A Review of the Four Dimension Antenna Arrays *

Transcription

1 Sep. 26 Journal of Electronic Science and Technology of China Vol.4 No.3 A Review of the Four Dimension Antenna Arrays * YANG Shi-wen, NIE Zai-ping School of Electronic Engineering, University of Electronic Science and Technology of China Chengdu 6154 China Abstract The four dimensional (4D) antenna arrays introduce a fourth dimension, time, into conventional antenna arrays to offer greater flexibility in the design of high performance antenna arrays. This paper presents the tutorial on the study of 4D antenna arrays and the review of the recent research findings on 4D antenna arrays. Issues considered include the theory of 4D antenna arrays, different time modulation schemes, numerical simulation results, and some experimental results on their applications to low sidelobe designs. Throughout the discussion, some challenging issues on the study of 4D antenna arrays are highlighted. Key words antenna arrays; 4D antenna arrays; time modulation Antenna arrays are widely used in many high performance radio systems, such as those in the areas of radar, communication, and electronic countermeasures, navigation, etc. With rapid development of the technology in modern radio systems, antenna array are often required to offer high performance antenna characteristics with more and more stringent requirements, such as wideband, higher gain, low or even ultra-low sidelobes, etc. While Conventional antenna arrays can be considered as the radiation source distributions in space, usually of three dimensions [1]. As the requirements for antenna array parameters become more and more stringent, the error tolerance requirements of various factors in conventional antenna arrays, such as the precision of the array geometrical structure or the precision of the feeding networ, become even more stringent accordingly [2]. Consequently, the antenna array cost is tremendously high, which maes it unaffordable for commercial and industrial application. Therefore, it is naturally necessary to introduce an additional degree of design freedom, a fourth dimension, into conventional antenna arrays, which is the so often called in literature: time. The concept of the four-dimensional antenna can be dated bac to as early as 195 s. H.E. Shans and R.W. Bicmore obtained a sum pattern at the center frequency and a difference pattern at the first sideband frequency simultaneously, by using a parabolic dish antenna with a highly rotated primary horn feed [3]. The antenna can be considered as a preliminary four dimensional antenna, since it possesses the characteristics of time modulation. Thus, the 4D antennas are also termed as the time modulated antenna in the literature. In 1963, W. H. Kummer et al. extended the concept of four dimensional antennas to antenna arrays [4]. The time modulation was fulfilled by simple on-off switching of antenna elements in a predetermined sequence, so that, after the antenna output has been filtered, the resulting pattern will have reduced sidelobes. There are less stringent constraints on the antenna array errors, while only ordinary sidelobes for the static array are required, thus the cost was reduced dramatically. Furthermore, the time modulated arrays have great flexibility in the control of the aperture excitation, since the time parameter which tapers the distribution can be easily, rapidly and accurately adjusted. By using the time modulation technique in an 8-element wavegide slotted linear array in the X-band, Kummer et al. successfully realized a nearly ultra-low sidelobe ( 39.3 db ). Nevertheless, the sideband level of this ind of four dimensional antenna arrays is rather high, which means that a considerable amount of power was shifted to useless sidebands. In 1983, Lewis et al. introduced another technique to reduce the signal response entering the antenna array sidelobes [5]. The essence of Lewis idea is that, by moving the phase center of a phased array antenna in the plane of the aperture, signals radiated and received through the antenna sidelobes can be shifted out of the passband of the electronic system receiver, due to Doppler shift effect. Received * Supported in part by the National Natural Science Foundation of China (No )

