I Introduction
The everincreasing demand for wireless data is insatiable and affecting, immensely, the technology and the design of future wireless networks. In , mobile data traffic was about Exabytes per month, and based on Cisco’s forecasts [Cisco], it will exceed Exabytes per month by . Although wireless communication techniques have been developed to meet this demand, most of them will not suffice to satisfy exponentially increasing mobile data traffic volumes. Recently, numerous studies on 5G cellular networks have been reported. Nonetheless, there remain open questions about the final technologies of choice and 5G standards. According to [6824752], 5G will rely on the following three enabling technologies, the so called bigthree: (i) massive multipleinput multipleoutput (MIMO), (ii) millimeter wave (mmWave), and (iii) ultradensification. Interestingly, these technologies are not only compatible and congruent but also represent prerequisites for each other.
The frequencies between and GHz are referred to as mmWave. Due to the high path loss, so far mmWave systems were not at the center of mobile communications research, though undoubtedly they will play a major role in 5G [6736750]. The availability of huge amounts of bandwidth in the mmWave band paves the way to serving mobile users with high data rates [6824746]. Furthermore, the implementation of massiveMIMO in mmWave systems can be easily realized via smallsize array antennas.
Telecommunication companies apply densification techniques (i.e., ultradense small cell deployment) to improve their areal spectral efficiency, in particular in highly congested regions. Due to the high path loss in the mmWave band densification is inevitable. In [6834753], it was shown through experimental measurements that the maximum range of mmWave base stations (BSs) is less than meters. The main problem raised by densification is how to serve all BSs with appropriate backhaul^{1}^{1}1 It sould be noted that in the terminology of cloudradio access network (CRAN) the word fronthaul indicates the link between remote radio head (RRH) and base band unit (BBU), while the term backhaul means the backbone infrastructure connecting BBUs to the core network. However, in this study, we use the term backhaul to indicate either fiber links between WBSs and central office or wireless links between UBSs and WBSs. solutions[6963798].
Ia Related Work
In[6588652], existing fibertothenode residential access networks are utilized to design a costoptimized optical fiber backhaul for small cells. In [7218503], the passive optical network (PON) architecture has been utilized as backhaul of heterogeneous networks. In [7306543] and [7115912], mixed freespace optic (FSO)/radio frequency (RF) and optical fiber backhaul networks were used to serve BSs. It was shown that the integration of optical fiber with other technologies is more practical and costeffective than leveraging only optical fiber backhaul solutions. More recently, in [7947084], authors provides an optimization framework to deploy mixed fiber and wireless backhauls for BSs, where the survivability of fiber backhaul has been investigated. In addition, authors in [7925837] proposed a cost effective fiber backhaul deployment and resource allocation optimization for integrated access and backhaul cellular networks where resources are shared dynamically between access and backhaul links.
Recently, selfbackhauling has been attracting an increasing amount of attention[Interdigital]. On the other hand, given the successful demonstrations of inband fullduplex (IBFD) radio systems [bharadia2013full], there is an emerging trend to utilize this technique in selfbackhauled wireless systems[7306541]. It is worth mentioning that in IBFD selfbackhauling, the same frequency band is simultaneously used for both backhaul and access links.
In [1230131], the authors investigated the cell planning problem for G cellular networks. They considered a set of candidate locations for BSs and selected optimal locations based on given traffic distributions and power consumption restrictions. In [6196268], the cell planning problem was investigated from an energyefficiency point of view by means of raytrace models. In [7450686], the authors proposed a costoptimized cell planning method, whereby the locations of macro and picoBSs as well as relay nodes were determined. It is worth mentioning that in [1230131]  [7450686], a finite set of candidate locations was examined in greater detail. In [7056465]
, the authors proposed a cell planning approach by considering infinite candidate locations and various user distributions. Moreover, they utilized metaheuristic algorithms to solve the cell planning problem under consideration. More recently, in
[7883847], the authors reviewed cell planning problems and also investigated the problem of cell planning for future cellular network.All the aforementioned studies considered traditional cellular networks using the ultrahigh frequency (UHF) band. In [7305743], the cell planning problem was resolved for mmWave cellular networks. The authors utilized a metaheuristic algorithm to obtain nearoptimum solutions. Furthermore, in [7450185], a new approach was proposed for solving the mmWave cell planning problem by leveraging the polygon computational geometry concept. Note, however, that in this study the issue of backhauling was not addressed. There were also some other studies on selfbackhauling. Among them is [7386685], where the authors investigated joint beamforming, power allocation, and spectrum assignment in a selfbackhauling twotier wireless network. Further, cell association and backhaul spectrum assignment were studied in [7505948]. These two studies optimized the aforementioned parameters for fixed BSs, whereas in this work we determine the locations of selfbackhauled BSs subject to satisfying the rate and coverage constraints.
