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Resource Allocation in the Cognitive Radio Network-Aided Internet of Things for the Cyber-Physical-Social System: An Efficient Jaya Algorithm^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. The Problem Formulation

#### 2.1. The Basic Model of OFDM Power Allocation in CRNs

#### 2.2. The Complex Model with User Rate Proportionality Constraints

## 3. The Proposed Solution Method Using the PA-Jaya Algorithm

#### 3.1. The General Idea of Jaya Algorithm

Algorithm 1 Jaya update procedure. |

Input: population matrix P, population size M, the number of variables $2N$, fitness vector f, the best and worst solution vectors: ${p}_{\mathrm{best}}$ and ${p}_{\mathrm{worst}}$Output: updated population matrix P, updated fitness vector ffor$m:=1\phantom{\rule{0.277778em}{0ex}}\mathrm{to}\phantom{\rule{0.277778em}{0ex}}M$dofor $n:=1\phantom{\rule{0.277778em}{0ex}}\mathrm{to}\phantom{\rule{0.277778em}{0ex}}2N$ do Choose a random number ${r}_{m,n,1}$ from [0,1]; Choose a random number ${r}_{m,n,2}$ from [0,1]; ${p}_{m,n}^{\prime}={p}_{m,n}+{r}_{m,n,1}({p}_{\mathrm{best},n}-|{p}_{m,n}\left|\right)-{r}_{m,n,2}({p}_{\mathrm{worst},n}-|{p}_{m,n}\left|\right)$; end for ${f}_{m}^{\prime}=J\left({P}_{m}^{\prime}\right)$; if ${f}_{m}^{\prime}>{f}_{m}$ thenfor $n:=1\phantom{\rule{0.277778em}{0ex}}\mathrm{to}\phantom{\rule{0.277778em}{0ex}}2N$ do ${p}_{m,n}={p}_{m,n}^{\prime}$; end for ${f}_{m}={f}_{m}^{\prime}$; end ifend for |

#### 3.2. PA-Jaya for the Fundamental Issue in the Cognitive OFDM Radio Network

Algorithm 2 The improved asynchronous Jaya update procedure. |

Input: population matrix P, population size M, the number of variables $2N$, the number of inner loops T, fitness vector f, the best and worst solution vectors: ${p}_{\mathrm{best}}$ and ${p}_{\mathrm{worst}}$Output: updated population matrix P, updated fitness vector ffor$m:=1\phantom{\rule{0.277778em}{0ex}}\mathrm{to}\phantom{\rule{0.277778em}{0ex}}M$dofor $t:=1\phantom{\rule{0.277778em}{0ex}}\mathrm{to}\phantom{\rule{0.277778em}{0ex}}T$ dofor $n:=1\phantom{\rule{0.277778em}{0ex}}\mathrm{to}\phantom{\rule{0.277778em}{0ex}}2N$ do Choose a random number ${r}_{m,n,1}$ from [0,1]; Choose a random number ${r}_{m,n,2}$ from [0,1]; ${p}_{m,n}^{\prime}={p}_{m,n}+{r}_{m,n,1}({p}_{\mathrm{best},n}-|{p}_{m,n}\left|\right)-{r}_{m,n,2}({p}_{\mathrm{worst},n}-|{p}_{m,n}\left|\right)$; end for break; end ifend for ${f}_{m}^{\prime}=J\left({P}_{m}^{\prime}\right)$; if ${f}_{m}^{\prime}>{f}_{m}$ thenfor $n:=1\phantom{\rule{0.277778em}{0ex}}\mathrm{to}\phantom{\rule{0.277778em}{0ex}}2N$ do ${p}_{m,n}={p}_{m,n}^{\prime}$; end for ${f}_{m}={f}_{m}^{\prime}$; end ifend for |

Algorithm 3 The improved PA-Jaya update procedure. |

Input: population matrix P, the number of subpopulations S, the number of population iterations D, the number of iteration intervals of subpopulation information exchange QOutput: updated population matrix Pfor$i:=1\phantom{\rule{0.277778em}{0ex}}\mathrm{to}\phantom{\rule{0.277778em}{0ex}}D$dofor $s:=1\phantom{\rule{0.277778em}{0ex}}\mathrm{to}\phantom{\rule{0.277778em}{0ex}}S$ do Update ${P}_{s}$ with the improved asynchronous Jaya algorithm; end forif i mod Q = 0 thenfor $s:=1\phantom{\rule{0.277778em}{0ex}}\mathrm{to}\phantom{\rule{0.277778em}{0ex}}S$ do Replace the worst individual solution in ${P}_{s}$ with the global best individual solution; end forend ifend for |

**Step 1: Parameter setting.**It starts with the setting of initial parameters, including the number of secondary users $\left(K\right)$, the number of variables $\left(2N\right)$, population size $\left(M\right)$, the number of population divisions $\left(S\right)$, the number of inner loops $\left(T\right)$, the number of iteration intervals of subpopulation information exchange $\left(Q\right)$, and the algorithm termination criterion. For the current situation, the termination criterion is set as the maximum number of iterations $\left(D\right)$, which means that the algorithm is terminated when it iterates more than this value.

**Step 2: PA-Jaya initialization.**Initial values of individual solutions can be randomly generated under the constraints in Equations (5) and (6). After finishing the same operation for all the variables in the whole population, the solutions matrix is well initialized.

**Step 3: Fitness evaluation.**Once all the candidate solutions are initialized, every individual solution is evaluated with the fitness function. Considering the practical problem in this article, the fitness function’s purpose is to get the maximum object value according to Equation (3).

