## Mahdi Baianifar , S. Mohammad Razavizadeh , Hossein Akhlaghpasand and Inkyu Lee## |

Parameter | Value | Parameter | Value |

SLL_{dB} | [TeX:] $$ 20dB $$ | [TeX:] $$ \theta_{3 \mathrm{d} \mathrm{B}} $$ | [TeX:] $$ 6^{\circ} $$ |

[TeX:] $$ \alpha_{N} $$ | 4 | [TeX:] $$ \alpha_{L} $$ | 2.5 |

[TeX:] $$ P_{f}, P_{f c} $$ | 100mW, 9.6W | [TeX:] $$ \eta f $$ | 4 |

[TeX:] $$ P_{m}, P_{m c} $$ | [TeX:] $$ 20,68.73 \mathrm{W} $$ | [TeX:] $$ \eta_{m} $$ | 3.77 |

[TeX:] $$ \left(M_{r}, m_{r}, \theta_{r}\right) $$ | [TeX:] $$ \left(10 \mathrm{dB},-10 \mathrm{dB}, 90^{\circ}\right) $$ | [TeX:] $$ \left(M_{t}, m_{t}, \theta_{t}\right) $$ | [TeX:] $$ \left(10 \mathrm{dB},-10 \mathrm{dB}, 30^{\circ}\right) $$ |

[TeX:] $$ \left(M_{r}^{f}, m_{r}^{f}, \theta_{r}^{f}\right) $$ | [TeX:] $$ \left(10 \mathrm{dB},-10 \mathrm{dB}, 90^{\circ}\right) $$ | [TeX:] $$ \left(M_{t}^{f}, m_{t}^{f}, \theta_{t}^{f}\right) $$ | [TeX:] $$ \left(10 \mathrm{dB},-10 \mathrm{dB}, 30^{\circ}\right) $$ |

[TeX:] $$ \beta_{1}, \beta_{2} $$ | [TeX:] $$ 0.003,0.006 $$ | [TeX:] $$ R_{f} $$ | [TeX:] $$ 30 \mathrm{m} $$ |

Fig. 3 as a function of the SINR threshold. The density of the MBS is [TeX:] $$ \lambda_{m}=4.973 \times 10^{-5} $$ and the curves are obtained under two different values of the blockage effect intensitity [TeX:] $$ \beta $$ as in table 1 and m = 5. It is observed that by increasing the 3DBF outperforms in comparison with the network in which the tilt angle is not optimized (marked as 2DBF in the figure) and also the proposed low complexity method have performance close the optimal solution resulted from the exhaustive search.

Fig. 4 illustrates the EE of the network in terms of the SINR threshold for [TeX:] $$ \lambda_{m}=8 \times 10^{-4} $$ and two values of [TeX:] $$ \beta $$ as in Table 1 under this scenario with m = 1. As we see in this figure, the EE of the network that adopts 3DBF is always improved in comparison with the 2DBF. This improvement is more than 100% in high SINR thresholds. In addition, in this figure, the EE performance of the proposed low-complexity method is compared with the optimum method based on the exhaustive search. As we see in the figure, the performance of the proposed lowcomplexity approach is the same as the optimal solution in almost all the SINR threshold and for both values of [TeX:] $$ \beta $$.

Fig. 5 presents the network EE with respect to the tilt angle for [TeX:] $$ \lambda_{m}=5.093 \times 10^{-6} $$ and m = 5. In this figure, the optimum tilt angles obtained by exhaustive search and the proposed lowcomplexity method are shown. Also, the dashed lines represent the tilt angle bounds obtained in (28). We see that both tilt angles are almost the same.

In Fig. 6, performance of the HetNet scenario is evaluated. This figure exhibits the effect of the FBSs density [TeX:] $$ \lambda_{f} $$ and the radius of the sleep region R_{c} on the optimum tilt angle that maximizes the coverage of the typical macro user. In this figure we see that by increasing the density of the FBSs, the optimum tilt angle slightly decreases. Also by increasing R_{c} or reducing the density of the FBSs, the coverage probability of the macro users increases, since interference from the FBSs is reduced.

Fig. 7 illustrates the coverage probability of the typical femto user in terms of R_{c} for case of [TeX:] $$ \sigma^{2}=5 \times 10^{-4} $$, which corresponds to [TeX:] $$ \mathrm{SNR}_{f}=P_{f} / \sigma^{2}=23 \mathrm{dB} $$. In this figure, we see that the lower bound obtained in (30) is very tight. It is observed that although the lower bound is obtained under assumption of an interference limited scenario, it is still quite tight in other scenarios.

