Antenna Decoupling by Common and Differential Modes Cancellation

672 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL . 69, NO. 2, FEBRUARY 2021

Antenna Decoupling b y Common and Differential

Modes Cancellation

Libin Sun , Graduate Student Member, IEEE,YueLi , Senior Member, IEEE, Zhijun Zhang , Fellow, IEEE,

and Hanyang Wang, Senior Member, IEEE

Abstract— In this article, a general decoupling method based

on a new perspective of common mode (CM) and differential

mode (DM) cancellation is proposed. For two closely spaced

antennas, the mutual coupling effect can be analyzed and solved

by exciting them simultaneously with in-phase (CM) and out-of-

phase (DM) signals. It is theoretically proved that, if CM and

DM impedances are the same, the mutual coupling effect between

two separated antennas can be totally eliminated. Therefore,

we can solve the coupling problem by CM and DM impedance

analysis and exploit the unique ﬁeld properties of characteristic

modes to assist in antenna decoupling in a physical intuitive way.

To validate the feasibility of this method, two practical design

examples, including the decoupling between closely spaced dipole

antennas and planar inverted-F antennas, are proposed. Both

design examples have demonstrated that the proposed method

can provide a systemic design guideline for antenna decoupling

and achieve better decoupling performance compared to the

conventional decoupling techniques. We forecast the proposed

decoupling scheme, with a simpliﬁed decoupling procedure, has

great potential for the applications of antenna arrays and multi-

input multi-output (MIMO) systems.

Index Terms— Antenna decoupling, common mode (CM), dif-

ferential mode (DM), mode cancellation, multi-input multi-output

(MIMO), mutual coupling.

I. INTRODUCTION

UTUAL coupling effect between antenna elements

is an intrinsic issue of antenna array o r multi-input

multi-output (MIMO) antenna system, which will signiﬁcantly

degrade the antenna efﬁciency and affect the diversity per-

formance [1]–[4]. To tackle this issue, plenty of decoupling

methods and techniques have been investigated to eliminate

the mutual coupling effect in antenna arrays. Speciﬁcally,

orthogonal mode method employs the orthogonal nature of

physical quantities, such as polarizations [5]–[10], r adiation

patterns [11], [12], and phases [13], [14] to design decoupled

MIMO antennas with a natural high isolation. However, it is

hard to solve the coupling problem between closely spaced

antenna elements with the same physical property by the

Manuscript received January 2, 2020; revised June 6, 2020; accepted July 2,

2020. Date of publication July 21, 2020; date of current version February 3,

2021. This work was supported by the National Natural Science Foundation

of China under Contract 61971254 and Contract 61525104. (Corresponding

author: Zhijun Zhang.)

Libin Sun, Yue Li, and Zhijun Zhang are with the Beijing National

Research Center for Information Science and Technology (BNRist), Tsinghua

University, Beijing 100084, China (e-mail: [email protected].cn).

Hanyang Wang is with Huawei Technology Ltd., Berkshire RG2 6UF, U.K.

(e-mail: [email protected]).

Color versions of one or more of the ﬁgures in this article are available

online at https://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/TAP.2020.3009427

orthogonal mode method. Accordingly, a serious of decoupling

techniques are presented to suppress the mutual coupling

effect between nearby elements in antenna arrays. Electro-

magnetic band gap (EBG) [15]–[17] and detected ground

structures (DGS) [18]–[23], both possess band-stop response,

can suppress the surface-wave coupling effect between antenna

elements. Neutralization line (NL) [24 ]–[28] and parasitic

elements [29]–[37] can provide a new coupling path with equal

amplitude but o ut-of-p hase to achieve the co upling cancella-

tion. Recently, a novel decoupling metasurface [38]–[41] is

proposed to solve the mutual coupling problem in large-scale

antenna arrays by the out-of-phase cancellation of coupled

waves and reﬂected waves. However, in the above decoupling

techniques, the characteristic modes of antenna elements are

not effectively exploited to assist in antenna decoupling, which

will make the decoupling process really complicated and time-

consuming. The coupler technology [42]–[44] can provide a

route to realize common mode (CM) and differential mode

(DM) for two symmetrical antenna elements. However, the

coupler should be ﬁnely modiﬁed to address the impedance

mismatching issue caused by the strong mutual coupling

between antenna elements [43], [44]. Therefore, the complex

and bulky feed network and asymmetric radiation properties

limit the application scenarios of this technology.

In this article, we propose a simple and efﬁcient decou-

pling method based on a new perspective of CM and DM

cancellation [45]. In our method, decoupling between two

symmetrical antenna elements is theoretically equivalent to

the impedance matching of CM and DM. Then, the unique

ﬁeld properties of CM and DM can be exploited to assist in

comprehendin g the coupling issue and eliminating the mutual

coupling effect by adjusting CM and DM impedances inde-

pendently. When we obtain the same impedance status for CM

and DM, the coupling current in the passive antenna element

can be canceled out absolutely by the superposition of CM and

DM. To validate the feasibility of this method, two practical

design examples, including the mutual coupling reduction

between closely spaced electric-type antennas (dipoles) and

magnetic-type antennas [planar inverted-F antennas (PIFAs)],

are proposed. Both design examples have demonstrated that

the proposed methodology could offer a systemic design

guideline, simpliﬁed decoupling procedure, and satisfactory

decoupling performance.

