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Concentric Circular Array Antenna Null Steering Synthesis by Using Modified Hybrid Ant Colony System Algorithm Ali Abdulhadi Noaman
Concentric Circular Array Antenna Null Steering Synthesis by Using Modified Hybrid Ant Colony System Algorithm Ali Abdulhadi Noaman Dept. of Electrical Engineering, University of Basra, Basra, Iraq [email protected] doi: 10.4156/ijact.vol2.issue2.14
Abstract In this article, a hybrid optimization method has been proposed consisting of modified ant colony systems (ACSs) and constrained nonlinear programming (NLP) to solve the problems of null synthesis of concentric rings circular array antenna consist of parallel center feeding dipoles elements with two complex nonlinear optimization problems. In the first problem, a synthesis of concentric circular array radiation pattern with many interface signals is considered. In the second problem, the hybrid optimization algorithm is used to achieve wide nulls in the concentric circular array radiation pattern. The optimization process is achieved by finding the optimal values of the excitation coefficients of each element in the circular rings array. Several examples are considered here to verify the validity of this method. The results obtained by this method show that it is possible to obtain an array radiation pattern with wide null width of 90o with a depth equal to -60dB and two nulls on both sides of the main lobe with about -112.9 dB depth level. Comparisons were made between the results of this proposed method and the results obtained by many other evolutionary optimization algorithms, and it is clearly shown that this method is more efficient and flexible in solving the problems of concentric circular array antenna performance optimization.
Keywords: Ant Colony System, concentric circular arrays, nonlinear programming. 1. Introduction Nowadays, a communication system is operating in the presence of many unwanted interferences. Furthermore, the desired signal and interferences are might be operating at the same carrier frequency such that these interferences cannot be eliminated by filtering. The optimal performance for a communication system in such a situation may be to maximize the signal-to-noise ratio (SNR) at the output of the system without causing any signal distortion. This would require adjusting the antenna pattern to cancel these interferences with the main beam pointed in the signal direction. Thus, the communication system is said to be employing an optimal antenna when the amplitude and the phase of the signal induced on each element are adjusted to achieve the maximum output SNR which is also referred to as signal to interference and noise ratio SINR [1]. Array antennas have many applications in radar, sonar, and satellite communication systems [2]. The array geometries that have been studied to increase the system capacity by reducing the co-channel interference, and increase the quality by reducing the fading effects include mainly uniform linear arrays [3-8], uniform rectangular [9], and circular arrays [10-11]. A linear array has excellent directivity and it can form the narrowest main-lobe in a given direction, but it does not work equally well in all azimuthally directions. The two dimensional array is generally superior to linear array in that the amount of ambiguity is reduced to two direction of arrivals (DOAs) and information on elevation and azimuth angle of the incoming signal can be extracted. Thus two dimension arrays have been widely used in 3-D beamforming. Concentric circular array antenna (Figure 1) has received considerable interest for its symmetric and compact structure among the other two dimension arrays. A concentric circular array antenna (CCAA) is an array that consists of many concentric rings of different radii and number of elements on its circumference. Since a concentric circular array does not have edge elements, directional patterns
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International Journal of Advancements in Computing Technology Volume 2, Number 2, June 30 synthesized with a concentric circular array can be electronically rotated in the plane of the array without a significant change of the beam shape (i.e., it can perform 360 degree scan around its center and the beam pattern can be kept invariant) [12]. CCAA is also favored in DOA and in narrowband and broadband beamforming applications [13-15]. In this work, a practical antenna element is used to include the element radiation characteristics in the synthesis process. The dipole antenna will be used which is a practical radiator and used in many communication applications. The half-wavelength dipole antenna will be selected since it is consider the most widely used types of antenna for the following reasons: its radiation pattern is omnidirectional in the H-plane, which is required by many applications (including mobile communications), its directivity is reasonable, it has a good trade-off between the directivity and size, and the input impedance is not sensitive to the radius and is about 73Ω , which is well matched with a standard transmission line of characteristic impedance 75 Ω or 50 Ω (with VSWR < 2)which is probably the most important and unique reason [16].
