Journal of Communications and Information Networks, 2018, 3(1): 1-14 doi: 10.1007/s41650-018-0004-7

Special Focus:Advanced Antenna Technologies for Future Wireless Applications

Time-Modulated Arrays: A Four-Dimensional Antenna Array Controlled by Switches

Chong He,, Lele Wang,, Jingfeng Chen,, Ronghong Jin,

School of Information Technology, Deakin University, Melbourne 3215, Australia

Corresponding authors: Ronghong Jin,rhjin@sjtu.edu.cn

作者简介 About authors

Chong He received his B. S. degree in electronic and information engineering and M. S. degree in electromagnetic and microwave technology from Huazhong University of Science and Technology, Wuhan, China, in 2007 and 2009 respectively, and the Ph. D. degree in electronic engineering from Shanghai Jiao Tong University, Shanghai, China, in 2015. Since 2016, he has been a postdoctor researcher in Department of Electronic Engineering, Shanghai Jiao Tong University. His research interests include phased arrays, DOA estimation, DBF, location and calibration techniques. E-mail:hechong@sjtu.edu.cn.

Lele Wang received his B. S. degree in applied physics from Hubei University of Education and M. S. degree in plasma physics from Huazhong University of Science and Technology, Wuhan, China. He is currently working toward his Ph. D. degree at Shanghai Jiao Tong University, Shanghai, China. His research interests include antenna arrays, unconventional array design, DBF, and weqsas DOA estimation. (Email:lele wang@sjtu. edu. cn) E-mail:lele_wang@sjtu.edu.cn.

Jingfeng Chen received his B. S. degree in electronics and information engineering and M. S. degree in signal and information processing from Nanjing University of Information Science & Technology, Nanjing, China, in 2009 and 2012, respectively. He is currently working toward his Ph. D. degree at Shanghai Jiao Tong University, Shanghai, China. His research interests include antenna arrays, unconventional array design, DBF, and DOA estimation. E-mail:laowu3917@163.com.

Dr.Jin is a Committee Member of the Antenna Branch of the Chinese Institute of Electronics,Beijing,China.He was a recipient of the National Technology Innovation Award,the National Nature Science Award,the 2012 Nomination of National Excellent Doctoral Dissertation (Supervisor),the Shanghai Nature Science Award,and the Shanghai Science and Technology Progress Award.(Email:rhjin@sjtu.edu.cn) E-mail:rhjin@sjtu.edu.cn.

Abstract

With the rapid development of modern electronic technologies, antenna arrays typically operate in very complex electromagnetic environments. However, owing to the various errors such as systematic errors and random errors, conventional antenna arrays have relatively high sidelobes. Time modulated arrays (TMAs), also known as four-dimensional (4-D) antenna arrays, introduce time as an additional dimension for generating ultra-low sidelobes at fundamental component and realizing real-time beam scanning by harmonic components. Recently, the harmonic components can also be developed for various new applications including wireless communications and radar systems. In this review, we introduce comprehensively the fundamental methodologies and recent applications of TMAs. This aims to stimulate continuing efforts for the understanding of TMAs and explore their applications in various aspects. The methods mentioned in this review include three aspects: sideband radiation suppression, power efficiency of TMAs, and applications of harmonic components. These methods either improve the existing TMAs or promote the practical applications of TMAs. First, to suppress the sideband radiation, a method using non-uniform periodical modulation is introduced. The proposed method has an advantage of low computation and can be easily used for synthesizing a real-time radiation pattern according to the environmental need. Next, a TMA structure using reconfigurable power dividers/combiner is introduced to improve the power efficiency of feeding network. Finally, three applications of harmonic component including direction finding, calibration method, and space division multiple access are separately introduced to illustrate the development potential of TMAs.

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Cite this article

Chong He. Time-Modulated Arrays: A Four-Dimensional Antenna Array Controlled by Switches. [J], 2018, 3(1): 1-14 doi:10.1007/s41650-018-0004-7

Ⅰ. INTRODUCTION

The ultra-low sidelobe antenna array is known for its ca-pacity to improve the signal-noise ratio, depress the undesirable effect caused by the output signal of the main beam, and highly increase the anti-jamming performance of the system. The key in synthesizing the pattern is to accurately calculate the parameters including the excited amplitude and distances between elements, in terms of the system requirement. A great amount of effort has been devoted to the effective synthesis of the desired pattern, including various optimization algorithms[1,2,3,4,5,6,7,8,9]However, the requirements of complicated hardware designs and the large dynamic range ratio of excitation render these methods difficult to be applied in a real operational system.

However, the situation changed in the later 1950s, when Shanks and Bickmore proposed a 4-D electromagnetic radiator to control antenna radiation characteristics[10]. Since the time was introduced in the design and the antenna parameters were periodically modulated to synthesize the radiation pattern, the antenna system can also be considered as a timemodulated array(TMA). In the 1960s, the 4-D antenna concept was expanded to the design of antenna arrays by Kummar et al. By simply switching the ON and OFF states of the antenna elements with a predetermined sequence, a TMA can be used to realize beam-scanning with sidebands and synthesize the ultra-low sidelobe level (SLL) pattern at the carrier frequency[11,12]. The constraints on the antenna array errors are less stringent, while only ordinary sidelobes for the static array are required[13,14]. It is noteworthy that because the time parameter can be easily, rapidly, and accurately adjusted, the requirement on the dynamic range of amplitude excitations need not be as rigorous as the traditional antenna array. However, owing to the low speed of the switches at radio frequencies, this technique did not receive much attention at that time.

Recently, with the development of the speed of radio frequency switches, the TMA has attracted great attention again by virtue of its advantages. In the early 21st century, Yang et al. utilized a differential evolution algorithm to suppress the sideband levels (SBLs)[15], which was caused by periodical switching of continuous signals and commonly generated simultaneously with the useful signal at the carrier frequency[16]. Soon after, great effort was made to effectively reduce the SBLs, including various optimization algorithms, such as simulated annealing, particle swarm optimization, hybrid ABC-DE algorithm, and multi-objective optimization[17,18,19,20]. Meanwhile, different TMA schemes[21,22,23] and the pulse-shaping strategy[24]were also proposed to minimize the SBLs. However, all of the SBLs-suppressing methods above are based on optimization algorithms that require significant time to synthesize the desired pattern. To solve this problem, we proposed a non-uniform period modulation method to suppress the SBLs[25]. By modulating the radio frequency switches with non-uniform periods instead of the traditional uniform periods, the SBLs of the TMA can be remarkably suppressed and ultra-low SLL patterns at the fundamental component can also be obtained. Moreover, the proposed method does not need complex optimization computations, which renders the TMA more efficient in engineering applications.