2 194 Journal of Electronic Science and Technology of China Vol.4 The phase center motion is achieved by illuminating only part of the total array elements and moving the illuminated part across the entire array electronically, which is apparently not convenient in practical implementation. Moreover, there were no experimental results to verify the theory. The ideas of Kummer s time modulation as well as Lewis s moving phase center are actually based on the same parameter: time. By introducing the additional degree of freedom, time, into conventional antenna arrays, antenna designers can have greater flexibility in the design of high performance arrays, such as low/ultra-low sidelobe arrays [6]. Thus, we can term all these types of antenna arrays as the 4D antenna arrays. The difference between Kummer s time modulation and Lewis moving phase center is that, the aperture sizes of the former case changes at each time instant, while those of the latter case do not. In recent years, the 4D antenna arrays have regained the research interests due to the need of realizing low/ultra-low sidelobe arrays. Yang et al. carried out a series of studies on 4D antenna arrays, including the moving phase center arrays with optimized static excitations [7], sideband suppression of time modulated arrays [8], power pattern synthesis of time modulated arrays [9], directivity and gain of time modulated arrays [1], different time modulation schemes [11], 4D planar arrays [12], linear arrays with bidirectional phase center motion [13], time modulated arrays with optimized time sequences [14], and the mutual coupling compensation in time modulated arrays [15], etc. Other researched such as Fondevila et al. also studied the possibility of uniformly excited 4D antenna arrays [16]. All the studies mentioned above demonstrate that the 4D antenna arrays are a promising candidate for realizing higher performance antenna array with lower costs. The goal of this paper is to provide both a brief tutorial on 4D antenna arrays for those involved in antenna array research as well as a review of some of the state-of-the-art findings in this re-emerging research field. The remainder of the paper is divided into three main parts. First, Section 1 provides a tutorial on the theory and analysis of the 4D antenna arrays with different time schemes. Topics on mutual coupling in 4D linear arrays were also covered in this section. Section 2 then presents some typical numerical simulation results of the design of 4D antenna arrays. Some experimental results on 4D antenna arrays are presented in Section 3. Finally, a short summary and discussion on possible future research activities are highlighted in Section 4. 1 Theoretical Tutorial Consider an N-element linear array of equally spaced identical array elements, each element is controlled by a high speed RF switch, and is excited with an amplitude A and phase α ( = 1,2,L, N). If a plane wave of frequency f is incident at an angle θ with respect to the normal of the array, the output signal from the array can be expressed as: N j2πft jα j( 1) β dsinθ = 1 E( θϕ,, t) = e ( θϕ, )e A e U ( t)e (1) where d is the element spacing, β = 2πf /c, c is the velocity of light in free space, e( θ, ϕ ) is the element pattern factor, A is the static excitation amplitude, and U (t) ( = 1,2,L, N) represents the periodic switch on-off time function for each element. Suppose that the transmitted pulse width is T, the pulse repetition frequency is prf, and the pulse repetition period thus is T p = 1/prf. The total E field E(θ,ϕ,t) in Eq.(1) is a periodic function of t, and can be expanded into a Fourier series: j2πmprft = m (2) m = E( θϕ,, t) C e where C m is the Fourier component, i.e. N C = e ( θϕ, ) a (3) m = 1 j( 1) βdsinθ j2πft me e and the amplitude a m has the following form: 1 a AU () t (4) Tp j2πmfpt m = e dt T p Various types of time modulation scheme can be represented by different U (t), which will be illustrated as follows. 1.1 Linear Arrays with VAS Linear arrays with Variable Aperture Sizes (VAS) are the first type of 4D antenna arrays [4,11]. The aperture size of the linear array varies at each time step (Fig.1(a)). For continuous state time modulation scheme, T = T p. Assuming that the th element is switched on for an interval of τ within each period T p, then U (t) is given by

3 No.3 YANG Shi-wen, et al.: A Review of the Four Dimension Antenna Arrays 195 1, t τ U () t =, otherwise (5) switched on at time instant μ 1 and switched off at μ 2, then U (t) is given by The space and frequency response of the array far-field pattern can be obtained from Eq.(2) with different frequency components separated by prf, namely, F d = mprf (m =,±1,L,± ). At the center frequency, the amplitude of the Fourier component for each element [4, 11] is given by τ a = A (6) T Thus, Eq.(6) can be used to synthesize specific low sidelobe patterns at f. 1 N/2 1 N/2 N/2+1 N/2+2 N (a) VAS (b) UPCM M M+1 N (c) BPCM Fig.1 4D Linear array with different types of time modulation scheme. The directivity of the 4D linear array with VAS can be evaluated for typical types of array elements, such as the isotropic elements, the parallel short dipoles, and the co-linear short dipoles [1]. Studies in Ref.