13540


FACTA UNIVERSITATIS  
Series: Electronics and Energetics Vol. 39, No 1, March 2026, pp. 105 - 121 

https://doi.org/10.2298/FUEE2601105M 

Original scientific paper  

EFFECT OF MUTUAL COUPLING IN SMART ANTENNA FOR 

MASSIVE MIMO SYSTEM-A TECHNICAL SURVEY AND 

DESIGN CONSIDERATIONS  

Manisha Mishra, Jibendu Sekhar Roy 

School of Electronics Engineering, KIIT Deemed to be University, Bhubaneswar, 

Odisha, India 

ORCID iDs: Manisha Mishra   https://orcid.org/0000-0002-9635-4000 

 Jibendu Sekhar Roy   https://orcid.org/0000-0002-3571-2708 

Abstract. The 5th and 6th (5G and 6G) generation wireless communications exploit large 

antenna arrays to serve a large number of users over large distances. In 6G sky 

communication, large antenna arrays will be used for communications with unmanned 

aerial vehicles (UAV), satellites and high altitude platforms (HAP) along with terrestrial 

infrastructures. The manuscript at hand dispenses an organized technical survey of the 

effects of mutual coupling in massive MIMO (mMIMO) (multiple input multiple output) 

systems, subsuming the effects on te direction-of-arrival (DoA) of the signals and digital 

beamforming, which substantiate the performance of the design of smart antenna (SA). 

The mutual coupling distorts the wave front of the incoming signal, resulting in an 

erroneous DoA estimation and majorly degrading other performances of the antenna 

array in an mMIMO system. An assortment of compensation techniques is elucidated 

since it is unfeasible to completely eliminate the mutual coupling. Further, some 

investigated results of isotropic antennas and dipole arrays are explicated, screening the 

mutual coupling effects. For practical antenna array design, compensation for the effect 

of mutual coupling is necessary, especially for densely populated arrays in an mMIMO 

system. Investigations on various methods of compensation of mutual coupling in 

antenna array design are surveyed. 

Key words: Smart antenna, Mutual coupling, Mutual impedance, Massive MIMO, 

Beamforming 

1. INTRODUCTION 

The capacity in wireless communication can be enhanced using a MIMO system which 

uses multiple antennas at both the transmitter and receiver ends [1-3]. At the receiving end, 

by combining the received signals from all the antennas, the fading effect can be reduced, 

which increases the signal-to-noise ratio (SNR) and minimizes the error rate. 5G wireless 

 
Received March 10, 2025; revised July 15, 2025, and August 11, 2025; accepted August 11, 2025 

Corresponding author: Jibendu Sekhar Roy 
School of Electronics Engineering, KIIT Deemed to be University, Bhubaneswar, Odisha, India 

E-mail: drjsroy@kiit.ac.in 

https://mail21.elfak.ni.ac.rs/owa/?ae=Item&t=IPM.Note&a=New&to=drjsroy%40kiit.ac.in&nm=Jibendu+Sekhar+Roy


106 M. MISHRA, J. S. ROY 

networks and 6G sky connections for the services of multiple users, need massive MIMO 

(mMIMO) systems where large antenna arrays with directive beams are used [4, 5]. The 

mMIMO system produces narrow targeted beams with low interference. The escalating 

technology and widening employment of wireless communications are enriching the 

present and future years. The very first model of smart antenna i.e. retrodirective antenna, 

was conferred by a patent in 1959 to L. C. Van Atta [6] for retrodirective beam formation. 

Smart antenna applications necessitate close analysis of the electromagnetic behaviour of 

the signals, particularly in regard to mutual coupling [7], [8]. The smart antenna arrays 

(SAA) [9-11] tilt the beam electronically to any desired user direction while producing a 

null in the direction of the interferer in a cellular network [12]. The SAA provides enhanced 

security in the network. The constraints of power utility and frequency reuse can be 

improved in a cellular network by employing digital beamforming using multiple antenna 

techniques [13-14]. The massive employment of antenna elements has two main effects: 

Spatial correlation for the propinquity of the elements as signal sources and mutual 

coupling due to small inter-element spacing [15-17]. Since the effect of mutual coupling 

changes impedance and radiation properties of an antenna array, it is necessary to consider 

the effect of mutual coupling in smart antenna design. After DoA estimation of the 

incoming signal, the smart antenna system in the base station forms the desired beam 

towards the user in a cellular network. So, the basics of mutual coupling with related 

supporting equations and the effect of mutual coupling in DoA estimation and 

beamforming should be known for the smart antenna design.  