Furthermore, many other approaches have been proposed to utilize these harmonic components from different perspectives, which are expected to enable various new applications in wireless and rader systems[26,27,28,29,30, [31,32,33,34,35,36,37,38,39]. Using the sideband signals, the TMAs were also used to estimate the arrival direction[27,28,29,30,31] and beam steering at the harmonic frequencies without additional phase weights[32,33,34,35]. Moreover, it was also used to realize a real-time reconfigurable wireless power transmission system[37], a single-sideband time-modulated phased array at the first positive sideband[38], and a secure communication scheme at the physical layer[39]. Inspired by the existing methods, we further developed the methods of direction finding[40] and single-sideband modulation. In these works, the mathematical expressions were deduced to calculate the incident direction using the fundamental and the first harmonic component, following which a simple S-band QSSB modulator was constructed to verify the single-sideband method. Meanwhile, recently, the TMA was also utilized for the space division multiple access(SDMA)in a single RF channel[41], parallel calibration of a phased array system[42], and phase gradient for detecting orbital angular momentum modes[43].

The low power efficiency of the TMA is known as one of the major disadvantages towards its real applications. The power loss in the feeding network, caused by the power absorption during the OFF state of the absorptive switches, is one of the most important reasons to reduce TMA efficiency. Several methods were proposed to address this problem by introducing several special structures, e. g. , using single-pole multi-throw switches to connect the array elements[44,45]. In Ref. [44], three-throw switches were used for realizing twochannel beam scanning, but part of the feeding power is still absorbed during the OFF state. Single-pole double-throw (SPDT)switches were used in Ref. [45]to avoid power loss in the feeding network. However, this resulted in the inflexible capabilities of the pattern synthesis and low aperture efficiency. To solve this problem, we proposed a TMA structure with reconfigurable power dividers/combiner(RPDC)to maximize the feeding network efficiency without losing either flexibility or aperture efficiency[46]. In this work, by using the RPDC instead of traditional absorptive switches in the feeding network, the power absorbed during the OFF state can be reused and the feeding power can be maximally utilized.

The remainder of this review are organized as follows. In section Ⅱ, the TMA principle and a method to suppress the sideband radiation are introduced. In section Ⅲ, for the sake of improving the efficiency of array, a TMA structure using RPDC to redistribute the absorbed energy is introduced. In section IV, the TMA applications based on three aspects are introduced, including direction finding, parallel calibration method, and SDMA. Conclusions and prospects are summarized in section V.

Ⅱ. FUNDAMENTAL PRINCIPLE OF THE TMA AND SIDEBAND RADIATION SUPPRESSION

A. TMA Theory

The TMA was first proposed by Shanks and Bickmore in the 1950s. They indicated that by periodically controlling the ON-OFF state of the element in an antenna array, the desired radiation pattern can be achieved. Recently, TMA has aroused renewed attention owing to its advantages of flexibility and low cost.

A typical structure of an N-element TMA is shown in Fig.1. N elements are equally spaced and operate on the receiving state. Each antenna is connected to a single-pole single-throw(SPST)switch, which is periodically modulated by field-programmable gate array(FPGA). Considering that all the elements are isotropic, the array factor can be given by

AF(θ,t)=ej2πFcatn=1NUn(t)ej(n1)KDsinθ,(1)

where θ denotes the incident angle with respect to the broadside direction, N is the number of switches, Fc is the carrier frequency of the incident signal, K=2πFc/c is the wave number, and D=λ/2 is the element spacing. Un(t)is the periodic function added on the nth element, which can be expressed as

Un(t)=m=gn(tmTp),(2)

Figure 1

Figure 1   A typical structure of the N-element TMA: (a)TMA diagram; (b) time sequence added to the nth channel


where Tp is the modulation period and gn(t)is a gate function

gn(t)={1,τon,ntτoff,n,0,0tτoff,ntTpn,(3)

where Tpn is the modulation period in the nth RF switch, and τon, n and τoff, n are the opening and closing instants in the nth RF switch, respectively. The periodic function Un(t)can be unfolded by the Fourier series as

Un(t)=kαnkej2πkFpnt,(4)

with Fpn = 1/Tpn being the modulation frequency. The Fourier coefficients αnk can be written as

αnk

=1Tpn0Tpngn(t)ej2πkFpntdt

={sin[πkFpn(τoff,nτon,n)]πkejπFpn(τoff,n+τon,n),k0,(τoff,nτon,n)Fpn,k=0,(5)

where αn0 is the fundamental component of the nth element, whose value is related to the duty ratio, and αnk is the kth harmonic component of the nth element. Substituting Eq. (4) and Eq. (5)into Eq. (1), the array factor can be rewritten as

AF(θ,t)=ej2πFctn=1N(k=αnkej2πkFpnt)ej(n1)KDsinθ

ej2πFctn=1Nαn0ej(n1)KDsinθ

+k=,k0n=1Nαnkej2π(FC+kFpn)tej(n1)KDsinθ.(6)

B. Sideband Radiation Suppression

The design complexity of an antenna array can be greatly simplified in a TMA. However, the undesired sideband radiations(SR)at the harmonic frequencies are generated simultaneously with the useful fundamental components, which results in an electromagnetic compatibility problem with other RF systems or self-expose. For a more efficient TMA, the sideband radiation level is to be suppressed. In recent years, many optimization algorithms including simulated annealing, particle swarm optimization, hybrid ABC-DE algorithm and multi-objective optimization[17,18,19,20] have been proposed to address this problem. The effective results and desired patterns have been acquired by the methods above. However, the large amount of computation is a major disadvantage of most optimization algorithms.

