Review Paper Geometric Configuration Optimization for Baseline Interferometry

Transcription

1 Research Jornal of Recent Sciences ISSN Vol. 2(5), 78-82, May (213) Res.J.Recent Sci. Reiew Paper Geometric Configration Optimization for Baseline Interferometry Abstract Aidin Gharahdaghi Amirkabir Uniersity of Technology (AUT), Tehran, IRAN Aailable online at: Receied 26 th December 212, reised 14 th Febrary 213, accepted 4 th March 213 One of the necessary parts for settlement of baseline interferometric arrays which are sed in radio astronomy is to design geometric configration of the array in a way that most effectie reslts cold be achieed. In VLBI imaging the plane coerage is a key factor for obtaining better sampling of signals. In this paper the configration of antenna arrays are optimized by means of PSO and its mlti-poplation ersion MPSO. By presenting some simlation reslts, effectieness of methods, especially for MPSO will be shown. Keywords: Baseline interferometry, antenna array optimization, particle swarm optimization. Introdction Obseration of distant astronomic objects has always motiated the people to inent and tilize high tech systems performing in oter space or on the Earth. Modern radio astronomy is not only based on single location telescopes, bt it astly ses the interferometric methods for arrays of antennas. VLBI (Very Large Baseline Interferometry) is the techniqe of obtaining samples of radio signals from astronomic objects by distant antennas on Earth-based array. This makes it possible to hae a larger eye on the sky by means of calclating correlation between signals from arios coples of antennas. Howeer the data samples are often not spatially rich, bt the effect of Earth rotation is to obtain broader region of obseration. It cold be shown that the isibility fnction V (, ) in plane is the Forier transform of radio sorce image I (x, y) in the xy plane 1. V (, ) = F [I (x, y)} (1) Howeer the effects of sampling, gain and noise of the channel shold be mentioned as conoltion of main isibility fnction by an oerall measrement fnction B (, ). V dirty (, ) = V(, ) * B (, ) (2) The dirty isibility fnction cold be inerse Forier transformed to gie the dirty image I dirty. I dirty (x,y) = F 1 {V dirty (, )} (3) One of the main tasks to be done after collecting obseration data is to deconole dirty signals to obtain estimation for sorce signal. Varios methods for deconoltion of VLBI images are introdced in literatre. The most basic and tilized one of those method is CLEAN algorithm 2, in which the reslt estimated image is obtained by iteratie processes on dirty signals. This method often needs some maniplations by hman ser. Some other deconoltion methods are also proposed based on the concept of entropy maximization 3. Entropy based methods are sitable mostly for data of high qality and enogh nmber of samples to estimate the probability density of data appropriately. By estimating sorce signal in a way maximizing some entropy measre, the deconoltion task cold be done. Some recent methods based on compressie sensing are proposed especially for the case of sparse data 4,5. Another task for increasing the performance of baseline interferometry is to optimize the configration of antenna array in a way that broader regions of plane cold be obsered and the final estimated reslt hae the most similarity to the pictre of radio sorce object. The task of configration optimization is often a pre-settlement operation for baseline interferometry. Bt for the case of space borne interferometric astronomy, the configration of spacecrafts cold be changed on demand. For optical telescopes array, the optimal configration problem is stdied in Mgnier et al. 6 Since the optimal selection of parameters for deep space network arrays is considered to be a complex problem, Jones 7 has sreyed some constraints on the array configration. Considering some sort of criteria sch as compactness of configration, minimm and maximm apertre, and flexibility, some reqirements are obtained for the optimm array design. By sing mltiobjectie optimization, Cohanim et al. 8 deeloped a design method for array of radio telescopes, which considers the imaging performance and cable length as its main objecties. In that paper, some well known array topologies are assmed and then some improements to them are obtained. A sieing algorithm for optimization of array configration is proposed in S et al. 9. The sieing algorithm remoes elements form array to fit the reslted coerage to a predefined sketch in the coerage plane. To remoe the points, some weights are assigned to the points in each iteration and those weights are sed to determine the points to be remoed. There is also recent interest in tilization of search based algorithms in designing arrays of antennas. Jin and Rahmat- International Science Congress Association 78