This article is organized as follows. In Section II, the

decoupling methodology of CM and DM cancellation is pre-

sented. In Section III, the design example of dipole antennas

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SUN et al.: ANTENNA DECOUPLING BY CM AND DM CANCELLATION 673

Fig. 1. Decoupling conditions for an arbitrary dual-antenna system from two

different perspectives. (a) Single-ended model and corresponding decoupling

condition. (b) CM and DM models and corresponding decoupling condition.

decoupling is reported with de tailed design guideline, antenna

performance, and comparison. In Section IV, the design exam-

ple of PIFAs decoupling is reported with detailed design guide-

line, antenna performance, and comparison. Finally, Section V

draws a conclusion of th is article.

II. P

RINCIPLE OF CM AND DM CANCELLATION

A. S-Parameters Analysis

Shown in Fig. 1(a) is the sketch diagram of an arbitrary

two-port antenna system. As we all know, the aim of antenna

decoupling is to let S

= 0 from the perspective of single-

ended S-parameters. Alternatively, as shown in Fig. 1(b),

we can also regard the two-port antenna system as a whole

and analyze it from the perspective of mixed mode (CM and

DM) S-parameters. The CM and DM S-parameters are [46]

cc11

= (S

+ S

)/2(1)

dd11

= (S

− S

+ S

)/2. (2)

Speciﬁcally, a symmetrical and reciprocal 2-port n etwork

satisﬁes the conditions of S

= S

and S

= S

. Therefore,

the CM and DM S-parameters for a symmetrical and reciprocal

two-port antenna system can be simpliﬁed to

cc11

= S

+ S

(3)

dd11

= S

− S

. (4)

Combined with (3) and (4), we have

= S

= (S

cc11

− S

dd11

)/2(5)

= S

= (S

cc11

+ S

dd11

)/2. (6)

In terms o f (5), we can conclude that the decoupling equation

of S

= 0 can be equivalent to S

cc11

= S

dd11

when we

consider the decoupling issue from the perspective of CM/DM

system. That is, for an arbitrary symmetrical and reciprocal

two-port antenna system, if CM and DM S-parameters are

the same, the mutual coupling effect between two separated

antennas can be totally eliminated. This conclusion could offer

a new insight into antenna decoupling, which will be analyzed

in d etail in Sections III and IV.

Fig. 2. Relationships of current distributions. (a) Port1 is driven and port2 is

loaded with 50 . (b) Port2 is driv en and port1 is loaded with 50 .

B. Current Analysis

To have an intuitive view of the decoupling principle from

the perspective of the CM/DM system, the relationships of

current distributions are reported in Fig. 2. When port1 is

driven and port2 is loaded with 50 , Ant1 is excited with

current I

with a strong coupled current I

on Ant2. Due

to the orthogonal nature of CM and DM, the CM current

=[I

, I

]

and DM current i

=[I

, −I

]

could

be regarded as a set of basis current of the two-port antenna

system. Accordingly, the currents I

and I

can be expressed

as the linear addition of basis currents i

and i

as shown

in Fig. 2(a), and it can be deduced as

P 1





= I

+ I

= αi

+ β i

1 − S

cc11





1 − S

dd11



−I



(7)

where α and β are the complex excitation coefﬁcients of CM

and DM basis currents, respectively, which are related to the

S-parameters of CM and DM.

When port2 is driven and port1 is loaded with 50 ,Ant2is

excited with current I

with a strong coupled current I

Ant1. Symmetrically, as shown in Fig. 2(b), currents I

and

can be expressed as the linear subtraction of i

and i

and it can be deduced as

P 2





= I

− I

= αi

− β i

1 − S

cc11





−

1 − S

dd11



−I



. (8)

According to (7), Table I summarizes some typical states

with different values of CM and DM S-parameters. As seen,

if CM and DM have the same S-parameter, the coupling

current in the passive antenna element I

can be canceled out

absolutely with a perfect isolatio n, whereas the difference in

CM and DM S-parameters will lead to the incomplete current

cancellation. Therefore, the key to antenna decoupling is to

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674 IEEE TRANSACTIONS ON ANTE NNAS AND PROPAGATION, VOL. 69, NO. 2, FEBRUARY 2021

TABLE I

OME TYPI CAL STATES WHEN FED THROUGH PORT1

Fig. 3. Model of two closely spaced dipoles separated by a distance of 0.2

and the corresponding current distributions by CM and DM excitations.

keep CM and DM impedances in the same state for achieving

a perfect current cancellation in the passive element.