To reduce the computation and to make the TMA more practicable, we proposed a non-uniform period modulation method to suppress the SBLs[25]. By modulating the RF switches with non-uniform periods instead of the traditional uniform periods, the SBLs of the TMA can be remarkably suppressed and ultra-low SLL pattern at the fundamental component can also be obtained. Moreover, the proposed method does not require complex optimization computations, which renders the TMA more efficient in engineering applications.

The radiation pattern at the fundamental component is only related to the duty cycle, not the modulation period. This implies the possibility in synthesizing the same pattern as that of the fundamental component by simply maintaining the duty cycle on different elements consistent with that of the conventional TMA. Since the elements are modulated by nonuniform modulation periods, the generated harmonic components have different frequencies. The SR level will drop because the powers of different harmonic radiation cannot be accumulated in space.

To illustrate the effect of non-uniform period modulation on sideband radiation level suppression, numerical simulations are carried out to examine the feasibility of the method and an eight-element linear TMA is also constructed to verify its effectiveness.

For instance, in a 30-element uniform linear TMA, the modulation frequencies of N RF switches are Fp1, Fp2, …, Fpn and the carrier frequency Fc is set as 2. 6 GHz. The modulation frequency Fpn is chosen as

Fpn=[30+0.5(n1)]MHz,n=1,2,,N.(7)

The Dolph-Chebyshev weighting is chosen to weight the RF elements to obtain the low SLL. The radiation patterns of the fundamental component and the maximum SR for the two kinds of modulations are compared in Fig.2. For the uniform period modulation, the maximum sideband level is approximately−12. 3 dB. However, for the non-uniform period modulation, the maximum sideband level is approximately−36 dB since the harmonic component power is distributed to different frequency spectra.

Figure 2

Figure 2   Comparison of the patterns between the uniform and non-uniform period modulations: (a)uniform period modulation; (b)non-uniform period modulation


To verify the performance of the TMA SR suppression method based on the non-uniform period, a simple S-band eight-element TMA was constructed. The element space of the array was set as 0.48λ and the work frequency was set as 2. 515 GHz. To achieve an SLL below−20 dB at the fundamental component, the weights of elements 1-3 and 6-8 were separately set as 0.58, 0.66, 0.88, and 0.99, 0.66, 0.58, respectively. The values were decided using the Dolph-Chebyshev weighting distribution. Meanwhile, elements 4 and 5 were always open. To verify the effectiveness of the proposed method, both the uniform and non-uniform period modulations were implemented on the TMA in the experiment. In the experiment of uniform period modulation, the modulation frequencies of all channels were set as 1 MHz. In the experiment of the non-uniform period modulation, channels 1-3 and 6-8 were set as 1 MHz, 1. 1 MHz, 1. 2 MHz, and 1. 9 MHz, 1. 8 MHz, 1. 7 MHz, respectively. The power patterns for the two kinds of modulations are shown in Fig.3. The normalized maximum SR level of the array with the uniform period modulation is −12. 1 dB. The TMA modulated by non-uniform period pulse sequences shows that the maximum SR level of the array can be reduced by−22. 9 dB, which is 10.8 dB lower than that of the uniform modulation method.

Ⅲ. IMPROVING TMA EFFICIENCY USING RPDC

A TMA has relatively low efficiency owing to the power absorption in the switches during the off state. In this part, a novel TMA structure using an RPDC is designed to improve the efficiency of the feeding network[46]. The RPDC can change the state dynamically in response to the external environment to minimize unnecessary DC power loss. Thus, the power absorbed during the off state can be evenly transferred to other array elements during the on state in the TMA. Moreover, the switching speed of an RPDC is approximately tens of nanoseconds, resulting in a wide bandwidth in the proposed TMA design for signal transmission.

As shown in Fig.4, a 2N-element array is symmetrical with respect to the center of the array, both the left and right Nelement arrays are separately connected to an N-way RPDC, which is periodically modulated by an FPGA. The transmitter transmits the signals that will be divided into two ways signals by the two-way Wilkinson power divider network. Subsequently, the two-way signals are divided into 2N-way signals by the N-way RPDC, which are transmitted by the antenna array.

The pulse sequence on the elements in a classic distribution using SPST is shown in Fig.5(a). To synthesize the same pattern as the TMA using SPST, the power ratios of different TMA elements using RPDC should be consistent with that of the conventional TMA using SPST. The control function of

Figure 3

Figure 3   Normalized power patterns of the fundamental and the maximum harmonic components under two kinds of modulations: (a)uniform period modulation; (b)non-uniform period modulation


Figure 4

Figure 4   TMA transmitting structure using RPDC with 2N elements


the TMA using RPDC can be written as

Unm,RPDC(t)=δnm(t)2N/KmRPDC

(m=1,,M,n=1,,2N,tn,onm,RPDCttn,offm,RPDC),(8)

Figure 5

Figure 5   Comparison of two different pulse sequence strategies: (a)pulse sequences of a conventional eight-element TMA using SPST; (b)pulse sequences of the improved eight-element TMA using RPDC


where M is the total number of time intervals of the RPDC switching in a period, and Tn,onm,RPDC and tn,offm,RPDCare the opening and closing instants of the nth element at the mth time interval, respectively. δnm(t) is the Kronecker delta function (δnm(t)=1 if the nth element at the mth time interval is excited, and δnm(t)=0 otherwise). KmRPDC is the number of simultaneously excited elements at the mth time interval. The durations of time intervals of the TMA using RPDC are derived as[46]

τnm,RPDC=

{2Nτ1SPST[2Nτ1SPST+m=1N12(Nn)(τn+1SPSTτnSPST)]1,m=12(Nm+1)(τmSPSTτm1SPST)[2Nτ1SPST+m=1N12(Nn)(τn+1SPSTτnSPST)]1,m2(9)

where τmSPST=(tn,offSPSTtn,onSPST)/Tp is the duty cycle of the excitation on the nth element using SPST. The efficiency of the feeding network of the TMA using RPDC can be calculated as

ηfeedingRPDC=n=12Nm=1Mδnm(t)τnm,RPDCKmRPDC.(10)

Owing to the periodic modulation of switches, undesired sideband radiations are generated with the required power pattern at the carrier frequency. The total power loss of the improved TMA is determined by[46]

PSRRPDC=n=12Nm=1M2N{δnm(t)KmRPDC[τnm,RPDC(1τnm,RPDC)]

r=1,rmMδnm(t)δnr(t)KmRPDCKrRPDCτnm,RPDCτnr,RPDC}.(11)

The efficiency improvement of the feeding network can be expressed as

ηfeedingImproved=ηfeedingRPDCηfeedingSPST,(12)

where ηfeedingSPST is the efficiency of the feeding network of the TMA using SPST. The efficiency of the input power can be expressed as

P0toal=Po/(P0+PSR)ηfeeding,(13)

where P0 is the fundamental component power and PSR is the sideband radiation power.

