# Performance of Millimeter Wave Dense Cellular Network Using Stretched Exponential Path Loss Model
## 1 Introduction  
Densifying a cellular network by deploying a large number of small cells per unit area, widely known as an ultra-dense network (UDN), is the most appealing approach to increase the per-user data rate by exploiting spatial reuse of frequency resources among users. Essential features of UDN include short transmission ranges with different propagation characteristics, and discrete obstructions cause significant attenuation than the conventional free space path loss. Moreover, the irregular deployment of dense infrastructure introduces increased interference different from the existing cellular network [1, 2, 3, 4, 5, 6]. On the other hand, the mmwave band scales up the network capacity and provides high data rates of multi-Gbps due to the abundant spectrum in the frequency range of 30-300 GHz. In addition, the propagation feature of mmwave signals, such as limited communication range, appears very attractive for UDN deployment. Accordingly, both of these are key inter-dependent technologies to address the requirements for enhanced coverage and capacity [7, 8, 9, 10]. However, deploying mmwave for outdoor cellular communication has several associated challenges, such as LOS link establishment, directional communication and severe penetration losses. Due to these limitations, the range of a direct path in mmwave is limited with highly probabilistic LOS communication. The probability of an LOS link between user equipment (UE) and base station (BS) depends on numerous factors, such as building density, terrain features and locations of UEs. Moreover, because of the high deployment cost of mmwave networks, LOS channels might not always be feasible, and NLOS links should be considered for coverage [11]. Mmwave channel measurements and field experiments have shown that the signal received from reflections, i.e., NLOS paths, helps cover the shadowed region behind blockages. These NLOS signals supplement the LOS signal to increase capacity substantially. For an mmwave testbed operating at 29 GHz, channel measurements have shown that an NLOS connection reflected from a site located 1200 feet away could provide a superior received signal than the LOS where foliage or street infrastructure may obstruct the LOS path. The NLOS-reflected signals from objects such as concrete and the ground are found to be highly supportive for mobile communication and can be used to maintain the connection with attractive data rates even if a mobile device has moved out of the LOS coverage [12]. Using network optimization tools, it has been analyzed that interference due to potential reflection in NLOS links is negligible, and the reflected paths can be leveraged as an alternative to the LOS paths [13; 14]. Performance evaluation of mmwave cellular network shows that in an environment with dense blockages, even if a large number of users connect to the BS through NLOS links, there is adequate coverage [15]. NLOS paths are also shown to facilitate localization and positioning in mmwave [16; 17]. \({}^{\rm HM}\)Consequently, when deploying mmwave technology in practice, it is necessary to understand what kind of performance can be obtained under a realistic outdoor environment that may have different blockages, such as different building densities, irregular town structures, etc. Hence, the modeling of NLOS links deserves special attention if sufficient coverage and rates are to be drawn. For system-level analysis, the presence of blockages in an environment is abstracted to a LOS probability function. The impact of blockages is incorporated into the system model by distinguishing the LOS and NLOS paths with separate path loss expressions. The LOS path is shown to have behaviour similar to free space having a path loss exponent value of 2, while depending upon the environmental factors and obstacles density, the NLOS path loss exponent, has a greater value than the LOS exponent [13]. For analytical tractability, almost all prior works use the exponential blockage model [18; 19; 20; 21; 22] or the ball blockage model [23; 24; 25; 26].