III. D

ESIGN EXAMPLE OF DIPOLE ANTENNAS

To demonstrate the feasibility and features of the pro-

posed CM and DM cancellation method, a design example

of decoupling between two closely spaced dipole antennas is

proposed in this section. As we all know, decoupling between

closely spaced dipole antennas is a classic problem. And

parasitic scatter [29], [30] is the well-known approach fo r

the dipole antennas decoupling, however, it suffers from a

narrow bandwidth. Here, based on the CM and DM cancel-

lation method, we propose a simple and efﬁcient structure to

decouple between closely spaced dipoles with an enhanced

bandwidth performance.

A. Design Guideline

Fig. 3 shows two λ/2 resonant dipole antennas separated by

a distance L

of 40 mm (0.2 λ

). To analyze the coupling prob-

lem from the perspective of CM and DM, the corresponding

current distributions with in-phase and out-of-phase excitations

are illustrated in Fig. 3. When fed with in-phase signals, com-

mon currents are driven on two dipoles and the center plane

can be equivalent to a virtual PMC plane. On the contrary,

when fed with out-of-phase signals, differential currents are

driven on two dipoles and the center plane can be equivalent

to a virtual PEC plane. As seen, the excited current strength of

DM is higher than CM, which leads to the incomplete current

Fig. 4. Evolution procedure of dipole decoupling and corresponding Smith

charts of CM and DM. Detailed dimensions: L

= 40 mm, L

= 96.5 mm,

Ls = 17 mm, and C = 0.25 pF. (a) Case1: closely spaced dipoles separated

by 0.2 λ

. (b) Case2: two horizontal strips are added in-between. (c) Case3

(proposed): a vertical strip and lumped capacitance are added between two

horizontal strips. (d) Smith charts of CM impedance. (e) Smith charts of DM

impedance.

cancellation in the passive element as analyzed in Section II-B.

Consequently, we should tune CM and DM impedances

to the same state for matching the current strengths of

CM and DM.

The evolution procedure of the dipole antenna decoupling

as well as the corresponding Smith charts of CM and DM

impedances in the evolution procedure are proposed in Fig. 4.

As shown in Fig. 4(d) and (e) (red line), in Case1, the CM

impedance is much higher than 50  while the DM impedance

is much lower than 50 . The impedance discrepancy between

CM and DM leads to the strong coupling between two

dipoles. Although many approaches can realize the impedance

tuning of CM and DM, the interaction b etween CM and

DM impedances makes the tuning process very complicated.

Accordingly, it is crucial to ﬁnd a way to adjust CM and

DM impedances independently. Fortunately, the unique ﬁeld

properties of CM and DM make the independent impedance

tuning possible, which can be summarized as the following

two steps.

Step1: Insert two symmetrical horizontal strips between

dipole antennas as shown in Fig. 4(b). Due to the center PMC

boundary condition for CM, the horizontal strips cannot excite

effective current in CM as shown in Fig. 5(a). On the contrary,

as shown in Fig. 5(b), the center PEC boundary condition for

DM can support a strong current distribution in the horizontal

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SUN et al.: ANTENNA DECOUPLING BY CM AND DM CANCELLATION 675

Fig. 5. Simulated current distributions in (a) Case2 with CM excitation, (b)

Case2 with DM excitation, (c) Case3 with CM excitation, and (d) Case3 with

DM excitation.

Fig. 6. Smith charts of (a) CM and (b) DM impedances with the variation

of inserted capacitance C.

strips for DM. Consequently, the horizontal strips can adjust

DM impedance independently while CM impedance keeps

unchanged as shown in Fig. 4(d) and ( e) (blue line). Speciﬁ-

cally, Ls is a key parameter for DM impedance matching and a

good DM impedance matching is achieved when Ls = 17 mm.

Step2: I nsert a vertical strip and a lumped capacitance

between two horizontal strips as shown in Fig. 4(c). For

CM, the center PMC boundary condition can support a strong

current distribution in the vertical strip, as shown in Fig. 5(c).

On the contrary, as shown in Fig. 5(d), the center PEC

boundary condition for DM cannot support effective current

in the vertical strip. Therefore, the vertical strip can adjust

CM impedance independently while DM impedance keeps

unchanged as shown in Fig. 4(d) and (e) (green line). However,

the vertical strip cannot make a sufﬁcient impact on the

CM impedance, hence a lumped capacitance is inserted in-

between for further adjustment. Fig. 6 shows the inﬂuence

of the inserted capacitance on CM and DM impedances. As

shown in Fig. 6(a), the CM impedance can hardly match

to 50  when without the capacitance. With the variation

of capacitance, the CM impedance is sharply altered and it

achieves an optimized matching status when C = 0.25 pF.

On the contrary, the DM impedance is not affected by the

capacitance C, as shown in Fig. 6(b), due to the center virtual

PEC boundary.

