# Backhaul-Aware Dimensioning and Planning of Millimeter-Wave Small Cell Networks

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. System Model and Problem Description

#### 2.1. System Model

_{M}∪ B

_{S}of base stations, where B

_{M}are the MCs and B

_{S}are the SCs, all managed by a certain operator. The access network serves a set U of user equipments (UEs), each demanding a capacity of D

_{u}. The sub-6 GHz and mmWave bands are used for access transmissions in MCs and SCs, respectively. In the BH network, each MC has a high-speed optical fiber connection, while each SC j can connect either to another SC or directly to a MC using an mmWave LOS link with a capacity C

_{j}

^{BH}. In this way, the SCs can act as aggregator nodes to relay UE data. The required LOS between the access and BH nodes limits the area of interest to a set S

_{b}

^{LOS}of candidate sites for placing the SC b. The spectrum in the access network is organized in resource blocks (RBs) that are allocated to the nodes in a semi-persistent manner to meet current demands [21]. Each UE u is allocated a fraction W

_{u}of the spectrum allocated to its serving node. Non-overlapped mmWave spectrum in the V-band is allocated for access and BH networks. The V-band is selected because of its unlicensed or lightly licensed spectrum use. Due to the attenuation effects of oxygen absorption, this band can be effectively used to connect closely spaced SCs with short links that are daisy-chained and aggregated for transport to the network core [4]. Let W

^{BH}be the bandwidth dedicated to the BH in each node. Beamforming is employed in the BH network to enable simultaneous transmissions (beams) to different nodes using the same RBs. However, SCs acting as relays in a multi-hop BH link will use time or frequency multiplexing for transmissions with the nodes at the previous and next hops. The SCs can communicate directly with the other nodes through the X2 protocol, which is an ultra-fast broadband-related protocol that allows mobile operators to use different topologies to offload traffic.

_{u,r}be the Signal-to-Interference-plus-Noise Ratio (SINR) of this UE when transmitting on the RB r, defined as:

_{j}is the cell load factor of the node j, π

_{j,r}is a function that takes the value 1 when the RB r is allocated to the node j and the value 0 otherwise, I can take the value of M or S depending on the cell type (i.e., MC or SC) and p

_{N}is the noise power measured in one RB. The cell load factor is defined as the relation between the service demand and cell capacity according to the work in [32]. The spectral efficiency SE

_{u,r}of the UE u in the RB r is calculated from the γ

_{u,r}based on the following SINR mapping [34]:

_{max}is the maximum achievable spectral efficiency with link adaptation; γ

_{min}and γ

_{max}are the minimum and maximum SINR values, respectively; and ρ specifies the attenuation factor, which represents implementation losses. The capacity offered by the node b to the UE u is expressed as:

_{b}is the subset of RBs allocated to the serving node b. The fraction W

_{u}allocated to the UE depends on the resource scheduling scheme. For example, assuming a round-robin scheme, it is given by:

_{RB}is the spectral occupancy of a RB (e.g., 180 kHz assuming a subcarrier spacing of 15 kHz) and U

_{b}is the subset of UEs served by the same node b.

^{m}is the main-lobe width and A

_{max}and A

_{min}are the main and side-lobe gains, respectively. The antenna beams in the BH are aligned, so that the effective gain on BH links is A

^{2}

_{max}. Each candidate SC location in the area of interest has a probability of LOS propagation from a given BH node. This probability is taken from the 3GPP models in [36], which are applicable to frequencies up to 100 GHz. Unlike what happens with the UEs in the access links, an improvement of the LOS probability is applied to the BH links due to the local planning activities. According to the model presented in [37], the LOS probability p′ after local planning optimization is determined as follows:

_{x}, c

_{y}), where c

_{x}and c

_{y}are the x- and y-coordinates. The parameter Δd represents the correlation distance, d

_{E}stands for the Euclidean distance and M × N is the total number of grid points that are considered in the area of interest. Since the independent LOS visibility variable is Boolean to represent LOS and NLOS states, the obtained value of the correlated variable is rounded to the nearest 0 or 1. From this information, the set S

_{b}

^{LOS}of candidate sites for placing an SC can be obtained. The same exponential spatial filter is also applied to the shadow fading in order to provide spatial consistency.

