# A Power Control Algorithm Based on Chicken Game Theory in Multi-Hop Networks

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. System Model

_{t}(i) from port #i is shown in Equation (1). The system’s supposition is that there is ideal rake combining, and the TPC works well enough to accurately value sending power. In addition, a fading channel with Rayleigh [35] is supposed as the L-path, so no diversity is applied in multi-hop relay networks [36,37,38,39,40,41,42]. Transmit power P

_{t}(i) from port #i is expressed below:

_{req}is the required received signal power. Between nodes #i and #j, there is some definition, including shadowing decay η

_{i,j}(dB), l-th path plurality path gain ξ

_{i,j}, path loss exponent α, and the distance d

_{i,j}. If the ensemble average operation is E[*], then the result is $E\left[{\left|{\xi}_{i,j}\right|}^{2}\right]=1/L$ independent plurality gaussian variables in which the zero-mean [43] is {ξ

_{i,j}}. In order to unify this article, “i” and “j” are used to symbolize nodes #i and #j.

_{r}(1) from the mobile terminal #i = 0 is given by

_{t}(0) can be written as

_{r}(i) of port #i is the total of all the received power from all the previous ports and is derived by

_{total}is calculated by totaling the transmit powers as follows:

_{r}(i) = P

_{req}, by using TPC, the transmit power P

_{t}(i − 1) of port #(i − 1) is derived via

_{r}(i) received from previous ports #0~#(i − 1) at port #i is larger than the required received power P

_{req}, i.e., P

_{r}(i) ≥ P

_{req}, port #(i − 1) can be fired from the constructed route, i.e., P

_{t}(i − 1) = 0. The transmit power P

_{t}(i − 2) of port #(i − 2) is given as:

_{norm}using MHMRC diversity [9] is described as the average total transmit power following the route normalized by that of a single-hop case, i.e., P

_{norm}= E[P

_{total}]/E[P

_{single-hop}], where P

_{total}is calculated by Equation (5) and P

_{single-hop}is calculated by Equation (1) with i = 0 (mobile terminal) and j = n (central port). Therefore, P

_{norm}is derived as follows:

_{t}(j) is derived from Equation (3) for port #j = 0 and from Equation (6) for ports #j = 1~n − 1, displacing i − 1 by j. P

_{t}(j) is derived recursively from Equation (6). Due to P

_{t}(0)∝P

_{req}, it can be easily accepted that P

_{t}(j)/P

_{req}is not a function of P

_{req}. Consequently, P

_{norm}is an independent variable relative to P

_{req}. In Equation (8), considering the fact that two operations of expectation and addition have been done, the algorithm complexity of P

_{norm}is O(n

^{3}).

## 3. Distributed Chicken Game Algorithm Power Control

_{norm}and is not any more complex than P

_{norm}. Therefore, the complexity of the proposed algorithm should be O(n

^{3}).

## 4. Simulation Analyses

Algorithm 1 Power control |

1: Initialize the local table. |

2: FUNCTION INIT () |

3: {if t = 0 Then P_{i} = P_{max}; P^{i}_{infer} = 0; |

Initialize (native_form); |

4: Endif;} |

5: update the local table once system get a new message. |

FUNCTION Deal Message (HI/HELLO) |

6: {if I get HELLO Then update(native_form); Endif;} |

7: determine whether system need to transmit the message according to evaluate the cost from native form. |

8: FUNCTION Send Message (M) |

9: {if i transmits M Then u < = find_payoff(native_form); |

10: Pi < = calculate_trans_power(u); |

11: If M = message then add_infer_area (P^{i}_{infer}); |

12: Endif; |

13: Endif;} |

- Maximum energy power control algorithm (MAXPCA), by which all the nodes in the networks choose the highest transmission power;
- Minimum energy power control algorithm (MINPCA), by which all the nodes in the networks choose the lowest sending power;
- Distributed chicken game algorithm to power control (DCGAPC), which is the method proposed in this article.

- Reachability—ratio of the figures of the correct messages received compared to the figure of the actual messages received.
- Average latency—how long it takes for a broadcast message to be sent from the source node to all nodes in the network.
- Capacity—maximum data transmission rate for the link with the lowest processing power in the network.
- Energy efficiency—the ratio of the sum figure of the messages received compared to the energy consumed in broadcasting each unit.