B. Decoupling Performance

After the above two steps, both CM and DM impedances

are in the same matching status. Accordingly, the mutual

Fig. 7. Simulated (a) S

and (b) S

in Case1, Case2, and Case3.

Fig. 8. Simulated current distributions (a) without and (b) with the decoupling

structure when fed through port1.

Fig. 9. Simulated radiation pattern of the proposed decoupled dipole antennas

at 1.5 GHz when fed through port1. (a) E-plane. (b) H-plane.

coupling between port1 and port2 can be canceled out accord-

ing to (5). The single-ended S-parameter in the evolution

procedure is shown in Fig. 7. As seen, the original isolation

between two dipole antennas is only 7.5 dB. After inserting

the proposed decoupling structure, the isolation is obviously

improved to better than 40 dB at 1.5 GHz as well as a

satisfactory decoupling bandwidth. Meanwhile, S

bandwidth

almost keeps unchanged with the insertion of the proposed

decoup ling structure.

To physically demonstrate the decoupling performance,

the current distributions without and with the decoupling

structure is proposed in Fig. 8. If without the decoupling

structure, two dipoles are strongly coupled due to the radiated

wave effect. After inserting the proposed decoupling structure,

the coupled current in port2 is totally canceled out owing to

the complete cancellation of CM and DM currents.

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676 IEEE TRANSACTIONS ON ANTE NNAS AND PROPAGATION, VOL. 69, NO. 2, FEBRUARY 2021

TABLE II

OMPARIS ON OF THE DECOUP LING PERF ORMANCE BETWEEN CLOSELY

SPACED DIPOLE ANTENNAS

The radiation p attern of the proposed decoupled dipole

antennas when fed through port1 is presented in Fig. 9 .

As seen, an “8”-shaped copolarized radiation pattern is formed

with a cross-polarization level of −14 dB in E-plane. The

omnidirectional radiation in H-plane is slightly affected due

to th e inﬂuence of inserted strips and passive element, which

leads to a gain variation of 4.7 dBi in H-plane.

To highlight the merits of our decoupling scheme,

the decoupling performance of closely spaced dipole antennas

is compared in Table II. In addition, the proposed decoupling

scheme is also suitable when the element distance is smaller,

such as 0.1 λ and 0.075 λ, the optimized results of which

are also included in Table II. As seen, our decoupling scheme

possesses much better bandwidth performance than the con-

ventional decoupling technique [29], [30]. Moreover, in our

scheme, the unique ﬁeld properties of characteristic modes are

effectively analyzed and exploited to assist in designing the

decoupling structure instead of performing complex network

analysis.

IV. D

ESIGN EXAMPLE OF PIFA ANTENNAS

The decoupling performance of closely spaced electric-

type antennas (dipoles) is demonstrated in Section III.

In this section, the d ecoupling performance of closely spaced

magnetic-type antennas (PIFAs) is proposed to validate the

universality of the proposed CM and DM cancellation method.

A. Design Guideline

Fig. 10(a) shows two strongly coupled PIFAs with a side-

by-side distance of d = 2 mm (0.01 λ

).ThePIFAsare

modeled in the air medium with a proﬁle of 8 mm (0.04 λ

The two PIFAs are directly fed b y metal probes at port1 and

port2, respectively. The E-ﬁeld distributions of CM and DM

are illustrated in Fig. 10(b) and (c), respectively. With the in-

phase excitation, the common E-ﬁeld distribution is excited

in two PIFAs, which enables y-direction equivalent magnetic

currents. On the contrary, with the out-of-phase excitation,

a differential E-ﬁeld is excited in two PIFAs, which cancels the

y-direction equivalent magnetic currents. However, th e center

and fringe radiation apertures can be effectively excited, which

enables an x -direction equivalent magnetic currents as shown

in Fig. 10(c). Therefore, CM radiates an x-polarized ﬁeld

while DM radiates a y-polarized ﬁeld.

Fig. 10. (a) Model of two extremely closely spaced PIFAs with a side-by-

side distance d = 0.01 λ

. (b) Vector E-ﬁeld distribution of CM with in-phase

excitation. (c) Vector E-ﬁeld distribution of DM with out-of-phase excitation.

For the PIFA structure, there are many parameters to tune

the CM and DM impedance matching and bandwidth. For

CM, the impedance matching and bandwidth can be tuned

by the size of the ground plane, i.e., W

and L

[47]. For

DM, the impedance matching and bandwidth of the center slot

depend on the width of slot, i.e., d and the width of PIFA, i.e.,

, while that of the fringe radiated magnetic currents depend

on the size of the ground plane, i.e., W

and L

. To quantify the

inﬂuence, the simulated CM and DM impedance bandwidth

with the variation of d, W

,andL

is demonstrated

in Fig. 11. As shown in Fig. 11(a), with the increasing of

the center slot width d , the radiation capacity of DM can be

signiﬁcantly enhanced with an increased impedance bandwidth

while the bandwidth of CM almost keeps unchanged. As

shown in Fig. 11(b), with the increasing of the width of PIFA

, the bandwidth of DM can also be signiﬁcantly enhanced

due to the radiation enhancem ent of the center slot while the

bandwidth of CM almost keeps unchanged. As shown in Fig.

