In the mobile system covering big areas, many small cells are often used. And the base antenna’s azimuth angle, vertical down angle, and transmit power are the most important parameters to affect the coverage of an antenna. This paper makes mathematical model and analyzes different algorithm’s performance in model. Finally we propose an improved Tabu search algorithm based on grid search, to get the best parameters of antennas, which can maximize the coverage area and minimize the interference.
In mobile communication systems, such as the current 2G and 3G networks, small cells divided by the base stations are used to cover the entire region. So the base station should have the best possible coverage area in order to improve the quality of service (QoS). As to base station antenna, the most important factors that affect the cell coverage are antenna’s azimuth angle, vertical down angle, and transmit power. As to the terminal, we think there are two targets which have to be considered. They are RSRP (Reference Signal Receiving Power) and SINR (Signal to Interference plus Noise Ratio) [
Recent antenna parameter adjustment algorithms are mainly based on experience and manual adjustment. Besides, we can use some optimization algorithms, such as Powell search algorithm, and intelligent algorithms such as GA (Genetic Algorithm) [
In this study, we propose an improved TS algorithm based on Grid Search to solve the problem of antenna parameter adjustment and optimization. By combining both the TS algorithm and the Grid Search strategy, the advantages of both approaches can be maintained and developed. At the same time, it can be found that the time consuming of the optimization process can be reduced efficiently, and the final optimization results guarantee that it can get the global optimum, compared with that of the exhaustive attack method (EAM) in the computer simulations.
This paper mainly discusses the application of intelligent TS algorithm in antenna parameters optimization problem. By using Tabu Search algorithm based on grid search and changedpace onedimensional search, we can get a global extreme in short time. Finally, we use multicell joint adjustment to get a better cell coverage. Section
In modern mobile communication system, we often use cell coverage to solve the problem of signal coverage of the whole system. The entire region is divided into several cells according to antenna of base station. The terminal directly communicates with the base which it belongs to. The cellular network is a typical model of cell coverage [
A typical cellular network unit.
But the shape of the base coverage as well as the number of sectors is adjusted with the actual needs in practical engineering. As shown in Figure
A base station distribution scene in Norway.
As the distribution of base stations and directions of antennas have no rules to follow, we can only adjust antennas parameters to maximize the coverage area. To simplify the mathematical model, in practical engineering we just consider three major parameters. They are antenna’s azimuth angle
Antenna’s horizontal angle.
Figure
In Figure
Antenna’s vertical angle.
3D figure of antenna.
Assume
When the objective function gets best solution
According to cost231hata propagation model, we define RSRP and SINR as follows.
Terminal’s RSRP calculation formula is as shown:
Assuming that the transmit power is distributed in all of a reference signal, the terminal SINR calculation can be written as
As previously mentioned, solving objective function is an NPC problem, because its complexity grows exponentially with the increase in the number of sectors. We cannot use a polynomial to describe the function, so any algorithm based on derivative cannot be used in this paper. In practical engineering, we often use some algorithm independent of derivative such as Powell search algorithm. Powell search does not require the objective function’s derivative, and the iterative process is relatively simple. However in this scene model, considering antenna’s adjustable minimum scale, Powell’s search direction will lose conjugate after several rounds. In practical engineering, we firstly optimize the RF parameters with continuous range of values. Secondly we take the nearest discrete value to be the optimization result. But Powell search also has a problem that it is easy to fall into the local extreme trap. The optimization result is not really a global solution.
Intelligent algorithm can also be used in this scene such as Genetic algorithm which is widely used in solving engineering problems [
Partly efficiency comparison between GA and Powell algorithm.
In Figure
Completely efficiency comparison between GA and Powell algorithm.
By analyzing the actual performance of intelligent and nonintelligent algorithm, we can get he following conclusion. (1) Nonintelligent algorithm like Powell search has fast convergence speed; (2) nonintelligent algorithm like Powell search is easy to fall into local extreme trap; and (3) GA’s lifting speed is too slow.
Based on the above conclusions, we choose another intelligent algorithm, which is the Tabu Search. The reason to select TS in solving this engineering problem depends on the following facts. Firstly, as an intelligent algorithm, TS can avoid local extreme trap and reach the global optimization [
Choose an arbitrary initial solution
Choose a solution
Update the memory
Update
As shown in Algorithm
The solution of the scene should be as the form of
In a grid search problem, we can consider that the search direction is the direction of the initial point to its near point. Then, if we just consider the parameters of azimuth and vertical angle, it should be a twodimensional grid. And there are 8 search directions that are up, down, left, right, topleft, bottomleft, topright, and bottomright. In this scene model, it should be a threedimensional grid and there are 26 search directions.
After determining the search direction, we can get a maximum in every search direction by calculating objective function. Theses local maximum points form a new candidate field. Choose the biggest in the field. If it is not in the Tabu list, put it into Tabu list and it becomes next round’s initial point. If it is better than the “best solution” in the list, it becomes the new “best solution.” If the improvement of objective function
Searching the maximum on one direction, we use changedpace onedimensional search. Intelligent adjustment step makes the decrease in the number of searches to improve the algorithm speed. The process is shown in Figure
The process of changedpace onedimensional search.
In Figure
Besides, in the local extreme search, we can record the objective function of one point which has been searched. Next time the algorithm reaches this point, we do not need to calculate the objective function again.
In above algorithm, the system calculates from sector 1 to
This loop calculation has two problems: (1) the calculation of sector
Another base station distribution scene in Norway.
In Figure
Considering the efficiency of algorithm, multicell adjustment consumes more time in every one round, but the performance also get surprising improvement in one round. For performance comparison, we also use the IWO optimization approach in [
Efficiency comparison between three algorithms.
In Figure
Time consuming of two adjustment schemes in different platform.
In Figure
In the process of algorithm, the order of optimization is decided by the division of bases’ group. We define bases close on the distance being in the same group, and the details are as follows.
Firstly choose the topleft base to be the initial base and choose the base which is near to initial base to be one group.
Optimize the parameters in this group; the order of sector optimization is random.
After optimizing the parameters, record the cells which have been optimized in the list.
Choose the base which is the nearest to this group, but which has not been optimized, to be the next initial base. Choose the base which is near initial base to be one group.
If the added base has been in the optimized list and its distance to initial base is over some threshold, throw this base.
Repeat this process until all the bases are optimized.
We randomly choose 5 actual base scenes in Norway and separately use Powell and improved TS algorithm to make simulation and account their results. Table
Experiment parameters.
Tabu list length ( 
Multicell number ( 
Aspiration criterion  Max iteration number 