^{−7}~e

^{−8}level/magnitude. However, MINPCA generates less interference with e

^{−10}~e

^{−11}level/magnitude due to its low sending power. DCGAPC shows the least interference, with only e

^{−11}level/magnitude. Because this algorithm can regulate the sending power via the condition of the channels, its interference is less than the other two methods.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Kudoh, E.; Adachi, F. Study of a multi-hop communication in a virtual cellular system. In Proceedings of the WPMC—Wireless Personal Multimedia Communiations, Yokosuka, Japan, 19–22 October 2003. [Google Scholar]
- Behzad, A.; Rubin, I. Impact of power control on the performance of Ad hoc wireless networks. In Proceedings of the INFOCOM 2005, Miami, FL, USA, 13–17 March 2005; pp. 102–113. [Google Scholar]
- Wang, J.; Zou, N.; Zhang, Y.; Li, P. Study on Downlink Performance of Multiple Access Algorithm based on Antenna Diversity. ICIC Express Lett.
**2015**, 9, 1221–1225. [Google Scholar] - Xu, H.; Guo, C.; Zhang, L. Optimal Power Control in Wireless Powered Sensor Networks: A Dynamic Game-Based Approach. Sensors
**2017**, 17, 547. [Google Scholar] [CrossRef] [PubMed] - Zhao, W.; Shao, F.; Ye, S.; Zheng, W. LSRR-LA: An Anisotropy-Tolerant Localization Algorithm Based on Least Square Regularized Regression for Multi-Hop Wireless Sensor Networks. Sensors
**2018**, 18, 3974. [Google Scholar] [CrossRef] [PubMed] - Katranaras, E.; Imran, M.A.; Tzaras, C. Uplink capacity of a variable density cellular system with multicell processing. IEEE Trans. Commun.
**2009**, 57, 2098–2108. [Google Scholar] [CrossRef] [Green Version] - Wang, C.L.; Ku, S.J. Novel Conversion Matrices for Simplifying the IFFT Computation of an SLM-Based PAPR Reduction Scheme for OFDM Systems. IEEE Trans. Commun.
**2009**, 57, 1903–1907. [Google Scholar] [CrossRef] - Lu, G.; Wu, P.; Aronsson, D. Peak-to-Average Power Ratio Reduction in OFDM Using Cyclically Shifted Phase Stages. IET Commun.
**2007**, 1, 1146–1151. [Google Scholar] [CrossRef] - Wang, J.; Zhang, S.; Zhang, J. Multi-hop maimal ratio combining (MHMRC) diversity based on virtual cellular network. J. Jilin Univ.
**2011**, 41, 533–536. [Google Scholar] - Sklar, B. A primer on turbo code concepts. IEEE Commun. Mag.
**1997**, 35, 94–101. [Google Scholar] [CrossRef] - Lin, S.; Costello, D.J., Jr. Error Control Coding: Fundamentals and Applications; Prentice Hill: Upper Saddle River, NJ, USA, 1983. [Google Scholar]
- Li, S.E.; Li, R.; Wang, J.; Hu, X.; Cheng, B.; Li, K. Stabilizing Periodic Control of Automated Vehicle Platoon with Minimized Fuel Consumption. IEEE Trans. Transp. Electrif.
**2017**, 3, 259–271. [Google Scholar] [CrossRef] - Zou, Q.-F.; Tan, X.-Z.; Liu, M.; Ma, L. Low complexity frequency domain iterative equalization based on minimum mean square error for single carrier systems. Jilin Daxue Xuebao (Gongxueban)
**2015**, 45, 2062–2068. [Google Scholar] - Tian, P.; Xiao, X.; Wang, K.; Ding, R. A Hierarchical Energy Management System Based on Hierarchical Optimization for Microgrid Community Economic Operation. IEEE Trans. Smart Grid
**2016**, 7, 2230–2241. [Google Scholar] [CrossRef] - Chen, J.; Li, J.; Yang, S.; Deng, F. Weighted Optimization-Based Distributed Kalman Filter for Nonlinear Target Tracking in Collaborative Sensor Networks. IEEE Trans. Cybern.
**2017**, 1, 1–14. [Google Scholar] [CrossRef] [PubMed] - Li, P.; Li, M.; Feng, J. Multi-Feedback Interference Cancellation Algorithms for OFDM Systems over Doubly-Selective Channels. Algorithms
**2015**, 8, 484–513. [Google Scholar] [CrossRef] [Green Version] - Vasudevan, K. Coherent Detection of Turbo-Coded OFDM Signals Transmitted Through Frequency Selective Rayleigh Fading Channels with Receiver Diversity and Increased Throughput. Wirel. Pers. Commun.
**2015**, 82, 1623–1642. [Google Scholar] [CrossRef] [Green Version] - Shu, S.; Qu, D.; Li, L.; Jiang, T. Invertible Subset QC-LDPC Codes for PAPR Reduction of OFDM Signals. IEEE Trans. Broadcast.
**2015**, 61, 290–298. [Google Scholar] [CrossRef] - Zhao, D.-W.; Zhao, H.-L.; Ma, Y.-K.; Jia, M. Enhanced scaled selection combiner for decode-and-forward systems with adaptive modulation. Jilin Daxue Xuebao (Gongxueban)
**2016**, 46, 671–677. [Google Scholar] - Wan, L.; Zhou, H.; Xu, X.; Huang, Y.; Zhou, S.; Shi, Z.; Cui, J.-H. Adaptive Modulation and Coding for Underwater Acoustic OFDM. IEEE J. Ocean. Eng.
