Characteristics mode analysis based wideband Sub-6 GHz flexible MIMO antenna using a unique hybrid decoupling structure for wearable applications

This article presents a compact flexible four-element multiple input multiple output (MIMO) antenna for Sub-6 GHz wearable applications. A wideband monopole antenna with a modified edge tapered radiator and a lowered ground plane is replicated to form a four-element antenna. The proposed antenna is fabricated on a flexible polyethylene terephthalate (PET) substrate and holds an overall dimension of 65 × 56 × 0.25 mm3. The antenna has a measured bandwidth of 3.55–5.3 GHz with a peak gain of 4.9 dBi. A novel hybrid decoupling structure with a neutralization line in the radiator and a unique defective ground structure (DGS) suppresses the coupling current and provides isolation better than −24 dB throughout the bandwidth. The antenna design evolution is explained using characteristics mode analysis (CMA). The MIMO diversity performance is relatively good with MIMO diversity metrics showing envelope correlation coefficient (ECC) < 0.001, diversity gain > 9.99, total active reflection coefficient (TARC) < −10 dB, channel capacity loss (CCL) < 0.3 bps Hz−1 and multiplexing efficiency (ME) < −0.5. Specific absorption rate (SAR) analysis of the antenna is performed to check the antenna’s suitability in wearable applications and the proposed antenna exhibits 0.745 W kg−1 and 0.326W kg−1 for 1g and 10g of tissue respectively which is much less than the permissible international standards.