To achieve the radiation pattern of Chebyshev distribution (SLL=−30 dB) and Taylor distribution (SLL=−30 dB, n¯=2)at the carrier frequency, the corresponding improved pulse sequences obtained according to Eq. (9) are in Fig.6 (a) and (b), respectively, where the color depths denote the excitation values at different time intervals.

The efficiency improvement of the feeding network ηfeedingImproved is shown in Fig.7. When the number of elements is fixed at 6 or 16, the efficiency improvements increase with the decrease in SLLs. Meanwhile, as the element increases from 6 to 16 and the SLL is fixed at −30 dB, the efficiency improvement of the feeding networks with Chebyshev and Taylor distributions were almost unchanged and is approximately 34. 88% and 34. 19%, respectively. The maximum efficiency improvements are 43. 99%, 43. 10% with 2N=6, and 52. 60%, 46. 31% with 2N=16, respectively.

A six-channel TMA is designed to verify the feasibility and validity of the proposed TMA with an RPDC. The measured and simulated results for different SLLs are shown in Tab.1. ∆G and∆SBL are the differences in the TMA gains and SBLs, respectively. The measured gain values are shown to be consistently a little lower than the simulated ones, which may be attributed to the higher insertion loss of the RPDC in the single-path mode. The measured and simulated values of the gains rise from 0.98 dB to 1. 65 dB and 1. 2 dB to 1. 88 dB with the SLL decreasing from−20 dB to−30 dB.

Figure 6

Figure 6   Pulse sequences of(a)Chebyshev distribution; (b)Taylor distribution with SLL=−30 dB of TMA using RPDC(2N=16,d=0. 5λ)


Ⅳ. TMA APPLICATIONS

A. Direction Finding

By utilizing the additional information of the harmonic components, the TMA is capable of finding the RF source direction. In 2007, a direction-finding concept using a twoelement TMA was first proposed in Ref. [27]by finding the null of the first harmonic component. In 2010, A. Tennant[28] designed a two-element antenna to estimate the direction by adding a mechanical phase shifter on an element array. In the same year, compared with the conventional classic multiple signal classification(MUSIC)method, a higher resolution was achieved[30]. In 2014, Q. Zhu[47] proposed the multiple sum and difference patterns in the TMA to estimate the direction. In this method, the TMA was divided into two subarrays, which could calculate the incident angle of the signal using the beaming characteristics of two sub-arrays. In 2016, the direction finding of acoustic signals was conducted in TMA[48].

Figure 7

Figure 7   Improved efficiency of TMA using two different distributions


Table 1   Performance comparison of simulated and measured results

SLL=−20 dBSLL=−25 dBSLL=−30 dB
∆G∆SBL∆G∆SBL∆G∆SBL
simulated/dB1.20−2.891.60−2.301.88−2.32
measured/dB0.98−2.611.27−2.461.65−2.21

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The stretcher can be removed if we performed a numerical analysis directly to the harmonic characteristic directly. With the signal of different incident directions, the incident angle can be calculated by analyzing the relationship between the fundamental and harmonic components.

The system outline of the direction finding using the TMA is shown in Fig.8. Two-element antennas and a simple frontend construction is the focus in the TMA direction finding method. The receiver system is controlled by the switch and the switch frequency is controlled by an FPGA with modulation frequency Fp. The output signal of the antennas is processed by a down converter, a low-pass filter, a digitalto-analog converter, and a spectrum analyzer. Finally, the measured result of the incident direction is displayed on the computer. The far-field signal at frequency Fc enters the array, with incident direction θ. The signal is modulated by an SPDT RF switch with modulation period Tp, and the duty cycle of each element is 50%. The received signal modulated by the SPDT switch can be written as

s(t)=U(t)ej2πFct,(14)

where U(t)is a periodical function expressed as

U(t)={1,(n1)Tpt(n0.5)TpejKDsinθ,(n0.5)TptnTp,nZ,(15)

where K=2πFc/c is the wave number and D=λ/2 is the element spacing. U(t)can be unfolded by the Fourier series as

U(t)=n=αkej2πkFpt,(16)

where αk is the Fourier coefficient of the kth harmonic:

αk={1+ejKDsinθ2,k=0,j(ejkπ1)2kπ(1ejKDsinθ),k0.(17)

Substituting k=0, 1 into Eq. (17), the fundamental component α0 and the first harmonic component α1 are obtained by

{α0=1+ejKDsinθ2,α1=jπ(1ejKDsinθ).(18)

According to Eq. (17), the incident angle θ can be calculated by

θ=arcsin(2KDarctanπα12α0).(19)

The performance of the proposed method is shown in Fig.9. The solid and the dashed curves represent the absolute and relative errors of direction finding, respectively. The maximum absolute and relative errors are approximately 0.5°and 6%, respectively. The standard deviations of the absolute and relative errors are 0.28°and 2. 3%, respectively. The standard deviations of direction finding under different signal-to-noise ratios(SNRs)are shown in Fig.9(b). When the incident direction of the far-field source is at+30°, the mean square error (MSE)decreases from 0.6°to 0.03°with the SNR increasing from−10 dB to 20 dB.

The measured results of direction finding are shown in Tab.2. The estimation errors are less than 5°, and their standard deviation is 3. 3°. The error in the measured results may be caused by the amplitude and phase imbalance between the two channels, power measurement errors, the mutual coupling characteristic between two antenna elements, or the multipath in the surrounding environment.

