Low Sideband Radiation Beam Scanning at Carrier Frequency for Time-Modulated Array by Non-Uniform Period Modulation

Abstract

A novel beam scanning method utilizing the carrier frequency component for time modulated array (TMA) is proposed and a significant algorithm based on the non-uniform period modulation is implemented to suppress the maximum sideband radiation (SR) level. The signal in each channel is modulated by a pair of high-speed radio- frequency (RF) switches and totally three or four delay lines with different phases. In each modulation period, three selected delay lines are connected successively with proper pulse durations to keep the switches in ”ON” states constantly and ensure the maximum efficiency in the feeding network. Additionally, in order to suppress the relatively higher SR generated by both switches and delay lines, each channel of the TMA system has a different modulation period, which will separate the harmonic components of different elements on the frequency axis. A desired relatively low maximum SR level without complicated optimization is obtained compared to uniform period modulation and optimization algorithms. Several numeric simulations are brought out to examine the performance of the proposed methods, and the results for comparison to existing methods are also provided. A group of experiments have been done to verify its effectiveness.

Full text

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 68, NO. 5, MAY 2020 3695
Low Sideband Radiation Beam Scanning at Carrier
Frequency for Time-Modulated Array by
Non-Uniform Period Modulation
Gang Ni , Chong He ,Member, IEEE, Jingfeng Chen , Yiqing Liu , and Ronghong Jin ,Fellow, IEEE
Abstract— A novel beam scanning method utilizing the car-
rier frequency component for time-modulated array (TMA) is
proposed and a significant algorithm based on the non-uniform
period modulation is implemented to suppress the maximum
sideband radiation (SR) level. The signal in each channel is
modulated by a pair of high-speed radio-frequency (RF) switches
and totally three or four delay lines with different phases. In each
modulation period, three selected delay lines are connected
successively with proper pulse durations to keep the switches
in ON states constantly and ensure the maximum efficiency
in the feeding network. Additionally, in order to suppress the
relatively higher SR generated by both switches and delay lines,
each channel of the TMA system has a different modulation
period, which will separate the harmonic components of different
elements on the frequency axis. A desired relatively low maximum
SR level without complicated optimization is obtained compared
with uniform period modulation and optimization algorithms.
Several numeric simulations are brought out to examine the
performance of the proposed methods, and the results for
comparison to existing methods are also provided. A group of
experiments have been done to verify its effectiveness.
Index Terms—Beam scanning, non-uniform period modula-
tion, sideband radiation (SR), time modulated array (TMA).
I. INTRODUCTION
TIME-modulated array (TMA) was first proposed and
experimentally constructed by Shanks and Bickmore
in 1960s [1], [2]. By controlling high-speed radio-frequency
(RF) switches periodically in the RF front of each channel,
the signals transmitted or received through the TMA are mod-
ulated by the ON–OFF gate function. And an ultralow side
lobe level (SLL) can be obtained with proper time sequences
imposed on the RF switches. The main superiority of TMA is
that it takes time as an extra designed freedom to generate the
equivalent amplitude and phase excitation, which will achieve
a larger dynamic range of excitation compared with traditional
phased arrays. Unfortunately, undesired harmonic components
occur at each harmonic frequency simultaneously since the
periodic pulse modulation, leading to the decline of array
Manuscript received September 15, 2019; revised November 27, 2019;
accepted December 27, 2019. Date of publication February 3, 2020; date of
current version May 5, 2020. This work was supported by the NSFC under
Grant 61901263, in part by the SAST Independent RD Plan under Grant
ZY2018-23, and in part by the 2018 Independent Innovation Project of CSIC
722 Research Institute. (Corresponding author: Chong He.)
The authors are with the Department of Electronic Engineering, Shanghai
Jiao Tong University, Shanghai 200240, China (e-mail: hechong@sjtu.edu.cn).
Color versions of one or more of the figures in this article are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TAP.2020.2969889
gain and spectral interference in other RF systems working
on harmonic frequencies.