Introduction
Wireless wearable technology has been showing exponential growth ever since its evolution and has gained the deep focus of researchers in the past few years.The broad arena of wearable technology applications including health monitoring, skin cancer detection, flexible biosensors, implantable wearables, sports, military applications, IoT (Internet of Things), and many more has led to a sudden increase in device usage by 90% from 2015 to 2020 [1,2].High-speed communication with uninterrupted service is essential in the above-mentioned applications which makes 5G communication a promising opportunity for the same.According to the 3rd generation partnership project (3GPP), there are two frequency ranges for 5G NR.The mid-band operates at Sub-6 GHz (<6 GHz band).The higher band called the millimeter wave band operates at a range of 24-300 GHz.The sub-6 GHz band attracts researchers due to its exclusive property of stronger penetration capability and feasible long-distance communication with a large cell coverage area [2].Antennas being the backbone of deployment of any wearable wireless technology, flexible microstrip antennas are ruling the wearable market due to their peculiar characteristics like high flexibility, lightweight, and conformality [3].
The design of a conformal microstrip antenna for wearable applications is a very challenging task due to the high backward radiation which in turn affects the human tissues [4].An intense level of electromagnetic (EM) radiation gets absorbed in the human body and is transformed into heat.The effect of EM radiation is investigated by calculating the Specification Absorption Rate (SAR) which quantifies the permissible amount of radiation that the human body can absorb.According to international standards, the permitted limit is restricted to 1.6 W kg −1 (1g tissue) and 2 W kg −1 (10g tissue) at any specific part of the body [5,6].
Severe scattering and reflections in the vicinity of the human body due to multipath fading on-body communication link drastically affects any reliable communication, and therefore a technology called multiple input multiple output (MIMO) systems where multiple antenna elements are employed is highly recommended.MIMO systems improve the channel capacity by minimizing the need for a large spectrum with reduced transmission power in a multipath fading environment [7].However, the implementation of conformal MIMO systems faces several challenges including better isolation, directional radiation characteristics, and maintaining stable bandwidth [8].Numerous approaches are seen in the literature for improving the isolation between the inter-elements such as incorporating slots [9,10], stubs [11,12], metamaterial [13], defected ground plane (DGS) [2,14], electromagnetic band gap structures (EBG) [15], neutralization lines (NL) [16] or hybrid (combination of any two of the specified techniques) [7].Even though the above-mentioned techniques help provide the isolation, optimizing the MIMO antenna decoupling structures maintaining the operating bandwidth, stable gain, radiation efficiency, and desired directional radiation patterns with a low antenna volume is challenging [17,18].
Literature shows several wearable MIMO antennas covering Sub-6 GHz band.A Sub-6 GHz MIMO antenna with a defective ground structure is proposed in [2] to get an improved isolation among the antenna elements.The antenna integrated on the wrist showed satisfactory SAR limits, however, the gain of the antenna is affected due to the defects created in the ground plane due to the back radiation which deteriorates the gain of the antenna.A two-element antenna is proposed in [10] for mid band applications.The ground structure incorporates a T-shape stub to improve the isolation.The antenna shows a satisfactory directional radiation pattern and satisfactory gain, but the antenna bandwidth remains low.A wideband textile MIMO antenna is proposed in [11] for wearable applications.A slotted T-shaped stub integrated DGS provides isolation better than −18 dB between the elements.However, the SAR value for 10g of tissue was considerably high for the above antenna which is not suitable for real-time wearable applications.In [12], a two-element MIMO antenna is proposed for wearable applications.
A pair of symmetrical stubs incorporated in the ground plane contribute to an isolation of −22 dB along the bandwidth.Even though the body effects of the proposed MIMO antenna have been performed to compare the antenna characteristics, the rate of absorption of radiation in the human body for the proposed antenna is found missing which is crucial in any wearable applications.A wideband wearable MIMO antenna in [19] using a neutralization line gives a good impedance bandwidth and better isolation of −32 dB, however, the measured peak gain of the antenna is low which is not satisfactory in real-time on-body applications.An all-textile conformal array antenna is proposed in [20] for wearable devices.The antenna provides omnidirectional radiation characteristics with a low profile and a low SAR value, however, the peak gain achieved for the wearable array antenna is low.The above literature shows that there are a limited number of wearable MIMO antennas with satisfactory performance in all characteristics for Sub-6 GHz applications.The MIMO antennas in [2,19] and [20] have a low gain value.Reference [10] gives a MIMO antenna with low bandwidth.In both of the designs in [11] and [12] the antenna shows a directional type of radiation with satisfactory isolation; however, the antennas have a large profile.The current literature reveals that designing a wearable antenna with less deviation in the antenna performances keeping a low profile, satisfactory gain, and at the same time maintaining good MIMO performances and a reduced SAR value is a very challenging task for the researchers working on wearable antenna designs.In the above literature, [11,19] and [20], the MIMO antennas utilize textile materials which provide a significant degradation in its performance when utilized for human body interactions since the textile absorbs moisture and thereby degrades the antenna performance drastically [19].Therefore, researchers in recent times have been utilizing various polymer-based substrates like Kapton, Polyethylene Terephthalate (PET), conductive polymers, liquid crystal polymers (LCP), and polydimethylsiloxane (PDMS) due to their exclusive electrical and mechanical properties [21].
Therefore, considering all these significant parameters of the wearable antenna design, a compact fourelement wearable Sub-6 GHz antenna fabricated on a PET substrate is proposed in this article.The design uses a novel hybrid decoupling structure with a unique DGS and a neutralization line in the radiator for better isolation.The antenna has been performed with characteristic mode analysis to optimize the design and understand the resonance behaviour and radiation characteristics of the proposed antenna.
In most of the above referred literature, the isolation is achieved using a DGS alone, however, here the authors utilize a neutralization line along with a unique DGS making it a hybrid decoupling structure which is seen rare in the literature exclusively for flexible Sub-6 GHz MIMO applications.A satisfactory result in bending analysis, a very low SAR value, and good MIMO diversity metrics values are other focuses of this article.The proposed four-element antenna shows a measured impedance bandwidth of 3.55-5.3GHz with S11 less than −10 dB and an overall dimension of 65 × 56 × 0.25 mm 3 .The antenna provides an isolation greater than −24 dB over the entire bandwidth.SAR values fall well below the international standards with 0.745 W kg −1 and 0.326 W kg −1 for 1g and 10g of tissues respectively at 4.1 GHz.The main contributions of this paper are summarized as follows: • The evolution of a single-element antenna is analysed exclusively using CMA to study the resonance behaviour of the antenna.This article applies CMA as an aid in tracking modes, sorting and helps in antenna design evolution by manipulating modes using eigenvalue-based parameters and related far-field and current distribution.
• A unique hybrid decoupling structure utilizing the neutralization line and DGS has contributed to enhanced isolation of −24 dB over the bandwidth.
• The bending analysis of the antenna is done across the x and y-axis along different radii according to the body curvatures where the antenna is placed.
• Specific Absorption Rate is performed to check the feasibility of the antenna for wearable applications by putting the antenna over a three-layer phantom model that possesses variable material and dielectric characteristics.
The entire article is organized as follows: The design of the single-element antenna is explained in section 2. Section 3 explains the proposed four-element MIMO antenna and its analysis.Antenna analysis of the proposed four-element MIMO antenna for wearable applications is explained in section 4 followed by Results and Discussion in section 5 and Conclusion in section 6 respectively.