IB Paper Contributions and Organization
This paper makes the following three main contributions: Selfbackhauled mmWave cell planning: In this paper, a general optimization model is proposed for mmWave small cell planning. We consider both fiber and wireless backhauling techniques. Accordingly, two types of BSs are deployed, BSs with either fiber or wireless backhaul. At BSs with wireless backhaul, the IBFD technique is used to realize selfbackhauled implementation. To satisfy, both, given coverage and capacity constraints with minimum number of either BSs, we propose a multiobjective optimization problem to simultaneously determine number of required BSs with fiber, wireless backhaul, and the optimum locations for BSs. Furthermore, an infinite set of candidate locations is considered.
Joint cell and fiber backhaul planning: We also formulate another multiobjective optimization problem for joint cell and fiber backhaul planning. The multiobjective problem contains two parts. One part optimizes the cell planning problem and the other one minimizes deployment costs. To reduce the cost of fiber installation, we leverage existing dark fibers and determine the best locations for installing optical splitters. We utilize a metaheuristic approach to solve this multiobjective problem.
Efficient metaHeuristic algorithm:
To solve the above problems we develop an efficient metaheuristic algorithm based on the wellknown nondominated sorting genetic algorithm (NSGAII). We compare our proposed algorithm to metaheuristic alternatives utilizing particle swarm optimization (PSO), tabu search (TS), simulated annealing (SA), and ant colony optimization (ACO). Our simulation results reveal the superiority of the NSGAII based algorithm to the considered alternatives in terms of the obtained objective and speed of convergence. In addition, by means of simulation, we examine the impact of the probability density function (PDF) used to change the positions of BSs and tune this PDF to improve the objective of both cell planning and joint cell and backhaul planning problem.
It is worth mentioning that all the considered features for the radio access network are in accordance with the 3GPP standards [5Gstandard1] [5Gstandard2].
The remainder of the paper is organized as follows. Section II describes the system model. In Section III, the proposed cell planning and joint cell and fiber backhaul planning are formulated. Section IV presents the proposed metaheuristic algorithms. Numerical results and performance evaluation are presented in Section V. Finally, Section VI concludes the paper.
Ii System Model
Iia Network Architecture
In our system model, we consider small cells operating in the mmWave band and define two types of smallcell base stations, namely, wired base station (WBS) and unwired base station (UBS). As shown in Fig. 1, WBSs are served with fiber backhaul and UBSs are connected to WBSs via wireless backhaul.
For UBSs, the wireless backhaul is implemented by means of IBFD, referred to as IBFD wireless selfbackhauling [jain2011practical][7817893]. With this technique, the same frequency band is simultaneously used for both access and backhaul. The main issue of this technique is the selfinterference between access and backhaul links. Hopefully, this interference can be mitigated efficiently by using separated highly directional antennas, thus providing sufficient distance between transmitter and receiver antennas, and utilizing advanced cancellation techniques in both digital and analog domains to remove residual interference [6832464]. Let denotes the residual selfinterference noise in the backhaul link in the downlink direction, where is the percentage of residual selfinterference and is the transmission power of access links.
