ANTENNA PLACEMENT OPTIMIZATION FOR CELLULAR NETWORKS Hammad Hafiz, Harjeet Aulakh and Kaamran Raahemifar

Electrical and Computer Engineering Ryerson University Toronto Canada

ABSTRACT

Long Term Evolution (LTE) cellular networks are currently implemented in many countries at very high speed. Since manual cell planning is a time consuming process and subject to errors and inefficiency, there is a need for automated approaches to optimize coverage, capacity and quality of cellular networks in less amount of the time. This paper studies the application of branch and bound algorithms to solve the Antenna Placement Problem (APP) in Cellular networks. We are investigating the optimal placement of trans-receiver antennas in cellular systems. Our optimization framework imposes no constraints on the location of the antennas. Based on a branch and bound search technique, we adopt a formulation that is suitable for node placement optimization in various cellular network scenarios. We have shown that optimal placement of antennas within the coverage area can significantly improve the efficiency of wireless networks. We achieved the optimal placement topologies for different numbers of antennas and illustrate that the circular deployment is not optimum in all cases. Finally, we showed the optimal placement solutions through MATLAB simulations.

Index Terms—Cellular networks, Antenna placement,

Cluster head, Branch and Bound search, coverage area and Quality of Service.

1. INTRODUCTION Cellular network planning is a multi-objective optimization problem, which involves deciding on the number of Base Stations, their configuration such as power, type of antennae, height of the tower, etc., and locating BSs in the geographical area. A new generation cellular system looks forward to increasing its network capacity and coverage, as well as minimizes the interference and improves the Quality of Service (QoS). One methodology to minimize the interference, both in the uplink and the downlink of cellular networks, is to decrease the overall transmit power by Base Stations [1]. In addition, by decreasing the access distance between the transmitter and the receiver, these antenna systems has a direct impact on the energy efficiency of the cellular network.

Figure 1: Structure of antenna system in cellular networks [2]

Optimal placement of antennas has been a significant subject of attention in wireless networks [2], [3]. Optimizing the location of the antennas for obtaining the minimum bit error rate in linear cells [4], maximizing the coverage of a cellular network [1] or finding the optimum radius for antenna deployment of antennas [3] are some examples of the benefits of antenna placement optimization in cellular systems. In different words, the capacity increase (or equally the power saving) of antenna systems is largely influenced by antenna locations. Many of the studies on the placement optimization of antennas [5] impose restrictions on the topology of the network, such as linear cells or antennas deployed along a circle. The remaining of this paper is outlined as follows. First in Section II, we discussed the related work. In Section III, we formulated the optimization problem and introduce the branch and bound technique used for solving the placement optimization problem. In Section IV the MATLAB simulation with comparisons and graphs are shown. This paper is concluded in Section V.

2. RELATED WORK Tzung-Pei Hong and Cheng-Hsi Wu [4] et al. proposed the weighted clustering algorithm (WCA) for identifying cluster heads in mobile networks. A mobile ad hoc network can be modeled as composing of nodes and links, which is usually represented by a graph G = (V,E) , where V represents the set of nodes and E represents the set of

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links. They assume the transmission radii for all nodes are the same. The following formula is used to calculate the combined weight (Wv) of a node v as a cluster head:

Where v is the serial number (ID) of a mobile node, △v is the degree difference of node v, Dv is the sum of the distances between v and its neighbors, Mv is the mobility speed of node v, Tv is the cumulative time in which node v acted as a cluster head, and wi is the weighted coefficient for the i-th factor. The degree of a node v is the number of nodes within its transmission radius, not including itself. The degree difference is thus the difference between the degree of a node v and a predefined ideal node number M in a cluster. Wv is used to determine the goodness of a node as a cluster head. The lower the Wv value is, the better v acts as a cluster head. Limitation of this approach is that the base stations were randomly generated to compute the system lifetime from the application nodes. Also, additional limitation for selection of cluster heads in mobile wireless sensor networks. Efrat [6] et.al has addressed the problem of finding an optimal base-station location. They split the problem into two parts: (i) for a given base station location and (ii) finding an optimal base-station location by using part (i) over a discrete set of locations. They show that problem (i) can be expressed as a linear programming problem, which can be solved in polynomial time. For problem (ii), they show that restricting the base-station to the locations of the mobile nodes achieves a constant-factor approximation for maximizing lifetime and present a (1 − ε) - approximation by discretizing the search space into a limited number of points. Limitation of this approach is that it only considers line of sight sensors in the optimal sensor placement problem. Buragohain [7] et al deals with the sub-problem of finding an optimal routing scheme to maximize the lifetime of the network when the base station’s location is fixed. With the use of assumption that transmission and reception of 1 bit of data uses 1 unit of energy irrespective of the distance of transmission/reception, they prove that the problem is NP-complete. Limitation under their scheme is that the number of levels of the transmission tree is not restricted and also it only considers a time synchronization model for computing aggregates. Hou [8] et al. has presented the extension of the life of the network by moving the base-station to different locations. In their model, the base-station has an unlimited supply of power. The idea is that since the sensors around the base-station consume more energy than others (because they work as the relay for other sensors), one can move the base-station to different locations, to balance the battery