Design of single-element antenna 2.1. Design methodology
A modified edge tapered rectangular monopole antenna with a lowered ground plane is fabricated on a flexible Polyethylene Terephthalate substrate with a dielectric permittivity of 3.2 and a loss tangent of 0.022 to achieve a Sub-6 GHz band.Initially, in antenna 1, a single rectangular patch is designed to resonate at 4.6 GHz whose length (L) and width (W) are calculated using the mathematical equations given in [14].Figure 1(a) shows the evolution stages of the single-element antenna.The second stage (antenna 2) has a lowered ground plane.Stage 3 (antenna 3) introduces a modified radiator with two semi-circular slits and in the final stage (antenna 4) proposes, the radiator with tapered edges.
Figure 1(b) shows the corresponding reflection coefficient stages.Antenna 1 has a low bandwidth as seen in the figure since the antenna is a typical patch antenna that is known to exhibit a very low fractional bandwidth of only a few percent.In antenna 2, the ground plane is further lowered to enhance the impedance bandwidth.Lowering the ground plane modifies the current flow and thus alters the quality factor, contributing to an increased bandwidth.Though this stage contributed a bandwidth of 3.8-5.2GHz with a S11 below −10 dB, the impedance of the antenna is seen to be very low.In antenna 3, two semi-circular slits are etched from the radiator to improve the impedance matching.As seen in figure 1(b), the antenna 3 has an improved impedance matching with a bandwidth of 3.2-4.6GHz with S11 less than −10 dB.To further increase the bandwidth, in antenna 4, the edges of the radiator are tapered by cutting small rectangles from the bottom of the patch.These tapers increase the current path length which results in broader bandwidth as shown in figure 1(b).
The entire design evolution of the single-element antenna is investigated using CMA as a tool which is explained in the upcoming subsection.Figure 2 shows the configuration of the single-element antenna.

Mathematical modeling
This section explains the mathematical modeling of the single-element antenna.The wide bandwidth is achieved by modifying the rectangular monopole antenna as shown in figure 1(a).For understanding the mathematical interpretation of the single element antenna in terms of its resonant frequency, the radiator of the antenna with its iterations is shown in figure 3.
The semi-circular slits carved out from the rectangular radiator disturb the current distribution of the antenna which increases the effective LC and thereby shifts the resonance to the lower region.To further increase the bandwidth of the antenna, rectangular tapers are made at the edges of the radiator, that increases the effective length of the radiator and thus improves the bandwidth.As the proposed antenna is monopole in nature, the resonant frequency of the antenna is calculated using (1) [22].´mm s −1 ), and eff e is the effective dielectric constant of the substrate that can be estimated by (2).
( ) e e e = + + -+ and L p represents the maximum length of the radiator given by (3).y represents the perimeter of the semicircle given by 2π(x1)/2 where x1 is the radius of the semicircle (7 mm), and x represents the overall perimeter of the rectangular cuts.