In this paper, a technical survey on the impact of mutual coupling in adaptive smart 

antenna, for 5G and 6G large array applications is reported. The objective of this paper is 

to survey the methods of analysis of mutual coupling effect in antenna arrays for densely 

populated arrays for the application to mMIMO systems, including the survey on the 

compensation methods of mutual coupling effect. The aim of this paper also includes the 

comparison of analysis and compensation methods for mutual coupling effects in antenna 

arrays. In section 2 the simulated results for isotropic and dipole antennas are presented to 

show the effect of mutual coupling on smart antenna parameters. In section 3, the impact 

of mutual coupling on DoA Estimation is described. In Section 4 research reports on the 

effect of mutual coupling in adaptive beamforming in smart antennas are reviewed. The 

research works on different methods of compensation of mutual coupling in smart antenna 

are surveyed in section 5. In section 6 a discussion on the effect of mutual coupling on 

antenna arrays used for mMIMO, UAV, and HAP is included. After this technical survey, 

a brief conclusion is added in section 7 where the importance of this survey and the deficit 

of research work on the effect of mutual coupling on smart antennas are presented. The 

topics covered in this technical survey provide useful information for the design of densely 

populated large antenna arrays. 

2. MUTUAL COUPLING IN SMART ANTENNA 

In an antenna array, part of the energy is coupled with the nearby ones [18] and the 

radiation characteristics appreciably differ from the stand-alone antenna features. The 

beam patterns with mutual coupling effects show higher side lobe levels and a broader 

main lobe, thereby reducing the directivity of the array [19]. In an mMIMO system, the 

radiation beams of the array system must be very directive with lower side lobe levels. The 



 Effect of Mutual Coupling in Smart Antenna for Massive MIMO System-A Technical Survey  107 

effect of mutual coupling [20-21] becomes dominant in a densely populated array. For 5G 

and 6G wireless communications, the mMIMO systems can use the sub-6GHz band, where 

dipole antennas can be used as array elements. The design of a dipole array is easier 

compared to other antenna arrays. The paper [22] investigates the effect of mutual coupling 

in a smart environment for a linear isotropic array, where inter-element distances are varied 

to observe the variations of beam direction and half-power beamwidth (HPBW) due to the 

mutual coupling (Fig. 1). The signal processing algorithm, least mean square (LMS) 

algorithm, is used for generating adaptive radiation beams and nulls. In this simulation 

work for a smart antenna of dipole array, the number of antennas N=12, beam direction 

(BD) =200, null direction (ND) =300 and µ=0.0001. 

 

 

Fig. 1 Variation of beam direction and beamwidth (HPBW) for an isotropic array 

The simulated results of smart antenna of isotropic elements, for various beam direction 

(BD) and null direction (ND) by varying the inter-element spacing, are tabulated in Table 

1. In Table 1, when the element spacing is less, the BD and ND are far from the desired 

BD and ND. For low values of element spacing, HPBW is wide, which means due to the 

mutual coupling effect, the directivity decreases (directivity is inversely proportional to the 

HPBW). The SLL is very poor due to the mutual coupling effect for low element spacing. 

In a dense antenna array (say, inter-element spacing d<0.3λ) the mutual coupling is 

more. For a dipole SA, the impact of mutual coupling in beamforming is investigated. If 

two transmitting dipole antennas are excited by the voltage sources Vs1 and Vs2, the coupled 

voltages V12 and V21 are [23]  

 𝑉12 =  𝑍12𝐼2 (1) 

 𝑉21 =  𝑍21𝐼1 (2) 



108 M. MISHRA, J. S. ROY 

Source internal impedances of antennas 1 and 2 are Zg1 and Zg2, and Z11 and  Z22 are the 

antenna self-impedances. The Z12 and Z21 are the mutual impedances when antenna 2 and 

antenna 1 are excited, respectively. Original electrical characteristics are changed due to 

mutual coupling between the two antennas. Reciprocity theorem is used to determine the 

current In at n-th antenna, with the equivalent model of Fig. 2. 