consumption among all sensors. They considered two versions of the problem: (i) The number of base-station locations is finite (C-MB), and (ii) The number of base-station locations is infinite (U-MB). They provide a polynomial-time algorithm for the C-MB problem and a (1−ε)-approximation algorithm for the U-MB based on discretizing the space into a set of finite locations. Limitation of this model is that it does not consider how to determine the optimum time to move the base station to new sensors.

3. BRANCH AND BOUND SEARCH TECHNIQUE Several heuristics have been proposed to choose cluster heads (CH) in a group of cell phone users. These include (i) Highest-Degree heuristic (ii) Lowest-ID heuristic and (iii) Node-Weight heuristic. In our approach we have assumed several things to deploy B & B technique for optimal placement of antennas. These things includes: 1: The squared space area, 2: The mobile terminals (users) are represented as nodes, 3: Heterogeneous network, 4: Applications nodes (AP) are also called cluster header (CH), 5: A node x is considered to be a neighbor of another node y if x lies within the transmission range of y, and 6: The neighbors of a CH become members of that cluster and can no longer be executed in algorithm after one node has chosen as CH. We have deployed the mentioned algorithm using B & B technique to obtain the following constraints e.g. Cost (Installation), energy (signal quality) and coverage area.

Figure 2: Overview of Clustering Technique

We have deployed the mentioned algorithm using B & B technique to obtain the following constraints e.g. Cost (Installation), energy (signal quality) and coverage area. Wireless network consists of nodes, cluster header/application nodes, and one or several base stations (BSs). Energy of the wireless network elements can be described as follows: Nodes < Cluster header < Base Station. Each cluster of nodes is allocated with at least one cluster header (CH) (see Fig. 2). Our goal is to place the cluster header in such a way, in a square space, so that we have maximum coverage, signal quality, minimum installation cost and improved QoS (future work). We have taken different scenarios in which we considered

different parameters to find out the optimized location for the cluster header to cover the maximum number of nodes. And if the node lies out of that range then we analysis it by considering the following two options. 1: Do we want to serve the node with the same cluster header with weak signals (less quality of service) or 2: Do we want to place another antenna to get the services for that node. Intelligently we may want to get the services from the same cluster header as placing another antenna for just one/two nodes may not be cost efficient solution. To provide a solution to this thing, whereby we don’t want to place another antenna just to serve one/two nodes, we have also implemented logic to optimally cover this node with enhanced antenna range. We can realize the trade-off that if we want to deploy the antennas with less range then we may have the scenarios in which some nodes lies outside the range of the antenna but those nodes have to be served by the same cluster header to have optimal distribution. But on the other hand, if we deployed antennas with larger range to cover the all nodes in specified vicinity then we can eliminate the above scenarios but we may have to pay in terms of antenna cost (with larger coverage area). The steps involved in B & B search technique optimization process are shown in the figure 3 below. Here are the steps that we have taken to implement B & B search technique. 1. Average of X =1/ ∑ 2. Neighbors N (v) ={v’| distance (v,v’)≤Rv} 3. Compute the Euclidean distance for every node. 4. Neighborhood calculation (see matrix below for generalized basic logic steps) and choosing proper CH. 1 631 36

After implementing our desired criteria (nodes<R) and logic we are eliminating row and column. Repeating all this for remaining nodes until each node is assigned to a cluster (this way we traversed the whole matrix). At the end we are left with 1x1 matrix. 8 1232 36

15 1833 36

22 2434 36 29 3035 36 [36]