11(c), the bandwidth of DM is enhanced with the shrunk

of the width of the ground plane W

because the radiation

capacity of the fringe magnetic currents can be enhanced with

a weakened surface-wave effect on a small ground plane. Also,

the bandwidth of CM almost keeps unchanged with the shrunk

of W

. As shown in Fig. 11(d), with the shrunk of the length

of the ground plane L

, the bandwidth of CM is decreased

while that of DM is enhanced, thus it is an effective degree

of freedom to match the bandwidth of CM and DM.

Based on the above analysis, in addition to the intrinsic

parameters and the element distance of PIFAs, the size of the

ground plane is also a signiﬁcant factor to match CM and DM

impedances, hence we can tune CM and DM impedances to

the same state with a self-decoupled performance by simply

adjusting the size of the ground plane. As illustrated in Fig. 12,

there are also two steps to fulﬁll coupling reduction for the

strongly coupled PIFAs.

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SUN et al.: ANTENNA DECOUPLING BY CM AND DM CANCELLATION 677

Fig. 11. Simulated CM and DM impedance bandwidth with the variation of

(a) side-by-side distance d, (b) width of PIFA W

, (c) width of the ground

plane W

, and (d) length of the ground plane L

Fig. 12. Evolution procedure of the PIFA decoupling. Only the dimension

of the ground plane is altered in the decoupling process. Detailed dimensions:

= 43 mm, W

= 28 mm, d = 2 mm, L

= 8 mm, and H

= 8 mm.

Step 1: Reduce the length L

of the ground plane as shown

in Case2 of Fig. 12. With the shrunk of L

, the CM impedance

can be adjusted independently and tuned to a matched status

while the DM impedance almost remains unchanged, as shown

in Fig. 13 (blue line).

Step 2: Reduce the width W

of the ground plane as

shown in Case3 of Fig. 12. With the shrunk of W

,theDM

impedance can be adjusted independently and tuned to a

matched status while the CM impedance remains unchanged,

as shown in Fig. 13 (green line).

B. Decoupling Performance

With the same impedance status for CM and DM, the strong

coupling between two closely spaced PIFAs can be can-

celed out according to (5). The single-ended S-parameters in

the evolution procedur e are presented in Fig. 14. As seen,

the original isolation between two PIFAs is only 7.5 dB when

the ground plane dimension is 120 × 120 mm

.However,

Fig. 13. Smith chart of (a) CM and (b) DM impedances.

Fig. 14. Simulated (a) S

and (b) S

in the evolution process.

Fig. 15. Simulated isolation at 1.5 GHz with the v ariation of (a) length of

the ground plane L

(when W

= 80 mm) and (b) width of the ground plane

(when L

= 65 mm).

the mutual coupling can be absolutely eliminated and the

isolation b etween two PIFAs can be improved to better than

22.2 dB if the ground plane is shrunk to 65 × 80 mm

without adding any extra decoupling structure. Meanwhile,

the matched bandwidth is also enhanced to 1.46∼1.52 GHz

with the reduction of the ground plane dimension. That is,

a n ovel self-decoupling phenomenon is realized between two

extremely closely spaced PIFAs by simply modifying the size

of the ground plane.

To further demonstrate the effect of the ground plane size

on the element isolation, the simulated isolation at 1.5 GHz

with the variation of L

and W

is proposed in Fig. 15. As

shown in Fig. 15(a), the isolation at 1.5 GHz has an optimal

value of 51.5 dB when L

= 62.5 mm. The isolation will

be deteriorated with a smaller or larger length L

of the

ground plane. Note that the ﬁnal d imension of L

is chosen to

65 mm to balan ce the radiation pattern and manufactur ability.

As shown in Fig. 15(b), the isolation at 1.5 GHz also has an

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678 IEEE TRANSACTIONS ON ANTE NNAS AND PROPAGATION, VOL. 69, NO. 2, FEBRUARY 2021

Fig. 16. Vector E-ﬁeld distributions for the decoupled PIFAs with (a) CM

excitation, (b) DM excitation, (c) port1 excitation, and (d) port2 excitation.

Fig. 17. Photograph of the self-decoupled PIFAs.

optimal value of 38.4 dB when W

= 77.5 mm. Note that the

ﬁnal result of W

is chosen to 80 mm to balance the radiation

pattern and manufacturability.