**Step 4: Solution update.**In each parallel subpopulation, by comparing the fitness function value of each candidate solution, we can easily select the best and the worst solutions. Hence, we are able to modify the old solution with the proposed asynchronous Jaya iteration strategy. Let ${P}_{i,m}={\left\{{p}_{i,m,n}\right\}}_{n=1}^{2N}$, ${P}_{i,m}^{\prime}={\left\{{p}_{i,m,n}^{\prime}\right\}}_{n=1}^{2N}$, and let $J(\xb7)$ be the mathematical operation in Equation (3), respectively. Then, the update of the candidate solution is checked by assessing

**Step 5: Convergence criterion.**The stopping condition is checked. Once the searching process reaches the maximum number of iterations, the loop is terminated and the optimum solution is obtained.

#### 3.3. PA-Jaya for the User Fairness Issue in Cognitive OFDM Radio Network

#### 3.4. Computational Complexity Analysis for PA-Jaya

## 4. Simulation Results and Analyses

#### 4.1. Simulation Setup

#### 4.2. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Flowchart of the PA-Jaya algorithm for the cognitive orthogonal frequency division multiplexing (OFDM) radio network power allocation model.

**Figure 8.**Comparison of different algorithms for the fairness indicator with different user numbers.

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

BER | ${p}_{e}$ | ${10}^{-5}$−${10}^{-1}$ |

Transmit BER | $\delta $ | 5 dB |

Noise spectral density power | ${N}_{0}$ | ${10}^{-7}$ W/Hz |

Interference factor | ${S}_{k,n}$ | ${10}^{-6}$ W |

Subcarrier bandwidth | ${W}_{c}$ | 0.315 |

Total system upper power limit | ${p}_{\mathrm{total}}$ | 1−30 W |

User-acceptable maximum interference limit | $\frac{{I}_{\mathrm{th}}}{{F}_{n}}$ | ${10}^{-3}$−${10}^{-2}$ W |

The number of secondary users | K | 8 |

Population size | M | 30 |

Total number of subcarriers | N | 64 |

The number of subpopulations | S | 3 |

The iteration interval of subpopulation communicate | Q | 10 |

The number of inner loop | T | 10 |

Total number of iterations | D | 200 |

Parameter | SA | GA | PSO | DE | ICO | Jaya | PA-Jaya |
---|---|---|---|---|---|---|---|

Initial temperature | 100 | – | – | – | – | – | – |

Reannealing interval | 100 | – | – | – | – | – | – |

Population size | – | 30 | 30 | 30 | 30 | 30 | 30 |

Scaling factor | – | – | – | 0.3 | – | – | – |

Crossover factor | – | 0.3 | – | 0.1 | 0.3 | – | – |

Mutation factor | – | 0.1 | – | – | 0.1 | – | – |

Initial inertia weight | – | – | 0.9 | – | – | – | – |

Convergence inertia weight | – | – | 0.4 | – | – | – | – |

Local acceleration constant | – | – | 2 | – | – | – | – |

Global acceleration constant | – | – | 2 | – | – | – | – |

Cloning proportion | – | – | – | – | 0.2 | – | – |

Generation | GA | PSO | ICO | SA | DE | Jaya | PA-Jaya |
---|---|---|---|---|---|---|---|

0 | 28.35 | 25.83 | 26.68 | 15.75 | 26.15 | 26.90 | 27.04 |

20 | 31.53 | 31.19 | 27.37 | 32.45 | 30.24 | 37.23 | 38.43 |

40 | 32.76 | 32.45 | 29.23 | 32.45 | 34.02 | 38.02 | 40.01 |

60 | 32.76 | 33.08 | 32.19 | 36.86 | 36.23 | 38.27 | 41.27 |

80 | 32.76 | 33.08 | 33.74 | 36.86 | 37.49 | 38.40 | 41.90 |

100 | 32.76 | 33.08 | 34.30 | 36.86 | 37.80 | 38.78 | 42.21 |

120 | 32.76 | 33.08 | 34.50 | 36.86 | 38.12 | 39.00 | 42.53 |

140 | 32.76 | 33.08 | 34.50 | 37.80 | 38.12 | 39.22 | 42.84 |

160 | 32.76 | 33.08 | 34.52 | 37.80 | 38.12 | 39.34 | 42.84 |

180 | 32.76 | 33.08 | 34.52 | 37.80 | 38.12 | 39.53 | 42.84 |

200 | 32.76 | 33.08 | 34.52 | 37.80 | 38.12 | 39.63 | 42.84 |

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## Share and Cite

**MDPI and ACS Style**

Luo, X.; He, Z.; Zhao, Z.; Wang, L.; Wang, W.; Ning, H.; Wang, J.-H.; Zhao, W.; Zhang, J.
Resource Allocation in the Cognitive Radio Network-Aided Internet of Things for the Cyber-Physical-Social System: An Efficient Jaya Algorithm. *Sensors* **2018**, *18*, 3649.
https://doi.org/10.3390/s18113649

**AMA Style**

Luo X, He Z, Zhao Z, Wang L, Wang W, Ning H, Wang J-H, Zhao W, Zhang J.
Resource Allocation in the Cognitive Radio Network-Aided Internet of Things for the Cyber-Physical-Social System: An Efficient Jaya Algorithm. *Sensors*. 2018; 18(11):3649.
https://doi.org/10.3390/s18113649

**Chicago/Turabian Style**

Luo, Xiong, Zhijie He, Zhigang Zhao, Long Wang, Weiping Wang, Huansheng Ning, Jenq-Haur Wang, Wenbing Zhao, and Jun Zhang.
2018. "Resource Allocation in the Cognitive Radio Network-Aided Internet of Things for the Cyber-Physical-Social System: An Efficient Jaya Algorithm" *Sensors* 18, no. 11: 3649.
https://doi.org/10.3390/s18113649