5. Plotting the network distribution

6. Plotting cluster header with corresponding served nodes. 7. Plotting the antenna range

4 EXPERIMENTAL RESULTS AND DISCUSSIONS Generally antenna gain is a parameter which measures the degree of directivity of the antenna's radiation pattern. A high-gain antenna preferentially radiates in a particular direction. Normally, the antenna gain, or power gain of an antenna is defined as:

Gain = , where U is the radiation intensity. In our research we have considered two different scenarios. In the first scenario, we have taken the fact into the consideration that we have chosen antennas with optimized range. That being said, antenna with small range possesses the less gain (less expensive) and orientation of the antenna is relatively inconsequential. This scenario also realizes the fact that the nodes sitting in the vicinity of the cluster header (antenna) may also be served intelligently by the same CH/antenna. Below is the Algorithm Flow Chart (Figure 4). Our program intelligently allocates the nodes to the best available CH. As it is not an optimal idea to place another antenna just to serve one/two nodes, these nodes may get the services from nearby antenna at some cost. In the second scenario we have presented antennas with longer range. Although we need the less number of antennas to cover the same area but we may pay the cost in terms of gain (more expensive antennas). Examples of both scenarios are laptop Wi-Fi antenna and dish antenna on a spacecraft. The algorithm flow chart, see Fig. 3, has been shown to grasp the basic idea. 4.1 Simulations Results

Form a matrix of elements

Make Matrix diagonal zero and chose a radius R

Sort the rows and perform

Neighborhood Calculations

CH = highest density

Sort Node < R (high

to low)

Count # of nodes that satisfies: Node <R

Remove correspondin

g row and column of

chosen node

Repeat process for all nodes

Finding the Euclidean distance

Figure 3: Steps for B & B Search Technique

Figs. 5 to 7 show the results of our program. Beside the improvement in efficiency we have the same optimized output with indicated covered area compared to the preceding logic output. The time analysis of the program is also presented to show the efficiency of our program.

In the profile summary “Self Time” is the time spent in a function excluding the time spent in its child functions. So efficiency can easily be visualized. Our program is so generalized that it even can take care of 1500 nodes (tested) compared to the 30 nodes which were executed last year by another group. This is the significant improvement. In the outputs below “N” represents the number of nodes while “Criteria” represents the method of selecting the area range by cellular antenna. Optimized placement criteria means that the antenna is placed in such a way that it optimally cover the nodes. Although some of the nodes may not be covered under the same CH range but they may be served by the same CH with the compromise on QoS (Quality of Service). On the other hand range extender means that we are placing antenna with higher range so that all of the approximate nodes should be in the range of CH/antenna but with no compromise on QoS.

Figure 5: N=500, Criteria = Optimized Placement Layer1

Figure 6: N=500, Criteria = Optimized Placement Layer2

Start

Finding the Euclidean

distance and setup R

Neighborhood Calculations

Traversing whole matrix and choosing

proper CH with specific criteria

Optimization Criteria & Range Selection

Remove processed Row and Column

Data Gathering for CH and Antenna Range

Stop

Yes

No

Plotting nodes cluster

distribution with served CH

Figure 4: Algorithm flow chart

Figure 7: N=500, Criteria = Range Exte

4.2 Graphs and Comparisons Figs. 8 to 10 show the graphical represeoutput. X-axis represents the number of axis represents the unit of time i.e. secondstime of the execution is higher the effiprogram would be. For the better represegraph we are only taking the nodes up to 10did the execution of the program for N=15the program are also tabulated below. It can easily be visualized by these grprogram is more generalized and performcompared to the one executed last year by Our program has the drastic change in thethe program after N=30.

Figure 8: Number of Nodes versus Ti

4.3 Comparisons Our program produced the same optimizedpreceding logic does, with the improvemenIn table 1 we have presented the comparisoefficiency of our program compared to thelast year by another group considering the s

0.520.59

0.532

0.6270.54

0.5330.609

0.68

0

0.2

0.4

0.6

0.8

1

0 20 40 60

Our Program (s)

53.9470.65

88.88

94.69

97.67

0.00

20.00

40.00

60.00

80.00

100.00

120.00

0 20 40

Improvemen

ender

entation of the nodes while y s. So lesser the

ficiency of the entation of the 00. But we also 500. Results of

raphs that our mance efficient

another group. e efficiency of

ime

d output as the nt in efficiency. on showing the e one executed ame scenarios.