Characteristic mode analysis
The design evolution of the single-element antenna using CMA has been elaborated in this subsection.The theory of characteristic mode analysis (CMA) has been helpful ever since its evolution in understanding the physical phenomenon of the conducting structure and contributes to its design optimization.
CMA analysis is based on an impedance matrix that considers a combination of eigen currents and values as depicted in equations ( 4) and (5) [23,24].
The total current associated with any conducting structure is the summation of currents of all the individual modes.On the other hand, the electric field is related to J n and n b which is the nth mode current and weighting coefficient respectively.
The modal current J n ( ) is determined by the structure of the conductor.Modal weighting coefficient can otherwise be written as: where V i n is the modal excitation coefficient which measures the coupling between the applied excitation and the conductor's mode and n l is the eigen value which is the ratio of the stored energy to emitted energy.The eigenvalues provide information regarding the radiating behavior of the associated mode.Moreover, a corresponding mode resonates when 0.
n l = The impedance matrix is given by where R and X represent the real and imaginary parts of the impedance matrix Z [23,24].
Modal significance (MS) and characteristic angle (CA) are the two crucial parameters when any antenna is investigated using CMA which is described by equations (8) and (9).Each mode related to any antenna structure has a unique MS which depends on the respective antenna structure.This further gives insight into the significant and non-significant modes of any antenna structure.The modal significance ranges from 0 MS 1. Furthermore, the bandwidth of each mode is a frequency range where MS is greater than a value of 0.707 (any mode having value greater than 0.707 within the operating range is significant) and a mode reaches resonance when MS is unity (MS 1) = [23].
MS j Coefficients of CMA and their significance [23,24].
Characteristic angle n a provides the phase lag between the E-field of the antenna and the surface current.n a has a phase difference of 180  for the resonating mode when 0.
n l = The modes store energy when the value of n a is within the value of 90  or 270 .
 Mode contributes to storing the magnetic field when 90  < n a < 180  (inductive) and storing the electric field when 180  < n a < 270  (capacitive) [23, 24].The three coefficients and their significance in characteristic mode analysis are summarized in table 1.
CMA as an optimization technique for antenna design can be utilized in different aspects of analysis like feed optimization, pattern optimization, impedance matching optimization and many more [23].However, this article applies CMA as a helpful aid in the tracking of modes including mode tracking and sorting, and thereby helps in antenna design evolution stages by manipulating modes using eigenvalues and corresponding parameters as well as related far field and current distribution.The analysis is performed using CST Microwave Studio simulation tool.
The evolution stages of the proposed antenna design are studied through CMA.The wider bandwidth of the antenna is achieved through interpreting the current distribution and corresponding far fields and modal significance of each antenna stage estimated at its corresponding resonant frequency.Each antenna is performed with CMA using the integral solver in CST Microwave Studio simulation tool.The modal significance and other eigen value-based parameters are used to interpret the significant and non-significant modes in each stage.Moreover, the current distribution of all analysed mode provides an insight about the region of maximum current concentration.This would help us in optimizing the design further to meet the desired structure.The first stage involves a rectangular patch resonating at 4.6 GHz with a bandwidth ranging from 4.57-4.65GHz with S11 less than −10 dB.CMA of antenna 1 is investigated and eigenvalues, MS, and CA of the same are analysed at 4.6 GHz (resonant frequency of antenna1) as shown in figures 4(a)-(c).
It is evident that in the bandwidth of interest, only mode 1 and mode 3 have a value close to zero and thus contribute to the antenna resonance and other modes are either inductive or capacitive which can be considered as the higher-order modes which does not contribute to radiation in the frequency range.This could be further confirmed if we check the modal significance plot in figure 4(c).From the MS graphs, mode 1 and mode 3 show a value of unity in the frequency range of operation.However, mode 3 reaches its resonance at 4.7 GHz which is close to the operating frequency of stage 1.Therefore mode 3 has utmost modal significance than all the other modes considered.The characteristic angle plot also gives information about the resonance of the antenna.Mode 3 has a CA value of 180  near resonance points and hence proves more significant than other modes having inductive and capacitive characteristics.Figure 5 shows the current distribution and far-field characteristics of the first five fundamental modes at 4.6 GHz.It is seen that in all the modes the current is concentrated near the patch edges and the ground.Considering significant mode 3, the current is out of phase and therefore lowering the ground plane would disturb the surface current thereby reducing the quality factor and improving the bandwidth.
The ground plane is lowered by adequate parametric analysis thus resulting in the evolution of antenna 2. The eigenvalues and the related parameters for stage 2 are investigated for the frequency of 4.5 GHz (resonant    The far-field properties and surface current distribution of stage 2 are shown in figure 7.This stage contributes to a bandwidth ranging from 3.8 to 5.2 GHz with S11 less than −10 dB.The impedance matching at this stage is low as mode 1 and mode 2 show almost similar values of modal significance which causes impedance mismatch due to the superposition of these modes.Therefore, to alleviate this problem and to achieve better impedance matching and wideband characteristics two slits are carved from the radiator in antenna 3. From the current distribution plots in figure 7 in stage 2, it is seen that the current is more concentrated towards the edges of the radiator.Therefore, two slits are carved out from the edges of the radiator with adequate parametric analysis.Cutting slits alter the current path and thus shift the resonance frequencies.The eigenvalue, MS, and CA plots of stage 3 calculated at frequency of 4 GHz (resonant frequency of stage 3) are shown in figures 8(a)-(c).It is seen that no modes show similar modal values for stage 3, thereby achieving better impedance matching.All modes except mode 5 are significant in this stage with an MS value greater than 0.707 within the corresponding operating frequency range.The eigenvalue of mode 4 shows resonance close to the resonance frequency of stage 3 and thus contributes more to the radiating field of the antenna.
The far-field plots and surface current distribution of antenna 3 are displayed in figure 9.As observed in the corresponding plot, the antenna exhibits an omnidirectional radiation pattern.This stage improved the impedance matching with a bandwidth of 3.2-4.6GHz with S11 less than −10 dB.
To further increase the bandwidth, surface current distribution of antenna 3 is considered and most of the current is concentrated on the bottom edge of the patch and near the partial ground structure for all the significant modes.Therefore, tapers are created at the edges of the radiator where rectangular cuts are carved from the radiator edge thus improving the bandwidth.
Cutting the edges of the patch increases the length of the current path and thus contributes to better impedance matching [25].The eigenvalue, CA, and MS plots of the proposed single-element antenna (antenna 4) is estimated at resonant frequency of 3.5 GHz (resonance of stage 4) are shown in figures 10(a)-(c).The modal significance shows the first three modes are significant as this shows an MS value greater than 0.707 in the corresponding resonance frequency (3.5 GHz) and thus contribute to resonance [23].Therefore, those modes are considered to be prominent, and other modes can be neglected since it does not contribute to the antenna resonance.The current distribution and the patterns of the first five fundamental modes of antenna 4 are shown in figure 11.The current is more concentrated near the ground plane, edges of the patch, and the feedline and contributes to the desired wideband operation with good impedance matching.
CMA analysis is done in this work in order to provide the optimization of the structure by investigating the modal significance and the corresponding current distribution of each analysed mode of all stages using the Integral Solver in CST Microwave Studio.Modal significance gives the insight about the most significant modes in each stage.Further, mode currents have been investigated and based on this, the region of maximum current concentration for all the analysed modes of individual stages has been observed.Tapers and modifications (parasitic elements) in the structure are made in the region of maximum current concentration to achieve the wider impedance bandwidth.Thus, this analysis has helped in achieving a desired wider impedance bandwidth with satisfactory radiation characteristics, with the interpretation of characteristic modes and related current distribution.