In the recent decades, aiming to suppress or eliminate har-
monic components of specific harmonic frequencies, numerous
algorithms and time modulation strategies were proposed and
experimentally verified [3]–[10]. Evolutionary optimization
algorithms, such as the simulated annealing (SA) [3], dif-
ferential evolution (DE) [4], genetic algorithm (GA) [5], and
particle swarm optimization (PSO) [6], were implemented to
control the sideband radiation (SR) level by optimizing the
turning on/off instants of the RF switches. Bekele et al. [7]
took the pulse shape as a new designed freedom to optimize
the SR level. And mathematical method was used to suppress
sidelobes and sidebands in [8]. Additionally, pulse shifting [9]
and fixed-bandwidth elements [10] were exploited to achieve
low SR loss. The sideband levels (SBLs) were suppressed
conveniently and significantly by utilizing non-uniform period
modulation [11] in further study, and the SR power under
non-uniform period modulation was investigated in [12]. More
recently, the utilization of SR has become a hot research
orientation. The unique properties of harmonic components
of the modulated signals were explored and implemented in
various fields. For instance, in [13]–[15], the direction of
arrival (DOA) was estimated by the sidebands and carrier com-
ponent. Efficient beam steering methods utilizing the harmonic
components was validated in [16]. Besides, SR also plays a
significant role in harmonic beamforming [17], multiple-beams
pattern synthesis [18], [19], cognitive radio systems [20], and
sidelobe blanking radar system [21].
Unlike the harmonic components in each harmonic fre-
quency, no additional phases are introduced at the carrier
frequency component, which means it is hard to achieve beam
scanning using the carrier frequency component without phase
shifters. To break through the limitations, a phase modulation
method was proposed in [22]. The proposed structure utilized
several delay lines to generate equivalent phases at the carrier
frequency component, whereas the static attenuators or much
“OFF” time in the RF switches caused considerable power
loss. In [23], an improved phase modulation structure was
designed to eliminate the OFF times or attenuators. The always
ON states of the two delay line branches avoided the power loss
in the absorptive switches remarkably. However, the paired
switches, extra power dividers and combiners in each channel
introduced nonnegligible insertion loss, resulting in the decline
of efficiency in actual application. Additionally, both the
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3696 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 68, NO. 5, MAY 2020
methods in [22] and [23] utilized the evolutionary optimization
algorithms to realize the relatively low SR level. It is difficult
to converge to the optimal time sequences when the scale of
the TMA is very large.
In this article, a new beam-scanning method based on
the carrier frequency component is proposed and the novel
non-uniform period modulation is exploited to suppress the
maximum SR generated in the harmonic frequencies. In the
TMA structure, three or four delay lines totally with different
phases are configured in each channel and three of them are
connected in each period to achieve beam scanning and keep
the RF switches in ON states constantly. It is worth noting that
the simple structure and the always ON states will avoid the
absorptive switches and reduce the power loss in the feeding
network significantly as in [23]. Meanwhile, the elements of
TMA system are modulated by different frequencies. With
proper modulation frequencies in each channel, the sidebands
of different harmonic frequencies and different elements can-
not accumulate in space, so a relatively low maximum SR level
without complicated optimization can be obtained. Besides,
the non-uniform period modulation method will have a better
SR suppression performance as the array scale increases.
This article is organized as follows. Section II presents
the theory of the proposed method. Section III provides
the numeric simulations to examine the performance of the
proposed method. In Section IV, two 16-elements linear TMAs
were constructed to verify the effectiveness of the proposed
method. Finally, conclusions are drawn in Section V.
II. PRINCIPLE
A. Theory of TMAs
Consider an N-element uniform linear TMA with element
spacing dand working on transmitting state. Assume that the
antenna elements are isotropic and the array is considered to
transmit a sinusoidal wave of frequency fc. The far-field factor
of the TMA is shown as
AF(θ, t)=ej2πfct
N

n=1
AnejφnUn(t)ej(n−1)Kdsinθ(1)
where K=2π/λ is the wavenumber and λis the carrier
wavelength. θis the angle with respect to the normal direction
of the array. Anand φnare the static amplitude and phase
excitation of the nth element. And Un(t)is the periodical
function controlling the states of the nth high-speed RF switch,
which is given as
Un(t)=
∞

m=−∞
gn(t−mTpn)(2)
where Tpn represents the modulation period. In general, gn(t)
is a gate function written as
gn(t)=1,ton,n<t≤tof f,n
0,0<t≤ton,nor tof f,n<t≤Tpn
(3)
where t0n,nand t0ff,nrepresents the opening and closing
instants of the nth RF switch.