  𝑉2 = 𝑍21𝐼1 + 𝑍22𝐼2 = −𝐼2𝑍𝐿 (3) 

        𝐼2 = −
𝑍

21

𝑍
22

+𝑍𝐿
𝐼1 (4) 

 𝐼𝑛 = − ∑
𝑍𝑛𝑚

𝑍𝑛𝑛+𝑍𝑔
𝐼𝑚

𝑁−1

𝑚=0,𝑚≠𝑛
 (5) 

Table 1 Variation of smart antenna parameters with inter-element spacing 

No. of antenna 
elements 

Element 
Spacing ‘d’ 

Desired BD, 
ND (Deg) 

Obtained 
BD, ND (Deg) 

HPBW 
(Deg) 

SLLmax 

(dB) 

N=12 0.5λ  20,  30  20,  30 8.8 -11.8 

0.3 λ  16.1,  30 12.9 -5.6 

0.25 λ  13.6,  30 15.2 -4.5 

0.2 λ  10.8,  30 18.3 -3.5 

0.5 λ  -20,  -10  -20,  -10 9 -12.5 
0.3 λ  -23.6,  -10 13.6 -5.7 

0.25 λ  -25.7,  -10 16.3 -4.7 

0.2 λ  -28.9,  -9.7 20.7 -3.9 

0.5 λ  -10,  0  -10,  0 8.8 -13.2 
0.3 λ  -13.2,  0 13 -6.1 

0.25 λ  -15.3,  0 15.5 -5.1 
0.2 λ  -18.5,  0.2 18.8 -3.8 

N=20 

0.5λ  20,  30  20,  30 5.3 -12.74 
0.3 λ  19.8,  30 8.8 -12.23 

0.25 λ  18.7,  30 10 -8.74 
0.2 λ  16.8,  30 11.7 -6.23 
0.5 λ  -20,  -10  -20,  -10 5.5 -13.63 
0.3 λ  -20,  -10 9 -13.10 

0.25 λ  -21.4,  -10 10.5 -9.45 
0.2 λ  -23,  -10 12.5 -6.95 
0.5 λ  -10,  0  -10,  0 5.2 -13.76 

0.3 λ  -10.8,  0 8.6 -12.98 

0.25 λ  -11.4,  0 11.2 -10.1 

0.2 λ  -12.5,  0 11.8 -7.02 



 Effect of Mutual Coupling in Smart Antenna for Massive MIMO System-A Technical Survey  109 

 

 

Fig. 2 Equivalent model for two dipole antennas 

A linear antenna array of N number of co-linear dipole antennas is shown in Fig. 3.  

 

Fig. 3 Array of dipole antennas 

For dipole length of ‘l’, propagation constant β, the radiation field is [12] 

  𝐸(𝜃) = 𝑗𝜂
𝐼𝑜𝑒−𝑗𝛽𝑟

2П𝑟
[

cos(
𝛽𝑙

2
cos 𝜃)−cos(

𝛽𝑙

2
)

sin 𝜃
] (6) 

I0 is the excitation current and η is the free-space impedance (120πΩ). Total radiated field 

for N number of dipoles, with mutual coupling is   

 𝐸𝑡𝑜𝑡𝑎𝑙(𝜃) = ∑ 𝐼𝑛𝐸(𝜃)𝑒𝑗(𝑛−1)(
2П𝑑

𝜆
cos 𝜃+𝛼)𝑁

𝑛=1  (7) 

The array factor is  

 𝐴𝐹(𝜃) = ∑ 𝐼𝑜𝑒𝑗(𝑛−1)(
2П𝑑

𝜆
cos 𝜃+𝛼)𝑁

𝑛=1  (8) 

Where α is the progressive phase shift. The effect of mutual coupling on the radiation 

beam by varying dipole spacing with N=16, BD=25 Deg, ND=15, and µ=0.0001 and using 

the LMS algorithm is simulated and is shown in Fig. 4 (a). In Fig. 4(b), the variations of 

beam direction and HPBW for the half-wave dipole array are shown. 



110 M. MISHRA, J. S. ROY 

 

(a) 

 

 

 

(b) 

Fig. 4 (a) Radiation pattern; (b) Variation of beam direction and HPBW 

In [20] an optimal beam generation method is extended, evaluating the active element 

patterns along with the impedance matrix, effective even in severe coupling effects. The 

MIMO systems [15] in wireless communication are expected to be one of the key 

technologies in the future using spatial diversity and spatial multiplexing [24] techniques. 

The problem of computation of mutual coupling for wire antenna arrays was solved by the 

method of moment (MoM) in numerical electromagnetic code in 1970s [25-28]. Here, the 

technical survey for the effect of mutual coupling on SA design is described separately in 

two sections as effect on DoA estimation and effect on adaptive beamforming. A separate 

section is included on the literature survey for compensation methods of mutual coupling 

in the design of antenna array. 