Design of four-element antenna 3.1. Design methodology and decoupling mechanism
The four-element antenna is designed by positioning a pair of single elements horizontally adjacent to each other separated by 8 mm from edge to edge of the individual elements.This pair is mirrored along the X-axis separated by 9 mm from edge to edge which is commuted at less than λ/4 where λ is the wavelength corresponding to 4.1 GHz as shown in figure 12(a).Placing the antenna elements close to each other creates mutual coupling which is evident in the current distribution plot shown in figure 12(b).
The evolution of the proposed four-element antenna is shown in figure 13.The first stage (Antenna 1) consists of a connected ground structure.The second stage (Antenna 2) consists of a unique DGS with slotted vertical and horizontal stubs integrated into the ground plane.Small vertical slits are carved out in the ground   The connected ground plane slightly improves the isolation; however, the antenna's reflection coefficient deviates in the following iteration.A unique DGS has improved the isolation by maintaining the reflection coefficient of the antenna.The rectangular slots in the ground plane of individual elements help in the bandwidth enhancement.To further enhance the isolation, a neutralization line is employed in the radiating plane (figure13(c)).The current distribution of the four elements with and without the neutralization line at the resonant frequency of 4.1 GHz is depicted in figure 14.This is done by exciting port 1 and terminating all the other ports.The coupling effect is very severe without the proposed decoupling structure.Therefore, a hybrid decoupling structure that comprises a neutralization line and a unique defective ground structure has provided improved isolation among the inter-elements.
The defective ground structure comprises a combination of horizontal and slotted vertical branches.The stubs incorporated in the ground plane create an alternate current path and thus reduce the coupling effects.Incorporating DGS could not provide the satisfactory isolation expected for a MIMO system.
To further enhance the isolation between the inter-elements, a rectangular neutralization line (NL) is introduced in the radiator.NL generates fields in the adjacent elements that have a magnitude that is out of phase and thus neutralizes the coupling current and thereby improves the isolation [24].The current distribution in figure 14 shows that the decoupling structure has the maximum current concentration.The S-parameters of the proposed antenna with respect to different evolution stages are shown in figures 15(a)-(b).
The current concentration in the ground and the NL ensures that the coupling current has been only concentrated in the decoupling structure and thus adjusting the corresponding length and width of the slots in the ground plane and the neutralization line performed through parametric analysis results in the enhanced isolation of better than −24 dB throughout the frequency range.The geometry of the proposed four-element antenna is shown in figure 16.

Equivalent circuit model of the proposed decoupling structure and antenna
This section explains the equivalent circuit model of the proposed hybrid decoupling structure and the antenna.For ease of analysis, the equivalent circuit model of the proposed antenna and the decoupling structure are investigated separately.The simulated S-parameters of the proposed antenna are realized using the circuit theory and the impedance method where the antenna is validated using the lumped circuit [7,26].The proposed decoupling structure can be modeled with a combination of lumped inductive and capacitive components (LC circuits).The proposed hybrid decoupling structure is modeled using the LC circuit) as illustrated in figure 17.The tuning of the corresponding lumped elements and further optimization is done using the NIAWR software.The conductive part between port1 and port2 is represented by inductance L2.The gap between the radiating part of the lowered ground plane is indicated by capacitance C2 and C3.The slotted and stub-integrated defective structures connected to the lowered ground are modeled as a combination of parallel LC tank circuits represented by L8-C4-L9.This is symmetrically replicated to the other side to form the LC circuit corresponding to the ground plane.The neutralization line in the radiator on the other hand (L1-C2), is coupled to the proposed DGS using the coupling capacitance indicated by CC1 and CC2, CC3 and CC4.This combination provides a band-stop characteristic contributing to enhanced isolation.The corresponding LC circuit is then tuned for each value of inductance and capacitance values to achieve the isolation S12 corresponding to the simulated transmission coefficient values.The corresponding tuned values of the LC circuit and the corresponding transmission coefficient are depicted in figure 17.
The equivalent circuit of the decoupling structure is further extended to form the entire equivalent circuit of the proposed four-element antenna.The equivalent circuit of the single-element antenna is initially designed and connected to the decoupling structure through a coupling capacitor.The antenna resonance is modeled using parallel RLC (Rx-Lx-Cx) components (that correspond to the real and imaginary part of the antenna impedance) that are connected to the decoupling structure through the inductance Ly as shown in figure 18(a).The excitation of the entire structure is provided using 50Ω ports.The entire circuit is tuned to match the