**2015**, 40, 327–336. [Google Scholar] [CrossRef] - Marina, M.; Arno, T.; Emmeric, T.; Vallozzi, L.; Vermeeren, G.; Joseph, W.; Rogier, H.; Martens, L. Diversity Performance of Off-Body MB-OFDM UWB-MIMO. IEEE Trans. Antennas Propag.
**2015**, 63, 3187–3197. [Google Scholar] [CrossRef] [Green Version] - Chai, E.; Shin, K. Low-Overhead Control Channels in Wireless Networks. IEEE Trans. Mob. Comput.
**2015**, 14, 2303–2315. [Google Scholar] [CrossRef] - Wang, J.; Cao, F.; Zou, N. Multi carrier system joint receiving method based on MAI and ICI. Jilin Daxue Xuebao (Gongxueban)
**2018**, 41, 301–305. [Google Scholar] - Al-Awami, A.; Saif, W.A.; Zerguine, A.; Zidouri, A.; Cheded, L. An Adaptive Equalizer Based on Particle Swarm Optimization Techniques. In Proceedings of the ISSPA 2007, Sharjah, UAE, 12–15 February 2007; pp. 12–15. [Google Scholar]
- Hu, M.; Li, Y.; Lu, X.; Zhang, H. Tone Reservation to Minimize Nonlinearity Impact on OFDM Signals. IEEE Trans. Veh. Technol.
**2015**, 64, 4310–4314. [Google Scholar] [CrossRef] - Bishwarup, M.; Timothy, T.; Visotsky, E.; Vook, F.W.; Ghosh, A.; Nam, Y.-H.; Li, Y.; Zhang, C.; Zhang, M.; Luo, Q.; et al. 3D channel model in 3GPP. IEEE Commun. Mag.
**2015**, 53, 16–23. [Google Scholar] - Guido, R.; Conforti, D. A hybrid genetic approach for solving an integrated multi-objective operating room planning and scheduling problem. Comput. Oper. Res.
**2017**, 87, 270–282. [Google Scholar] [CrossRef] - Qiu, X.; Sha, X.-J.; Mei, L. Hybrid carrier CDMA multi-antenna system based on weighted-type fractional Fourier transform. Jilin Daxue Xuebao (Gongxueban)
**2013**, 43, 218–222. [Google Scholar] - Guillermo, D.; Rey, P.A.; Wolff, P. Solving the operating room scheduling problem with prioritized lists of patients. Ann. Oper. Res.
**2016**, 258, 395–414. [Google Scholar] - Guo, M.; Wu, S.; Li, B.; Song, J.; Rong, Y. Integrated scheduling of elective surgeries and surgical nurses for operating room suites. Flex Serv. Manuf. J.
**2016**, 28, 166–181. [Google Scholar] [CrossRef] - Wang, S.; Roshanaei, V.; Aleman, D.M.; Urbach, D.R. A discrete event simulation evaluation of distributed operating room scheduling. IIE Trans. Healthc. Syst. Eng.
**2016**, 6, 236–245. [Google Scholar] [CrossRef] - Mauve, M.; Widmer, J.; Hartenstein, H. A survey on position-based routing in mobile ad hoc networks. IEEE Netw.
**2001**, 30–39. [Google Scholar] [CrossRef] - Huang, C.; Yates, R. Rate of convergence for minimum power assignment algorithms in cellular radio systems. Wirel. Netw.
**1998**, 4, 223–231. [Google Scholar] [CrossRef] - Holland, G.; Vaidya, N. A rate adaptive MAC protocol for multi-hop wireless networks. In Proceedings of the 7th Annual International Conference on Mobile Computing and Networking, ACM MobiCom, Rome, Italy, 16–21 July 2001. [Google Scholar]
- Daou, I.; Kudoh, E.; Adachi, F. Transmit power efficiency of multi-hop MRC diversity for a virtual cellular network. IEICE Trans. Commun.
**2005**, E88-B, 3643–3648. [Google Scholar] [CrossRef] - Daou, I.; Kudoh, E.; Adachi, F. Transmit power efficiency of multi-hop hybrid selection/MRC diversity for a DS-CDMA virtual cellular network. In Proceedings of the 62th IEEE VTC, Dallas, TX, USA, 25–28 September 2005. [Google Scholar]
- Luo, J.; Ye, D.; Xue, L.; Fan, M. A survey of multicast routing protocols for mobile Ad-Hoc networks. IEEE Commun. Surv. Tutor.
**2009**, 11, 78–91. [Google Scholar] - Adachi, F. Wireless past and future-evolving mobile communication systems. IEICE Trans. Fundam.
**2001**, E84-A, 55–60. [Google Scholar] - Sun, Q.; Zeng, X.; Chen, N. A Cross-layer Designed Power Control Algorithm for Wireless Ad Hoc Networks. In Proceedings of the 10th IEEE International Conference on High Performance Computing and Communications, Dalian, China, 25–27 September 2008; pp. 478–485. [Google Scholar]
- Lee, W.C.Y. Mobile Cellular Telecommunication Systems; McGraw-Hill: New York, NY, USA, 1989. [Google Scholar]
- Han, G.Y.; Song, J. Extensions of the I-MMSE Relationship to Gaussian Channels with Feedback and Memory. IEEE Trans. Inf. Theory
**2016**, 62, 5422–5445. [Google Scholar] [CrossRef] - Zhang, J.; Wang, J.; Zhang, S. Pseudorange Measurement Method Based on AIS Signals. Sensors
**2017**, 17, 1183. [Google Scholar] [CrossRef] - Zheng, K.; Hu, Q.; Zhang, J.B. Positioning Error Analysis of Ranging-Mode Using AIS Signals in China. J. Sens.
**2016**, 2016, 6928961. [Google Scholar] [CrossRef]