 Effect of Mutual Coupling in Smart Antenna for Massive MIMO System-A Technical Survey  111 

3. EFFECT OF MUTUAL COUPLING IN DIRECTION OF ARRIVAL ESTIMATION 

One of the imperative measurements in signal processing is the estimation of  the DoA 

of narrowband signals. The estimation of DoA is an explicit way out for the quality of 

service degradation owing to the handoff problem. Several approaches can be employed 

for DoA estimation, like, minimum variance distortionless response algorithm, the multiple 

signal classification (MUSIC) algorithm, maximum entropy, and the estimation of signal 

parameters via the rotational invariance (ESPRIT) algorithm. The ESPRIT algorithm 

presumes all the array elements to have similar radiation patterns, as a result of which 

mutual coupling impinges on the estimation error directly. Underlining the effects of 

mutual coupling, particularly in circular antenna arrays, a mutual coupling matrix is given 

for the received signal x(t), giving the equation [29] 

 𝑥(𝑡) = ∑ 𝑎𝑀𝐶(𝜑𝑘)𝑠𝑘(𝑡) + 𝑛(𝑡)𝐾
𝑘=1  (9) 

Here, 𝑎𝑀𝐶(𝜑𝑘)is the array steering vector taking mutual coupling into consideration. S(t)  

is a Kx1 signal vector and n(t) is the  Nx1 noise vector.  

Liao et al. [30] propose subspace-based techniques for DoA evaluation and tracking 

with the effects of coupling. At times, the high-resolution DoA schemes like ESPRIT may 

fail due to coupling. Generally, the calibration algorithms assume DoAs as time invariant, 

but real systems are time varying. In the papers [31-32], the authors describe that among 

the used DoA estimation approaches, the maximum-likelihood method gives the best 

asymptotic performance but at the cost of high computational complexity. So, SAGE 

algorithm which is a modification of expectation maximization is proposed.  

In the network theory approach for DoA estimation [11], an array of N elements is 

considered as N+1 terminals of a linear, bilateral network that responds to an outside 

source. A relation between normalized impedance matrix Z0 (normalized to the load 

impedance) and open circuit voltages V0 at the antenna terminals is established as [7] 

 V𝑍0 =  𝑉0 (10) 

Where, V is the element output voltage. 

Using network model approach, signal-to-interference-plus-noise-ratio (SINR) of the 

SA is estimated as 

 𝑆𝐼𝑁𝑅 = 𝑃𝑑/𝑃𝑎 (11) 

 𝑃𝑎 =  ∑ 𝑃𝑖𝑘
𝑚
𝑘=1 + 𝑃𝑛 (12) 

Where, Pd is the desired output signal power, Pik is the output interference power and Pn is 

the output thermal noise power. 

In comparison with the ESPRIT algorithm, the stated method is appropriate for 

applications in cylindrical array structure. The approach of angles of arrival degrades as 

the mutual coupling varies with the identical vectors of the array, altering the covariance 

matrix. DoA estimation for the uniform linear array (ULA) using the MUSIC algorithm 

supposedly degrades as the mutual coupling by the interactions between receiving antenna 

elements isn’t ignorable and the prior data about the array doesn’t hold true. In the subspace 

approach of the MUSIC algorithm, eigenvectors for the signal space and the noise span are 

orthogonal to each other [33]. The Root-MUSIC algorithm [34], based on polynomial 

rooting, reduces the computational complexity of the MUSIC algorithm and is more apt 



112 M. MISHRA, J. S. ROY 

for fewer array elements with low SNR. The DoAs θ1,θ2, , …..θk, are computed by the 

conventional algorithms to construct the new transformation matrix using the coupling 

coefficients [35]. This algorithm response is quite good even in multipath or unknown 

conditions. 

4. EFFECT OF MUTUAL COUPLING IN BEAMFORMING OF ADAPTIVE SMART ANTENNA 

In an array antenna, when one antenna is excited and radiates, part of the energy is 

coupled to the second, inducing a current as a result of which it starts radiating even if it is 

not excited. Mutual coupling intrudes into the beamforming pattern in an array and needs 

to be examined thoroughly for the adaptive signal processing step. Quite a few adaptive 

algorithms [36] have been helpful for beamforming, such as least mean square (LMS), 

recursive least squares, conjugate gradient method, constant modulus algorithm [21], and 

so on. The idea is to form maximum gain beam(s) in the desired path, nullifying the 

intruder’s direction. It is always chosen to place a deeper null in the interferer direction, 

but in a real environment mutual coupling exceedingly undermines it. A lot of studies have 

concluded that SINR lessens as the interferer comes close to the desired direction. Phase 

distribution and current magnitude in a dipole array are changed due to mutual coupling, 

distorting the vectors and giving rise to peaks and nulls in directions from the desired ones. 