Decomposing Un(t)into Fourier series
Un(t)=
∞

k=−∞
αn,kej2πkFpnt(4)
where Fpn =1/Tpn is the modulation frequency in the nth
element. Let τn=(t0ff,n−ton,n)/Tpn represents the pulse
duration of the nth element normalized by modulation period
Tpn, the Fourier coefficients αn,kare given as
αn,k=1
Tpn tof f,n
ton,n
gn(t)e−j2πkFpntdt
=τnsinc(π kτn)e−jπkFpn (tof f,n+ton,n),k= 0
τn,k=0.(5)
Finally, the far-field array factor is given as
AF(θ, t)
=
∞

k=−∞
N

n=1
Anejφnαn.k·ej2π(fc+kFpn )tej(n−1)Kdsinθ.(6)
For simplicity, the static amplitude Anand phase φnare
selected as uniform in the following discussion.
B. Principle of Beam Scanning With Carrier Components
As shown in (5), the Fourier coefficient at the center
frequency carries no phase under the given gate function,
whereas the Fourier coefficients at the harmonic frequencies
carry equivalent phases related to harmonic orders and open-
ing/closing instants. Since the first harmonic frequency com-
ponent accounts for the largest share of the power compared
with other harmonic frequency components, it is convenient
and efficient to achieve beam scanning utilizing the additional
phase in the first harmonic frequency [16], which is given by
αn,1=βn
|αn,1|=ωn
(7)
where the ωnand βnrepresent the certain distribution of
amplitude and the equivalent phase.
However, the undesired harmonic frequencies radiation is
hard to suppress in the meanwhile. Additionally, (5) shows the
amplitude of the Fourier coefficient at the center frequency is
relatively larger when the pulse duration is long, which means
efficient methods can be applied to achieve beam scanning at
the carrier frequency.
In this article, several fixed delay lines with different phases
are applied to each channel to achieve beam scanning. The
typical structure of the TMA system is shown in Fig. 1. The
RF switches of each channel are connected with Mfixed delay
lines whose phase delays range from 0 to γM, stepping by
2π/M. Meanwhile, three selected delay lines out of the M
fixed delay lines are connected successively in one modulation
period to keep the switches in the “ON” states invariably, which
could avoid the power loss in the absorptive switches.
In order to obtain a dynamic excitation phase βn(γm≤
mod(βn,2π) < γm+1)inthenth element, the nth switch turns
to the mth delay line with phase γmwhen ton,n1≤t<ton,n2,
turns to the (m+1)th delay line with phase γm+1when
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NI et al.: LOW SR BEAM SCANNING AT CARRIER FREQUENCY FOR TMA 3697
Fig. 1. TMA structure for beam scanning.
Fig. 2. Amplitude and phase of gate function.
ton,n2≤t<ton,n3, turns to the (m+2)th delay line with
phase γm+2when ton,n3≤t<Tpn. Thus, the equivalent
modulation signal has both uniform amplitude and phase,
which is shown by Fig. 2.
Similarly, defining τn,i=(t0ff,ni −ton,ni )/ Tpn,i=1,2,3
as the ith pulse duration of the nth element normalized by
modulation period Tpn, and to keep the switches in ON states
invariably, τn,isatisfies
3

i=1
τn,i=1(8)
then, the modulation gate function can be arranged as
gn(t)=⎧
⎪
⎨
⎪
⎩
ejγm,0≤t<τ
n,1Tpn
ejγm+1,τ
n,1Tpn ≤t<(τ
n,1+τn,2)Tpn
ejγm+2,(τ
n,1+τn,2)Tpn ≤t<Tpn.
(9)
According to the (5), the Fourier coefficients αn,kis shown
as
αn,k=⎧
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎩
3

i=1
τn,iejγm+i−1,k=0
3

i=1
τn,isinc(π kτn,i)e−j2kπξni ejγm+i−1,k= 0
(10)
where ξni represents the ith pulse center of the nth element,
given by
⎧
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎩
ξn1=τn1
2
ξn2=2τn1+τn2
2
ξn3=τn1+τn2
2.
(11)
Fig. 3. Composition of the carrier frequency component.
Thus, the Fourier coefficients at the center frequency αn0
can be decomposed as the sum of three vectors in the complex
space shown in Fig. 3.