**Figure 3.**The distributed chicken game algorithm power control (DCGAPC) layer design model. ID: identification; SNR: signal-to-noise ratio.

Nodes ID | Distance | Interference | Gain |
---|---|---|---|

ID1 | d_{i1} | p^{1}_{infer} | u_{i1} |

ID2 | d_{i2} | p^{2}_{infer} | u_{i2} |

ID3 | d_{i3} | p^{3}_{infer} | u_{i3} |

… | … | … | … |

Parameters (Unit) | Values |
---|---|

Simulation area (m^{2}) | $500\times 500$ |

Figure of the nodes | 50 |

Communications protocol | CSMA/CA (Carrier Sense multiple Access/Collision Avoidance) |

Route protocol | Flooding |

Bandwidth (Mbps) | 2 |

Required BER (Bit Error Ratio) | 10^{−2} |

The max sending power of the node(mw) | 2.5 |

The max coverage radius of the node(m) | 230 |

SNR(dB) | 13 |

Path decay parameter | $\alpha $ = 3–4 |

Standard deviation of the shadowing loss | $\sigma =4~10\text{}\mathrm{dB}$ |

Number of paths | L = 16 |

Power delay profile | Exponential |

Decay factor | $\gamma =0~10\text{}\mathrm{dB}$ |

Environmental noise (dBm) | −120 |

DCGAPC (s/packet) | 0.01–2 |

Traffic Rate (Packets/s) | Average Received Packets in MAXPCA (Packets/s) | Average Received Packets in DNGAPC (Packets/s) | Average Received Packets in MINPCA (Packets/s) |
---|---|---|---|

100 | 18,521.23 | 17,099.79 | 14,582.11 |

50 | 23,019.76 | 22,693.27 | 20,004.04 |

34 | 26,888.89 | 26,573.79 | 19,192.84 |

25 | 21,078.25 | 20,505.26 | 12,365.07 |

20 | 16,891.68 | 16,462.47 | 10,921.1 |

17 | 14,114.03 | 13,728.13 | 9737.36 |

15 | 12,094.9 | 11,760.88 | 8717.33 |

13 | 10,575.78 | 10,290.26 | 7850.96 |

11 | 9402.22 | 9174.83 | 7157.29 |

10 | 8443.6 | 8255.2 | 6513.05 |

© 2019 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/).

## Share and Cite

**MDPI and ACS Style**

Wang, J.; Zhengpeng, Y.; Gillbanks, J.; Sanders, T.M.; Zou, N.
A Power Control Algorithm Based on Chicken Game Theory in Multi-Hop Networks. *Symmetry* **2019**, *11*, 718.
https://doi.org/10.3390/sym11050718

**AMA Style**

Wang J, Zhengpeng Y, Gillbanks J, Sanders TM, Zou N.
A Power Control Algorithm Based on Chicken Game Theory in Multi-Hop Networks. *Symmetry*. 2019; 11(5):718.
https://doi.org/10.3390/sym11050718

**Chicago/Turabian Style**

Wang, Jinpeng, Ye Zhengpeng, Jeremy Gillbanks, Tarun M. Sanders, and Nianyu Zou.
2019. "A Power Control Algorithm Based on Chicken Game Theory in Multi-Hop Networks" *Symmetry* 11, no. 5: 718.
https://doi.org/10.3390/sym11050718