H 3 = -j o  rs K E J' o K E r D E e jsz , (A.11) E r3 = j  s K E J ' o  K E r  D E e jsz . (A.12) REFERENCES 1. D. Kajfez and P. Guillon, Dielectric resonators, Artech House, Boston, 1986. 2. C.-C. Chen and L. Peters, Buried unexploded ordnance identification via complex natural resonances, IEEE Trans Antennas Propagat 45 (1997), 1645–1654. 3. J. Steisel, Ame ´lioration de la de ´tection des mines antipersonel par la caracte ´risation des configurations de champs e ´lectromagne ´tiques pro- pres a ` la ge ´ome ´trie du proble `me, Engineering dissertation, Universite ´ Catholique de Louvain, 2002. 4. M. Storme, I. Huynen, and A. Vander Vorst, Characterisation of wet soils in the 2-18 GHz frequency range, Microwave Opt Technol Lett 21 (1999), 333–335. © 2003 Wiley Periodicals, Inc. MOVING PHASE CENTER ANTENNA ARRAYS WITH OPTIMIZED STATIC EXCITATIONS Shiwen Yang, Yeow Beng Gan, and Anyong Qing Temasek Laboratories National University of Singapore EW2 #03-01, Engineering Drive 3 10 Kent Ridge Crescent Singapore 119260 Received 11 December 2002 ABSTRACT: The in-band sidelobe levels of a moving phase center antenna array can be significantly lowered by applying a static excita- tion amplitude distribution, which is more economical and convenient to implement than those employing dynamic excitation distribution. This paper describes a differential evolution algorithm method for determin- ing the static excitations, via application to a 40-element linear array. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 38: 83– 85, 2003; Published online in Wiley InterScience (www.interscience.wiley. com). DOI 10.1002/mop.10977 Key words: antenna arrays; moving phase center; differential evolution 1. INTRODUCTION Ultra-low sidelobe levels (SLLs) in antenna arrays are extremely difficult to achieve in practice through conventional excitation amplitude tapering, due to various errors such as systematic errors and random errors [1]. A time-modulation method [2, 3] was proposed to realize ultra-low SLLs, by introducing time as the additional degree of freedom to relax the stringent error-tolerance requirements in conventional antenna arrays. Subsequently, Lewis and Evins [4] proposed another technique to reduce the SLLs by moving the phase center of a phased array antenna to Doppler shift sidelobe signals, out of the radar receiver’s passband. The phase center motion was achieved by sequentially controlling the RF switches in the feed lines of the array elements. One advantage of the moving phase center array, in comparison to the time-modu- lated array, is that the speed of the phase center motion is much faster than that of any target, thus leading to potential applications in airborne or space-borne radar. However, the excitation ampli- tude distributions in [4] should be kept dynamically across the entire array, which apparently was not convenient in practical implementation. To the authors’ knowledge, no further report on the work carried out in [4] has been reported since then. In this paper, a new method to reduce the sidelobe levels within the passband, based on static excitation amplitude distribution, is proposed. By using the static excitation amplitude distribution, only conventional RF attenuators or amplifiers are needed in the practical implementation. The static excitations are obtained through a global optimization technique based on the differential evolution (DE) algorithm [5]. 2. METHOD An N-element linear array of /2 equally spaced isotropic elements is considered (Fig. 1). In this array, M consecutive elements ( M  N) are sequentially switched (as in [4]), to transmit a rectangular pulse of width T = 1/ B, with a pulse repetition frequency prf . B is the radar receiver’s passband, and the “switch-on” time step is  = T/( N - M + 1). The time-dependent array factor is given by F , t  = e j2f0t  k=1 N A k U k  t   e jk-1 sin  , (1) where f 0 is the center frequency,  is the angle measured from the broadside direction, A k is the static excitation amplitude of the k th element (independent of time), and U k is the “switch-on” time for the k th element. The space and frequency responses of the array factor can be obtained by representing Eq. (1) as a Fourier series Figure 1 N-element moving phase center linear array with M elements switched on Figure 2 Normalized power patterns of the 40-element linear array with a moving phase center, excited by a static -30-dB SLL Taylor n  distri- bution ( n  = 5): — f 0 ;--- f 0 + prf ; ...... f 0 + 2prf MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 38, No. 1, July 5 2003 83