^{b}is determined as:

^{b}; ${G}_{{h}^{b},b}^{BH}$ is the channel gain (i.e., path loss and shadow fading) between the SC and its BH node; ${L}_{{h}^{j}}^{BH}$ represents the cell load factor of the BH node h

^{;}${A}_{{h}^{j}}({\theta}_{b})$ and ${A}_{b}({\theta}_{{h}^{j}})$ are the transmitter and receiver antenna gains in the direction determined by the nodes b and h

^{j}, respectively; and ${p}_{N}^{BH}$ stands for the noise power measured in the bandwidth of the BH network, W

^{BH}. Note that this expression assumes a single polarized MIMO system. Although cross-polarization helps reduce the undesired radio interference, it requires the use of special antennas and is more sensitive to interference and rain [39]. The cell load factor of BH nodes is given by the traffic load of their served SCs, connected with either direct or multi-hop links. The spectral efficiency $S{E}_{b}^{BH}$ of the SC b is obtained using Equation (2). Lastly, the corresponding capacity ${C}_{b}^{BH}$ offered by this SC is determined as:

#### 2.2. Problem Description

_{0}= B

_{M}

_{,0}∪ B

_{S}

_{,0}of base stations that has previously been deployed in certain locations s

_{b}

_{0}, where b

_{0}∈ B

_{0}stands for the node. We define the variable z

_{s}

^{SC}∈ {0,1} at location s ∈ S to indicate with value 1 that an SC is deployed there. Likewise, z

_{s}

^{MC}∈ {0,1} indicates the locations of the MCs. The variable x

_{i,j}∈ {0,1} specifies that the node i is backhauled via the node j and y

_{u,j}∈ {0,1} indicates that the UE u is served by the node j. For simplicity, we consider that the cell sizes and maximum distance for BH link availability are such that any SC can be backhauled to the MC through one SC at most, which implies the multi-hop BH link to be limited to two hops. In addition, the problem is focused on the downlink because of the asymmetric nature of data traffic. Given this, the SC dimensioning and planning problem can be expressed as follows:

_{S}is the maximum number of SCs that can be backhauled by a certain SC. The objective is to minimize the deployment cost (i.e., the number of newly deployed SCs) while guaranteeing the UE demands. In classical cellular planning, the deployment of new base stations is motivated by the insufficient quality of the radio links between the UEs and the base stations. In this way, Equation (11) represents the quality of service in the access network, unifying both coverage and capacity constraints for the UEs.

## 3. Proposed Dimensioning and Planning Algorithm

^{b}indicates the BH node for the node b and p

_{b}

^{RX}is the received power from b. The UE demand D

_{u}is expressed as traffic density, with d

_{x,y}representing the traffic demand in the grid point (c

_{x}, c

_{y}). The function F(·) is a filter to smooth the traffic demand variable. Dimensioning is based on iteratively adding a new SC to the planning problem until the network (both access and BH) capacity is enough to satisfy the UE demands (Steps 2–3 in Algorithm 1). The planning problem, where the number of SCs is invariant, is divided into two stages: the first aims at optimally placing the SCs based on the UE demands (Steps 4–7 in Algorithm 1), while the second further optimizes the location of the SCs to satisfy the required capacity in the BH links (Algorithm 2).

Algorithm 1 CEBA dimensioning and planning algorithm | |

Input: initial solution: q = [_{0}x, z], B^{SC}_{S}_{,0}; z, B^{MC}_{M}_{,0}, D_{u}, N_{S}, α, β | |

1: | initialize q ← q, B_{0}_{S} ← B_{S}_{,0} |

2: | while constraints in (11) or (12) are not met |

3: | add a new SC, |B_{S}| ← |B_{S}| + 1 |

4: | use k-means to partition ω = (c_{x}, c_{y}, F(d_{x,y})) in |B_{S}| clusters and obtain centroids s_{b}, b ∈ B_{S} |

5: | optimize s_{b} by applying the steepest-ascent method n times to the function F(d_{x,y}) |

6: | select |B_{S,0}| elements b ∈ B_{S} having the smallest d_{E} (s_{b}, s_{b}_{0}) and replace them by b_{0} ∈ B_{S,}_{0}, B_{S}_{,0} ⊂ B_{S};update s _{b}, z^{SC} |

7: | assign BH node to each b ∈ B_{S}: h^{b} = arg_{c} max p_{c}^{RX} with c ∈ B_{M} and s_{b} ∈ S_{c}^{LOS}; if not possible, try withc ∈ B _{S} only if c has LOS BH with 1-hop link; update x |

8: | if ∃ b ∈ B_{S} | b has NLOS BH or b does not satisfy (14) then |

9: | execute Algorithm 2, backhaul-aware optimization |

10: | end if |

11: | end while |

Output: optimized q and B_{S} |

Algorithm 2 Backhaul-aware optimization algorithm | |

Input: q = [x, z^{SC}], B, {s_{b}}, N_{S} | |

1: | forb ∈ B_{S} |

2: | if b has NLOS BH then |

3: | create a set C of candidate BH nodes: C ← B\{b, nodes with NLOS BH or 2-hop BH link} |