As illustrated in Fig. 1, we utilize a passive optical network (PON) architecture to realize the fiber backhaul. This architecture has been standardized as a promising scheme to realize fibertothex (FTTx) deployments, where the x may represent a home, building, neighborhood, or curb [6289432]. The main components of a PON consist of the optical line terminal (OLT), passive power splitter, and optical network units (ONUs). Generally, a PON has a treeandbranch topology, whereby the OLT and ONUs serve as the root and leave nodes, respectively. The OLT is located at the central office (CO) and performs resource allocation among ONUs, and ONUs reside at subscriber premises. In our model each WBS is connected to an ONU serving a single PON subscriber.
In this paper, we focus on the latest standard of PONs, the socalled NextGeneration Passive Optical Network 2 (NGPON2), which is specified in ITUT recommendation G.989.2 [ITU]. In NGPON2, multiple subscribers are served by utilizing hybrid time and wavelength division multiplexing (TWDM), where each subscriber transmits at the maximum data rate of Gbps [7389581]. By leveraging wavelength division multiplexing (WDM), it is also possible to implement a pointtopoint connection between the OLT and any ONU, which is desirable for WBS backhaul as it provides guaranteed lowlatency backhaul with a dedicated capacity of Gbps.
Interestingly, NGPON2 is backwardcompatible with previous PON standards such as GPON, which is widely used in FTTx deployments [7389581]. To provide fiber backhaul for small cells, we leverage preinstalled GPON equipment and only upgrade the OLT and splitter. As shown in Fig. 1, conventional GPON subscribers (denoted as FTTx subscriber) may be served beside WBSs over the common fiber infrastructure.
In the proposed joint cell and fiber backhaul planning, by taking existing FTTx feeder fibers into account we determine the optimal locations for installing new splitters and deploying new distribution fibers. In our approach, the goal is to minimize the cost of new required facilities for fiber backhaul planning. However, we assume there is no available distribution fiber at the optimum place of a WBS, and a new distribution fiber branch is installed to connect that WBS to the existing fiber infrastructure.
IiB mmWave Propagation and Blockage Model
Two main attributes of cellular networks are capacity and coverage, whereas the most critical design parameter in mmWave networks is path loss. With electromagnetic waves, the increase of path loss exponent is much higher in non lineofsight (NLOS) than lineofsight (LOS) systems, especially for higher frequencies such as mmWave [rappaport2013millimeter]. Clearly, in mmWave cellular networks, LOS channels are preferable to increase the spectral efficiency.
The wellknown path loss model (in dB) for mmWave cellular network is as follows [singh2015tractable]:
(1) 
where and denote the path loss at closein reference distance and the path loss exponent, respectively. Furthermore, we have , where
represents the lognormal shadowing variance,
denotes the position of nodes in Cartesian coordinates, and is the Euclidean distance. Note that as well as are different for LOS and NLOS.The high path loss in mmWave systems limits the communication range to very short distances. However, this limitation can be partially alleviated by using directional antennas. In this study, we assume steerable array antennas at BSs for access link and highly directional horn antennas for backhaul links, whereby and denote the array gain of the access link at BSs and user equipment (UE), respectively, and represents the array gain for the backhaul link at BSs. Furthermore, we assume that a perfect array beam matching is performed for both access and backhaul links.
In [6840343], a stochastic blockage model was derived for mmWave channels based on random shape theory and stochastic geometry. It was shown that when the blockage is modeled as a rectangle Boolean scheme, the probability of the channel status (LOS or NLOS) is given by
(2) 
where denotes the link distance and is a parameter that is determined by the density and average size of the blockages in a specific environment. For convenience, the notation and parameters are summarized in Table I.
Notation  Parameter  Notation  Parameter 

access link transmission power  backhaul link transmission power  
residual selfinterference percentage for duplex link  path loss at 1  
path loss exponent  path loss for  
shadowing variance  location of BSs  
users distribution in  average of users in  
position in Cartesian coordinates  and  users and UBSs association indicator, respectively  
successful detection indicator  array gain  
SINR  SINR threshold for detection  
lower bound for successful detection probability  interference  
large constant for penalty  crowding distance  
, , and  available bandwidth for each sector, resource block, and th user, respectively  , , , , , and  sets of users, pixels, BSs, WBSs, UBSs, and FAPS, respectively 
average data rate and resource block for each user in the downlink, respectively  costs of implementing WBS and UBS, respectively  
th Pareto front  thermal noise  
achieved and requested data rate for th user  th object  
vector of objects  ,  number of WBSs and UBSs, respectively  
constraint relaxation  FAP selection  
indicator to determine if th is connected to th FAP  and  costs of selecting FAP, distribution, and feeder fibers, respectively  
line of sight indicator  FAP capacity 
Iii Problem Formulation
Iiia Assumptions and Preliminary Parameters
In this paper, we design a cellular network over an area of size divided into subareas, , whereby each subarea () has a unique user spatial distribution () with a different average number of users per unit area ().