Figure 1. CCAA with two rings and N antennas for each ring In this paper, the synthesis process will be done with minimum number of antenna elements so as to reduce the overall design cost of the CCAA. A concentric circular array antenna of two rings with 25 elements uniformly distributed on each ring circumference is considered here. A hybrid optimization method consists of the ant colony systems (ACSs) and the constrained nonlinear programming (NLP) is developed to solve the nulling synthesis optimization problems of CCAA consisting of half wavelength center-fed parallel dipoles. The dipole elements are identical and oriented perpendicular to the plane of the CCAA. The excitation coefficients of the dipole elements are changed by using the hybrid ACS (HACS) to control the null placement and with reach the minimum depth levels. The antenna elements of the two rings will be feeding by using the same feeding network so that the total number of excitation variables will be twenty five variables. This paper describes in detail how to use the HACS to obtain the optimal excitation coefficients of the antenna elements and examine the adaptation and efficiency of the proposed optimization method by considering several design examples. Moreover, a comparison process between the simulation results of HACS and with those results obtained by using many other evolutionary optimization methods will be considered so as to examine whether the HACS has better optimization performance.
2. Ant colony system The basic idea behind ACS optimization can be summarized as follows. Ants are members of a family of insects with socialized behavior living in an organized colony. These families of ants are able to find the best way into a very complex set of mazes using these features to establish food collection
145
Concentric Circular Array Antenna Null Steering Synthesis by Using Modified Hybrid Ant Colony System Algorithm Ali Abdulhadi Noaman routes from the nest. Even though learning capabilities are very limited, the complexity of the organization of the colony allows a very efficient communication among individuals, based upon tactile and chemical media. Every expedition in searching of food sources liberates chemical secretions called pheromones in order to establish all paths used in the collection process. This allows other ants to follow-up all the food sources. It is established that shorter paths will tend to have a higher magnitude of the secretion deposits and, therefore, these routes will be preferred by new explorers. Ant colony system (ACS) is one of ant colony algorithms (ACO). ACS differs from basic ant system algorithm (AS) in three main points. First, it exploits the search experience accumulated by the ants more strongly than AS does through the use of a more aggressive action choice rule. Second, pheromone evaporation and pheromone deposit take place only on the arcs belonging to the best-so-far tour. Third, each time an ant uses a path (a, b( to move from node a to node b it removes some pheromone from the path to increase the exploration of alternative paths. In particular, ACS is the most aggressive of the different ACO algorithms and returns the best solution quality for very short computation times [17]. The first application of ACS was the traveling salesman problem (TSP). The ACS algorithm of TSP will be modified here so that it can be used to evaluate the optimal excitation coefficients.
A. Nodes and path generation Since the path selections of an ant in each iteration are limited, a discrete solving space is needed. The excitation coefficients will be express on plane O-XY as shown in Figure 2. First, Q lines will be draws which have equal length and separation and perpendicular to X-axis. Each amplitude excitation variable will be represented by four lines while the phase will be represented by six lines, so the total number of the excitation coefficient variables will be Q/10, where Q represents the total number of bits. The x coordinates (i) of these lines are represented by numbers 1~Q. Then each of these lines will be divided equally into sixteen portions and thus seventeen nodes are generated on each line. Each node (j) of the seventeen nodes represent respectively by numbers 0~16 which are possible values of the digit corresponding to the line. When the ant moves and reaches to any node of the end line Q, it completes a tour and its moving path can be represented by the following path {O, node (x1,y1j) node (x2.y2j) ... node (xQ, yQj)}. The amplitude and the phase values of the excitation coefficient of the first antenna element of the two rings (Figure 2) can be extracting from the previous path by using the following formula: I1=y1j*100+y2j*10-1+y3j*10-2+y4j*10-3 α1=y101j*102+y102j *101+y103j*100+y104j*10-1+y105j*10-2+y106j *10-3
(1)
The same above formula is used to find the rest values of the excitation coefficients by changing the coordinates of the specified variables.