As can be seen form Fig. 3, the equivalent amplitude ωnand
phase βnof the nth element are the combination of τn1ejγm
and τn2ejγm+1mainly, and τn3ejγm+2contributed by the third
modulation delay line is used to avoid the power loss caused by
the absorptive switches. From the complex space, the general
solution of τn1,τn2,andτn3to satisfy the distribution of
amplitude ωnand phase βn(γm≤mod(βn,2π) < γm+1)
is described as
⎧
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎩
τn1=ωn(sinφ2−si nφ3)+sinγ1
2sinγ1−si nγ2
τn2=ωn(sinφ1+si nφ3)−sinγ2
2sinγ1−si nγ2
τn3=−ωn(sinφ1+si nφ2)+sinγ1
2sinγ1−si nγ2
(12)
where φ1,φ2,φ3are given as
⎧
⎪
⎨
⎪
⎩
φ1=mod(βn,2π) −γm
φ2=γm+1−mod(βn,2π)
φ3=γm+2−mod(βn,2π).
(13)
To satisfy τn1,τ
n1,τ
n1≥0 and any distribution of amplitude
ωn, only M=3 and 4 are applicable, which means that it
is feasible when the total number of the delay lines is 3 or
4. Thus, the beam scanning can be achieved when the three
chosen delay lines are connected successive in one modulation
period with the pulse durations computed by (11). Different
from the methods in [22] and [23], an extra delay line is
connected in each modulation period to keep the switches in
ON states constantly and ensure the maximum efficiency in
the feeding network.
C. Theory of SR Level Suppression
When utilizing the carrier component to realize the beam
scanning, the SR is considered harmful to the bandwidth of
the transmitted signals and should be suppressed with effective
methods.
Moreover, the array factor (1) indicates that the power of
the harmonic components in all elements can be accumulated
in space when the modulation frequency is uniform (Fp1=
Fp2= ··· = FpN =Fp), which means the high-level
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3698 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 68, NO. 5, MAY 2020
Fig. 4. Spectrum of the modulated signals with a three-element TMA.
(a) Uniform period modulation. (b) Non-uniform period modulation.
SR is produced in some directions. The maximum SR is
described as
(MAXSR)Uniform
=max
k∈Z,k=0
N

n=1
αn,kej2π(fc+kFp)tej(n−1)Kdsinθ.(14)
Unlike the evolutionary algorithms in [22] and [23], in this
article, the non-uniform time modulation is applied to the
beam scanning method referring to the works in [11]. Noticing
that the carrier component does not have modulation frequency
dependence, so the proper variations of modulation frequency
to connect the three delay lines do not affect the carrier
frequency component. Whereas, by exploiting the non-uniform
modulation frequency (Fp1= Fp2= ··· = FpN = Fp)to
all elements, the generated harmonic components will have
different harmonic frequencies. Then, the power of harmonic
components cannot accumulate in space, which leads to the
decline of SR level efficiently. The improved maximum SR is
arranged as
(MAX SR)Non−uniform
=max
n;k∈Z,k=0(|αn,kej2π( fc+kFp)tej(n−1)Kdsinθ|). (15)
To illustrate the point, an example of modulated signal based
on non-uniform and uniform period modulation is shown
in Fig. 4. After time modulation, the original sinusoidal signal
occurs on every harmonic frequency fc+kFpn.Andthe
harmonic components of each element under non-uniform
period modulation scatter over the frequency axis and cannot
accumulate together, while the harmonic components under
uniform period modulation converge on the frequency axis and
cause the relatively high SBLs. In the meantime, the carrier
frequency components of both methods keep the same with
no modulation frequency dependency.
In order to avoid the aliasing of the sidebands, the difference
of modulation frequency between any two elements should
be great enough. Besides, if the first few sidebands of any
two elements are not in the same frequency, it is reliable to
consider that the maximum SR comes from the first harmonic
frequency components. Hence, the maximum SR utilizing the
non-uniform modulation periods can be rearranged as (16).
And it is worth pointing that the last maximum SR comes
from the Fourier coefficients of a certain element
MAX SRNon−uni f orm
=max
n
3

i=1
τn,isinc(π kτn,i)e−j2kπξni ejγm+i−1.(16)
Although non-uniform period modulation can scatter the
harmonic components of different elements along the fre-
quency axis, certain harmonic components in one element may
have the same frequencies as certain harmonic components in
another element when the harmonic frequency is high enough.
However, the problem can be solved effectively if the common
multiples between any two modulation frequencies are much
larger than modulation frequencies. With the larger common
multiples, the accumulated harmonic components of certain
elements will have the higher frequencies and cannot become
the main contribution of SR.
III. NUMERIC RESULTS
In this section, the effectiveness of the proposed method is
evaluated, and the performance under different conditions are
analyzed through several numeric simulations.