5  3  Tabu list is full  10 


Search ace length ( 
TS adjustment law  Propagation  Number of 


1  Single/multicell joint  Cost231 

Then we can get result as shown in Figure
Result comparison with five scenes.
As shown in Figure
Robustness refers to reliability of the system. When some accident occurs, the system should still work. In our paper, when adjusting the antenna’s azimuth and vertical angles in practical engineering, the adjusted error will lead to deviation between actual result and theoretical value. So we have to consider the change of SINR and RSRP here.
In engineering, we cannot adjust the antenna’s parameter very accurately. For example the calculated angle should be 120 degrees, but the actual adjusted result may be 120.5 degree. Robustness test requires that, under such deviation, the system still have a stable performance.
Now we set the optimized result to be the benchmark. Randomly change the parameters including azimuth and vertical down angles. The error range is up to 1 degree, but in fact the practical deviation in engineering is less than 1 degree.
As shown in Figure
Robustness test results.
As the antenna parameter adjustment is an NPC problem, we cannot prove that we can obtain the optimal solution in theory. Now we make simulation to prove that our optimized result is very near to the optimal solution. We choose a relatively small scene (scene 3) and use exhaustive attack method to get the optimal solution. Exhaustive attack method’s complexity is exponential complexity, and it consumes much more time than the TS algorithm. At the same time, we also introduce the IWO optimization approach in [
In Figure
Exhaustive method test.
This paper discusses how to get a set of parameters of base antenna to improve the coverage of the whole region. By building up the corresponding scene model and mathematical model, we propose an improved TS search algorithm and compare it with some other algorithm to analyze its advantage. We make robustness test to prove it can work well when accident occurs. This means the algorithm is very strong. We make optical test to prove our algorithm can get a global extreme and not easy to fall into local extreme trap. Besides, we propose a multicell joint adjustment process by analyzing the base distribution. The proposed approach can also be utilized in other application scenes, such as the indoor wireless positioning or localization and indoor visible light communications.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research work is supported by the National High Technology Research and Development Program of China under Grant no. 2013AA013602 and jointly funded by the Beidou Navigation Satellite System Management Office (BDS Office) and the Science and Technology Commission of Shanghai Municipality under Grant no. BDZX005.