B. Edge selection rule The ants traveling strategy is based on a probabilistic function that considers two things. Firstly, it counts the edges it has traveled accumulating their length and secondly it senses the trail (pheromone) left behind by other ants. The transition rule can be explained as follows. If an ant k reaches to some line, such as line Li (i=1~Q), then it will be move to a node j (j=0~16) from the seventeen nodes of the next line Li+1 chosen according to the so called pseudorandom proportional rule [17] given by: arg max x i , y iu . x i , y iu , j u j ik J ,
146
if q qo if q qo
(2)
International Journal of Advancements in Computing Technology Volume 2, Number 2, June 30 where jik contains all of the nodes on line Li, τ(xi, yij) is the amount of pheromone, η(xi, yij) is the desirability of the node (xi, yij), β is a parameter to control the influence of desirability, q is a random variable uniformly distributed over [0, 1], qo is the tunable parameter (0
Concentric Circular Array Antenna Null Steering Synthesis by Using Modified Hybrid Ant Colony System Algorithm Ali Abdulhadi Noaman Dept. of Electrical Engineering, University of Basra, Basra, Iraq [email protected] doi: 10.4156/ijact.vol2.issue2.14
Abstract In this article, a hybrid optimization method has been proposed consisting of modified ant colony systems (ACSs) and constrained nonlinear programming (NLP) to solve the problems of null synthesis of concentric rings circular array antenna consist of parallel center feeding dipoles elements with two complex nonlinear optimization problems. In the first problem, a synthesis of concentric circular array radiation pattern with many interface signals is considered. In the second problem, the hybrid optimization algorithm is used to achieve wide nulls in the concentric circular array radiation pattern. The optimization process is achieved by finding the optimal values of the excitation coefficients of each element in the circular rings array. Several examples are considered here to verify the validity of this method. The results obtained by this method show that it is possible to obtain an array radiation pattern with wide null width of 90o with a depth equal to -60dB and two nulls on both sides of the main lobe with about -112.9 dB depth level. Comparisons were made between the results of this proposed method and the results obtained by many other evolutionary optimization algorithms, and it is clearly shown that this method is more efficient and flexible in solving the problems of concentric circular array antenna performance optimization.
Keywords: Ant Colony System, concentric circular arrays, nonlinear programming. 1. Introduction Nowadays, a communication system is operating in the presence of many unwanted interferences. Furthermore, the desired signal and interferences are might be operating at the same carrier frequency such that these interferences cannot be eliminated by filtering. The optimal performance for a communication system in such a situation may be to maximize the signal-to-noise ratio (SNR) at the output of the system without causing any signal distortion. This would require adjusting the antenna pattern to cancel these interferences with the main beam pointed in the signal direction. Thus, the communication system is said to be employing an optimal antenna when the amplitude and the phase of the signal induced on each element are adjusted to achieve the maximum output SNR which is also referred to as signal to interference and noise ratio SINR [1]. Array antennas have many applications in radar, sonar, and satellite communication systems [2]. The array geometries that have been studied to increase the system capacity by reducing the co-channel interference, and increase the quality by reducing the fading effects include mainly uniform linear arrays [3-8], uniform rectangular [9], and circular arrays [10-11]. A linear array has excellent directivity and it can form the narrowest main-lobe in a given direction, but it does not work equally well in all azimuthally directions. The two dimensional array is generally superior to linear array in that the amount of ambiguity is reduced to two direction of arrivals (DOAs) and information on elevation and azimuth angle of the incoming signal can be extracted. Thus two dimension arrays have been widely used in 3-D beamforming. Concentric circular array antenna (Figure 1) has received considerable interest for its symmetric and compact structure among the other two dimension arrays. A concentric circular array antenna (CCAA) is an array that consists of many concentric rings of different radii and number of elements on its circumference. Since a concentric circular array does not have edge elements, directional patterns
144
International Journal of Advancements in Computing Technology Volume 2, Number 2, June 30 synthesized with a concentric circular array can be electronically rotated in the plane of the array without a significant change of the beam shape (i.e., it can perform 360 degree scan around its center and the beam pattern can be kept invariant) [12]. CCAA is also favored in DOA and in narrowband and broadband beamforming applications [13-15]. In this work, a practical antenna element is used to include the element radiation characteristics in the synthesis process. The dipole antenna will be used which is a practical radiator and used in many communication applications. The half-wavelength dipole antenna will be selected since it is consider the most widely used types of antenna for the following reasons: its radiation pattern is omnidirectional in the H-plane, which is required by many applications (including mobile communications), its directivity is reasonable, it has a good trade-off between the directivity and size, and the input impedance is not sensitive to the radius and is about 73Ω , which is well matched with a standard transmission line of characteristic impedance 75 Ω or 50 Ω (with VSWR < 2)which is probably the most important and unique reason [16].