2 Research Jornal of Recent Sciences ISSN Vol. 2(5), 78-82, May (213) Samii 1 introdced PSO (particle swarm optimization) method for designing arios configrations of radio antenna arrays to obtain maximm coerage and minimm sidelobe leel of the synthesized beam. A comparatie stdy of three different approaches for the task of radio antenna array optimization is presented in Olieri et al. 11. The three methods incldes GA (genetic algorithm), ADS (almost difference sets) and PSO. In this paper it is shown how to improe PSO in a way that optimm soltions of problem cold be fond faster and more accrately. The main improement in PSO sed here, is to define mltiple sbpoplations of particles rather than only one poplation. The method is sed to find locations of antennas to hae an optimm coerage, and satisfaction of some constraints on problem. In section 2, the PSO and its improed mltipoplation ersion are discssed, then the procedre of soling optimal configration problem by those methods are described and simlation reslts are presented in section 3. PSO and MPSO Particle swarm optimization is one of the astly sed search based optimization algorithms and proposed by Kennedy and Eberhart 12. In recent years, PSO is tilized to sole many optimization problems in arios applications 13. The conentional PSO is based on swarm intelligence of some nmber of simlated particles which search the space of possible soltions and share the information abot their location fitness with other particles in poplation. By means of some simple pdating eqations, the positions of particles change in each iteration and conerge to some optimm soltion in search space. The main procedre of PSO is as follows. The fitness fnction of the problem is defined to assign a fitness measre to eery position (soltion) in parameter space. Seeral particles are positioned randomly in the search space. The best position de to fitness fnction among all particles is named as gbest and for eery particle i, the best preios position is named as pbest i. Then the pdated elocity of particles are calclated from those information as below: i (t+1) + w (t) + r 1 c 1 (gbest x i (t)) + r 1 c 1 (ρbest i x i (t)) (4) In this eqation, w is inertia factor, r 1 and r 2 is random nmbers and c 1 and c 2 are some constant nmbers. After pdating elocity ectors for each particle, the new position of particles are calclated by adding the elocity ector to crrent position. x i (t + 1) = x i (t) + i (t+ 1) (5) The procedre contines iteratiely till some criteria (sch as exceeding some predefined nmber o iterations) is met. In conentional PSO, all the particles are assmed to be from a single poplation and share information with all other ones. Bt it might be appropriate for some problems to hae more than one poplation, independent to each other or haing some kind of information sharing. In MPSO (mlti-poplation PSO), for each sbpoplation k there is a gbest k. A particle in a sbpoplation is affected only by information within that same sbpoplation. In this paper it is shown that MPSO cold be more effectie than conentional PSO for the problem of optimal geometric configration of baseline interferometric antenna arrays. Optimization of Array Configration In this section the geometric configration of an example array is optimized by PSO and MPSO. The locations for antennas in a sqare area shold be determined in a way that best plane coerage cold be achieed. The Earth rotation effects are also considered. For the first case, the problem is to decide locations of for antennas in a limited area. This problem is soled by means of both PSO and MPSO. The geometric configration and corresponding plane coerage as soled by PSO are depicted in figres 1 and 2 respectiely Figre-1 for for antennas determined by PSO International Science Congress Association 79

3 Research Jornal of Recent Sciences ISSN Vol. 2(5), 78-82, May (213) The same problem is also soled by means of MPSO with eqialent parameters. The reslts are shown in figres 3 and 4. The coerage as reslted by tilizing MPSO shows better characteristics of coering more areas in plane. To show how MPSO cold find the soltion faster than PSO, in figre 5 conergence cres of the two methods are shown. This two cres show that the MPSO method has fond the soltion that minimizes objectie fnction faster than PSO. 15 plane coerage Figre-2 Reslted coerage for configration shown in figre Figre-3 for for antennas determined by MPSO International Science Congress Association 8

4 Research Jornal of Recent Sciences ISSN Vol. 2(5), 78-82, May (213) For another case, the problem of choosing locations for ten antennas is also soled by means of MPSO which shows good reslts as seen by coerage characteristics. The reslted 15 configration and corresponding coerage are shown in figres 6 and 7. plane coerage Figre-4 Reslted coerage for configration shown in figre 3 PSO MPSO Figre-5 Conergence cres (Objectie in each iteration) for PSO and MPSO Figre-6 for ten antennas determined by MPSO International Science Congress Association 81

5 Research Jornal of Recent Sciences ISSN Vol. 2(5), 78-82, May (213) 15 plane coerage Conclsion In this paper the problem of optimizing array configration for baseline interferometry is addressed and soled by means of PSO and MPSO. Simlation reslts showed that both PSO and MPSO cold be sed appropriately for selecting optimal locations for antennas in order to obtain good characteristics of plane coerage. The reslts showed that MPSO cold be more effectie than PSO as it is faster in finding better soltions. References 1. Middelberg E. and Bach U., High resoltion radio astronomy sing ery long baseline interferometry, Reports on Progress in Physics, 71(6), 6691 (28) 2. Clark B.G., An efficient implementation of the algorithm CLEAN, Astronomy and Astrophysics, 89(3), (198) 3. Bajkoa A.T., Mlti-freqency synthesis of VLBI images sing a generalized maximm entropy method, Astronomy reports, 52(12), (28) 4. Sksmono A.B., Deconoltion of VLBI images based on compressie sensing, In Electrical Engineering and Informatics, 29, ICEEI 9. International Conference On, 1, (29) 5. Li F., Cornwell T.J. and De Hoog F., The application of compressie sampling to radio astronomy, Astronomy and Astrophysics, 528(A31), 1-1 (211) 6. Mgnier L.M., Rosset G. and Cassaing F., Apertre configration optimality criterion for phased arrays of optical telescopes, JOSA A, 13(12), (1996) Figre-7 Reslted coerage for configration shown in figre 6 7. Jones D.L., Geometric Configration Constraints for Large Deep Space Network Arrays, The Interplanetary Network Progress Report, 42(157), 1-9 (24) 8. Cohanim B.E., Hewitt J.N. and De Weck O., The Design of Radio Telescope Array Configrations sing Mltiobjectie Optimization: Imaging Performance erss Cable Length, The Astrophysical Jornal Spplement Series, 154(2), 75 (28) 9. S Y., Nan R.D., Peng B., Roddis N. and Zho J.F., Optimization of interferometric array configrations by sieing points. Astronomy and Astrophysics, 414(1), (24) 1. Jin N. and Rahmat-Samii Y., Analysis and particle swarm optimization of correlator antenna arrays for radio astronomy applications, Antennas and Propagation, IEEE Transactions on, 56(5), (28) 11. Olieri G., Caramanica F. and Massa A., Hybrid ADSbased techniqes for radio astronomy array design, Antennas and Propagation, IEEE Transactions on, 59(6), (211) 12. Kennedy J. and Eberhart R., Particle swarm optimization. In Neral Networks, 1995, Proceedings, IEEE International Conference On, 4, (1995) 13. Banks A., Vincent J. and Anyakoha C., A reiew of particle swarm optimization. Part II: hybridisation, combinatorial, mlticriteria and constrained optimization, and indicatie applications, Natral Compting, 7(1), (28) International Science Congress Association 82