DSpace at VNU: Parallel computing in genetic algorithm for adaptive array antenna

PARALLEL COMPUTING IN GENETIC ALGORITHM FOR ADAPTIVE ARRAY ANTENNA Le Quang Thao*, Dam Trung Thong*, Nguyen Thi Ngoc Minh+ * Department of Radiophysics, Faculty of Physics Vietnam National University, College of Science Hanoi, Vietnam thaolq@vnu.edu.vn + Scientific and Technological Institutes of Military Radar Institute 17 Hoang Sam, Hanoi, Vietnam minh_viet08447@yahoo.com Keywords: adaptive array antenna; genetic algorithm; parallel computing; parallel genetic algorithm; Abstract This paper presents how parallel computing could apply into genetic algorithm for adaptive array antenna There are some constrains in this algorithm that prevent parallel computing to reduce the benefits in time cost Therefore, instead of using normal model of parallel computing, we apply parallel genetic algorithm for adaptive array antenna to have an interesting result which benefits in the deep NULL Introduction As the developed of technology, more and more wireless devices are used Therefore, it’s possible to got interference signal from undesired devices which located in some directions These signals would reduce the desired signal and make our device lost the information In order to reject these signals, adaptive array antenna or smart antenna is used more popular This antenna could change its far-field pattern to put the NULL in some directions that may have interference or undesired signals This could be a parabolic or directional antenna which could steer whole antenna to avoid these signals With this model, we could only reduce a small part of noise Phased array antenna is the evolution of adaptive array antenna by its ability in changing far-field pattern with only a changing in its phased shifting and amplitude weighting of each element So with this kind of antenna, if we have a set of suitable phased shifting and amplitude weighting, we could put a deep NULL at any direction There are many algorithms for computing these variables For example, Least Mean Square Algorithm, Howells-Applebaum, which are presented in [3, 5] But many researches [4, 6] have shown that Genetic Algorithm is the best suitable for adaptive array antenna because it could converse quickly and be easy to apply in an array antenna with arbitrary number of elements Parallel computing has opened new chance to reduce the computational cost in many difficult problems, such as databases, data mining, advance graphics and virtual reality, collaborative work environments … [2] It could be done on a multi-core computer or in a number of same computers in network or in Graphic Processing Unit (GPU) Applying this algorithm to genetic algorithm in adaptive array antenna would have some special results in time cost and characteristic of the far-field pattern In this paper, we parallel genetic algorithm for an adaptive array antenna in a computer cluster We also make comparison with the normal model of genetic algorithm to show the advantages of parallel genetic algorithm Phased array antenna Phased array antenna is a group of antenna elements which could digitally change the phased shifting and amplitude weighting These elements in the group can be arranged in many shaped to make many kinds of phased array antenna, for example, linear array antenna, nonlinear array antenna, circular array antenna, planar array antenna, etc For simple, in this paper, we only discuss about linear array antenna (shown in figure 1) in which the elements are arranged in a line with equally distance Figure 1512 Example of linear phased array antenna The far field pattern of linear array antenna in mathematical form is shown in the following equation: N AF = ¦ wn e jΨn n =1 have interference signals To apply the genetic algorithm, we have to use a genome which contains all phased shifting and amplitude weighting of all elements in antenna This algorithm will reproduce new genome which present better optimized from initial one Where: wn = anejĮn : amplitude complex weight at element n, which presents the phased shifting and amplitude weighting for this element Ȍn : phase due to element position and observation direction This variable depends on configuration of antenna N: number of elements in the array Base on this equation, we have the far-field pattern of a linear array antenna with 20 elements in the form of figure Changing the phased shifting or amplitude weight of each element in this antenna would result to change the far-field pattern in both main beam and side lope This is principle for using this antenna in adaptive array antenna Figure Flow chart of genetics algorithm Parallel computing Parallel computing is an evolution of sequential computing [2] that base on the idea that many workers in a factory could make more products than only one In computing, we could split a huge computational cost to many parts and distribute to different processors to at the same time (shown in figure 4) Figure Far-field pattern of 20x1 linear array antenna Full papers must be typed in English This instruction page is an example of the format and font sizes to be used Genetic algorithm Genetic algorithm (GA) is a global search and optimization methods that simulate the metaphor of natural biological evolution [2, 6] By generating a number of potential solutions (or population) and applying the principle of survival of the fitness, it produces successively better approximations to a solution After a number of generations, by the process of selecting and reproducing, it creates new population which is