Figure 1. CCAA with two rings and N antennas for each ring In this paper, the synthesis process will be done with minimum number of antenna elements so as to reduce the overall design cost of the CCAA. A concentric circular array antenna of two rings with 25 elements uniformly distributed on each ring circumference is considered here. A hybrid optimization method consists of the ant colony systems (ACSs) and the constrained nonlinear programming (NLP) is developed to solve the nulling synthesis optimization problems of CCAA consisting of half wavelength center-fed parallel dipoles. The dipole elements are identical and oriented perpendicular to the plane of the CCAA. The excitation coefficients of the dipole elements are changed by using the hybrid ACS (HACS) to control the null placement and with reach the minimum depth levels. The antenna elements of the two rings will be feeding by using the same feeding network so that the total number of excitation variables will be twenty five variables. This paper describes in detail how to use the HACS to obtain the optimal excitation coefficients of the antenna elements and examine the adaptation and efficiency of the proposed optimization method by considering several design examples. Moreover, a comparison process between the simulation results of HACS and with those results obtained by using many other evolutionary optimization methods will be considered so as to examine whether the HACS has better optimization performance.
2. Ant colony system The basic idea behind ACS optimization can be summarized as follows. Ants are members of a family of insects with socialized behavior living in an organized colony. These families of ants are able to find the best way into a very complex set of mazes using these features to establish food collection
145
Concentric Circular Array Antenna Null Steering Synthesis by Using Modified Hybrid Ant Colony System Algorithm Ali Abdulhadi Noaman routes from the nest. Even though learning capabilities are very limited, the complexity of the organization of the colony allows a very efficient communication among individuals, based upon tactile and chemical media. Every expedition in searching of food sources liberates chemical secretions called pheromones in order to establish all paths used in the collection process. This allows other ants to follow-up all the food sources. It is established that shorter paths will tend to have a higher magnitude of the secretion deposits and, therefore, these routes will be preferred by new explorers. Ant colony system (ACS) is one of ant colony algorithms (ACO). ACS differs from basic ant system algorithm (AS) in three main points. First, it exploits the search experience accumulated by the ants more strongly than AS does through the use of a more aggressive action choice rule. Second, pheromone evaporation and pheromone deposit take place only on the arcs belonging to the best-so-far tour. Third, each time an ant uses a path (a, b( to move from node a to node b it removes some pheromone from the path to increase the exploration of alternative paths. In particular, ACS is the most aggressive of the different ACO algorithms and returns the best solution quality for very short computation times [17]. The first application of ACS was the traveling salesman problem (TSP). The ACS algorithm of TSP will be modified here so that it can be used to evaluate the optimal excitation coefficients.
A. Nodes and path generation Since the path selections of an ant in each iteration are limited, a discrete solving space is needed. The excitation coefficients will be express on plane O-XY as shown in Figure 2. First, Q lines will be draws which have equal length and separation and perpendicular to X-axis. Each amplitude excitation variable will be represented by four lines while the phase will be represented by six lines, so the total number of the excitation coefficient variables will be Q/10, where Q represents the total number of bits. The x coordinates (i) of these lines are represented by numbers 1~Q. Then each of these lines will be divided equally into sixteen portions and thus seventeen nodes are generated on each line. Each node (j) of the seventeen nodes represent respectively by numbers 0~16 which are possible values of the digit corresponding to the line. When the ant moves and reaches to any node of the end line Q, it completes a tour and its moving path can be represented by the following path {O, node (x1,y1j) node (x2.y2j) ... node (xQ, yQj)}. The amplitude and the phase values of the excitation coefficient of the first antenna element of the two rings (Figure 2) can be extracting from the previous path by using the following formula: I1=y1j*100+y2j*10-1+y3j*10-2+y4j*10-3 α1=y101j*102+y102j *101+y103j*100+y104j*10-1+y105j*10-2+y106j *10-3
(1)
The same above formula is used to find the rest values of the excitation coefficients by changing the coordinates of the specified variables.
B. Edge selection rule The ants traveling strategy is based on a probabilistic function that considers two things. Firstly, it counts the edges it has traveled accumulating their length and secondly it senses the trail (pheromone) left behind by other ants. The transition rule can be explained as follows. If an ant k reaches to some line, such as line Li (i=1~Q), then it will be move to a node j (j=0~16) from the seventeen nodes of the next line Li+1 chosen according to the so called pseudorandom proportional rule [17] given by: arg max x i , y iu . x i , y iu , j u j ik J ,
146
if q qo if q qo
(2)
International Journal of Advancements in Computing Technology Volume 2, Number 2, June 30 where jik contains all of the nodes on line Li, τ(xi, yij) is the amount of pheromone, η(xi, yij) is the desirability of the node (xi, yij), β is a parameter to control the influence of desirability, q is a random variable uniformly distributed over [0, 1], qo is the tunable parameter (0