Figure 9: Number of Nodes v

Figure 10: Number of Nodes versus Time First column of the table representsSecond, third and fourth column shoin seconds. And at the end; fiftimproved efficiency of our progravisualize that as the number of program is more efficient. And thtowards 100% when we take morenodes compared to the preceding loghalts after N=100. (-ve sign showefficiency).

5. CONCLUSIO A branch and bound search algorithin this paper to solve the antenna plVersatility of our algorithm compalogic is that the performance of thdepend on the number of nodes/cluinitial matrix, and radius of the antmuch more generic and performprogram can handle about 1000 nodimprovement. Our program handles have taken two different scenarios and range extender, and both of th

82

0.591

0.665

80 100

7

98.88

99.20

99.49

99.70

99.76

60 80 100

nt (%)

versus Time

(Efficiency improvement)

the number of nodes. ows the execution time th column, show the am. As we can easily

nodes increases our is efficiency reaching e nodes i.e. over 100 gic where the program ws that we gain the

ON

hm has been proposed acement problem. The ared to the preceding he algorithm does not uster header or on the tenna. Our program is mance efficient. Our des in 12s, a significant

100 nodes in 0.6s. We i.e. optimal placement hem do not affect the

efficiency of our program, an advantage of our approach. Looking at the graphs we conclude that as the number of nodes is increasing the efficiency increases accordingly. Table 1 also shows that we have achieved the 99% efficiency at N=70. This keeps growing until we hit the 100 nodes for 100% efficiency.

In each iteration the branch and bound search algorithm choose the randomly generated initial values and the number of covered users must be analyzed from the results of a single run of the algorithm. Then we analyzed the performance for each set of nodes to evaluate the performance of our program. The randomly selected node matrix makes branch and bound algorithms a powerful tool in solving the antenna placement problem. The algorithm performance was evaluated assuming a flat square area. Further work can include development of algorithms so that terrain features can also be considered.

6. REFERENCES

[1] Job Munyaneza, Anish Kurien and Ben Van Wyk, “Optimization of Antenna Placement in 3G Networks using Genetic Algorithms,” IEEE 3rd International Conference on Broadband Communications, Information Technology & Biomedical Applications, 2008 [2] Sina Firouzabadi and Andrea Goldsmith “Optimal Placement of Distributed Antennas in Cellular Systems,” IEEE 12th International Workshop on Signal Processing Advances in Wireless Communications, 2011 [3] Eunsung Park, Sang-Rim Lee, and Inkyu Lee “Antenna Placement Optimization for Distributed Antenna Systems,” IEEE Transactions on Wireless Communications, Vol. 11, No. 7, July 2012

[4] Tzung-Pei Hong and Cheng-Hsi Wu “An Improved Weighted Clustering Algorithm for determination of application nodes in heterogeneous Sensor Networks” Department of computer science and information engineering national university of Kaohsiung. Volume 2, Number 2, April 2011, 2011 ISSN 2073-4212. [5] M. Chatterjee, S. K. Das, and D. Turgut, “WCA: a weighted clustering algorithm for mobile ad hoc networks”, Cluster Computing, Vol. 5, No. 2, pp. 193-204, 2002. [6] A. Efrat, S. Har-Peled, and J. Mitchell. Approximation algorithms for two optimal location problems in sensor networks. In Proc. 2nd International Conference on Broadband Networks, pp. 714–723, 2005. [7] C. Buragohain, D. Agrawal, and S. Suri. Power aware routing for sensor databases. In Proc. 24th Annual Joint Conference of the IEEE Computer and Communications Societies, vol. 3, pp. 1747–1757, 2005. [8] Y. Shi, Y. Hou, and A. Efrat. Algorithm design for base station placement problems in sensor networks. In Proc. 3rd International Conference on Quality of Service in Heterogeneous Wired/Wireless Networks, page 13, ACM, 2006.

Table 1: Program execution performance table

N Our Program (s)

Preceding logic (s)

Impr- ovement (s)

Impr-ovement (%)

10 0.52 1.129 0.609 -53.94 20 0.59 2.01 1.42 -70.647 30 0.532 4.784 4.252 -88.880 40 0.627 11.819 11.192 -94.695 50 0.54 23.173 22.633 -97.670 60 0.533 47.794 47.261 -98.885 70 0.609 76.227 75.618 -99.201 80 0.682 134.462 133.78 -99.493 90 0.591 196.267 195.67 -99.699 100 0.665 282.352 281.68 -99.764 500 3.171 Halted - -100

1000 13.643 Halted - -100 1500 28.661 Halted - -100