[1] show that 4D linear arrays will suffer more or less reduction in directivity (typically around 1. db), due to the power shift to sidebands. 1.2 Linear Arrays with UPCM The idea of 4D Linear arrays with Unidirectional Phase Center Motion (UPCM) were firstly proposed in Ref.[5] and later were systematically studied in Refs.[7, 11]. The phase center of the illuminated subarray moves in unidirection from the left to the right during each cycle, thus referred to as UPCM array (Fig.1(b)). For the uniform phase center motion, a group of M consecutive elements out of N array elements are switched on at each time instant, and swept electronically across the full array. This gives rise to the phase center movement. If the th element is p M M+1 N where 1, μ1 t μ 2 U () t =, otherwise μ1 = max[,( M) τ ] μ 2 = min[ τ,( N M + 1) τ] (7) and the uniform time step τ = T/(N M+1). Similarly, the space and frequency response can be obtained from Eq.(2), and the amplitude of the Fourier component at the center frequency is μ2 μ1 a = A (8) T 1.3 Linear Arrays with BPCM 4D linear arrays with a Bidirectional Phase Center Motion (BPCM) were conceived and systematically studied in Ref.[13]. This type of 4D linear array provides wider radar passband width than the UPCM scheme for discontinuous state. The phase center of the illuminated subarray moves bidirectionally during each cycle, namely, left-right-left (Fig.1(c)). For the continuous scheme, U (t) is given by 1, t τ U1() t =, otherwise p (9) 1, μ1 t μ2 U() t = 1, μ3 t μ4, (1< N M) (1), otherwise 1, ν t ν, otherwise < (11) 1 2 U () t =, N M N where μ 1, μ 2, μ 3, μ 4, ν 1 and ν 2 are different time instants used to define the BPCM scheme [13]. In a similar procedure, the space and frequency response of the BPCM array can be obtained using Eq.(2), while the amplitude of the Fourier components at the center frequency can be used to synthesize the required static amplitude distribution and the switch-on time sequences. 1.4 Linear Arrays with Optimized Time Sequences Apart from the aforementioned three types of typical 4D linear arrays, the time modulation of the 4D array can be directly optimized by Genetic Algorithm

4 196 Journal of Electronic Science and Technology of China Vol.4 (GA) as well [14]. The on-off status of the RF switches reminds us of the same behavior in the simple GA (SGA) [14]. If we use a gene gq to represent the on-off status of the th element and at the qth time step (e.g., g q =1 when the switch is on), then the entire on-off switching time sequences for the N elements numbered from the array center to the array edge can be represented by a chromosome χ, namely, χ = g g Lg g g Lg Lg g Lg Lg g L g (12) N N N 1 2 L 1 2 L 1 2 L 1 2 L In a similar way, the radiation patterns at each harmonic frequency F d = mprf (m=, ±1,, ± ) can be obtained by Eq.(2), and the amplitude of the Fourier component for each element is given by a m [ πmτ ] L jπ sin = g πm q= 1 e mτ (2q 1) q (13) where τ = τ/t p. Using the SGA, the chromosome length is L N, and the cost function can be selected to suppress the Sidelobe Level (SLL) and Sideband Level (SBL) simultaneously, namely, f ( χ) = w SLL ( χ) + w SBL ( χ) (14) ( n) ( n) ( n) 1 f 2 max f+ mprf where (n) is the number of evolution generations, SLL is the sidelobe level at the center frequency f, SBL max is the maximum sideband level at selected m sideband frequencies, w 1 and w 2 are the corresponding weighting factors for each term. 1.5 Mutual Coupling Compensation in 4D Linear Arrays Similar to those in conventional antenna arrays, mutual coupling effects also exist in 4D antenna arrays, but they are more complicated by the dynamic excitations of the array elements. Based on the combination of the measured complex embedded element patterns and the Differential Evolution (DE) algorithm [17-18], a practical mutual coupling compensation approach for 4D linear arrays with VAS was proposed in Ref.[15]. The excitations A and τ in Eq.(6) are for 4D arrays without considering mutual coupling effect and should be compensated. Suppose that A % and τ% are the compensated complex static amplitude (including its phase) and switch-on time interval for the th element, respectively, then the th order amplitude of the Fourier components of the far-field response becomes to τ w = A % % (15) T p Consequently,a complex excitation vector w = {w (=1,2, L,N)} is to be determined. After w is determined, A % and τ% can be obtained. For uniform excitations, the amplitudes of A % for all the elements are the same while their phases are different. In order to determine w, the complex embedded element patterns in the plane of the linear array can be measured by sequentially exciting one of the elements while terminating the others. The actual array pattern for a given set of w is a linear combination of the active element patterns, namely, N E( w, θ ) = w E ( θ ) (16) = 1 The DE algorithm [17-18] is then used to match the actual array pattern with the desired pattern E d (θ) in the plane of the linear array and obtain the optimized complex weights w, with the cost function given by M ( n) ( n) = d θi i i= 1 f ( w) E ( ) E ( w, θ ) (17) where n is the number of evolution generations, and M is the total number of specified elevation angles. 