Consider a 16-element uniform linear TMA systems with
the center frequency fc=2.6 GHz and λ/2 space between
elements. Assume that all antenna elements are isotropic. In all
the following simulations with non-uniform period modula-
tion, the non-uniform modulation frequencies are chosen as
linear growth, which is shown as
Fpn =[30 +0.5(n−1)]MHz,n=1,2,...,16.(17)
Therefore, the gate function controlling the states of the nth
RF switch is written as
gn(t)=⎧
⎪
⎨
⎪
⎩
ejγm,0≤t<τ
n,1/Fpn
ejγm+1,τ
n,1/Fpn ≤t<(τ
n,1+τn,2)/Fpn
ejγm+2,(τ
n,1+τn,2)/Fpn ≤t</Fpn .
(18)
The Dolphy–Chebyshev weights are used to weight the RF
elements in order to obtain the low SLL less than −30 dB at
the carrier frequency component.
To steer at the desired angle θ, the desired phase of each
element is calculated by
βn=−(n−1)Kdsin(θ). (19)
According to the desired phase βnof the nth element,
three delay lines γm,γm+1,andγm+2are selected by γm<
mod(βn,2π) < γm+1. Then, let the phase of Fourier coeffi-
cient αn0be equal to βnand calculating the pulse duration
τn1,τn2,andτn3based on (12) and (13).
A. Performance
In the first example, to analyze the maximum SR perfor-
mance with different total number of delay lines, consider two
TMA systems with the same structure. The elements of one
TMA system are connected with three different delay lines
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NI et al.: LOW SR BEAM SCANNING AT CARRIER FREQUENCY FOR TMA 3699
Fig. 5. Beam patterns of the carrier frequency component and the maximum
SR levels under non-uniform period modulation.
Fig. 6. Relationship between maximum SR level and scanning angle.
(0,2π/3and4π/3), while the another one has four different
delay lines (0,π/2,π, and 3π/2). Fig. 5 plots the beam
patterns of the carrier frequency component and the maximum
SR with three and four delay lines. The designed steering
angle is 25◦. And a low SLL less than −30 dB is achieved
at the carrier frequency component. In Fig. 5, when the total
number M equals to 3, the maximum SR is −16.36 dB, while
it drops to −21.12 dB when M equals to 4.
Furthermore, the variations of maximum SR levels when
the scanning angel changes are shown in Fig. 6. It is observed
that the structure with four delay lines has a relatively low SR
level as a whole. And the average SR levels of three and four
delay lines are −16.83 dB and −20.44 dB, respectively. Thus,
the simpler structure with three delay lines has the higher SBL,
and the SR level of another structure obtains a 4.76 dB decline
with an extra delay line. The corresponding time sequences of
different delay lines are shown in Figs. 7 and 8, respectively.
It can be seen that the three pulse durations keep all the
RFswitchesalwaysinON state, which will maximum the
efficiency of the feeding network. In order to get a lower SR
Fig. 7. The non-uniform time sequences of the three delay lines for beam
scanning at 25◦(M =3).
Fig. 8. Non-uniform time sequences of the four delay lines for beam scanning
at 25◦(M =4).
and compare it with the results in [22] and [23] easily, the total
number of delay lines is chosen as four to finish the rest of
the simulations.
For completeness, the 30 order harmonic components
of 16 elements (n =1,2,...,16; k =1,2,...,30) obtained
from the non-uniform period modulation are shown in Fig. 9,
which are calculated by
|αn,kej2π(fc+Fpn )tej(n−1)Kdsinθ|.(20)
As is shown in Fig. 9, each element radiates all order
harmonic components corresponding with the designed mod-
ulation frequency, and the maximum level of the first-order
harmonic components is 6.17 dB larger than the maximum
level of the second-order harmonic components. So, it is safe
to conclude that the maximum SR comes from the first-order
harmonic components.
To further illustrate the performance of this method,
Fig. 10 shows the variations of SR level versus the number of
elements. As can be seen, the maximum SR level decreases
significantly when the element scale increases.
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3700 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 68, NO. 5, MAY 2020
Fig. 9. Harmonic components of the 16 elements obtained from non-uniform
period modulation, where Eirepresents the element i, i =1,2,...,16.
Fig. 10. Maximum SR level versus the number of elements.
B. Comparison
As a comparison, consider the same TMA structure with
the uniform period modulation and four different delay lines.
