## Tae-Yoon Park , Jong-Won Han and Een-Kee Hong## |

Network attributes | Normalized value |
---|---|

Throughput | 1 |

Total power consumption | 0.78231216218 |

Total traffic load | -0.68542154223 |

The high-loaded cell ratio | -0.45332123119 |

Total number of UEs in a cell | -0.14532152127 |

The inter-cell distance | The inter-cell Distance |

Total number of edge area UEs | -0.04234400663 |

Total center area UEs | 0.00234520121 |

The delay-sensitive UE ratio | -0.08293145131 |

throughput Among 8 network attributes, five network attributes that have meaningful correlation with UE throughput were selected. Five attributes were selected as follows.

Total power consumption (TPC): Power consumption is proportional to the number of active SCs. As the number of active SCs increases, the number of UEs per cell decreases and wider bandwidths can be allocated to UEs. The higher power consumption is, the more the gain of UE throughput. When the power of SCs is 30 dBm, the total power consumption of the network is as follows

Total traffic load (TTL): Total traffic load represents the sum of the traffic loads of UEs distributed in network. Increasing the amount of traffic to be processed leads lowering the throughput per UE.

The high-loaded cell ratio (TCR): The high-loaded cell ratio represents the percentage of SCs with a higher system load than 0.5 [6]. The system load is defined by the sum of the average traffic load in (2) divided by the maximum data rate in (3).

Since the radio resource per UE is limited in high-loaded cell, the lower UE throughput is provided in the higher high-loaded cell ratio network.

Total number of UEs in a cell (TU): As the number of UEs in a SC increases, the radio resources per UE decreases. Even though each traffic load of UE is different, the number of UEs is one of import network attributes for SC on/off.

The inter-cell distance (TD): The shorter distance between active cells causes the higher inter-cell interference and results in reducing UE throughput. And it is advantageous because the distance between cell and UE is short when the turned off SC UE is handed over to the neighbour cell. By selecting a cell having shorter TD to be turned off, the longer TD is achieved and it gives a positive effect on throughput.

To analyse the correlation between the five network attributes and the UE data throughput, we use a multiple linear regression analysis. We can figure out the impact of each network attributes on UE throughput based on correlation analysis and determine the criteria for SC on/off. Multiple linear regression analysis can be used to estimate the correlation between various dependent and multiple independent variables. Fig. 2 is an example of the model obtained through the analysis.

The model of multiple linear regression analysis is follows

[TeX:] $$\bar{x}$$ is the input variables of each network attribute, and is the slope coefficients for variables. In the ith simulation, [TeX:] $$y_{0}(i)$$ and [TeX:] $$y_{k}(i)$$ are the throughputs of the kth UEs before and after performing SC on/off, respectively. Since it is difficult to find out the exact values of , we adjust the values iteratively to minimize the estimation errors on determining values. The process of finding the minimum value described above is called the gradient descent method.

The weight is updated by using the gradient for each parameter calculated by differentiating the error function for all data by weight. At this time, the value that determines how much gradient to use is called the learning rate. The equations for error are as follows

[TeX:] $$L_{i}$$ is the sum of squared errors of the UE throughput predictions of the ith simulation, [TeX:] $$\hat{y}_{k}(i)$$ is the predicted throughput of the kth UE in the ith simulation. NS is total number of simulations used for multiple linear regression analysis, and r(= 5) is

the number of considered network attributes. We find the point m that shows the minimum prediction error.

where is the learning rate. If the slope is a positive value, the value decreases as the value of increases. With a high learning rate, we can cover more ground each step, but we risk overshooting the lowest point since the slope of the hill is constantly changing. With a very low learning rate, we can confidently move in the direction of the negative gradient since we are recalculating it so frequently. A low learning rate is more precise, but calculating the gradient is time-consuming.

The proposed SC on/off process is performed by two stages. In the first stage, we gather the training data for multiple linear analysis through simulations. In the second stage, SC on/off processes are applied with the multiple linear analysis result, and its performances are evaluated.

First stage: We run the simulations repeatedly as many as possible to get the training data for multiple linear regression analysis. The simulation is processed as follows:

UE throughput depends on the various attributes of the network. Through system-level simulation under the various network conditions, the throughputs of UEs are gathered to achieve training data. SCs and UEs are randomly deployed with PPP, cell association processes are carried out based on the largest RSRP, and the values of network attributes, xr(i) and all UEs throughput [TeX:] $$u(i)=\left(u_{0}(i), u_{2}(i), \cdots, u_{K n}-1(i)\right)$$ are stored. Based on these achieved simulation data, we find optimal values of with multiple linear regression analysis.

Second stage: We choose the proper SCs to be turned off based on the optimal values of , and the SC on/off process is carried out. The simulation is processed as follows.

Based on the training data acquired through the first stage, correlation between network attribute and UE throughput is evaluated. We examine how much each network attribute have an impact on UE throughputs. For example, when increasing the total power consumption by 1 W, the throughput increases by 0.5 bps/W. In this way, a model is created by considering the correlation between the network attributes and UE throughput. The initial weighting values in (10), are randomly designated, the values of are adjusted to reduce the estimation errors in (11) with linear regression model. Based on the final model that shows the minimum prediction error, it is possible to select cells to be turned off. While the condition to support the minimum required UE throughput is satisfied, we can find several sets of SCs to be turned off. Among the candidate, we choose the set to provide the best NEE.

Fig. 3 illustrates an example of multiple linear regression analysis created by the algorithms mentioned above. The current UE throughput can be adjusted to the target UE throughput by predicting the change in throughput based on multiple linear regression analysis.