Antenna analysis for wearable applications 4.1. Bending analysis of the proposed four-element antenna
The conformability of the antenna is a relevant analysis when we consider any flexible antenna, especially for wearable applications.When the antenna is placed at various parts of the human body, the antenna bends according to the distinct curvature of the body parts at different locations of the human body.While bending the antenna across any radius, antenna's effective length gets altered and thereby detunes the antenna performance [1,3].The proposed antenna performance when bent for the x-axis (Rx-axis) and y-axis (Ry-axis) across different radii is investigated concerning the body curvature at different parts like leg, hand, thighs, etc as shown in   However, a slight shift in the frequency is noticed when bent across the y-axis as shown in figures 20(c)-(d).The gain value of the antenna showed a drop in the maximum bent condition when the antenna is bent at a 40 mm radius.The bandwidth of the antenna also shows a negligible drop since the effective length of the antenna gets altered due to bend and thereby shifting the frequency.The effect of all bending cases on all the parameters are not plotted due to brevity.However, for easy understanding, the S-parameter variations of the extreme bend condition for both x and y axis bend

SAR analysis of the proposed four-element antenna
When the antenna is kept near proximity of the human body, a fraction of radiated power gets absorbed by body due to the lossy human tissues [1][2][3].To check the feasibility of the antenna for practical applications, SAR analysis is performed by placing the antenna on a three-layer phantom model, having a dimension of 100 × 100 × 27 mm . 3This model consists of skin, fat, and muscle having different thicknesses, electrical as well as mechanical properties.SAR can be computed using equation (10).
where s is the conductivity of the tissue in S/m, E is rms electric field in V/m, and r is the tissue mass density in kg m −3 .
Any on-body communication scenario needs the antenna to be placed less than 5 mm from the surface of the skin.Therefore, the proposed MIMO antenna is kept at 5 mm from the skin layer imitating the real-time scenario of placing the antenna over the clothes that have a thickness of approximately 1-6 mm [17].SAR is calculated for 1 g and 10 g of tissue at the resonant frequency of 4.1 GHz.The input power of 100 mW is selected for calculating the SAR at the resonance frequency of 4.1 GHz which is the maximum permissible power that can be fed to the antenna as per the international guidelines for wearable applications [27][28][29].The dielectric properties of the human body tissues vary with frequencies [4].The properties of different tissues at 4.1 GHz are given in table 3 which is taken from the ITIS foundation database [30].
The simulated SAR value for 1 g and 10 g of tissue at 4.1 GHz is 0.745 W kg −1 and 0.326 W kg −1 respectively which is below the international standards.Figure 22 shows the simulated SAR results with the three-layer tissue model.

Results and discussion
This section describes the simulated and experimental findings of the proposed four-element Sub-6 GHz antenna.The antenna parameters such as scattering parameters, radiation pattern, MIMO diversity parameters, and the on-body loading measurement results are elaborated in this section.The antenna design and corresponding results and analysis are carried out in ANSYS HFSS simulation tool.The simulated and measured results are in line.However, slight deviations are seen due to fabrication and cable losses and testing system tolerance.The simulated and measured gain versus frequency of the proposed MIMO antenna is shown in figure 24(c).The peak measured gain of the proposed antenna is 4.9 dBi is achieved.However, a slight deviation in the gain curve is seen due to negligible cable losses.Figure 24(d) shows the photograph of the anechoic chamber set up for the radiation pattern measurement of the proposed antenna.

MIMO diversity characteristics
To validate MIMO antenna performance in real-time applications, different diversity parameters including envelope correlation coefficient (ECC), diversity gain (DG), mean effective gain (MEG), total active reflection coefficient (TARC), channel capacity loss (CCL) and multiplexing efficiency (ME) are investigated.ECC is one of the main metrics in investigating any MIMO system.ECC defines the correlation between the antenna elements and can be calculated using the S-parameters using the equation (11) given in [31,32].
The acceptable value of ECC is <0.5 for ideal MIMO applications.DG represents the transmission power loss when the diversity mechanism is performed in the MIMO system.TARC on the other hand provides the ratio of the incident to the radiated power of the MIMO system.MEG represents the ratio of power received by the diversity antenna to the isotropic antenna in any fading environment.The desirable value of MEG and DG is less than −3 dB and −10 dB respectively.The variation in the power of the MIMO antenna under test to the ideal MIMO antenna is termed multiplexing efficiency.CCL causes the loss of the channel capacity of the MIMO system.The desirable value of CCL is 0.4 bps/Hz.The aforementioned parameters can be computed using the equations (12)-( 16) [32].
where q is varies 0 to 180 degrees.
where R Y is the receiver antenna's correlation matrix given by: where , i j h h are total efficiency and ij r is the correlation between the ith and jth element respectively.ME is estimated using the CST Microwave Studio simulation tool.The proposed antenna exhibits ECC < 0.001, TARC < −10 dB, DG > 9.9, MEG ratio ∼ 0 dB, CCL < 0.3 bps Hz −1 , and ME < −0.5 over the entire bandwidth as shown in figure 25.