Both the simulation and experimental results verify the feasibility of the proposed method. The proposed directionfinding system requires only two switches and a single RF channel, which can greatly promote the development of a simple and low-cost direction-finding technology. Moreover, the amount calculation of the proposed method principally concentrates on a two-point discrete Fourier transform (DFT), which facilitates the development of real-time direction finding.

Figure 8

Figure 8   Block diagram for TMA direction finding


Figure 9

Figure 9   Performance of the proposed method: (a) absolute and relative errors of the direction of arrival results; (b) MSEs of the direction-finding errors under different SNRs


B. Parallel Calibration Method by Time Modulation

The inconsistency, coupling and element failure of array elements affect greatly the performance of the active arrays, and must be considered when designing active arrays. Two kinds of classic serial channel mismatch calibration methods exist: the rotating-element electric-field and vector (REV) method and the phase-toggling method. These methods have some deficiencies, such as the requirement for many measurements when using the REV method, and the needs for measure between the calibration source and sink when using the phasetoggling method. Compared with the two calibration methods, the parallel calibration method is more efficient, and performs well for the large-phased arrays with very small calibration time slots. The proposed method has two primary advantages: first, it can be a fast far-field calibration method with no measurement between the calibration source and sink; second, auxiliary calibration elements are not required.

Table 2   Direction finding experiment results of the TMA

directionα0α1estimationabso.errorrela.error
/dBm/dBm/%
0−32.02−53.844.74.7
5−31.3−50.366.51.530
10−32.09−47.0311.31.313
15−32.16−41.4318.93.916
20−32.51−39.4823.73.718.5
25−33.22−38.9126.61.68
30−35.08−37.7234.24.214

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The principle of the calibration method based on time modulation is that the spectrum of the calibration signal after the periodic phase modulation is decided by the complex gains (S21 parameters) of all RF channels. Subsequently, through analyzing the harmonic frequency characteristics, their complex gains can be calculated in parallel. For example, for the receiving calibration, the calibration steps are as follows: First, a planar sinusoidal wave from a far-field source enters the phased array. Next, the periodic phase modulations are sequentially added to each phase shifter, thus changing the phase shifter of the corresponding channel from 0° to 180°. Subsequently, the combined calibration signal is sampled to create the spectrum analysis. Finally, the obtained harmonic characteristic is used to calculate the complex gains of the RF channels in parallel.

The array calibration diagram based on the TMA is shown in Fig.10. First, the phased array receives a planar sinusoidal calibration signal from the far field. Second, the received RF signals in all elements are periodically modulated by the controller, and the modulated signals are combined together by the power combiner. Third, the combined RF signal is converted down to IF and sampled by the A/D converter to the digital signal. Fourth, the spectrum of the digital calibration signal is estimated by the DFT. Finally, the estimated harmonic spectrum is utilized to calculate the channel mismatches of all RF channels in parallel. Assuming that gn represents the complex gain of the nth channel, the modulation cycle Tp is divided into N equal parts and the phase shift of the corresponding channel increases by 180°during one time slot. The gn of the nth channel is expressed as

gn(t){gn,n1NTp+mTptnNTp+mTp,gn,mTptn1NTp+mTp,(20)

where m∈Z, gn(t) is the periodic complex signal, which can be unfolded by the Fourier series as

gn(t)=k=Gk,nej2πkFpt,(21)

where Fp=1/Tp is the modulation frequency and Gk, n is the Fourier coefficient of the kth harmonic in the nth RF channel, which is calculated as follows

Gk,n=1Tp0Tpgn(t)ej2πkFptdt

={N2Ngn,k=0,jgnkπ(ej2πkN1)ej2πkN,k0.(22)

After using the power combiner, the calibration signal contained the fundamental and the harmonic components. The fundamental component Γ0 and the harmonic components Γ1, Γ2, …, Γn−1 are expressed as follows

{Γ0=n=1NN2NejKDsinθejKDsinθΓk=n=1Nj(ej2πkN1)kπejKDsinθejn(2πkN+KDsinθ)gn,k0,kZ,(23)

where D is the element spacing, and K is the wave number. To simplify the calculation, we set

{uk=2πkN+KDsinθ,bk={Γ0NN2ejKDsinθ,k=0,ΓkkπejKDsinθj(ej2πkN1),k0.(24)

Substituting Eq. (24)into Eq. (23), the system of linear equations of complex gains and the harmonic components are obtained as follows:

(eju0ej2u0ejNu0eju1ej2u1ejNu1ejuN1ej2uN1ejNuN1)g=b,(25)

where g and b are the complex gain vector and harmonic characteristic vector, respectively. Finally, the complex gain gn of each channel was calculated in parallel by solving the system of linear equations.

Figure 10

Figure 10   Array calibration diagram based on time modulation


Two numerical simulations are provided to examine the performance of the proposed method. In the first simulation, a 30-element uniform linear array with element spacing λ/2 is calibrated in parallel. The signal enters in the array with the incident angle θ =20°. The first channel is set as the reference and the amplitudes of the remaining RF channels are assumed to obey the uniform distribution in the range of[0.75, 1. 25], and their initial phases obey the uniform distribution in the range of[−30°, 30°]. The carrier frequency Fc and the sampling frequency Fs were set as 0.1 GHz and 1 GHz, respectively. The phase modulation period Tp was fixed as 3 µs. The calibration results and errors of the amplitude and phase estimations are plotted for comparison in Figs. 11 and 12, respectively.

Figure 11

Figure 11   Amplitude estimation results and errors: (a)amplitude comparison between the estimated results and the preset values; (b)amplitude estimation errors


Figure 12

Figure 12   Phase estimation results and errors: (a)phase comparison between the estimated results and the preset values; (b)phase estimation errors


Figure 13

Figure 13   Mean square errors of amplitude and phase estimation with the proposed method under different SNRs: (a) amplitude estimation MSEs under different SNRs; (b)phase estimation MSEs under different SNRs


In Figs. 11(a)and 12(a), the statistical MSEs of the amplitude and phase estimation are 0.2 dB and 1. 5°, respectively. In Figs. 11(b)and 12(b), the maximum and minimum amplitude estimation errors are approximately 0.5 dB and−0.2 dB when the channel numbers are 11 and 15, respectively. The maximum and minimum phase estimation errors are approxi mately 2. 6 dB and−3. 7 dB when the channel numbers are 17 and 14, respectively.