Without loss of generality, we assume that all users request the same average data rate and denote the average data rate in the downlink by . Here, it is important to note that this assumption will be generalized in the next subsection by assuming different data rate demands for each user. With regard to the average data rate, we also assume that at least resource blocks should be dedicated to each user to satisfy her demand. Hence, the largest number of users that can be supported by each BS is obtained as follows:
(3) 
where indicates the number of sectors of each BS; and denote the available bandwidth of each sector and resource block (RB), respectively; and is the floor function. The smallest number of BSs to satisfy the users’ data traffic demand in each subarea is computed as
(4) 
where is the size of subarea and represents the ceiling function. Consequently, the smallest total number of BSs required to serve all data requests in is given by
(5) 
It is worth mentioning that the number of WBSs has to be equal or larger than since all traffic is steered by WBSs.
Next, the number of required BSs to satisfy the coverage constraint is given by
(6) 
where is the coverage area of each BS. Then, we initialize our algorithms by feeding into them. It should be noted that , which is , is also a variable of our optimization problem. Thus, the final value of might differ from its initial value. In fact, by means of these primary calculations the optimization process, will be elaborated upon, can be reduced significantly.
IiiB Cell Planning Formulations
Let the following matrices represent the location of BSs:
(7a)  
(7b)  
(7c) 
where indicates the
th BS position in the Cartesian system. For the sake of simplicity and without loss of generality, we assume that all BSs have the same height. Let the binary variable
denotes the association state of the th user to the th BS, as obtained as follows:(8) 
where and denote the set of BSs and users, respectively. Indeed, with this variable we can indicate whether the ’th BS is the nearest BS to the ’th user or not. Using the same definition, we can now define a binary variable indicating the nearest WBSs to UBSs; it is set to if the ’th WBS is the nearest WBS to the ’th UBS, and otherwise. Moreover, let indicate if the th user receives the minimum power from her associated BS for detection or not, which is given by
(9) 
where is the received SINR at th user of the th BS. Furthermore, denotes the lower bound of the probability and is the SINR threshold for the successful detection. is given by
(10) 
where indicates the transmitted power of the access link. shows the path loss as a function of the distance between the th BS and the th user. and denote the array gain of the access link at BSs and UEs, respectively. In addition, and denote the thermal noise and the corresponding interference that the th user suffers from the interfering BSs, respectively. Note that (9) and (10) specify access links. Similarly, we define the following variables for backhaul links:
(11) 
(12) 
where in (11) denotes the set of UBSs, is the SINR threshold for successful detection, and is the lower bound of the successful detection probability. In (12), denotes the transmission power of the backhaul link, is the path loss between two BSs at distance , and represents the array gain of the backhaul link. Further, we use and to represent the selfinterference from the access link and neighboring UBSs, respectively.
The primary goal of our cell planing framework is to maximize the number of users served with their requested data rates, , which is accepted as crucial aim for 5G. Accordingly, we set the objective function of the cell planning problem to minimize the total number of users which are not satisfied with their demanded rates.
(13) 
where and indicate the desired and actual data rate of the th user, respectively. The indicator function in (13), , equals if the condition is satisfied, and otherwise. Here, is a given constant and is given by
(14) 
where is the bandwidth dedicated to the th user from its associated BS.