The vector E-ﬁeld distributions for the proposed decoupled

PIFAs are illustrated in Fig. 16. Fig. 16(a) and (b) shows

the CM and DM E-ﬁelds with in-phase and out-of-phase

excitations, respectively. Although the E-ﬁeld distributions

in Fig. 16(a) and (b) are similar to those in Fig. 10(b) and (c),

however, the E-ﬁeld strengths of CM and DM are changed to

the same with each other. As early analyzed in Section II-B

and Fig. 2, the single-ended ﬁeld distribution can be regarded

as the superposition of CM a nd DM ﬁelds. When CM and

DM E-ﬁelds possess equal strength, the E-ﬁeldinthepassive

PIFA can be completely canceled out as shown in Fig. 16(c)

and (d).

C. Measured Results

To demonstrate the performance of the proposed self-

decoupling PIFAs, a prototype was fabricated as shown

in Fig. 17. The prototype is manufactured by 0.3 mm thick

brass (σ = 1.5×10

S/m) plates with the laser cutting process.

Two copper pillars are soldered with the PIFAs as the f eeding

Fig. 18. Simulated and measured S-parameters of the self-decoupled PIFAs.

Fig. 19. Simulated and measured normalized radiation pattern of the self-

decoupled PIFAs at 1.5 GHz when fed through port1. (a) E-plane. (b) H-plane.

probes. And two 50  SMA connectors are employed beneath

the ground plane for antenna test.

The measured S-parameter is plotted in Fig. 18, showing

a good agreement with the simulated results. Both simulated

and measured results demonstrate a −10 dB S

bandwidth of

1.46–1.52 GHz (4.0%). Across the matched bandwidth, a high

measured isolation of better than 20.0 dB is realized.

The simulated and measured E-plane and H-plane normal-

ized radiation patterns when fed through port1 are presented

in Fig. 19(a) and (b), respectively. The rad iation pattern fed

through port2 is symmetrical to that of port1, which is not

shown for brevity. As seen, a directional radiation pattern with

a low cross-polarization in the broadside direction is realized

in both planes. However, the backward radiation is increased

because of the reduction o f the ground plane.

The simulated and measured total efﬁciency is shown in Fig.

20. Across the desired band, the simulated efﬁciency is

84.0%−99.9%, while the measured one is 86.4%−95.9%. The

ultralow loss of air medium and the good impedance matching

and isolation performance contributes to the proposed high

antenna efﬁciency.

To evaluate the diversity performance of the proposed

self-decoupled PIFAs, the simulated and measured envelope

correlation coefﬁcients (ECCs) are presented in Fig . 20. The

ECCs are deduced by the simulated and measured far E-ﬁelds

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SUN et al.: ANTENNA DECOUPLING BY CM AND DM CANCELLATION 679

Fig. 20. Simulated and measured total efﬁciency and ECC of the self-

decoupled PIFAs.

Fig. 21. Simulated (a) CM and (b) DM impedances with the variation of

under a large ground plane (120 × 120 mm

based on the formulation [48]

≈|ρ



‚

(θ, ϕ) sin θdθdϕ

‚

(θ, ϕ) sin θdθdϕ ·

‚

(θ, ϕ) sin θdθ dϕ



(9)

where

= E

θ,i

(θ, ϕ) · E

∗

θ,j

(θ, ϕ) + E

ϕ,i

(θ, ϕ) · E

∗

ϕ,j

(θ, ϕ). (10)

Here, E

θ,i

and E

ϕ,i

are the complex electric ﬁeld of port i

in the elevation and azimuth planes, respectively. As shown

in Fig. 20, both simulated and measured results demonstrate

a good diversity performance for the proposed self-decoupled

PIFAs with ECCs < 0.02 across the desired band.

D. Other Decoupling Scheme

It should be noted that the proposed self-decoupling design

scheme with a modiﬁed ground plane size is not suitable for

the application when the size of the ground plane is strictly

ﬁxed, such as mobile phone antennas. Therefore, to ﬁt different

application scenarios, other parameter to tune CM and DM

impedances, within a ﬁxed ground plane of 120 × 120 mm

is also proposed. As analyzed in Section IV-A, the width W

PIFA shows a signiﬁcant impact on the impedance bandwidth

Fig. 22. Simulated S-parameters with an increased W

for self-decoupling

under a large ground plane. Detailed dimensions: L

= 120 mm, W

120 mm, L

= 43 mm, W

= 52 mm, d = 2 mm, L

= 13 mm, H

= 8 mm.

TABLE III

OMPARIS ON OF THE DECOUP LING PERF ORMANCE BETWEEN CLOSELY

SPACED PIFAS

of DM. Fig. 21 shows the simulated CM and DM impedances

with the variation of W

under a ground plane of 120 ×

120 mm

. As seen, with the increasing of W

, both of the CM

and DM impedances shift upward to the inductive region, but

the variation of DM impedance is severer than CM impedance.

