using Multi-Objective Optimization. *Technologies*. 2018; 6(4):117.
https://doi.org/10.3390/technologies6040117

**Chicago/Turabian Style**

Sámano-Robles, Ramiro. 2018. "On the Throughput Region of Wireless Random Access Protocols with Multi-Packet Reception Using Multi-Objective Optimization" *Technologies* 6, no. 4: 117.
https://doi.org/10.3390/technologies6040117