It is worth mentioning that another critical aspect of cell planning is to minimize capital expenditure (CAPEX). Hereupon, in addition to the cellular network rate, implementation cost is also involved in our cell planning procedure. Obviously, the major CAPEX of cellular network has its roots in BSs implementation and feeding them with appropriate backhauls. Therefore, we model the major cost of cell planning as follows:
(15) 
where and are indicating the costs of implementing WBS and UBS and feeding them with suitable backhaul, respectively. Given the aforementioned definitions and assumptions, our cell planning problem can be formulated as follows:
(16)  
subject to:  
(17)  
(18)  
(19)  
(20)  
(21)  
(22) 
Objects: The optimization problem has two objectives, and . Thus, we have a multiobjective problem here. Obviously, these two objects are conflicting since having a good coverage implies having more BSs, which is costly.
Coverage constraints: Constraint (IIIB) insures the coverage of deployed cells, where denotes the total number of elements in a set, and is a constant, relaxing the constraint. Furthermore, we divide the entire region into enough small areas called as pixels, in which and are denoting the pixel set and SINR at the middle of the th pixel, respectively. Note that is computed using (9) for a user located at the center of th pixel. Constraint (18) is included to associate UBSs to WBSs. It is worth mentioning that in our cell planning each UBS is served by a single WBS.
Limitations of WBSs: Due to the limited fiber backhaul capacity, energy constraint, and computation processing, the total number of UBSs served by each WBS is less than , as stated in (19).
Capacity Constraints: Clearly, the total spectrum of UBSs assigned to users has to be less than its capacity, which is given by (20). The same approach can be employed for WBSs, while accounting for their distinctive feature of supporting both access and backhaul links simultaneously.
Two different approaches can be applied to allocate the bandwidth of WBSs to access and backhaul links: static or dynamic allocation. In static allocation, the bandwidth of each WBS is divided into two subbands, which are separately dedicated to access and backhaul links. Conversely, in dynamic allocation, the WBS bandwidth is divided among access and backhaul links dynamically according to current traffic loads and bandwidth requests. Clearly, dynamic allocation enables more flexibility and efficiency. It is worth mentioning that this functionality can be easily implemented in cellular networks thanks to the advent of software defined wireless network (SDWN)[6994333] as well as cloud radio access network (CRAN)[6898939]. Constraint (IIIB) guarantees that the total bandwidth of a given WBS allocated to its associated access and backhaul links is less than its available bandwidth. In addition, constraint (22) is included to satisfy an acceptable amount of users, in which, is a relaxing constant (similar to in (IIIB)).
IiiC Joint Cell and Fiber Backhaul Planning
In this subsection, we optimize both the cell planning and fiber backhaul designing problems. We assume that there are some predeployed fiber access points (FAPs) that are randomly distributed across the area. Furthermore, we assume that there are enough dark feeder fibers associated with these FAPs. Our goal is to leverage these dark feeder fibers and FAPs to implement NGPON2 architectures as the backhaul of WBSs.
Let the binary variable indicates the selection state of FAPs, which is if the th FAP is selected, and otherwise. In addition, we define a binary variable , which is set to if the th WBS is connected to the th FAP; otherwise it is set to .
To formulate the cost of the fiber backhaul in our planning problem, we define some parameters in the following. Let indicate the cost of selecting an FAP and installing an optical splitter at it. The costs to utilize feeder fiber and deploy distribution fibers per unit length are denoted by and , respectively. Furthermore, let indicates the distance between the th FAP and the th WBS. Similarly, let represents the distance between the central office and the th FAP.
Given the aforementioned parameters, the total cost of deploying fiber backhaul based on an NGPON2 architecture () can be modeled as follows:
(23) 
We apply the same procedure utilized in the previous subsection for cell planning.
Finally, we can summarize the multiobjective joint cell and fiber backhaul planning as follows:
(24)  
(25)  
(26)  
(27)  
where , , and are given in (14), (15), and (23), respectively. Also, constraint (25) ensures that only one splitter is associated with each WBS. Constraint (26) states that each WBS is connected to a selected FAP and constraint (27) accounts for the capacity limitations of the fiber backhaul, which guarantees that the total number of WBSs connected to a specific FAP does not exceed the fiber capacity allocated to that FAP ().