The second simulation involves the accuracy of the proposed calibration method under different SNRs. The simulation parameters are the same as those in the first simulation. The simulation results shown in Fig.13 indicate that with the increase in the SNR, the MSEs of the amplitude and phase estimation decrease steadily. If the SNR of the received signal is larger than 15 dB, the MSEs of the amplitude and phase estimation are less than 0.2 dB and 1°, respectively.

Figure 14

Figure 14   Measured results of amplitude and phase characteristics of four channels by vector network analyzer(VNA): (a)amplitude characteristics; (b)phase characteristics


A four-channel S-band RF circuit was constructed and calculated in parallel. The calibration procedure is as follows. First, a 2. 6 GHz sinusoidal calibration signal is divided equally into four parts by a power divider. Second, in each RF channel, the SPST RF switch substitutes the phase shifter to control the channel for simplicity. Third, after the modulation, the calibration signals of four channels are combined by a power combiner. Finally, the combined signal is input to an oscilloscope to acquire the data that is used to calculate the mismatches of the four channels in parallel.

The acquired data is used to create the harmonic analysis. The Fourier coefficients Γk (k=0, 1, 2, 3) at Fc, Fc+Fp, Fc+2Fp, and Fc+3Fp are substituted into Eq. (25) to calculate the complex gains of four channels. We solve the linear system described in Eq. (25) and obtain the complex gains of four channels. The amplitudes and phases of four channels(S21parameters)are plotted in Fig.14. As shown in Fig.14(a), the amplitudes of four channels almost decreased with the increase in the frequency. In Fig.14(b), the phases of four channels are nearly the same at different frequencies.

The calculated and measured complex amplitudes and phases of four channels at 2. 6 GHz are listed in Tab.3. The calculated results appear to differ greatly compared to the measured results, because they are not normalized. We set the first channel as the reference for both the calculated and measured results. The amplitude and phase of the first channel are 0 dB and 0°, respectively. The amplitudes and phases of the other channels are normalized to the first channel. Subsequently, the calculated and measured channel mismatches of four channels are listed in Tab.4. As shown, the amplitude estimation errors between the measured and calculated results are less than 0.1 dB, and the phase estimation errors are less than 0.5°.

Table 3   Comparison of the calculated and measured complex gains at 2. 6 GHz

channel1234
calculated amplitudes/dB−35.28−35.89−36.56−35.87
calculated phases/°−135.69−139.86−146.94−143.04
measured amplitudes/dB−15.81−16.46−17.11−16.45
measured phases/°−53.72−58.14−65.12−61.22

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Table 4   Comparison of calibration results between calculation and measurement

channel1234
calculated amplitudes/dB0−0.61−1.28−0.59
measured amplitudes/dB0−0.65−1.30−0.64
calculated phases/°0−4.17−11.25−7.35
measured phases/°0−4.42−11.40−7.50
amplitude estimation errors/dB0−0.04−0.020.05
phase estimation errors/°00.250.150.15

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C. Space Division Multiple Access Based on TMA

SDMA is a good solution to mitigate the lack of resources in communication systems. Generally, the multi-beam antenna or the smart antenna is used for the system. The TMA is a new approach proposed recently with advantages in hardware complexity and cost. Its principle is that the powers of the users’signals in different directions can be redistributed to different order harmonic components.

In the simulation, a six-element array with element spacing λ/2 is designed. The normalized patterns of the fundamental and harmonic components are plotted in Fig.15. As shown in Fig.15, the patterns of the fundamental and harmonic components point to different directions. The solid curve indicates the pattern at Fc, which points to the normal direction θ0. The dashed and dotted curves represent the patterns of the ±1st harmonic components, which point to ±θ1(±19. 5°). The dashed dot and short-dashed lines indicate the pattern of the ±2nd harmonic components, which point to ±θ2(±41. 8°). The maximum radiation powers of the first and second harmonic components are−0.4 dB and−1. 7 dB, respectively.

Figure 15

Figure 15   Multi-beam characteristic of a simple TMA


In the uplink, if three users transmit the signals s1(t), s2(t), s3(t)with the same carrier frequency Fc, from θ0, +θ1, −θ2, respectively, the combined signal is

sRX(t)=F0(θ0,t)s1+F1(θ1,t)s2(t)ej2πFpt

+F2(θ2,t)s3(t)ej4πFpt,(26)

As shown in Eq. (26), the users’signals are modulated to different carrier frequencies according to their incident direction. In the downlink, to transmit the three users’signals to θ0, +θ1, −θ2 with the carrier frequency Fc, the signal before the TMA should be

sTX(t)=s1(t)+s2(t)ej2πFpt+s3(t)ej4πFpt.(27)

Finally, the three users’ signals can be transmitted with the same carrier frequency Fc. s1(t), s2(t), s3(t) radiate to θ0, +θ1, −θ2, respectively.

A simple S-band six-element TMA was designed to test the method. The TMA operates at 2. 525 GHz, with an element spacing of 5. 77 cm. Six channels were periodically opened in sequence. Each channel’s open time is 1/6 µs and the modulation frequency Fp is 1 MHz. The power patterns of the fundamental and harmonic components are plotted in Fig.16. As shown, the pattern at the fundamental component points to the normal direction 0°; the pattern at the ±1st, ±2nd harmonic components point to approximately ±20°, ±45°respectively. Compared to Fig.15, the sidelobes of the experimental results ascend, which may be caused by the mismatches among the six elements, the rising and falling times of the switches, etc. The high sidelobes may cause the interference with other sig nals. However, it can be suppressed effectively by methods such as amplitude weighting.