On-body measurement
The antenna performance in the interaction with the human body is reported in this section.The proposed fabricated antenna is placed on various locations of the realistic human (chest, thighs, and arm) which is considered relative to different curvature of the human body and the results are investigated as shown in figures 26(a)-(c).The antenna showed minimal deviation in the bandwidth when placed on the chest as it is like a planar surface with minimal deviations in its curvature compared to the other parts.When placed on arm and thigh the antenna showed a deviation in its bandwidth and resonance since the variation in bending alters the antenna's effective length and thus shifts the resonance.The dielectric characteristics including the conductivity, temperature, and dielectric constant values of the human body tissues also lead to the deviation in the antenna characteristics [33].The measured reflection coefficient of the antenna when placed in the above-specified locations is shown in 26(d).

Comparative analysis
This section provides a comparative analysis of the proposed design with the existing flexible MIMO antennas in the literature as shown in tables 4 and 5.In [5], the antenna has a comparatively good gain and low SAR values, however, the impedance bandwidth is less compared to the proposed antenna.Reference [11,13,34] show good gain values in the compromise of a large antenna volume.Moreover, in [11], the SAR value shows a higher value which is not suited for real-time body measurements.Reference [19] provides better isolation, however, the antennas show a low gain value.Reference20] shows less gain and bandwidth compared to the proposed antenna.The proposed antenna in this regard, provides a satisfactory gain, with a compact profile, and wider impedance bandwidth and exhibits a low SAR value which is within the international standards without any specific methodology implemented to reduce the same while keeping it at 5 mm from human body interaction.

Conclusion
A compact, wideband, flexible four-element Sub-6 GHz antenna is proposed for wearable applications.A unique decoupling structure with a neutralization line and a DGS contributes to isolation better than −24 dB.The MIMO diversity parameters like ECC, DG, TARC, MEG, ME, and CCL are investigated, and the antenna shows good results with values ECC <0.001, DG >9.99, TARC <−10 dB, MEG <−4, ME <−0.5 and CCL <0.3 bps Hz −1 proving its feasibility for real-time MIMO applications.Characteristic mode analysis (CMA) has been investigated to optimize the structure by identifying the significant and non-significant modes through modal significance and related current distribution as well as far-field patterns.Modifications are made on the structure in the region of maximum current concentration to achieve the desired wider bandwidth.The proposed antenna has an impedance bandwidth of 3.55-5.3GHz with S11 less than −10 dB which conforms to a wideband operation with satisfactory peak gain (4.9 dBi) and omni directional radiation characteristics.A bending analysis of the antenna is performed to investigate the conformal nature of the antenna and the results show that the antenna satisfies a good bending profile with minimal deviation in the scattering parameters.SAR analysis shows an acceptable figure (0.745 W kg −1 and 0.326W kg −1 for 1g and 10g) that confirms its suitability in 5G wearable applications.The on-body measurement results are satisfactory, which proves the suitability of the proposed antenna in the applications mentioned in the article.

Figure 1 .
Figure 1.Design of single element antenna (a) evolution stages (b) Reflection coefficient of all stages.

Figure 3 .
Figure 3. Designed layout of the radiator for mathematical modeling.

Figure 5 .
Figure 5. Surface current distribution and radiation patterns of the first five modes of antenna 1.

Figure 7 .
Figure 7. Surface current distribution and radiation patterns of the first five modes of antenna 2.

Figure 9 .
Figure 9. Surface current distribution and radiation patterns of the first five modes of antenna 3.

Figure 11 .
Figure 11.Surface current distribution and radiation patterns of the first five modes of antenna 4.

Figure 12 .
Figure 12.Four-element antenna without connected ground (a) schematic (b) current distribution at 4.1 GHz.

Figure 13 .
Figure 13.Evolution stages of the proposed four-element antenna (a) with the connected ground (b) with unique DGS (c) with proposed decoupling structure (unique DGS and NL).
plane symmetrically behind the feedline to improve impedance matching.The final stage (Antenna 3-proposed) consists of a neutralization line incorporated with the unique DGS in stage 2.

Figure 15 .
Figure 15.S-parameter plots of proposed four-element Sub-6 GHz flexible antenna with evolution stages of decoupling structure (a) Reflection coefficient (b) Isolation.
coefficient of the proposed four-element antenna as shown in figure 18(b).The values of the RLC components along with the inductance value that connects the decoupling structure are only mentioned in figure 18(a) since the LC values of the decoupling structure have been mentioned in figure 17(a).

Figure 19 .
Figure 19.Bending analysis of the proposed four-element antenna along the x and y-axis.

Figure 20 .
Figure 20.S-parameters of the proposed four-element antenna in bending scenario (a) reflection coefficient of R(x-axis) bend (b) transmission coefficient of R(x-axis) bend (c) reflection coefficient of R(y-axis) bend (d) transmission coefficient of R(y-axis) bend (e) reflection coefficient comparison of R(x-axis) 20 mm bend (f) transmission coefficient of R(x-axis) 20 mm bend (g) reflection coefficient comparison of R(y-axis) 40 mm bend (h) transmission coefficient comparison of R(y-axis) 40 mm bend.

