#
Performance of Resource Allocation in Device-to-Device Communication Systems Based on Evolutionally Optimization Algorithms ^{†}

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. System Models

_{l}-th UE transmits the signal to the lth relay station by the channel gain ${h}_{{u}_{l},l}^{(n)}$. The lth relay station relays the transmission to the base station using the nth resource block (RB). However, when the u

_{j}-th D2D UE transmits signal to the lth relay station, the interference link gain ${g}_{{u}_{j},l}^{(n)}$ will be transmitted to the lth relay station.

_{l}-th UE to the lth relay with the nth RB; and ${x}_{{u}_{j}}=1$ or 0. Each UE can only use one RB, with ${x}_{{u}_{j}}=1$ indicating one RB and ${x}_{{u}_{j}}=0$ indicating no RB. Furthermore, ${U}_{j}$ is the set of D2D UEs in the jth relay area; ${P}_{{u}_{l},l}^{(n)}$ and ${P}_{{u}_{j},l}^{(n)}$ are the transmission power of the u

_{l}-th UE and the u

_{j}-th CeUE, respectively; ${P}_{{u}_{l},l}^{(n)}$${g}_{{u}_{j},l}^{(n)}$ is the interference link gain from the u

_{j}-th CeUE to the lth relay; ${\sigma}^{2}={N}_{0}{B}_{RB}$. ${N}_{0}$ is power spectral density of the added white Gaussian noise (AWGN); and ${B}_{RB}$ is bandwidth of a RB. Similarly, the unit power SINR of the second hop can be expressed by:

_{l}can be obtained by:

## 3. PSO-Based Resource Allocation

**s**

^{pbest}. After this, the global experience is referred from the group’s best moving experience as the global best, which is denoted by

**s**

^{gbest}. According to the above-mentioned types of data with an iterative evolution, the final convergence obtains the optimal solution.

**s**

_{i}. The particle is uniformly distributed in the solution space. A total of 13 RBs and 3 relay stations are available. The moving velocity of the first particle in the (g + 1)-generation is expressed by:

_{1}and c

_{2}are the acceleration coefficients, which is called the individual factor and social factor, respectively. Generally, the factors are set by ${c}_{1}=2$ and ${c}_{2}=2$. The rand() is the random function that is uniformly distributed in the range of [0,1].

- (1)
- Initialization (g = 1): Generate the positions of M particles with ${s}_{i}^{1}$, i = 1, ..., M and velocity; and ${v}_{i}^{1}$, i = 1, ..., M. One example of the position of a particle ${s}_{i}^{1}$ can expressed by ${s}_{1}^{1}$ = [1 1 3 4 5 6│ 2 8 3 11 11 13│1 6 7 8 4 9].
- (2)
- Calculate the objective function value of all particles according to Equation (8) and find the ${s}^{pbest}$ and ${s}^{gbest}$ for this generation. One example of ${s}^{pbest}$ and ${s}^{gbest}$ can be ${s}^{pbes{t}_{1}}$ = [1 1 3 4 5 6]; ${s}^{pbes{t}_{2}}$ = [7 8 9 10 11 12]; ${s}^{pbes{t}_{3}}$ = [1 3 4 5 7 6] and ${s}^{gbest}$ = [3 4 5 6 7 5│7 8 9 10 11 12│1 3 4 5 7 6], respectively.
- (3)
- Let g = g + 1. According to step (2), we calculate the speed and position of the next generation (g + 1) particle after one generation calculation. After this, One example of the position can be ${s}_{1}^{1}$ = [2 3 1 4 5 6│9 7 6 11 13 10│1 6 7 8 4 9].If the number of generations g < G, return to step (2) to update the individual optimal solution and the population optimal solution. One example can be: no change in the previous ${s}^{pbes{t}_{1}}$ by ${s}^{pbes{t}_{1}}$ = [1 1 3 4 5 6]. However, the other two individual optimal solutions is updated by ${s}^{pbes{t}_{2}}$ = [9 7 6 11 13 10] and ${s}^{pbes{t}_{3}}$ = [2 7 8 9 3 5], respectively. Moreover, the new ${s}^{gbest}$ is updated according to the object function by ${s}^{gbest}$ = [2 3 1 4 5 6│ 9 7 6 11 13 10│1 6 7 8 4 9].
- (4)
- If the number of generations is g = G, the calculation ends.

**cw**

_{1}and

**cw**

_{2}are added to Equation (13) to speed up optimization searching in this present study. This PSO is called Refined PSO (RPSO). After this, its next generation of evolution speed of particle ${s}_{i}^{g+1}$ can be obtained by:

- (1)
- $c{w}_{1}({u}_{l})=1$ for when the RB of the u
_{l}-th UE in ${s}^{pbest}$ does not conflict with the RBs of other relay stations. - (2)
- $c{w}_{1}({u}_{l})=0$ for when the RB of the u
_{l}-th UE in ${s}^{pbest}$ conflicts with the RBs of other relay stations once. - (3)
- $c{w}_{1}({u}_{l})=3$ for when the RB of the u
_{l}-th UE in ${s}^{pbest}$ conflicts with the RBs of other relay stations more than once.