And the uniform frequency in all the RF elements is 30 MHz.
Since the modulation frequency does not affect the carrier fre-
quency component, the beam patterns of the carrier frequency
component with uniform and non-uniform period modulation
will overlap together if the phases and weights distribution
keep the same. And the normalized pulse durations and time
sequences of the two methods are the same obviously to meet
the same distributions in the meanwhile.
Fig. 11 shows the simulated power spectrums under
non-uniform and uniform period modulation. The designed
steering angle is also 25◦. And a low SLL less than −30 dB
at the carrier frequency component is obtained. The corre-
sponding time sequences are the same as Fig. 8. As can be
seen, comparing with the results of uniform period modulation,
the harmonic components under non-uniform period modula-
tion scatter over the frequency axis with the corresponding
non-uniform modulation frequencies steps. And the power
of the maximum SR under non-uniform period modulation
is much lower than that uniform period modulation. And
Fig. 12 plots the beam patterns of the carrier frequency
Fig. 11. Simulated power spectrum under non-uniform and uniform period
modulation.
Fig. 12. Beam patterns of the carrier frequency component and the harmonic
components under uniform period modulation.
component and the harmonic components under uniform
period modulation. As can be seen, the SBL SBL1and
SBL2under the uniform period modulation are 0.072 and
−12.05 dB, respectively. Therefore, comparing to the results
under the non-uniform period modulation when M =4
in Fig. 5. The power of the maximum SR level decreases
by 21.192 dB after utilizing the non-uniform period modu-
lation. And it is worth noting that the maximum SR under
non-uniform period modulation comes from a single harmonic
component of a certain element.
To illustrate the performance of the beam scanning method
with non-uniform period modulation, the comparison of SLL
and Max SR level to the methods in [22] and [23] is provided
in Table I. In the comparison, all the methods use a 16-element
uniform linear TMA with λ/2 spacing between elements and
have four different delay lines to achieve beam scanning.
As can be seen clearly from Table I, under the same condi-
tions, the proposed method has preferable maximum SR level
when SLL is −30 dB, and the maximum SR level increases
slightly when SLL is −40 dB. Additionally, the methods
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NI et al.: LOW SR BEAM SCANNING AT CARRIER FREQUENCY FOR TMA 3701
Fig. 13. Simulated comparison of total efficiency.
Fig. 14. Constructed TMA for experiment in the outfield.
TAB L E I
PERFORMANCE COMPARISON TO EXISTING RESULTS
in [22] and [23] consume much computation resources to con-
verge to the optimal time sequences because of the evolution-
ary optimization algorithm, and the computation cost increases
significantly when the number of elements is large, while the
proposed method based on non-uniform period modulation
only need to configure different modulation frequencies to
each element and has a better result with a large number of
elements.
Furthermore, the TMA structure of the proposed method
only needs a pair of switches and one power divider or
combiner in each channel to achieve low SR beam scan-
ning without ON times and static attenuators, while the
method in [23] needs two pair of switches and paired power
dividers or combiners in each channel when applied to the
actual application. Besides, when the link losses are not
considered, the efficiency comparison results in all scanning
angles between the proposed method and the method in [23]
Fig. 15. Insertion loss and relative phase of four delay lines and the two
SP4T switches in channel 1. (a) Insertion loss. (b) Relative phase.
are plot in Fig. 13. Both the carrier frequency components
are utilized to achieve a low SLL less than −30 dB with
Dolphy–Chebyshev weights. And the total efficiency of TMA
is given by η=ηf·Pf0/( Pf0+PSR),where Pf0is the power
of carrier frequency component and PSR is the total power
of SR. And ηfrepresents the ideal efficiency in the feeding
network. ηfsatisfies ηf=1 since the switches in both the
methods are always in ON states. It can found that both the
total efficiency are about 25%, and the proposed method have a
high efficiency in certain angle such as 0◦and 30◦. The mean
efficiencies of the proposed method and method in [23] are
28.48% and 27.22%, respectively. Therefore, the simplification
of the structure did not result in a decrease in efficiency.
IV. EXPERIMENTAL RESULTS
To verify the performance of the proposed method, a group
of experiments finished in the outfield have been conducted
in this section. A uniformly excited 8-element TMA with
four delay lines of different phases (0,π/2,π, and 3π/2) are
implemented. And to measure the patterns, the TMA works
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3702 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 68, NO. 5, MAY 2020
Fig. 16. Non-uniform and uniform time sequences of the four delay lines
for beam scanning at −25◦.
on the receiving state. Both uniform and non-uniform period
modulation methods are designed to achieve the uniform
amplitude distribution at the carrier frequency component.