Figure 16

Figure 16   Measured power patterns of the fundamental and harmonic components


Ⅴ. CONCLUSION AND FUTURE WORK

TMAs are a kind of 4-D antenna array that introduce time as an additional dimension for the generation, detection, and modulation of electromagnetic beams, enabling novel applications including generating ultra-low sidelobes at the fundamental component and realizing real-time beam scanning by harmonic components. TMAs have attracted extensive attention owing to their advantages such as design flexibility and low cost. Herein, we have presented a general review on the recently developed modulation technologies and practical applications using TMAs. This includes the suppression of sideband radiation susing non-uniform periodical modulations. The efficiency improvement in the TMA feeding network using an RPDC was introduced and compared to the conventional TMA. Finally, TMA applications were introduced in three aspects: direction finding, array calibration, and spacedivision multiple access.

While significant progresses have been achieved in the last few years, continuing efforts are encouraged to stimulate further developments and applications in the field of TMAs. In particular, the impact of using non-ideal characteristics of RF switches in real situations, including the switching speed and the rising and falling edges, requires further consideration. Direction finding of related sources, which has shown enormous potential practicability in wireless communications and radar systems, is another valuable research direction.

The authors have declared that no competing interests exist.
作者已声明无竞争性利益关系。

Reference

P. J. Bevelacqua , C. A. Balanis .

Minimum sidelobe levels for lineararrays

[J]. IEEE Trans.Antennas Propag, 2007, 55(12): 3442-3449.

[Cited within: 1]

G. Cardone , G. Cincotti , M. Pappalardo .

Design of wide-bandarrays for low sidelobe level beam patterns by simulated annealing

[J]. IEEE Transactions on Ultrasonics Ferroelectrics&Frequency Control, 2002, 49(8): 1050-1059.

[Cited within: 1]

N. H. Farhat , B. Bai .

Phased-array antenna pattern synthesis bysimulated annealing

[J]. Proceedings of the IEEE, 1987, 75(6): 842-844.

[Cited within: 1]

V. Murino , A. Trucco , C. S. Regazzoni .

Synthesis of unequaly spaced arrays by simulated annealing

[J]. IEEE Transactions on Signal Processing, 1996, 44(1): 119-122.

[Cited within: 1]

R. L. Haupt .

Thinned arrays using genetic algorithms

[J]. IEEE Trans.Antennas Propag, 1994, 42(7): 991-993.

[Cited within: 1]

F. J. Ares , J. A. Rodriguez , E. Villanueva , et al.

Genetic algorithm in the design and optimization of antenna arraypatterns

[J]. IEEE Trans.Antennas Propag., 1999, 47(3): 506-510.

[Cited within: 1]

H. M. Elkamchouchi , M. M. Hassan .

Array pattern synthesis approach using a genetic algorithm

[J]. IET Microwaves,Antennas&Propagation, 2014, 8(14): 1236-1240.

[Cited within: 1]

T. H. Ismail , Z. M. Hamici .

Array pattern synthesis using digitalphase control quantized particle swarm optimization

[J]. IEEE Trans.Antennas Propag., 2010, 58(6): 2142-2145.

[Cited within: 1]

G. Oliveri , A. Massa .

Bayesian compressive sampling for patternsynthesis with maximally sparse non-uniform linear arrays

[J]. IEEE Trans.Antennas Propag., 2011, 59(2): 467-481.

[Cited within: 1]

H. E. Shanks , R. W. Bickmore .

Four-dimensional electromagneticradiators

[J]. Canadian Journal of Physics, 1959, 37(3): 263-275.

[Cited within: 1]

H. E. Shanks .

A new technique for electronic scanning

[J]. IEEE Trans.Antennas Propag., 1961, 9(2): 162-166.

[Cited within: 1]

W. H. Kummer , A. T. Villeneuve , T. S. Fong , et al.

Ultra-low sidelobes from time-modulated arrays

[J]. IEEE Trans.Antennas Propag., 1963, 11(6): 633-639.

[Cited within: 3]

S. W. Yang , Z. P. Nie .

A review of the four dimension antennaarrays

[J]. Journal of Electronic Science and Technology of China, 2006, 4(3): 193-201.

[Cited within: 1]

W. Q. Wang , H. C. So , A. Farina .

An overview on time/frequency modulated array processing

[J]. IEEE Journal of Selected Topics in Signal Processing, 2017, 11(2): 228-246.

[Cited within: 1]

S. Yang , Y. B. Gan , A. Qing .

Sideband suppression in time modulated linear arrays by the differential evolution algorithm

[J]. IEEE Antennas Wireless Propag.Lett., 2002, 1(1): 173-175.

[Cited within: 1]

J. C. Bregains , J. Fondevila-Gomez , G. Franceschetti , et al.

Signal radiation and power losses of time-modulated arrays

[J]. IEEE Transactions on Antennas&Propagation, 2008, 56(6): 1799-1804.

[Cited within: 1]

J. Fondevila , J. C. Bregains , F. Ares , et al.

Optimizing uniformly excited linear arrays through time modulation

[J]. IEEE Antennas&Wireless Propagation Letters, 2004, 3(1): 298-301.

[Cited within: 2]

L. Poli , P. Rocca , L. Manican , et al.

Handling sideband radiations in time-modulated arrays through particle swarm optimization

[J]. IEEE Transactions on Antennas&Propagation, 2010, 58(4): 1408-1411.

[Cited within: 2]

S. Pal , S. Das , A. Basak .

Design of time-modulated linear arrays with a multi-objective optimization approach

[J]. Progress in Electromagnetics Research B, 2010, 23(23): 83-107.

[Cited within: 2]

J. Yang , W. T. Li , X. W. Shi , et al.

A hybrid ABC-DE algorithm and its application for time-modulated arrays pattern synthesis

[J]. IEEE Transactions on Antennas&Propagation, 2013, 61(11): 5485-5495.

[Cited within: 2]

S. Yang , Y. B. Gan , A. Qing .

Design of a uniform amplitude timemodulated linear array with optimized time sequences

[J]. IEEE Transactions on Antennas&Propagation, 2005, 53(7): 2337-2339.

[Cited within: 1]

L. Poli , P. Rocca , L. Manica , et al.

Pattern synthesis in time modulated linear arrays through pulse shifting

[J]. IET Microwaves,Antennas&Propagation, 2010, 4(9): 1157-1164.