- (1)
- $c{w}_{2}({u}_{l})=1$ for when the RB of the u
_{l}-th UE in ${s}^{gbest}$ does not conflict with the RBs of UEs of other relay stations. $c{w}_{2}({u}_{l})=1$ for g > 10. - (2)
- $c{w}_{2}({u}_{l})=3$ for when the RB of the u
_{l}-th UE in ${s}^{gbest}$ conflicts with the RBs of other relay stations once or more times in g ≤ 10.

## 4. RB Allocation with GA Discussion

## 5. Simulation Results

#### 5.1. PSO

_{1}= c

_{2}= 2, M = 10 and random allocation methods. The random method (Rand) is performed by randomly allocating the RBs to the UEs in each generation. However, the system retains the best results for the next generation based on the same object function as SPSO. From Figure 4, it is easy to observe that the proposed SPSO outperform the Rand at the 20th iterations and significantly improve the system capacity to 16 UEs at the 100th iterations, which is 2 UEs more than that of Rand.

_{1}= c

_{2}= 2. Compared with the Rand, SPSO algorithm can improve the efficiency by about 17–20% for K = 18 and 24. Moreover, the proposed RPSO algorithm can improve the efficiency by 18–24% compared to Rand.

#### 5.2. GA

#### 5.3. QoS Based Capacity Maximization

_{l}.

## 6. Discussion

^{N}× (26N + 38) addition and 13

^{N}× 117 multiplication operations to find the optimal solution. The computational complexity of these two applied algorithms is far less than the comprehensive search method but a sub-optimal solution can be obtained.

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**Simulation results comparisons between SPSO and random allocation method with M = 10 and K = 18.

**Figure 7.**System performance comparisons in 200 generations for (

**a**) throughput and (

**b**) system capacity with K = 18.

System bandwidth (MHz) | 2.5 |

Bandwidth of subcarrier (Hz) | 1500 |

Number of RBs | 13 |

Radius of the coverage area of relay station (meter) | 200 |

Distance between base station and relay station (meter) | 125 |

Number of CeUE | 9, 12, 15 |

Number of D2D pairs | 3, 6, 9 |

Minimum distance between base station and UEs (meter) | 10 |

Power of relay station (P_{l}, dBm) | 30 |

Power of UEs (P_{u}, dBm) | 23 |

Minimum throughput requirements of CeUEs (R_{th_C}, Kbps) | 128 |

Minimum throughput requirements of D2D pairs (R_{th_D}, Kbps) | 256 |

Standard deviation of Shadowing fading between relay and BS (dB) | 6 |

Standard deviation of Shadowing fading between UEs and relay station (dB) | 10 |

Power Spectral density of AWGN (dBm/Hz) | −174 |

Maximal generations (G) | 200 |

Number of particles (M) | 10 |

Learning factors (c_{1} = c_{2}) | 2 |

Number of user equipment (K) (Including CeUE and D2D UEs) | 12, 18, 24 |

Number of relay station | 3 |

ID of RBs | 1–13 |

Number of UE (K) | 12 | 18 | 24 |
---|---|---|---|

a. ROSO | 12 | 16.66 | 18.89 |

b. SPSO | 12 | 16.52 | 18.3 |

c. Rand | 11.8 | 14.1 | 15.2 |

Gain_{1} (a−c)/c | 1.69% | 18.16% | 24.28% |

Gain_{2} (a−c)/c | 1.69% | 17.16% | 20.39% |

Generations (G) | 200 |

Number of chromosomes (M) | 10–500 |

Crossover rate (R_{c}) | 0.9 |

Mutation rate (R_{m}) | 0.07 |

K | 12 | 18 | 24 |

GA | 12 | 17.96 | 21.8 |

RPSO | 12 | 17.86 | 20.41 |

Rand | 12 | 15.08 | 16.27 |

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**MDPI and ACS Style**

Tan, T.-H.; Chen, B.-A.; Huang, Y.-F. Performance of Resource Allocation in Device-to-Device Communication Systems Based on Evolutionally Optimization Algorithms ^{†}. *Appl. Sci.* **2018**, *8*, 1271.
https://doi.org/10.3390/app8081271

**AMA Style**

Tan T-H, Chen B-A, Huang Y-F. Performance of Resource Allocation in Device-to-Device Communication Systems Based on Evolutionally Optimization Algorithms ^{†}. *Applied Sciences*. 2018; 8(8):1271.
https://doi.org/10.3390/app8081271

**Chicago/Turabian Style**

Tan, Tan-Hsu, Bor-An Chen, and Yung-Fa Huang. 2018. "Performance of Resource Allocation in Device-to-Device Communication Systems Based on Evolutionally Optimization Algorithms ^{†}" *Applied Sciences* 8, no. 8: 1271.
https://doi.org/10.3390/app8081271