2 Simulation Results To demonstrate the application of the theory on 4D linear array, this section presents some typical numerical simulation results for the synthesis of low sidelobe array patterns using 4D linear arrays with various time schemes. 2.1 Linear Arrays with VAS As the first example, a 16-element λ/2 spaced isotropic element 4D linear array with VAS is considered. The 4D linear array has the following parameters: T = 1 μs, prf = 1 Hz, f = 1.56 GHz. A As the first example, a 16-element λ/2 spaced isotropic element 4D linear array with VAS is considered. The 4D linear array has the following parameters: T = 1 μs, prf = 1 Hz, f = 1.56 GHz. A 4dB SLL discrete Taylor n (n = 7) pattern [19] is selected as the target pattern at f. Fig.2 shows the 3D space and frequency response of the uniformly excited linear array with VAS. It is observed that a 4 db SLL discrete Taylor n (n = 7) pattern is successfully synthesized at the center frequency. However, the SBL was found to be as high as 12.7 db, and the reduction in directivity is about 3.74 db. If a 3 db SLL discrete Taylor n distribution ( n = 5) is used as the static non-uniform 2

5 No.3 YANG Shi-wen, et al.: A Review of the Four Dimension Antenna Arrays 197 excitation amplitude distribution, the 3D space and frequency response is presented in Fig.3. It is observed that the SBL is only about 2.25 db, a 7.55 db improvement over the previous case. The estimated reduction in directivity is only about.63 db θ/( ) F d /MHz 9.2 Fig.2 Space and frequency response plot of the 16-element uniformly excited 4D linear array with VAS Power/dB θ/( ) F d /MHz 9.2 Fig.3 Space and frequency response plot of the 16-element non-uniformly excited 4D linear array with VAS Power/dB Pattern/dB Pattern (db) f f +prf f +2prf θ ( θ/( ) deg) Fig.4 Normalized power patterns of the 16-element 4D VAS linear array with suppressed sideband levels Using the DE algorithm, the SBL of the 4D linear array can be further suppressed [8]. Fig.4 shows the 2D normalized radiation patterns at the center frequency f, and 2 sideband frequencies f +prf and f +2prf. The sideband levels are successfully suppressed under 3 db, while the sidelobe levels remain below 4 db at the center frequency. 2.2 Linear Arrays with UPCM The example considered here for the 4D linear array with UPCM involves a 4-element isotropic linear array with λ/2 equal spacing, with 2 consecutive elements switched on and swept across the full array within transmitted pulse width T. The 4D array has the following parameters: N = 4, M = 2, T = 1 μs, prf = 125 Hz, and f = 1. GHz. The uniform time step τ is calculated to be about 47.6 ns, which implies an equivalent velocity of the moving phase center of about V = m/s. The maximum Doppler frequency shift is about 1 MHz. A 5 db SLL Chebyshev pattern was selected as the target pattern at the center frequency. Fig.5 presents the 3D space and frequency response of the 4D linear array with static excitations from Eq.(8). The SLLs within the passband B = 1/ T = 1 MHz are nearly about 5 db. The corresponding static excitation amplitude distribution is plotted in Fig.6, in comparison to the conventional 5 db SLL Chebyshev excitation. It is observed that the excitation amplitude of the 4D linear array with UPCM has a smaller dynamic range ratio, which is easier to implement in practice. Power/dB θ/( ) Fig.5 Space and frequency response plot of the non-uniformly excited 4-element 4D linear array with UPCM Normalized amplitude Amplitude F d /MHz.2 UPCM Excitation array by (15) -5dB SLL Chebyshev Element No. Element Number Fig.6 Comparison of the static excitation distribution of the 4D linear array with UPCM and a conventional 5dB SLL Chebyshev array 8 4 4