4: | for c ∈ C |

5: | given the locations s_{c}^{LOS} ∈ S_{c}^{LOS} having LOS with c, calculate: ${\widehat{s}}_{c}^{LOS}$= arg${s}_{c}^{LOS}$min d_{E} (s_{b},${s}_{c}^{LOS}$) |

6: | end for |

7: | set BH node for b: h^{b} = arg_{c} min d_{E} (s_{b},${\widehat{s}}_{c}^{LOS}$), update x |

8: | set location: s_{b} =${\widehat{s}}_{{h}^{b}}^{LOS}$, update z^{SC} |

9: | end if |

10: | end for |

11: | forb ∈ B_{S} |

12: | if constraint in (14) is not met for b then |

13: | create a set G of SCs backhauled by b |

14: | for g ∈ G |

15: | create a set C of candidate BH nodes: C ← B\{b,g, nodes with NLOS BH or 2-hop BH link} |

16: | for c ∈ C |

17: | given the locations s_{c}^{LOS} ∈ S_{c}^{LOS} having LOS with c, calculate: ${\widehat{s}}_{c}^{LOS}$= arg${s}_{c}^{LOS}$min d_{E} (s_{g},${s}_{c}^{LOS}$) |

18: | end for |

19: | calculate: h^{g} = arg_{c} min d_{E} (s_{g},${\widehat{s}}_{c}^{LOS}$), r^{g} = d_{E} (s_{g},${\widehat{s}}_{{h}^{g}}^{LOS}$) |

20: | end for |

21: | sort g ∈ G by r^{g} in descending order with new index g’ |

22: | for g’ ∈ G |

23: | if constraint in Equation (14) is met for h^{g’} then |

24: | set s_{g’} =${\widehat{s}}_{{h}^{g\prime}}^{LOS}$, update z^{SC} |

25: | set h^{g’} as BH node for g’, update x |

26: | end if |

27: | if constraint in (14) is met for b then |

28: | break |

29: | end if |

30: | end for |

31: | end if |

32: | end for |

## 4. Performance Evaluation

#### 4.1. Simulation Scenario and Setup

^{m}is set to 10° and the gains A

_{max}and A

_{min}are set to 12 and −2 dBi, respectively, unless stated otherwise [35]. The cell bandwidth W

^{BH}in the BH is fixed to 1 GHz, and it does not interfere with the access spectrum. Regarding the proposed algorithm, N

_{S}= 2 is set to limit the required capacity per BH link, α = 0.7 allows partial service degradation and β = 0.8 allows small congestion in BH links. The other relevant simulation parameters are shown in Table 1.

#### 4.2. Simulation Results and Discussions

^{2}, the impact of the BH network is appreciable on both indicators by comparing ESBA with ESIB. To understand the increased number of SCs, note that the distance between MCs and SCs is limited by the maximum allowed path loss. Consequently, for a low number of MCs in the scenario, multi-hop BH links may frequently be required to reach distant areas, increasing the number of SCs. For 3 MCs/km

^{2}, the BH impact is appreciable on the spectral efficiency and insignificant on the number of SCs. Since in this case there are more locations satisfying the LOS condition, multi-hop BH links are less probable. Thus, ESBA approximates the same number of SCs as in the ideal case given by ESIB. However, deviations from the optimal location due to the BH constraints still impact the spectral efficiency as shown in Figure 2d.

^{2}, CEBA increases the number of SCs, on average, by 26% in comparison with ESBA. Such an increase is accentuated for higher traffic demands. Looking at the spectral efficiency, as the traffic demand increases, CEBA approaches the ESBA’s curve as a consequence of the increasing number of deployed SCs. This behavior of CEBA changes drastically for MC densities above 2 MCs/km

^{2}. Specifically, for 3 MCs/km

^{2}and low-medium traffic demands, the number of SCs is only increased by 10% compared to ESBA (and ESIB). It also deviates significantly from the random case. This is due to the smaller distances between MCs and SCs, which minimize the SC relocations made by CEBA.

^{2}and CEBA planning method. Figure 3 shows the number of planned SCs and the average spectral efficiency measured in the BH network. It is observed that, for high traffic demands, the number of planned SCs is smaller for 18 and 25 dBi gains. This is due to an increase of about 1 bps/Hz in the spectral efficiency, as shown in Figure 3b. In particular, when the BH capacity condition defined in Equation (12) is checked in the main loop of CEBA’s Algorithm 1, it returns a true value, indicating that the BH links are not congested and, therefore, additional SCs are not needed. The improvement in the average spectral efficiency is more pronounced in the range of low-to-medium values of the antenna gain. Accordingly, 18 dBi gain provides a good trade-off between spectral efficiency and antenna complexity.