Fig. 14 shows the constructed TMA for the experi-
ments. The TMA received the sinusoidal wave from far-field.
Then, the received signals are periodically modulated by the
high-speed RF switches and delay lines in amplitude and
phase. After that, the modulated signals are combined together
by an 8-way power combiner and input to the Agilent E4447 A
spectrum analyzer. Meanwhile, to measure the power patterns
automatically, the TMA is fastened to tunable controlled by
programs. The center frequency fcof TMA is designed to be
at 1.16 GHz and the element spacing is half of the wavelength.
In the uniform period modulation, the modulation frequencies
are 0.1/64 MHz, while in the non-uniform period modulation,
the modulation frequencies are [0.1, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3,
1.4]/64 MHz, respectively.
In the experiment, two SP4T switches ADG904BRUZ [24]
from Analog Devices controlled by a Cyclone IV FPGA
EP4CE10F17 are exploited to select the four phase states and
integrated with delay lines on the PCB board. The typical
parameters under our experiment environment such as inser-
tion loss, return loss (on channel), return loss (off channel),
rise time, and fall time are −1.3 dB, −28.1 dB, −20.8 dB,
3 ns, and 7.5 ns, respectively. And since the minimum
modulation period is 45.7 μs(1.4/64 MHz), the switching
time is much less than the modulation period and can be
neglected. As for the delay lines, we plot snake-shaped lines
to implement the wanted phase shifts. The lengths and widths
of snake-shaped lines are calculated by the software TXline2.
Since the two SP4T switches are integrated with the four delay
lines, we measured the phase versus frequency curves and
amplitude unbalance as a whole. The total insertion loss and
the relative phase of four delay lines and switches in channel
1 are shown in Fig. 15. The relative phase and insertion loss
in other channel at 1.16 GHz is given in Table II. It can be
seen that the amplitude imbalance and relative phase error are
no more than 2.47 dB and 5.3◦.
Fig. 17. Measured power spectrum. (a) Non-uniform period modulation.
(b) Uniform period modulation.
TAB L E I I
INSERTION LOSS AND RELATIVE PHASE OF FOUR DELAY LINES
AND TWO SP4T SWITCHES IN ALL CHANNEL AT 1.16 GH
z
Fig. 17(a) and (b) plots the normalized power spectrums
of non-uniform and uniform period modulation, respectively.
The corresponding time sequences are plotted in Fig. 16.
The designed steering angle is −25◦. As can be seen from
Fig. 17(a), the harmonic components only contributed by
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NI et al.: LOW SR BEAM SCANNING AT CARRIER FREQUENCY FOR TMA 3703
Fig. 18. Measured power patterns of the uniform and non-uniform period
modulation. (a) Carrier frequency components. (b) Maximum SR components.
element 1 with modulation frequency 0.1/64 MHz are marked
in red, which satisfy the distribution of sinc(.) given in (5).
And as shown in the red envelope curve, the power of high
order harmonics in element 1 is lower than the power of
low order harmonics in other elements. So, the 8th to 14th
order harmonics marked in blue mainly come from the first-
order harmonics of element 2–8 individually, and the har-
monics marked in green mainly come from the second-order
harmonics of element 2–8 individually. Therefore, the mea-
sured result demonstrates that the harmonic components under
non-uniform period modulation scatter over the frequency axis.
Besides, compared with the power spectrum of uniform period
modulation in Fig. 17(b), the power spectrum of non-uniform
period modulation has a relatively lower SR level.
Furthermore, the normalized power patterns of the carrier
frequency components and maximum SR components are
plotted in Fig. 18 for comparison. As can be seen in Fig. 18(a),
the carrier frequency components of the two kinds of method
both point to −25◦and have similar performance. And due
to the reflection and multipath in the outfield, there are dif-
ferences between simulation results and experimental results.
In Fig. 18(b), the maximum SR component of uniform period
modulation is synthesized by the +1st harmonic compo-
nent in all elements, while the maximum SR component of
non-uniform period modulation is generated by the +1st har-
monic component in a single element. It can be seen that the
maximum SR levels of uniform and non-uniform period mod-
ulation are −11.98 and −21.33 dB, respectively. Therefore,
utilizing the proposed method based on non-uniform period
modulation, the maximum SR level decreases by 9.35 dB
compared with using the uniform period modulation. The
results verified the effectiveness of the proposed method to
suppress the SBLs significantly.