6 198 Journal of Electronic Science and Technology of China Vol Linear Arrays with BPCM A 16-element λ/2 spaced isotropic element 4D linear array with BPCM was considered. The 4D linear array following parameters: M = 14, T = 1 μs, prf = 1 Hz, f = 1.56 GHz. Non-uniform static excitations were used for the 4D linear array with BPCM [11]. The 3D space and frequency response is shown in Fig.7. The target pattern is also successfully synthesized at the center frequency. In this case, the SBL is quite low, which is about 29.1 db. The reduction in gain is estimated to be only about.28db. Fig.8 presents the corresponding switch-on time sequences and the static excitations. Power/dB θ/( ) F d /MHz 9.2 Fig.7 Space and frequency response plot of the 16-element non-uniformly excited 4D linear array with BPCM Element number. Element No T=Tp P Timt/μs e (μs) (a) Time sequences 2.4 Linear Arrays with Optimized Time Sequences As an example, a λ/2-spaced 4D linear array of 16 uniformly excited isotropic elements is considered to optimize the switch-on time sequences [14]. A minimal time step of τ = 1 μs is selected, and the modulation period T p = 1 μs, implying a modulation frequency of 1 KHz. The target is to suppress the SLL and SBL simultaneously. In the SGA, the code length is selected as L=1, and the chromosome length is 8. A population size of 2 is selected, and the crossover and mutation probabilities are selected as.9 and.4, respectively. 1 sideband patterns are considered in Eq.(14) to ensure that all the sideband patterns are indeed suppressed. Fig.9 shows the optimized far field patterns at the center frequency and at the first 2 sideband frequencies. The optimized SLL and SBL are 25.5 db and 24.6 db, respectively. Fig.1 shows the corresponding optimized switch-on time sequences. It is observed that the 6 elements at the center portion are excited at all time. Thus, only 1 RF switches are needed for the implementation. Pattern/dB (db) θ (deg) θ/( ) Fig.9 Normalized radiation pattern of the 16-element uniformly excited 4D linear array with GA optimized switch-on time sequences f f +prf f +2prf Normalized amplitude Amplitude BPCM array -4dB SLL D-Taylor ( n =7) = Element number No. (b) Static excitations Fig.8 Switch-on time sequences and static excitations of the 16-element non-uniformly excited 4D linear array with BPCM Element Element nmumber. No Time t/μs (μs) Fig.1 Corresponding GA optimized switch-on time sequences of Fig.9

7 No.3 YANG Shi-wen, et al.: A Review of the Four Dimension Antenna Arrays Simulation Results An L-band 16-element printed H-plane coupled dipole linear array with its associated feed networ was designed and constructed to verify the theoretical and numerical results of the 4D linear arrays [11,13-15]. The two arms of the printed dipole were printed on each side of a thin dielectric substrate with ε r = 2.2 and h =.7874 mm, and a tapered balun lins the element to a SMA connector. A Rohacell foam of thicness 12.7 mm was attached to each side of the substrate and the ground plane to provide better mechanical support. The array element spacing is half-wave length at GHz. Ansoft HFSS was used in the design of the printed dipole element and array. The designed and measured array bandwidth was greater than 3% for VSWR< 2.. The array pattern measurements were performed in a compact range. The measured realized gain for the uniformly excited array was 16.1 dbi at GHz. Commercial off-the-shelf components, such as power divider, high speed RF switches, attenuators and phase trimmers, were used to form the feed networ. The single-pole-single-throw absorptive RF switch has a switching time of less than 2 ns. A digital Complex Programmable Logic Device (CPLD) card generates the required time sequences to control the RF switches. The entire control box includes the RF feed networ, CPLD card and a small DC power supply. The entire 4D linear array assembly is shown in Fig.11. shows the measured gain pattern for the corresponding static linear array at GHz. The measured reduction in gain due to time modulation is.3 dbi. As can be seen from Fig.12, the relative SLL of the BPCM array is 34.5 db, and the isotropic SLL is 19.5 dbi, which is within 1 db of the ultra-low sidelobe category. The measured SBL is 29.9 db, which is in good agreement with the theoretical value of 29. db. Realized Realized Gain gain/db (dbi) BPCM array array Static Static array array θ θ/( ) (deg) Fig.12 Measured realized gain pattern of the 4D linear array with BPCM in comparison with that of the static array (f =1.575 GHz) Normalized power/db Normalized Power (db) Meas Measured -3dB SLL 3 db SLL D-Taylor n = 7 D -Taylor ( n=5) θ (deg) θ/( ) Fig.13 Comparison of theoretical pattern and measured pattern at 1.58 GHz 2 18 Measured gain Computed gain gain Measured SLL Fig.11 Assembly of the printed dipole 4D linear array For the continuous scheme 4D linear array with BPCM [13], a 4 db SLL discrete Taylor n (n = 7) pattern was selected as the target pattern. The static excitations and the switch-on time sequences for M=14, T = 1 μs and prf = 1 MHz were implemented in the RF feed networ. The measured realized gain pattern at GHz is shown by the solid line in Fig.12, and its realized gain reads 15. dbi. While the dashed line Gain/dB Gain (dbi) Frequency f/ghz (GHz) Fig.14 Measured gain, computed gain and measured SLL versus frequency For the experimental study of the mutual coupling compensation in the uniformly excited 4D linear arrays with VAS, the complex embedded element patterns SLL/dB (db)