Figure 21 .Figure 22 .
Figure 21.Simulated radiation patterns of the proposed four-element antenna in bending scenario (a) Rx bend-E plane (co and cross) (b) Rx bend-H plane (co and cross) (c) Ry bend-E plane (co and cross) (d) Ry bend-H plane (co and cross).

Figure 23 .
Figure 23.S-parameters of the proposed four-element antenna (a) Reflection coefficient (b) Transmission coefficient.

Figure 24 .
Figure 24.Measured results of the proposed four-element antenna (a) Simulated and measured radiation pattern (co E-plane) (b) Simulated and measured radiation pattern (co H-plane) (c) Gain over frequency (d) Radiation pattern measurement set up (anechoic chamber).

Figure 25 .
Figure 25.Diversity performance of the proposed antenna (a) ECC and DG (b) ME and CCL (c) MEG and TARC (d) TARC at different angles of incident wave.

figure 19 .
figure19.Therefore, the nearest average values of radius corresponding to the human body dimensions are considered[3].The antenna bent across three radii 20 mm, 30 mm, 60 mm, and 80 mm along the x-axis and 40 mm, 60 mm, and 80 mm along the y-axis as shown in figure19.The corresponding S-parameters of the antenna in the bending scenario are shown in figure20.The bending of the antenna in both the x-axis and the y-axis showed good performance.At the extreme condition of 20 mm in the x-axis bend, a shift in resonance from 4.1 GHz to 4.04 GHz was observed, however, there is no prominent shift in the bandwidth of the antenna.However, a slight shift in the frequency is noticed when bent across the y-axis as shown in figures 20(c)-(d).The gain value of the antenna showed a drop in the maximum bent condition when the antenna is bent at a 40 mm radius.The bandwidth of the antenna also shows a negligible drop since the effective length of the antenna gets altered due to bend and thereby shifting the frequency.The effect of all bending cases on all the parameters are not plotted due to brevity.However, for easy understanding, the S-parameter variations of the extreme bend condition for both x and y axis bend (20 and 40 mm respectively) are shown in figures 20(e)-(h).The radiation pattern of the antenna along the E-plane (co and cross) and H-plane (co and cross) in all the bending conditions is shown in figures 21(a)-(d).The antenna shows a omnidirectional radiation pattern along both axes.The summary of the antenna performance in the bending scenario is summarized in table 2.
figure19.Therefore, the nearest average values of radius corresponding to the human body dimensions are considered[3].The antenna bent across three radii 20 mm, 30 mm, 60 mm, and 80 mm along the x-axis and 40 mm, 60 mm, and 80 mm along the y-axis as shown in figure19.The corresponding S-parameters of the antenna in the bending scenario are shown in figure20.The bending of the antenna in both the x-axis and the y-axis showed good performance.At the extreme condition of 20 mm in the x-axis bend, a shift in resonance from 4.1 GHz to 4.04 GHz was observed, however, there is no prominent shift in the bandwidth of the antenna.However, a slight shift in the frequency is noticed when bent across the y-axis as shown in figures 20(c)-(d).The gain value of the antenna showed a drop in the maximum bent condition when the antenna is bent at a 40 mm radius.The bandwidth of the antenna also shows a negligible drop since the effective length of the antenna gets altered due to bend and thereby shifting the frequency.The effect of all bending cases on all the parameters are not plotted due to brevity.However, for easy understanding, the S-parameter variations of the extreme bend condition for both x and y axis bend (20 and 40 mm respectively) are shown in figures 20(e)-(h).The radiation pattern of the antenna along the E-plane (co and cross) and H-plane (co and cross) in all the bending conditions is shown in figures 21(a)-(d).The antenna shows a omnidirectional radiation pattern along both axes.The summary of the antenna performance in the bending scenario is summarized in table 2.

Figure 26 .
Figure 26.Image of On-body measurement of the proposed four-element antenna on (a) chest (b) arm (c) thigh (d)Measured reflection coefficient on chest, arm, and thigh.

Figure 23 (
b) shows the port-to-port isolation of the proposed antenna.The unique slotted and stub integrated defective ground structure and the neutralization line in the radiator contribute to enhanced isolation.The measured antenna isolation is better than −24 dB throughout the bandwidth.The radiation pattern of the proposed antenna is tested in the anechoic chamber.The proposed fourelement antenna shows an omnidirectional radiation pattern as shown in figures 24(a)-(b).

Table 2 .
Summary of bending analysis.

Table 4 .
Comparison of proposed antenna with other wearable mimo antenna in literature.

Table 5 .
Comparison of diversity parameters, isolation, and SAR value with known literature.Scattering parameters and radiation characteristics The scattering parameters of the proposed antenna are shown in figure 23.The antenna has a simulated and measured impedance bandwidth of 40.0%(3.6-5.4GHz) and 39.54% (3.55-5.3GHz).The S-parameter results are measured with R&S ZNB 40 Vector Network Analyzer.