The beam patterns with mutual coupling have higher side lobe levels, broad beamwidths 

and shallower nulls. In the papers [37, 38], the interaction between the antenna array 

components is described by a mutual impedance matrix [Z]. For computation, the methods 

presented are induced electromotive force, method of moments (MoM) and full-wave 

electromagnetic numerical computation. Wang et al. [39], exploiting mutual coupling 

between the antenna elements for the printed slot arrays, investigate its effects on the array 

bandwidth. In the paper [40] diversity gain of a two-port antenna is measured in a 

reverberation chamber. Variation of measured and computed diversity gains [41] with 

dipole separation is compared in Fig. 5.  

 

 

Fig. 5 Dipole array in MIMO system [41] 



 Effect of Mutual Coupling in Smart Antenna for Massive MIMO System-A Technical Survey  113 

A mathematical analysis for the estimation of error with mutual coupling outcome is done 
in [41]. The methods rely on the sum of eigenvalues of the channel correlation matrix. The 
increase in spatial correlation lowers the estimation error at the cost of the channel’s effective 
degree of freedom (EDOF) [42]. Studies have shown an improvement in channel capacity due 
to mutual coupling when antenna spacing at both the transmitting and receiving ends is between 
0.2λ and 0.4λ as a result of an increase in the EDOF. In [43, 44] effects of mutual coupling are 
highlighted in broad-side and end-fire cases with channel modelling. Experiments point out that 
the radiation pattern is the same for a half-wave dipole and isotropic source in the azimuthal 
angle, but mutual coupling changes the size of the back lobe due to variations in phase 
difference and element spacing, reducing the directivity. By varying the dipole length [45] in 
the array, maximum directivity increases up to a certain extent with an optimum length of 
around 1.2λ. Beyond it, the side lobe level rises. A smart antenna with an active frequency 
selective surface for user detection is presented [46], where due to an active element effect of 
mutual coupling on radiation beam characteristics can be reduced. A most recent article [47] 
has reported the achievement of low mutual coupling using a metamaterial patch antenna for 
two-port MIMO, which is suitable for ultra wideband (UWB) applications. 

A summary table comparing the surveyed works on mutual coupling in antenna arrays 
is presented in Table 2. 

Table 2 Summary table for the surveyed works on mutual coupling in antenna array 

Research 
Report 

The method of analyzing mutual coupling effect Antenna type Applications 

Ref [13] The concept of ‘extra port’ is introduced in the 
element-by-element based correction procedure to 
involve the mutual coupling effects. 

Linear dipole 
array. 

5G wireless 
communication,  
Wi-Fi, satellite 
communication. 

Ref [16] The performance of the large-scale adaptive 
antenna arrays, in the presence of mutual 
coupling is presented. An expression SINR of in 
the presence of strong interference signals, 
considering the mutual coupling between the 
array elements, is derived.  

Dipole 
antenna array. 

Massive MIMO 
system. 

Ref [20] An optimal beam forming method, in the 
presence of mutual coupling, is proposed. Using 
the active element patterns and the impedance 
matrix, a computationally efficient beam forming 
algorithm is obtained, which can manage all 
mutual coupling effects. 

Small and 
medium-size 
dipole antenna 
array. 

Vehicular 
communication. 

Ref [29] The full-wave electromagnetic analysis using 
Integral Equation 3D (IE3D) software is used for the 
antenna design in the presence of mutual coupling.  

Circular and 
concentric 
circular patch 
antenna arrays. 

CDMA wireless 
communication. 

Ref [35] The problem of mutual coupling in DOA 
estimation is solved by using the time-frequency 
analysis.  

Smart antenna 
of isotropic 
elements. 

 Massive MIMO. 

Ref [38] A Rayleigh fading channel with varying angle-of-
arrival spread is considered where maximum 
SNR beamforming weights are used for array 
beamforming in the presence of mutual coupling. 
These weights are further correlated with mutual 
coupling at the base station array. 

Smart 
antenna. 

Digital 
beamforming in 
CDMA system. 



114 M. MISHRA, J. S. ROY 

Ref [39] Linear antenna arrays with corporate feed and a 
closed-form expression of 
the reflection coefficient are derived at the input 
port of the feeding network to obtain mutual 
coupling coefficient for bandwidth enhancement. 

Slot arrays 
and a two-
element 
Vivaldi array. 