8 2 Journal of Electronic Science and Technology of China Vol.4 were measured and the coupling compensation procedures described in Section II were used to obtain the compensated switch-on time sequences and the excitation phases, which were then implemented into the RF feed networ [15]. A 3 db SLL discrete Taylor n (n = 5) pattern was selected as the target pattern at 1.58 GHz. Fig.13 shows the measured normalized far-field pattern at 1.58 GHz, in comparison with the theoretical 3dB SLL discrete Taylor n (n = 5) pattern. Good agreement between the theoretical pattern and the experimental pattern. The frequency response of the measured gain, computed gain and measured SLL across the frequency band are presented in Fig.14. The measured SLL fluctuates within 3dB across the frequency band. 4 Conclusions and Remars This paper has provided a tutorial on the theoretical analysis and design of the 4D linear arrays, and illustrated how time variables can be utilized in antenna array design. It has also offered a review of recent research activities and findings related to the theory, simulation, and experiments of the 4D linear array. This review has shown that by introducing a fourth dimension, i.e., the time, into the conventional linear antenna arrays, much flexibility is available for the design of antenna arrays. Consequently, the 4D antenna arrays are anticipated to be a robust candidate for the realization of high quality antenna arrays with stringent array characteristic requirements. Despite the promising success achieved, it should be pointed out that a number of challenging problems remain unsolved before the 4D antenna arrays are implemented into practice. We found that tolerance errors still should be taen into account to achieve ultra-low sidelobes, though in 4D antenna arrays, they are less stringent as compared to that in conventional arrays. For further studies, topics such as modulated pulses, full wave simulation of the 4D antenna arrays, 4D antenna arrays combined with signal processing, etc., may be further investigated. Furthermore, system compatibility of the 4D antenna arrays should be thoroughly studied before they can be applied to practical systems. Acnowledgement This wor was also supported in part by the Innovative Research Team Program of UESTC, China. References [1] Mailloux R J. Phased Array Antenna Handboo[M]. London: Artech House, [2] Schran H E. Low sidelobe phased array antennas[j]. IEEE Antennas Propagat., 1983, 25(2): 4-9. [3] Schran H E, Bicmore R W. Four-dimensional electromagnetic radiators[j]. Canad. J. Phys., 1959, 37(3): [4] Kummer W H, Villeneuve A T, Fong T S, et al. Ultra-low sidelobes from time-modulated arrays[j]. IEEE Trans. Antennas Propagat., 1963, 11(5): [5] Lewis B L, Evins J B. A new technique for reducing radar response to signals entering antenna sidelobes[j]. IEEE Trans. Antennas Propagat., 1983, 31(6): [6] Bicmore R W. Time versus Space in Antenna Theory[M]. New Yor: Academic Press, [7] Yang S, Gan Y B, Qing A. Moving phase center antenna arrays with optimized static excitations[j]. Microwave and Optical Technology Letters, 23, 38(1): [8] Yang S, Gan Y B, Qing A. Sideband suppression in time modulated linear arrays by the differential evolution algorithm[j]. IEEE Antennas and Wireless Propagation Letters, 22, 1(1): [9] Yang S, Gan Y B, Tan P K. A new technique for power pattern synthesis in time modulated linear arrays[j]. IEEE Antennas and Wireless Propagation Letters, 23, 2(1): [1] Yang S, Gan Y B, Tan P K. Evaluation of directivity and gain for time modulated linear antenna arrays[j]. Microwave and Optical Technology Letters, 24, 42(2): [11] Yang S, Gan Y B, Tan P K. Comparative study of low sidelobe time modulated linear arrays with different time schemes[j]. J. of Electromagnetic Waves and Applications, 24, 18(11): [12] Yang S, Nie Z. Time modulated planar antenna arrays with square lattices and circular boundaries[j]. Int. J. Num. Mod. Electron. Networ Devices Fields, 25, 18(5): [13] Yang S, Gan Y B, Tan P K. Linear antenna arrays with bidirectional phase center motion[j]. IEEE Trans. Antennas Propagation, 25, 53(5): [14] Yang S, Gan Y B, Qing A, et al. Design of a uniform amplitude time modulated linear array with optimized time sequences[j]. IEEE Trans. Antennas Propagation, 25, 53(7): [15] Yang S, Nie Z. Mutual coupling compensation in time modulated linear antenna arrays[j]. IEEE Trans. Antennas Propagation, 25, 53(12): [16] J Fondevila J, Brégains C, Ares F, et al. Optimizing uniformly excited linear arrays through time modulation[j].