Thus, the discrepancy between CM and DM impedances can

be reduced by increasing W

.WhenW

is increased to 52 mm,

the simulated S-parameters are presented in Fig. 22 (note

that the feed position is optimized to L

= 13 mm for a

good impedance matching). As seen, a good self-decoupling

performance with an isolation better than 16.3 dB and an

operating bandwidth of 5.0% is also realized.

E. Comparison

To highlight the advantages o f the proposed PIFA decou-

pling scheme, it is compared to the conventional decoupling

techniques for closely spaced PIFAs as listed in Table III.

The conventional decoupling techniques for closely spaced

PIFAs are DGS [21], [22] and NLs [25], [26]. The DGS

technique can achieve acceptable decoupling performance for

closely spaced PIFAs; however, the radiation pattern will be

affected by the resonant slot on the ground plane with a

strong backward leakage. The NL technique can realize a

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680 IEEE TRANSACTIONS ON ANTE NNAS AND PROPAGATION, VOL. 69, NO. 2, FEBRUARY 2021

good isolation performance when two PIFAs are separated by

some distance, but the decoupling performance is signiﬁcantly

degraded when the interdistance of two PIFAs is reduced to

0.03 λ

[26]. Consequently, compared to the above-mentioned

PIFA decoupling techniques, our proposed decoupling scheme

possesses the merits of self-decoupling (without extra decou-

pling structure), extremely closely spaced element distance

(0.01 λ

), moderate bandwidth, and good isolation perfor-

mance, which is a potential candidate for MIMO applications.

V. C

ONCLUSION

This article proposes a simple and efﬁcient decoupling

method based on a new perspective of CM and DM can-

cellation. In our method, the complex decoupling problem

can be transformed to the CM and DM impedance matching,

which provides a simpliﬁed perspective on antenna decou-

pling. Moreover, with the help of unique orthogonal ﬁeld

properties of CM and DM, the CM and DM impedances can be

adjusted independently to avoid the complex iteration process.

Two classic design examples, including the decoupling

between closely spaced dipoles and PIFAs, are proposed to

demonstrate the novelty of this method. For d ipole antennas,

by inserting two horizontal strips for DM impedance matching

and a capacitance-loaded vertical strip for CM impedance

matching, th e strong mutual coupling b etween two dipoles

can be suppressed with a superb bandwidth performance.

For PIFAs, by adjusting the size of the ground plane or the

width of PIFAs, the strong mutual coupling between two

extremely closely spaced PIFAs can be self-decoupled without

using any extra decoupling structure. Both design examples

have veriﬁed that the proposed decoupling method possesses

systemic design guideline, simpliﬁed decoupling procedure,

and satisfactory decoupling performance. We further envision

that this decoupling methodology could be applied in various

antenna types to solve the intricate coupling problem in a

systemic and intuitive way.

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Libin Sun (Graduate Student Member, IEEE)

received the B.S. degree from Xidian Univ e rsity,

Xi’an, China, in 2016. He is currently pursuing the

Ph.D. degree with the Department of Electrical and

Engineering, Tsinghua University, Beijing, China.

He has authored ove r ten journal papers, and holds

ﬁve granted Chinese patents. His current research

interest includes antenna design and theory, partic-

ularly in 5G mobile phone antennas, multi-input

multi-output (MIMO) and diversity antennas, circu-

larly polarized antennas, leaky-wave antennas, and

surface-wave antennas.

Mr. Sun was a recipient of the Outstanding Reviewer for the IEEE T

RANS-

ACTIONS ON ANTENNAS AND PROPAGATION in 2019 and the Honorable

Mention in the 2020 IEEE AP-S Student Paper Competition. He serves as

a Reviewer for se veral international academic journals, such as the IEEE

RANSACTIONS ON ANTENNAS AND PROPAGATI ON, the IEEE ANTEN-

NAS AND WIRELESS PROPAGATI ON LETTERS, IEEE A CCES S,theIET

Microwaves, Antennas & Propa gation,theIET Electr onics Letters,and

Microwave and Optical Technology Letters.

Yue Li (Senior Member, IEEE) received the B.S.

degree in telecommunication engineering from Zhe-

jiang University, Zhejiang, China, in 2007, and

the Ph.D. degree in electronic engineering from

Tsinghua University, Beijing, China, in 2012.

In June 2012, he was a Post-Doctoral Fellow

with the Department of Electronic Engineering,

Tsinghua University. In December 2013, he was a

Research Scholar with the Department of Electrical

and Systems Engineering, Uni versity of Pennsylva-

nia, Philadelphia, PA, USA. He was also a Visiting

Scholar with the Institute for Infocomm Research (I2R), A∗STAR, Singapore,

in 2010, and the Hawaii Center of Adv anced Communication (HCAC),

Uni versity of Hawaii at Manoa, Honolulu, HI, USA, in 2012. Since January

2016, he has been with Tsinghua University, where he is currently an Assistant

Professor. He is currently an Associate Professor with the Department of

Electronic Engineering, Tsinghua University. He has authored or coauthored

ove r 130 journal papers and 45 international conference papers, and holds

18 granted Chinese patents. His current research interests include metamateri-

als, plasmonics, electromagnetics, nanocircuits, mobile and handset antennas,

multi-input multi-output (MIMO) and di versity antennas, and millimeter-wave

antennas and arrays.