Avionic, UAV, 
HAP. 

Ref [40] This paper explains how MIMO and diversity 
antennas with mutual coupling can be analyzed 
by classical embedded element patterns. 

 MIMO antennas and 
diversity antennas. 

Ref [41] Scaled least square (SLS) and minimum mean 
square error (MMSE) are used to assess the effect 
of mutual coupling on the performance of 
training-based MIMO antenna systems.  

Wire dipole 
antenna 
arrays. 

MIMO antenna 
system. 

Ref [42] The issue of mutual coupling is addressed by 
applying an exact network theory framework to 
consider the mutual coupling effect in MIMO 
systems. This method includes a new power 
constraint that limits the radiated power in the 
presence of mutual coupling.  

Half-wave 
dipole array. 

MIMO wireless 
communication. 

Ref [43] A generic matrix coupling model, augmented by a 
matching network, is used to analyze the effects 
of mutual coupling to a channel matrix in the 
channel model. 

Uniform 
linear array of 
vertical dipole 
antennas. 

Massive MIMO 
system. 

Ref [47] The effect of mutual coupling are investigated by 
combining three methods: Cutting the radiating 
patch with a partial ground plane, shape 
modification of the patch, and the use of 
metamaterials. 

Metameerial 
patch antenna 
array. 

MIMO and UWB 
communications. 

5. METHODS OF COMPENSATION OF MUTUAL COUPLING EFFECT  

IN SMART ANTENNA DESIGN 

For the design of a smart antenna of a densely populated array, inter-element spacing 

may be as small as 0.2λ, and in this case it is necessary to consider the mutual coupling in 

the array design, and for this various methods are available. In [48], a new compensation 

matrix is proposed to minimize the effect of mutual coupling in antenna arrays. In [49], in 

receiving thin wire dipole arrays, it is compensated by measurement only. Also adding the 

compensated excitation weights improves the antenna efficiency [50]. The compensated 

weight Wi for each element is calculated by [51]  

 
1 1 1 (0)[ ] {[ ] [ ] } [ ] [ ]iW U S S W− − −= + −  (13) 

𝑊𝑖
(0)

is the zero mutual coupling weight of each array element, S is the mutual coupling 

coefficient between the array elements and [U] the unity matrix. As the decoupling methods 

depend on the applications of the system, one of the easiest to use is the element pattern 

method [52] categorized as the isolated element pattern method, which takes the  coupling-

free voltages, and the other is the coupled element pattern method, which obtains the 

received coupled voltages through the coupled radiation pattern from the array elements. 

The coupling between the array elements is given by a set of coefficients Cmn, relating the 

coupled and decoupled voltages [53] 



 Effect of Mutual Coupling in Smart Antenna for Massive MIMO System-A Technical Survey  115 

 𝐶𝑚,𝑛 =
𝑘𝑑

2П𝐸
0

∫
𝑔𝑚(𝑢)

𝑓(𝑢)

П/𝑘𝑑

−П/𝑘𝑑
𝑒−𝑗𝑛𝑘𝑑𝑢𝑑𝑢  (14) 

E0 is the amplitude of the incident plane wave, f(u) is the isolated element pattern, k is the 

wave number,  d is the uniform element spacing, gm(u) is the received signal at element  m, 

and  u is the sine of the angle θ from broadside. Thinned smart antenna is proposed to 

enhance the network performance using large antenna arrays [54]. Bellofiore et al., 

exemplify the use of eigenspace projections for improved performance of the algorithm, 

namely the eigensubspace projection algorithm, by adjusting the LMS weights and taking 

the impedance matrix into account as follows [55]  

   𝑤𝑜𝑝𝑡 = 𝑍−1𝑤𝑜𝑝𝑡 (15) 

Spatially multiplexing of local elements technique [56] delineates the approach of 

reducing the radio channels to one with no loss of the signal veracity. Mutual coupling 

effects can be estimated by considering an N- element antenna array as N-port network 

[57] as 

 ∑ (𝐼𝑁,𝑖𝑉𝑖 +
𝑍𝑁,𝑖

𝑍𝐿
𝑉𝑖) = ∑ 𝑉0𝑖

𝑁
𝑖=1

𝑁
𝑖=1

 (16) 

Where, N=1, 2,…..,  −
𝑍𝑡

𝑁,𝑁

𝑍𝐿
= 1 and i = 1,2,…N. ZN,i, 𝑉𝑖 and  𝑉0𝑖are the matrices. 