In this section, we evaluate the correlation between network attributes and UE throughput that is derived by multiple linear regression analysis and the validity is confirmed by the reliability test. The SC off process is applied based on the confirmed

multiple linear regression model and the performances of the proposed algorithm are analysed. Multiple regression analysis is the process to estimate the relationship between multiple independent variables and a dependent variable. The reliability of analysis is decreased when some of independent variables are highly correlated. Strong correlations between independent variables applied to the analysis may lead to unreliable prediction. This phenomena is known as multicollinearity. In order to solve this problem, we need to remove the strongly correlated independent variables and select proper independent variables. Fig. 4 shows the correlation tendency between network attributes and UE throughput. Total power consumption (TPC) and the inter-cell distance (TD) show a positive linear relationship. This means that the UE throughput tends to increase each network attribute increases. Total traffic load (TTL), the highload cell ratio (TCR) and the number of UE in a cell (TU) show a negative linear relationship. This means that the UE throughput tends to decrease as network attributes (TTL, TCR, TU) increases.

Fig. 5 shows the result of finding the correlation coefficient between UE throughput and network attributes. As long as the

Table 2.

Parameter value | |
---|---|

The number of deployed cells | 400 cells |

Maximum of UEs | 100 UEs |

Small cell transmit power | 10 dBm |

Small cell basic power | 20 dBm |

Required UE throughput | 100 Mbps |

Bandwidth | 20 MHz |

Thermal noise spectral density | -174 dBm/Hz |

training data is accumulated, the process is repeated and the accurate correlation coefficient is founded. It can be seen that TPC, TTL, and TCR that have higher correlation coefficient than others are the key attributes and have large impact on the UE throughput. Thus, the three attributes are mainly adjusted to turn off cells to ensure throughput of UEs. Fig. 6 shows the result of multicollinearity analysis. [TeX:] $$P_{r}$$ value is the indicator to confirm multicollinearity. Usually, if the value exceeds 0.5, it can be regarded that the corresponding independent variable has a strong correlation. This means that the variable is less reliable. The five network attributes used in the targeted multiple regression analysis have values less than 0.5, which means that these attributes considered are adequate in terms of correlation strength. This confirms that theses network attributes have sufficient reliability for the analysis.

In the general UDN environment, the number of SCs is assumed to be larger than the number of active UEs. In our simulation, the maximum number of SCs is set to 400 and the number of UEs is randomly selected with the exponential distribution. The maximum number of UEs is limited by 100.

Fig. 7 shows the network throughput normalized by 1 Hz bandwidth and 1 [TeX:] $$\mathrm{km}^{2}$$ area according to the number of SCs As the number of SCs increases, the gain of network throughput increases but the gain of cell densification is saturated. Thus, in terms of NEE, it is necessary to find the optimal number of SCs subject to guarantee the minimum UE throughput. We compare the total network power consumption SC on/off algorithms in Fig. 8. The number of SCs is set to 400. In the conventional algorithm, the SCs that have connections with UEs are activated, and the remaining SCs are in sleep mode. The basic power,

Pb represents the power consumption of sleep mode cell and is set to 20 dBm. The total power consumption of active cell is the sum of basic power and transition power, PT of 10 dBm [3]. The Random ON/OFF algorithm randomly selects additional 20% or 30% of the active cells in the above conventional SC on/off scheme and turns off. The proposed SC on/off with learning denoted by Proposed ON/OFF is the algorithm that predicts UE throughput through correlation between UE throughput and network attributes and selects the SCs to be turned off.

As the number of UEs increases, the total power consumption to support UEs is shown in Fig. 8. It is confirmed that the power consumptions of random on/off algorithms are less than that of the conventional algorithm. Learning on/off operates sufficient number of cells to satisfy the required UE throughput.

Fig. 9 shows the cumulative distribution function (CDF) of UE throughputs. The UE throughputs of random on/off algorithms are less than that of conventional SC on/off algorithm due to less cell densification gain. The proposed on/off algorithm improves the UE throughput with less active cells and results in improving NEE.

Fig. 10 shows NEE that represents how the network is operating efficiently. When the number of UEs is small, NEE of Random ON/OFF is lower than that of the conventional algorithm since the number of SCs is insufficient. Otherwise, as the number of UEs increases the NEE of random on/off is improved since the coverage of SCs is overlapped. The proposed ON/OFF with machine learning selects the proper set of SCs to be turned off that can handover the traffic load to neighboring cells without significant throughput loss. Compare to the conventional algorithm, the proposed algorithm shows more than 75% improvements of average network energy efficiency.

In this paper, we proposed a SC on/off algorithm that can provide sufficient UE throughputs with high network energy efficiency. The proposed SC on/off algorithms can predict the variation of UE throughputs with multiple linear regression analysis and determine which cells to be turned off. In addition, the

accuracy of the algorithm was improved through the reliability test. Performances of the proposed algorithms were compared with those of the conventional and random SC on/off algorithms.

Conventional algorithms improve energy efficiency, but often fail to guarantee minimum UE throughput. The higher average UE throughput with a network energy efficient manner can be achieved with the proposed SC on/off algorithm since it takes individual UE throughput into consideration. The proposed algorithms provided more than 75% gain in network energy efficiency while guaranteeing UE throughput. This confirms that our algorithm ensures sufficient minimum UE throughput and improves reasonably energy efficiency.

Een-Kee Hong received B.S., M.S., and Ph.D. degrees from the Department of Electrical Engineering, Yonsei University, in 1989, 1991, and 1995, respectively. From 1995 to 1999, he was with SK Telecom, Korea, as a Senior Member of the Research Staff. In 1999, he joined the Department of Electronic Engineering, Kyung Hee University, Yongin, Korea, where he is currently a Full Professor. He has been the chairman of the 5g Forum Frequency Committee since 2013, and has served as Vice President of the Korean Institute of Communications and Information Sciences(KICS) since 2018. His research interests includes Mobile communication and 5G.

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