Figs. 8 and 9 plot the optimal EE, the optimal radius of the sleep region and the optimal tilt angle, respectively, with [TeX:] $$ \epsilon_{m}=0.2, \epsilon=0.7, \gamma_{m}=\gamma_{f}=10 \mathrm{dB} $$. We can check that the proposed low complexity approach has only a minor degradation in the performance with respect to the exhaustive search.

In this paper, we have studied the EE maximization problem in the downlink of a 3D beamforming mmWave network. We have optimized the tilt angle of the BSs to maximize the EE in a homogeneous network and a two tier HetNet mmWave cellular network. In both scenarios, we have optimized the tilt angle of the MBS’s antenna to maximize the EE. In addition, in the second scenario, the optimization of the radius of the sleep region has also been considered. In addition, to reduce the complexity of the optimization problems, an efficient method based on bisection algorithm has been proposed to compute the optimal tiltangle. The proposed algorithms result in almost the same EE performance as the optimal method based on exhaustive search but with much reduced complexity.

Mahdi Baianifar received his B.Sc. degree in Electrical Engineering from University of Zanjan, Iran and M.Sc. in Electrical Engineering from Sharif University of Technology, Tehran, Iran in 2011 and 2013, respectively. Currently, he is a Ph.D. student at Iran University of Science and Technology (IUST). His research interests are in the area of wireless communication systems and specially in the area of mmWave networks and application of the stochastic geometry in wireless communications.

S. Mohammad Razavizadeh received his B.Sc., M.Sc. and Ph.D. degrees in Electrical Engineering from Iran University of Science and Technology (IUST), Tehran, Iran, in 1997, 2000 and 2006, respectively. From 2005 to 2011, he was with Iran Telecomm. Research Center, as a Research Assistant Professor. Since 2011, he has been with the School of Electrical Engineering at IUST, where he is currently an Associate Professor and also head of the communications group. His research interests are mailnly in the area of signal processing for wireless communication systems. He is a Senior Member of the IEEE.

Hossein Akhlaghpasand received his B.Sc. degree in Communications Engineering from University of Zanjan, Zanjan, Iran, in 2012. He studied for his M.S. degree in Wireless Communication Networks at University of Tehran, Tehran, Iran, in 2012-2014. Currently, he is a Ph.D. student at Iran University of Science and Technology, and his research interests are in the area of wireless communication systems and multiple-antenna networks.

Inkyu Lee received the B.S. degree (Hons.) in Control and Instrumentation Engineering from Seoul National University, Seoul, South Korea, in 1990, and the M.S. and Ph.D. degrees in Electrical Engineering from Stanford University, Stanford, CA, USA, in 1992 and 1995, respectively. From 1995 to 2001, he was a Member of Technical Staff with Bell Laboratories, Lucent Technologies, where he studied highspeed wireless system designs. From 2001 to 2002, he was with Agere Systems, Murray Hill, NJ, USA, as a Distinguished Member of Technical Staff. Since 2002, he has been with Korea University, Seoul, where he is currently a Professor with the School of Electrical Engineering. In 2009, he was a Visiting Professor with the University of Southern California, Los Angeles, CA, USA. He has authored over 160 journal papers in the IEEE. He has 30 U.S. patents granted or pending. His research interests include digital communications, signal processing, and coding techniques applied for next generation wireless systems. He was elected a member of the National Academy of Engineering in Korea (NAEK) in 2015. He was a recipient of the IT Young Engineer Award at the IEEE/IEEK Joint Award in 2006, and the Best Paper Award at APCC in 2006, the IEEE VTC in 2009, and ISPACS in 2013. He was also a recipient of the Best Research Award from the Korea Information and Communications Society in 2011, the Best Young Engineer Award from NAEK in 2013 and the Korea Engineering Award from National Research Foundation of Korea in 2017. He has served as an Associate Editor for the IEEE TRANSACTIONS ON COMMUNICATIONS from 2001 to 2011, the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS from 2007 to 2011, the IEEE Wireless Communication Letters from 2011 to 2013, and the IEEE ACCESS from 2016 to 2017. He was the Chief Guest Editor of the IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS Special Issue on 4G Wireless Systems in 2006. He is an IEEE Fellow and an IEEE Distinguished Lecturer.

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