V. C ONCLUSION
In this article, a novel beam scanning method utilizing
the carrier frequency component for the TMA is proposed
and the non-uniform period modulation is implemented to
suppress the maximum SR level generated in the harmonic
frequencies. Configuring three or four delay lines with dif-
ferent phases in each channel and connecting three of them
successively in each modulation period, the beam scanning at
the carrier frequency is achieved. And the always ON states
in each RF switch can ensure the maximum efficiency in the
feeding network. Moreover, the maximum SR level decreases
remarkably when exploiting the non-uniform period modula-
tion method. Compared with the existing approaches achieving
beam scanning at the carrier frequency, the proposed technique
has a simpler structure. Besides, no complicated optimization
computation is needed to obtain the time sequences when
achieving the similar maximum SR level, which means the
proposed method is more efficient and practical in actual appli-
cation. The simulation and experiment results demonstrate the
effectiveness of the proposed method both in beam scanning
and the decrease of the maximum SR level.
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Gang Ni received the B.S. degree in electronic
information engineering from Beihang University,
Beijing, China, in 2018. He is currently pursuing the
Ph.D. degree with Shanghai Jiao Tong University,
Shanghai, China.
His research interests include DOA estimation,
digital beamforming, and wireless communication.
Chong He (Member, IEEE) received the B.Sc.
degree in electronic and information engineering and
the M.S. degree in electromagnetic and microwave
technology from the Huazhong University of Sci-
ence and Technology, Wuhan, China, in 2007 and
2009 respectively, and the Ph.D. degree in electro-
magnetic and microwave technology from Shanghai
Jiao Tong University, Shanghai, China, in 2015.
From 2016 to 2018, he was a Post-Doctoral
Researcher with the Department of Electronic Engi-
neering, Shanghai Jiao Tong University, where he
has been an Assistant Professor since 2019. His research interests include
phased arrays, DOA estimation, digital beamforming, and location and mul-
tiaddress wireless communication.
Jingfeng Chen received the B.S. degree in elec-
tronics and information engineering and the M.S.
degree in signal and information processing from
the Nanjing University of Information Science and
Technology, Nanjing, China, in 2009 and 2012,
respectively, and the Ph.D. degree in electromagnetic
and microwave technology from Shanghai Jiao Tong
University, Shanghai, China, in 2018.
Since 2019, he has been a Post-Doctoral
Researcher with the Department of Electronic Engi-
neering, Shanghai Jiao Tong University. His research
interests include antenna arrays, unconventional array design, DBF, and DOA
estimation.
Yiqing Liu received the B.S. degree in information
technology and engineering from Southeast Uni-
versity, Nanjing, China, in 2018. He is currently
pursuing the M.S. degree with Shanghai Jiao Tong
University, Shanghai, China.
His research interests include wireless communi-
cation, digital beam forming, and pattern synthesize.
Ronghong Jin (Fellow, IEEE) received the B.S.
degree in electronic engineering, the M.S. degree in
electromagnetic and microwave technology, and the
Ph.D. degree in communication and electronic sys-
tems from Shanghai Jiao Tong University (SJTU),
Shanghai, China, in 1983, 1986, and 1993, respec-
tively.
In 1986, he joined the Faculty of the Department
of Electronic Engineering, SJTU, where he has been
an Assistant, a Lecturer, an Associate Professor,
and is currently a Professor. From 1997 to 1999,
he was a Visiting Scholar with the Department of Electrical and Electronic
Engineering, Tokyo Institute of Technology, Meguro, Japan. From 2001 to
2002, he was a Special Invited Research Fellow with the Communication
Research Laboratory, Tokyo, Japan. From 2006 to 2009, he was a Guest
Professor with the University of Wollongong, Wollongong, NSW, Australia.
He is also a Distinguished Guest Scientist with the Commonwealth Scien-
tific and Industrial Research Organization, Sydney, NSW, Australia. He has
authored or coauthored over 300 articles in refereed journals and conference
proceedings and coauthored four books. He holds about 60 patents in antenna
and wireless technologies. His current research interests include antennas,
electromagnetic theory, numerical techniques of solving field problems, and
wireless communication.
Dr. Jin is a Committee Member of the Antenna Branch of the Chi-
nese 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 Technol-
ogy Progress Award.
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