The above equation calculates decoupled open-circuit voltages V0i useful for array 

signal processing. The receiving mutual impedance method surmounts the inadequacy of 

parameters, judging the elements to be in the receiving mode and is terminated with known 

impedance [26-27]. The impedance varies as a function of the direction of the incoming 

signal and demands for an estimated current distribution. In [58], the mutual coupling effect 

is reduced by using a compensation network, which is realized with two couplers and a 

passive network based on a 2nd-order band-pass filter. Using S-parameters doesn’t serve 

the entire purpose, as it calls for the accurate modeling of the transmitting array only, 

failing to estimate the mutual coupling effects at the receiving array. An extended S-

parameter method (ESPM) encapsulates multiport antennas measuring reflection and 

mutual coupling coefficient [59-60] 

 𝐵 = 𝑆𝑐𝐴 (17) 

Where,  A is the column vector of incident waves and  B of reflected waves at each port. 

Sc  being the scattering matrix of the 2n-port network. The incident wave Ak and reflected 

wave Bk can be given as 

  𝐴𝑘 =
𝑉𝑘+𝐼𝑘

2
………. 𝐵𝑘 =

𝑉𝑘−𝐼𝑘

2
 (18) 

Vk and Ik are the port voltage and port current, k=1, 2,….,n. Earlier S-parameter-based 

method were confined to single antenna measurements, but the ESPM emphasizes accurate 

measurement of reflection and mutual coupling of multiport antennas. Furthermore, it 

extends to radiation pattern, radiation efficiency, and actual gain measurements [61]. The 

technique fits very well in the designing of decoupling and matching circuits for small 

antennas. A powerful and consistent decoupling method to minimize the coupling effects 

is a must for the present expansion of antenna array applications [62]. The methods of 



116 M. MISHRA, J. S. ROY 

compensation of mutual coupling effect in antenna array design, are presented in tabulated 

form in Table 3. 

Table 3 Comparison of methods of compensation of mutual coupling effect in array design  

Sl.  

No. 

Research 

Report 

Mutual coupling compensation method 

1.  Ref. [28] The report presents that the mutual coupling is not increased when mutual 

impedance between the thin wire dipoles is forced to keep constant. The 

method of moment is used for computation. 

2.  Ref. [48] A compensation matrix is proposed to make the modal excitation coefficients 

of each antenna element in an array equal to those obtained without 

considering the effect of mutual coupling. 

3.  Ref. [49] The characteristic mode analysis (CMA) can be used to develop a method for 

compensating the mutual coupling effect. Using the knowledge of CMA, a 

mutual coupling compensation matrix is constructed by obtaining the 

characteristic matrix and Z-matrix of a metallic antenna array and in this way 

compensation error can be reduced. 

4.  Ref. [52] The mutual coupling compensation may be considered as a matrix multiplication 

performed on the received-signal vector. This restores the received signals by the 

isolated elements in  the absence of mutual coupling. This technique is most 

practical for digital beamforming antennas. 

5.  Ref. [53] The method of compensating mutual coupling, presented here, uses the 

calculation of the coupling coefficients between the array elements to form 

a matrix. This matrix is used to compensate for the effects of mutual coupling 

for a planar antenna array. 

6.  Ref. [54] In thinning of the antenna array, some antenna elements remain ‘off’ which 

increases the inter-element spacing and reduces the mutual coupling effect. 

7.  Ref. [57] This report describes the importance of compensation of mutual coupling in 

array design and also describes the various compensation methods. 

8.  Ref. [58] The mutual coupling effect is reduced by using a compensation network and 

it is realized with two couplers and a passive network, based on a 2nd-order 

band-pass filter.  

9.  Ref. [59] The Impedance and mutual coupling characteristics are found after reducing 

the effect of the coaxial cables by synthesizing the measured S-parameters, 

and the unbalanced currents on the outside of the coaxial cables are canceled 

at feed points. 

10.  Ref. [60] The microstrip antenna arrays are fed by co-planar waveguide (CPW) and to 

minimize the mutual coupling effect, orientations of the patches are optimized.  