[Cited within: 1]

Q. Zhu , S. Yang , L. Zheng , et al.

Design of a low sidelobe time modulated linear array with uniform amplitude and sub-sectional optimized time steps

[J]. IEEE Transactions on Antennas&Propagation, 2012, 60(9): 4436-4439.

[Cited within: 1]

E. T. Bekele , L. Poli , P. Rocca , et al.

Pulse-shaping strategy for time modulated arrays-analysis and design

[J]. IEEE Transactions on Antennas&Propagation, 2013, 61(7): 3525-3537.

[Cited within: 1]

C. He , H. Yu , X. Liang , et al.

Sideband radiation level suppression in time-modulated array by nonuniform period modulation

[J]. IEEE Antennas&Wireless Propagation Letters, 2015, 14: 606-609.

[Cited within: 2]

Y. Z. Tong .

Time modulated linear arrays

[D]. University of Sheffield, 2013: 1-4.

[Cited within: 1]

A. Tennant , B. Chambers .

A two-element time-modulated array with direction finding properties

[J]. IEEE Antennas&Wireless Propagation Letters, 2007, 6(11): 64-65.

[Cited within: 3]

A. Tennant .

Experimental two-element time-modulated direction fnding arrays

[J]. IEEE Transactions on Antennas&Propagation, 2010, 58(3): 986-988.

[Cited within: 3]

A. Tennant , B. Chambers .

Direction finding using a four-element time-switched array system

[C]// Antennas&Propagation Conference,Loughborough, 2008: 3.

[Cited within: 2]

G. Li , S. Yang , Z. Nie .

Direction of arrival estimation in time modulated linear arrays with unidirectional phase center motion

[J]. IEEE Transactions on Antennas&Propagation, 2010, 58(4): 1105-1111.

[Cited within: 3]

A. O’Donnell , W. Clark , J. Ernst , et al.

Analysis of modulated signals for direction finding using time modulated arrays

[C]// Radar Conference,Philadelphia, 2016: 1-5.

[Cited within: 2]

G. Li , S. Yang , Y. Chen , et al.

A novel beam scanning technique in time modulated linear arrays

[C]// IEEE Antennas & Propagation Society International Symposium,North Charleston, 2009: 1-4.

[Cited within: 2]

Y. Tong , A. Tennant .

Simultaneous control of sidelobe level and harmonic beam steering in time-modulated linear arrays

[J]. Electronics Letters, 2010, 46(3): 201-202.

[Cited within: 2]

G. Li , S. Yang , Y. Chen , et al.

An adaptive beamforming in time modulated antenna arrays

[C]// International Symposium on Antennas,Kunming, 2008: 221-224.

[Cited within: 2]

L. Poli , P. Rocca , G. Oliveri , et al.

Harmonic beamforming in timemodulated linear array

[J]. IEEE Transactions on Antennas&Propagation, 2011, 59(7): 2538-2545.

[Cited within: 2]

Q. Zhu , S. Yang , P. Rocca , et al.

Signal-to-noise ratio and timemodulated signal spectrum in four-dimensional antenna arrays

[J]. IET Microwaves,Antennas&Propagation, 2014, 9(3): 264-270.

[Cited within: 1]

D. Masotti , A. Costanzo , M. D. Prete , et al.

Time-modulation of linear arrays for real-time reconfigurable wireless power transmission

[J]. IEEE Transactions on Microwave Theory&Techniques, 2016, 64(2): 331-342.

[Cited within: 2]

A. M. Yao , W. Wu , D. G. Fang .

Single-sideband time-modulated phased array

[J]. IEEE Transactions on Antennas&Propagation, 2015, 63(5): 1957-1968.

[Cited within: 2]

P. Rocca , Q. Zhu , E. T. Bekele , et al.

4-D arrays as enabling technology for cognitive radio systems

[J]. IEEE Transactions on Antennas&Propagation, 2014, 62(3): 1102-1116.

[Cited within: 2]

C. He , X. Liang , Z. Li , et al.

Direction finding by time-modulated array with harmonic characteristic analysis

[J]. IEEE Antennas&Wireless Propagation Letters, 2015, 14: 642-645.

[Cited within: 1]

C. He , X. Liang , B. Zhou , et al.

Space-division multiple access based on time-modulated array

[J]. IEEE Antennas&Wireless Propagation Letters, 2015, 14: 610-613.

[Cited within: 1]

C. He , X. Liang , J. Geng , et al.

Parallel calibration method for phased array with harmonic characteristic analysis

[J]. IEEE Transactions on Antennas&Propagation, 2014, 62(10): 5029-5036.

[Cited within: 1]

J. Chen , X. Liang , C. He , et al.

High-sensitivity OAM phase gradient detection based on time-modulated harmonic characteristic analysis

[J]. Electronics Letters, 2017, 53(12): 812-814.

[Cited within: 1]

Y. Tong , A. Tennant .

A two-channel time-modulated linear array with adaptive beamforming

[J]. IEEE Transactions on Antennas&Propagation, 2012, 60(1): 141-147.

[Cited within: 2]

G. Bogdan , Y. Yashchyshyn , M. Jarzynka .

Time-modulated antenna array with lossless switching network

[J]. IEEE Antennas&Wireless Propagation Letters, 2016, 15: 1827-1830.

[Cited within: 2]

J. Chen , X. Liang , C. He , et al.

Efficiency improvement of time modulated array with reconfigurable power divider/combiner

[J]. IEEE Transactions on Antennas&Propagation, 2017, 65(8): 4027-4037.

[Cited within: 4]

Q. Zhu , S. Yang , R. Yao , et al.

Direction finding using multiple sum and difference patterns in 4D antenna arrays

[J]. International Journal of Antennas&Propagation, 2014, 2014(2): 1-12.

[Cited within: 1]

A. O’Donnell , W. Clark , J. Ernst , et al.

Analysis of modulated signals for direction finding using time modulated arrays

[C]// IEEE Radar Conference,Philadelphia, 2016: 1-5.

[Cited within: 1]

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