better suited to the environment than the initial Based on the idea, the flow chart of this algorithm is created and shown in figure Figure Split task in parallel computing By sharing the work between many processors, the time cost for computing could be speed up (S) a number of time which is shown in Amdahl’s law [1]: In adaptive array antenna, we need to compute the phased shifting and amplitude weighting for each element in whole antenna in order to place a NULL in some directions that may 1513 S= (1 − P ) + P N It means that with a certain percentage of parallel work (P) we could only increase the speed up to a limited times while increasing the number of processors (N) (example in figure 5) Therefore, to get higher speed up number we should invest in increasing the percentage of parallel work in whole computation However, the time cost in a parallel system is also affected by ts (time required time for distributing work, transmitting and receiving data) So total time needed for computing a problem in parallel: Fortunately, we could use parallel genetic algorithm instead of parallel computing in each generation It means we would genetic algorithm in each computer of processor then combine the population of from all computer by the process of immigration There are more genes, especially good gene because we initialize and compute GA in different population in different computers With this model (Figure 6), although we couldn’t reduce the time cost, we would prevent the local minimized trap while putting NULL Simulation result t=ts+tc Therefore, for a problem in which the computational cost is not too high and need so much time in distributing, transmitting and receiving data, it is not benefited by applied parallel computing For example, in genetic algorithm, we have to all these things in each generation with a finite number of populations So if applied directly the parallel computing in this problem the time cost would be increased because of these required time Base on the theory, we have simulated the parallel genetic algorithm as well as normal genetic algorithm for a specific antenna in different cases: only interference signal and interference signals This antenna and our genetic algorithm have some configuration shown in table Item Number of antenna elements Distance between elements Population size Gene bits Gene size Chromosome bits Crossover probability Mutation probability Definition Value N d/λ M Q P=N-1 L=PxQ Pc Pm 20 0.5 50 15 19 285 50% 10% Table 1: This is an example of a table caption Our simulation results are shown in the figure 7, 8, NULL at -20 degree Figure Example of time speed up depend on number of processors Figure Model of parallel genetic algorithm Figure 1514 Simulation results: NULL at -20 degree From the simulation result, it’s obvious that parallel genetic algorithm has two advantages: First, from the figure and many other simulation results which is not mention in this article, the power in case of parallel genetic algorithm is often the same or higher than in normal genetic algorithm It means that parallel genetic algorithm produce the better suitable to the environment NULL at -30 degree Second, in case of more than one NULL, the parallel genetic algorithm makes all the NULL to be deeper There isn’t any local minimized like in the case of normal genetic algorithm It’s the advantage of parallel genetic algorithm Genetic algorithm produces the better suitable individual because it has more genes which are got from many other populations when initialized and applied genetic algorithm in different computer Conclusion Figure Simulation results: NULL at -30 degree This paper discusses about using parallel computing in adaptive array antenna Our simulation results have proved that parallel genetic algorithm is better in power and when there are more than one interference signals This problem is still opened and needed more research to figure out the best model Our future work will concentrate on how to reduce the time cost of this algorithm by apply parallel computing in cost function Figure NULL at 30 degree NULL at 20 degree NULL at -20 degree NULL at -30 degree References [1] Amdahl, G.M “Validity of the single-prosessor aproach to large scale computing capability”, AFIPS conference proceedings vol 30, Reston, Va., 1967, pp 483-485 [2] Blaise Barney, “Introduction to Parallel Computing”, Lawrence Livermore National Laboratory, 2010 [3] R T Compton, “Adaptive Antennas Concepts and Performance”, Englewood Cliffs, NJ: Prentice Hall, 1988 [4] R L Haupt, “Phase-only adaptive nulling with genetic algorithms”, IEEE AP-S Trans 45(5) pp 1009–1015, (June 1997) [5] R A Monzingo and T W Miller, “Introduction to Adaptive Antennas”, New York: Wiley,1980 [6] Le Quang Thao, Nguyen Ngoc Dinh, Dam Trung Thong, “Amplitude and Phase Adaptive Nulling with a Genetic Algorithm for Array Antennas”, 2nd AIMSEC, IEEE Proceeding volume pp.1887-1890, (2011) Simulation results: NULLs 1515 ... time for distributing work, transmitting and receiving data) So total time needed for computing a problem in parallel: Fortunately, we could use parallel genetic algorithm instead of parallel computing. .. applied parallel computing For example, in genetic algorithm, we have to all these things in each generation with a finite number of populations So if applied directly the parallel computing in this... in this antenna would result to change the far-field pattern in both main beam and side lope This is principle for using this antenna in adaptive array antenna Figure Flow chart of genetics algorithm