6. THE EFFECT OF MUTUAL COUPLING IN ANTENNA ARRAYS FOR FUTURE WIRELESS 

TECHNOLOGIES 

In this section the discussion on the effect of mutual coupling in millimeter wave 

mMIMO, UAVs and HAPs are presented. In millimeter wave mMIMO, UAV and HAPs 

different frequency bands are used, and therefore the effect of mutual coupling differs 



 Effect of Mutual Coupling in Smart Antenna for Massive MIMO System-A Technical Survey  117 

between antenna arrays (element spacing depends on wavelength). For MIMO and 

mMIMO systems, used frequency bands are the 2.4 GHz band, the 3.5 GHz band, the 5 

GHz band and for UWB communication, the 3.1-10.6 GHz band [63-65]. For millimeter 

wave (mmWave) mMIMO systems, the frequency band of 24-100 GHz is used in 5G 

mmWave deployments [66]. The popular frequency bands for 5G UAV are 900 MHz, 2.4 

GHz, and 5.8 GHz, whereas in 6G wireless communication, in addition to these bands, 

mmWave bands are also proposed [67]. The HAPs all over the world use different 

frequency bands, like frequency bands 21.4 - 22 GHz, 24.25 - 27.5 GHz, 31 -31.3 GHz,  

and 38 - 39.5 GHz [68]. In an mMIMO system the number of antennas in the array is large. 

Therefore, the mutual coupling effect directly affects the performance of mmWave 

mMIMO systems and should be considered in array design [69]. Mutual coupling effect 

degrades the matching efficiency and radiation pattern of the mMIMO system. In UAV 

communication, mostly light weight patch antennas, dipoles, or monopoles are used. At 

low frequencies, because of the space constraints in the device, the element spacing is low, 

and the mutual coupling effect should be taken into account in array design. The mutual 

coupling between the radiating patches can be controlled using varicap diodes [70]. Mutual 

coupling between the antenna elements modifies the reflection coefficient when monople 

antennas are used for UAV communication [71]. In [72] optimal optimal antenna element 

position in a limited plane is determined to minimize the mutual coupling effect for a sparse 

array for UAV application. The HAPs generally placed at an altitude of 18 to 20 km from 

the earth’s surface because the wind speed at that level is minimum. Therefore, high-gain 

antennas are required, and large array antennas are used. A MIMO-HAP diversity system 

is proposed in [73] which takes into account the effect of mutual coupling in the antenna 

system. This antenna array system consists of twelve electric dipoles, which are positioned 

on the twelve edges of a cubical configuration. A MIMO-HAP diversity system is used 

[74], where a power control method is used to minimize the mutual coupling effect in the 

array antenna. For low-profile and light-weight applications, like UAV and HAP, 

microstrip antenna arrays are the first choice in spite of the narrow bandwidth and low gain 

of a microstrip antenna. But multilayered micorstrip antenna can be used for bandwidth 

enhancement [75, 76].  One of the potential sources of performance degradation of 

micortsip array is mutual coupling between the antennas, and this performance degradation 

can be reduced by the selection of proper elements and proper orientation of the patches 

[14, 77]. A higher dielectric constant of the substrate of a microstrip antenna can increase 

the mutual coupling effect, whereas a lower dielectric constant reduces it but increases 

antenna size. If the substrate thickness is more, the mutual coupling effect in a microstrip 

array is less [78]. 

7. CONCLUSION  

The effect of mutual coupling in an SA affects antenna gain, beamwidth, radiation 

pattern, and input impedance. It also causes the shift of the main beam and null from the 

desired directions. These effects are severe for 5G and 6G wireless communications, where 

for long-distance communications large antenna arrays with relatively smaller antenna 

spacing are used. This paper presents in detail the effects of mutual coupling in direction 

of arrival estimation as well as adaptive beamforming of smart antennas separately, 

including the design considerations for large arrays, like mMIMO. The survey on the 



118 M. MISHRA, J. S. ROY 

different types of compensation methods is also included. Since smart antenna is one of the 

pivotal technologies in next-generation cellular communication, this paper can show the 

prospective direction of research on this topic. It is found that in most of the papers, authors 

have taken account of the effects of mutual coupling but not used compensation methods. 

Most of the papers reflect on the effect of mutual coupling on linear arrays using isotropic 

antennas. In realistic status, densely populated antenna arrays are planar. Because of their 

low-profile nature, microstrip antennas are useful for large array applications in 5G and 6G 

applications. The effect of mutual coupling in the case of a planar microstrip array is very 

significant because for a microstrip array, mutual coupling depends on the relative position 

of the microstrip antennas. The main contribution of this paper is to present the issue of 

mutual coupling in the design of densely populated antenna arrays for mMIMO systems. 

The paper describes the survey on the methods of analysis of the mutual coupling effect in 

array design along with the mutual coupling compensation methods. The future 

investigation is to review and analyze mutual coupling in lightweight planar arrays for 6G 

sky connection. Also, the future work will be to survey the experimental methods of 

compensating for the mutual coupling effect in antenna arrays. 

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