It should be noted that both and are the deployment costs of wireless and fiber networks. Therefore, they can be merged and treated as one object, , defined as . Thus, the planning objective can be rewritten as
Iv Proposed Cell Planning Algorithms
Generally, the cell planning problem, similar to the wellknown facility location problem [drezner2001facility], is NPHard [1230131]. Thus, obtaining its optimal solution for large areas with infinite BS candidate positions is not straightforward. Alternatively, metaheuristic algorithms such as tabu search, genetic algorithms, simulated annealing, and ant colony optimization can be used. The metaheuristic approaches for cell planning problem can be divided in two categories based on either finite or infinite candidate locations for BSs. Clearly, considering infinite candidate locations results in a better performance at the expense of higher computational complexity.
In this paper, we assume infinite candidates and utilize genetic algorithm to solve our cell planning problem. Furthermore, we use NSGAII to solve our planning problems to approach promising solutions. In what follow, first we start with introducing genetic algorithm then we follow NSGAII algorithm.
Iva Cell planning with metaheuristic algorithms
IvA1 Genetic Algorithm
The genetic algorithm (GA) starts with an initial random population (individuals) denoted by , where is the total number of individuals.
Let denotes the total number of iterations in GA. Let define and denoting the sets of selected individuals for crossover and mutation, respectively. Note that and are proportional to the total population . In each iteration, individuals are selected from the set and individuals are selected from the set for crossover and mutation, respectively. Different strategies may be applied for the selection step, either purely random selection or considering the cost function, for more information we refer interested readers to [996017].
Let denote the selected individuals for crossover. Then, in each iteration the crossover procedure is performed according to Eq. (28), and new individuals, and , are derived as follows:
(28a)  
(28b) 
where is the sign of the Hadamard production and is directly derived from to compute the summations represented in (28). It should be noted that and may have different number of elements, thus, the minimum dimension from the pair of and , or even the maximum dimension can be selected, where for the case of maximum selection random elements are added to which has less elements. Additionally,
is a random matrix defined as follows:
(29)  
in which and are selected based on one of the above approaches. In addition, we have where is an allone matrix with the same dimension as . Moreover, we determine the distribution of in (29) empirically from simulation results as follows:
(30) 
where is a small positive constant, enabling the search of more possible solutions. Based on , we have the following three different possibilities in each iteration: 1) transferring the locations of WBSs to the next iteration while merging the locations of UBSs, 2) transferring the locations of UBSs to the next iteration while merging the locations of WBSs, and 3) merging the locations of both WBSs and UBSs. Using this randomness implied by will help us keep the positions of those BSs that are appropriately located while merging the other. With this policy, we can significantly reduce the number of iterations and improve the performance of the optimization. Further details will be provided in our results below. Note that in the ordinary NSGAII we just have the third case, where we merge the locations of all BSs. Let assume () is selected for permutation, then, its th column ( is randomly selected within ) is mutated as follows:
(31a)  
(31b)  
(31c) 
where and
are zero mean Gaussian random variables with variances of
and , respectively. Furthermore, is a small enough positive constant denoting the mutation rate, and and denoting Cartesian coordinates. It should be noted that subscripts max and min are set to make sure we have most of the mutated individuals in the allowed area.To complete the proposed GA, the following penalty functions are included in the objective function of the planning problem, in which we categorize (IIIB), (19), (20), and (22) as inequality constraints (), and (18) as equality constraint ():
(32a)  
(32b)  
(32c)  
(32d) 
where is a vector denoting the optimization variables. Furthermore, and are the number of inequality and equality constraints, respectively; and are large enough positive violation coefficients for inequality and equality constraints, respectively. For instance, the penalty function for (IIIB) is:
(33)  
It should be noted that is a function of and . Finally, using the aforementioned penalty functions, the penalized objectives can be expressed as:
(34) 
Here, we use as a variable vector to abbreviate the variables and . Since the penalized objective equals the objective itself in the feasible set we use the same notation for them.
IvB Metaheuristic algorithms for the proposed multi objective problems
We utilize the wellknown NSGAII algorithm [srinivas1994muiltiobjective] to solve the considered multiobjective problems. In so doing, Algorithm 1 present GA procedure, afterward, we proceed to NSGAII for our proposed planning problems.