9 No.3 YANG Shi-wen, et al.: A Review of the Four Dimension Antenna Arrays 21 IEEE Antennas and Wireless Propagation Letters, 24, 3(1): [17] Kurup D G, Himdi M, Rydberg A. Synthesis of uniform amplitude unequally spaced antenna arrays using the differential evolution algorithm[j]. IEEE Trans. Antennas Propagation, 23, 51(9): [18] Yang S, Gan Y B, Qing A. Antenna array pattern nulling using a differential evolution algorithm[j]. Int. J. RF and Microwave Comput. Aided Eng., 24, 14(1): [19] Villeneuve A T. Taylor patterns for discrete arrays[j]. IEEE Trans. Antennas Propagation, 1984, 32(1): Brief Introduction to Author(s) YANG Shi-wen ( 杨仕文 ) was born in Sichuan Province, China, in He received the B.Sc. degree in electronic science from East China Normal University, Shanghai, China, in 1989, and M.Eng. degree in electromagnetics and microwave technology and Ph.D. degree in physical electronics both from the University of Electronic Science and Technology of China (UESTC), Chengdu, China, in 1992 and 1998, respectively. He joined the Institute of High Energy Electronics, UESTC, where he was first as a Teaching Assistant in 1992 and later became a Lecturer since From 1998 to 21, He was a Research Fellow at the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore. He was a Research Scientist at the Temase Laboratories, National University of Singapore, Singapore, during February 22 and January 25. He is currently a professor with the Department of Microwave Engineering, School of Electronic Engineering, UESTC. He has authored or co-authored over 5 journal and conference papers. He received the 3rd class of China National Technology Invention Award in His current research interests include antennas and antenna arrays, computational electromagnetics, and high power microwave components. Prof. Yang is a Senior Member of the Institute of Electrical and Electronic Engineering (IEEE) and a Senior Member of Chinese Institute of Electronics (CIE). He serves as a reviewer for IEEE Transactions on Antennas and Propagation, IEEE Transactions on Plasma Science, IEEE Microwave and Wireless Components Letters, Journal of Electromagnetic Waves and Applications, etc. NIE Zai-ping ( 聂在平 ) was born in Xi an, China, in He received the B.Eng. degree in 1968 and the M.Eng. degree in 1981 both from the UESTC (formerly now as the Chengdu Institute of Radio Engineering). He was a visiting scholar in the Electromagnetic Laboratory, University of Illinois at Urbana-Champaign from 1987 to He is currently a professor with the Department of Microwave Engineering, School of Electronic Engineering, UESTC, and Vice President of UESTC. He has authored or co-authored over 35 journal and conference papers. He has co-authored 3 technical boos including the first Handboo of Antenna Engineering in China. He was the first winner of the 2nd class of China National Science and Technology Progress Award in 22. His research interests include electromagnetic radiation, scattering, inverse scattering, wave and field in inhomogeneous media, computational electromagnetics, smart antenna technique in mobile communications and MIMO wireless communications, etc. Prof. Nie is a Senior Member of the Institute of Electrical and Electronic Engineering (IEEE) and a Fellow of Chinese institute of electronics (CIE).