Dr. Li was a recipient of the Issac Koga Gold Medal from the URSI

General Assembly in 2017; the Second Prize of the Science and Technology

Award of the China Institute of Communications in 2017; the Young Scientist

Awards from the conferences of ACES 2018, AT-RASC 2018, AP-RASC

2016, EMTS 2016, and URSI GASS 2014; the Best Paper Awards from the

conferences of CSQRWC 2018, NCMMW 2018 and 2017, APCAP 2017,

NCANT 2017, ISAPE 2016, and ICMMT 2016; the Outstanding Doctoral

Dissertation of Beijing Municipality in 2013; and the Principal Scholarship of

Tsinghua Univ ersity in 2011. He is serving as an Associate Editor for the IEEE

RANSACTIONS ON ANTENNAS AND PROPAGATION, the IEEE ANTENNAS

AND WIRELESS PROPAGATION LETTERS,andComputer Applications in

Engineering Education, and also on the Editorial Board of Scientiﬁc Reports.

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682 IEEE TRANSACTIONS ON ANTE NNAS AND PROPAGATION, VOL. 69, NO. 2, FEBRUARY 2021

Zhijun Zhang (Fellow, IEEE) received the B.S.

and M.S. degrees from the Uni versity of Electronic

Science and T echnology of China, Chengdu, China,

in 1992 and 1995, respectively, and the Ph.D. degree

from Tsinghua University, Beijing, China, in 1999.

In 1999, he was a Post-Doctoral Fellow with the

Department of Electrical Engineering, The Univer-

sity of Utah, Salt Lake City, UT, USA, where he was

appointed a Research Assistant Professor in 2001.

In May 2002, he was an Assistant Researcher with

the University of Hawaii at Manoa, Honolulu, HI,

USA. In November 2002, he joined Amphenol T&M Antennas, Vernon Hills,

IL, USA, as a Senior Staff Antenna Dev e lopment Engineer, and was then

promoted to the position of an Antenna Engineer Manager. In 2004, he joined

Nokia Inc., San Diego, CA, as a Senior Antenna Design Engineer. In 2006, he

joined Apple Inc., Cupertino, CA, USA, as a Senior Antenna Design Engineer

and was then promoted to the position of a Principal Antenna Engineer. Since

August 2007, he has been with Tsinghua Uni versity, where he is currently a

Professor with the Department of Electronic Engineering. He is the Author of

the book Antenna Design for Mobile Devices (W iley, First Edition in 2011 and

Second Edition in 2017).

Dr. Zhang served as an Associate Editor for the IEEE T

RANSACTIONS ON

ANTENNAS AND PROPAGATION from 2010 to 2014 and the IEEE ANTENNAS

AND

WI RELESS PROPAGATION LETTERS from 2009 to 2015.

Hanyang Wang (Senior Member, IEEE) received

the Ph.D. degree from Heriot-Watt University, Edin-

burgh, U.K., in 1995.

From 1986 to 1991, he served as a Lecturer and

an Associate Professor with Shandong Uni versity,

Jinan, China. From 1995 to 1999, he was a Post-

Doctoral Research Fellow with the University of

Birmingham, Birmingham, U.K., and the Unive rsity

of Essex, Colchester, U.K. From 1999 to 2000, he

was with Vector Fields Ltd., Oxford, U.K., as a

Software Development and Microwave and Antenna

Engineering Consultant Engineer. He joined Nokia U.K. Ltd., Farnborough,

U.K., in 2001, where he had been a Mobile Antenna Specialist for 11 years.

He joined Huawei Technology Ltd., Berkshire, U.K., after leaving Nokia,

where he is currently the Chief Mobile Antenna Expert and the Head of the

Mobile Antenna Technology Di vision. He is also an Adjunct Professor with

Nanjing University, Nanjing, China, and Sichuan University, Chengdu, China.

He holds over 40 granted U.S./European/Japan/Chinese patents. His current

research interests include small, wideband and multiband antennas for mobile

terminals, antennas, and antenna arrays for 5G mobile communications in

sub-6 GHz and mm-wave frequency bands. He has authored over 100 articles

on these topics.

Dr. Wang is a Huawei Fellow and an IET Fellow. He was a recipient of

the Title of Nokia Inventor of the Year in 2005, the Nokia Excellence Award

in 2011, the Huawei Individual Gold Medal Award in 2012, and the Huawei

Team Gold Medal Award in 2013 and 2014. His patent was ranked number

one among 2015 Huawei top ten patent awards. He is an Associate Editor of

the IEEE A

NTENNAS AND WIRELESS PROPAGATION LETTERS.

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