Generally, multiobjective optimization problems have more than one optimal solution. The set of these optimal solutions is referred to as the Pareto front. The Pareto front is defined as follows:
Definition 1: A solution vector , where indicates the th objective function, is a Pareto front or nondominated, if and only if there is no such that:
) and
) .
Similarly, dominates (), if and only if:
) , and,
)
Two approaches are utilized to find the optimal Pareto front set. The first one is based on decomposition, in which the multiobjective problem is formulated as an oneobjective optimization problem. The constraint, weighted sum, and goal attainment methods belong to this category [996017]. In this approach, however, multiple executions of these algorithms with various conditions is challenging. The second approach deals directly with the multiobjective optimization problem. In our study, we apply NSGAII, which belongs to the second category, as explained in more detail next.
NonDominated Sorting Genetic Algorithm II: This algorithm was introduced in [996017]
. It leverages GA for evolutionary computing and a specific sorting method referred to as nondominated sorting. The sorting method is used to rank the solutions of each iteration. In what follows, the parameters required to develop the proposed NSGAII algorithm are explained.
Let indicate a set for th individual, which is fulfilled for those individuals dominated by the th individual. In addition, a scalar is used to denote the time instances that the th individual is dominated by other individuals. The nondominated sorting procedure is explained in Algorithm 2. Note that in Algorithm 2, , where indicates the th Pareto front set, i.e., is a set of solution vectors, , which are dominated neither by themselves nor by the other solution vectors.
Ranking the solutions that are far apart from each other by using a prerogative approach is a promising approach to obtain a Pareto optimal solution. To implement this ranking method, we define the socalled crowding distance for the th answer as follows:
(35) 
where and are the two nearest solutions to from different sides and are in the same Pareto front as . Also, and are the two head solutions in each front. Note that the crowding distance for these two head solutions needs to be initialized with to avoid being omitted or ignored during this procedure. Solutions with a small crowding distance are likely to be excluded from the procedure in subsequent iterations.
The variables of the fiber backhaul planning problem are binary. Thus, the crossover and mutation procedures are obtained by modifying Eqs. (28) and (31). Assume that and are selected as parents. The binary crossover is then given by
(36) 
where , is the total number of FAPs, is a binary random vector whose elements are or with equal probability, and . Furthermore, the binary mutation for is given by
(37) 
where is a random integer number between and .
The proposed NSGAII procedure for our cell planning and joint cell and backhaul planning problem is shown in Algorithm 3.
V Results
Va System parameters for cell planning
We consider an area with mmWave BSs where some BSs have direct access to fiber (WBSs) while the remaining ones are supported by WBSs via wireless IBFD selfbackhauling. The cell planning takes different criteria such as capacity, coverage, and selfbackhauling into account. Specifically, parameters such as , , and are set to default values, as shown in Table I. In addition, we assume that the height of antenna in UEs and BSs is set ot m and m, respectively. As listed in Table II, the required bandwidth for a data rate of Mbps is approximately MHz. On the other side, we also have the dimensions of areas, hereupon, by using (6) we can obtain . Accordingly, by utilizing the concluded values , , and for each scenarios we can appropriately set up the optimization algorithms.
Cell Planning Parameters  

Parameter  Value  Parameter  Value 
dB  dB  
dBi  dBi  
dBi  
Noise Figure  dB  dBm/Hz  
+(BW)  
GHz  
MHz  
Watt  Watt  
dB  dB  
Genetic Algorithm  Network Costs  
Parameter  Value  Facility  Price 
Furthermore, the parameter settings for selfbackhauled mmWave, equipment costs including both backhaul and access components, and parameter values of our proposed NSGAII algorithm are listed in Table II. These parameter settings are taken from [6834753], [rappaport2013millimeter],[singh2015tractable], [6840343], [ranaweera2013design2], and [7499308]. We note that the NSGAII parameters are empirically set such that the best results are achieved.
Scenario Description  

Scenario  (Km)  (user/Km)  
Scenario I 

Comments
There are no comments yet.