^{2}. In general, this time increases with the traffic demand since more iterations are required to place additional SCs. Looking at the differences between methods, RSBA gives the lowest values since it follows a very simple logic for cell planning. Consequently, most of the simulation time is spent in network performance computation. The proposed method, CEBA, increases the simulation time with respect to RSBA by a factor of 2–3. This increment is mainly determined by the execution of the k-means, the steepest-ascent and the BH-aware optimization algorithms. Nevertheless, such an increase factor reveals a good trade-off between complexity and effectiveness of the solution. On the contrary, ESBA and ESIB provide the greatest values of the simulation time due to the high computational load of the exhaustive search approach. In particular, the increase factors are 25–37, which are considerably higher than those obtained by CEBA. Contrary to expectations, ESIB achieves larger simulation times than ESBA even though the BH network is not simulated. The underlying reason is that the set of candidate solutions that are evaluated by brute-force in the case of ESBA is smaller due to the required LOS condition.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Example network deployment for a traffic demand of 5 Gbps in the overall area for each evaluated algorithm. (

**a**) CEBA method; (

**b**) ESBA method; (

**c**) RSBA method; (

**d**) ESIB method.

**Figure 2.**Performance comparison in terms of number of SCs (#SCs) and spectral efficiency for different MC densities and traffic demands. (

**a**) #SCs for 2 MCs/km

^{2}; (

**b**) Spectral efficiency for 2 MCs/km

^{2}; (

**c**) #SCs for 3 MCs/km

^{2}; (

**d**) Spectral efficiency for 3 MCs/km

^{2}.

**Figure 3.**Evaluation in terms of number of SCs (#SCs) and spectral efficiency in the BH network for different values of the antenna gain. (

**a**) #SCs; (

**b**) BH spectral efficiency.

Parameter | Access | BH |
---|---|---|

Operating frequency (GHz) | MC: 5 SC: 60 | 60 |

Cell bandwidth (MHz) | MC: 100 SC: 250–1000 | 1000 |

Propagation—path loss | 3GPP model [36] | 3GPP model [36] |

MC antenna gain (dBi) | 12 | [12,13,14,15,16,17,18,19,20,21,22,23,24,25] |

SC antenna gain (dBi) | 10 | [12,13,14,15,16,17,18,19,20,21,22,23,24,25] |

MC transmit power (dBm) | 43 | 33 |

SC transmit power (dBm) | 25–33 | 30 |

Antenna height (m) | UE: 1.5, MC: 25, SC: 12 | MC: 25, SC: 12 |

UE service demand (Mbps) | 20 | - |

Number of demand realizations | 100 | 100 |

Method | Traffic Demand [Gbps] | |||
---|---|---|---|---|

1.0 | 3.0 | 5.0 | 7.0 | |

CEBA | 13.6 | 41.0 | 56.3 | 197.5 |

ESBA | 123.1 | 381.7 | 813.2 | 1444.3 |

RSBA | 4.1 | 12.3 | 30.5 | 53.9 |

ESIB | 150.0 | 419.4 | 771.1 | 1709.4 |

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**MDPI and ACS Style**

Muñoz, P.; Adamuz-Hinojosa, O.; Ameigeiras, P.; Navarro-Ortiz, J.; Ramos-Muñoz, J.J.
Backhaul-Aware Dimensioning and Planning of Millimeter-Wave Small Cell Networks. *Electronics* **2020**, *9*, 1429.
https://doi.org/10.3390/electronics9091429

**AMA Style**

Muñoz P, Adamuz-Hinojosa O, Ameigeiras P, Navarro-Ortiz J, Ramos-Muñoz JJ.
Backhaul-Aware Dimensioning and Planning of Millimeter-Wave Small Cell Networks. *Electronics*. 2020; 9(9):1429.
https://doi.org/10.3390/electronics9091429

**Chicago/Turabian Style**

Muñoz, Pablo, Oscar Adamuz-Hinojosa, Pablo Ameigeiras, Jorge Navarro-Ortiz, and Juan J. Ramos-Muñoz.
2020. "Backhaul-Aware Dimensioning and Planning of Millimeter-Wave Small Cell Networks" *Electronics* 9, no. 9: 1429.
https://doi.org/10.3390/electronics9091429