Design and Optimization of a Compact Super-Wideband MIMO Antenna with High Isolation and Gain for 5G Applications

: This paper presents a super-wideband multiple-input multiple-output (SWB MIMO) antenna with low proﬁle, low mutual coupling, high gain, and compact size for microwave and millimeter-wave (mm-wave) ﬁfth-generation (5G) applications. A single antenna is a simple elliptical-square shape with a small physical size of 20 × 20 × 0.787 mm 3 . The combination of both square and elliptical shapes results in an exceptionally broad impedance bandwidth spanning from 3.4 to 70 GHz. Antenna dimensions are optimized using the trust-region algorithm to enhance its impedance bandwidth and maintain the gain within a predeﬁned limit across the entire band. For that purpose, regularized merit function is deﬁned, which permits to control both the single antenna reﬂection response and gain. Subsequently, the SWB MIMO system is constructed with four radiators arranged orthogonally. This arrangement results in high isolation, better than 20 dB, over a frequency band from 3.4 to 70 GHz band. Further, the system achieves an average gain of approximately 7 dB below 45 GHz and a maximum gain equal to 12 dB for 70 GHz. The system exhibits excellent diversity performance throughout the entire bandwidth, as evidenced by the low envelope correlation coefﬁcient (ECC) (<3 × 10 − 3 ), total active reﬂection coefﬁcient (TARC) ( ≤− 10 dB), and channel capacity loss (CCL) (<0.3 bit/s/Hz) metrics, as well as the high diversity gain (DG) of approximately 10 dB. Experimental validation of the developed SWB MIMO demonstrates a good matching between the measurements and simulations.


Introduction
Over the years, the telecommunication industry has experienced a rapid growth due to the emergence of advanced technologies in wireless communication.To comply with the network and data traffic requirements, the fifth-generation (5G) technology has been deployed, providing broad bandwidth and data rates as high as multi-gigabits per second (Gbps) [1,2].In 5G technology, various frequency bands are employed across both microwave and millimeter-wave (mm-wave) spectra.A band of 3.5 GHz is utilized at sub-6 GHz with an enhanced bandwidth compared to the existing 4G bands [3].The mm-wave bands at 26, 28, 38, 50, and 60 GHz offer higher data rates than sub-6 GHz bands, mainly due to their wider bandwidth [4][5][6].The 5G networks enable vital technologies for deploying the Internet of Things (IoT).Consequently, it is crucial for IoT devices to be 5G-compliant [7].To achieve this, cost-effective, compact-sized, high-gain, and efficient antennas with broad bandwidth are essential [8].
Ultra-wideband (UWB) radio technology has gained significant attention for its low power consumption and high data rate, making it suitable for numerous applications.performance in terms of SWB , high gain (maximum of 12 dB), and low mutual coupling (<−20 dB).The system covers various wireless communication bands, including 5G sub-6 GHz, K/Ku-band, and 5G mm-wave.Upon manufacturing and testing the system, the simulation results were verified, and its real-world performance was assessed.The contributions of this work are summarized as follows: I.
Designed a compact antenna with a simple structure to attain both SWB and high gain performance; II.
An innovative optimization technique was employed to achieve an exceptionally wide bandwidth spanning from 3.4 to 70 GHz, with peak gain reaching 12 dB at 70 GHz.This optimization method employed a gradient-based algorithm with numerical derivatives and design-goal regularization to simultaneously optimize the structural dimensions, achieving both SWB and high gain, all while maintaining a low profile and compact size of 20 × 20 × 0.787 mm 3 ; III.
Implemented an orthogonal arrangement of a four-port SWB MIMO antenna to achieve isolation exceeding 20 dB and outstanding diversity performance, all without the need for any decoupling techniques.
The system exhibited a remarkable level of isolation and gain, while retaining a compact size and minimal complexity, surpassing the state-of-the-art structures.As the IoT and 5G technologies continue to shape smart cities, the SWB MIMO system developed in this study has promising applications in various areas including intelligent medical treatment, household and street management, energy management, and environmental well-being.

SIW-Based Series-Fed Dipole
A simple monopole antenna based on the elliptical-square shape is proposed in this work to achieve a super-wide operating frequency band.The design steps of the developed SWB antenna, as well as its configuration, are shown in Figure 1.The antenna was printed on a low-loss Rogers RT5880 substrate, which had a dielectric constant of 2.2, a tangent loss of 0.0009, and a thickness of 0.787 mm.The metallic copper layer had a thickness of 0.0175 mm.The initial stage involved selecting an elliptical patch that provided a broad frequency range, as shown in Figure 1a.A partial ground was incorporated to guarantee a wide impedance bandwidth [23].Additionally, a rectangular notch measuring 2 × 1 mm 2 was created on the ground plane to serve the same purpose [24].The design generated three frequency bands with broad impedance bandwidths, two below 20 GHz, and one above 41 GHz, namely 6.5−11.2GHz, 12.8−19.7GHz, and 41.7−70 GHz, as depicted by the reflection characteristics (marked as Step 1 in Figure 2).Afterwards, a square shape was integrated into the center of the elliptical shape to enhance the bandwidth, as depicted in Figure 1b.The inclusion of the square shape resulted in broadening the bandwidth below 20 GHz (3.6-19.7 GHz) and above 33 GHz (33.2-70GHz), as illustrated in Figure 2 (Step 2).
Although the elliptical-square shape offered two broad impedance bandwidths, rigorous optimization could further enhance the response and provide the SWB property.However, this process requires numerous EM simulations, which can be time-consuming and also requires human intervention after each simulation.Numerical optimization can help reduce the time necessary to adjust the structure dimensions.Since the antenna response often relies on appropriate refinement of its parameters and there exist no precise formulas for designing all antenna structures, implementing optimization methods is the most effective approach to achieve the desired outcome with less time and effort.This work utilized the trust-region local optimization procedure to identify optimal antenna dimensions and improve the impedance bandwidth.The details of the optimization process can be found in Section 3.
work utilized the trust-region local optimization procedure to identify optimal antenna dimensions and improve the impedance bandwidth.The details of the optimization process can be found in Section 3.

SWB Performance Optimization
The major objective of the design process was to ensure impedance matching of the antenna over the frequency range 3.4 ≤ f ≤ 70 GHz (covering the 5G microwave and mmwave bands), more specifically, to fulfill the condition |S11(x,f)| ≤ -10 dB for all f  F = [3.470.0] GHz, where x is a vector of adjustable parameters.Interactive manipulation of antenna geometry parameters using parameter sweeping or similar methods is not capable of identifying the optimum design, partly due to variable interactions, but also due to a very-broad range of operating frequencies to be controlled.In this paper, a rigorous numerical optimization was applied instead as outlined below.The designable parameters selected for the optimization process were gathered into a parameter vector x = [ay ax sl sw L2 sh] T , and all explained in Figure 1c.The search process was conducted over the design space X, demarked by the lower and upper bounds on the variables: 4 ≤ ax, ay ≤ 6 work utilized the trust-region local optimization procedure to identify optimal antenna dimensions and improve the impedance bandwidth.The details of the optimization process can be found in Section 3.

SWB Performance Optimization
The major objective of the design process was to ensure impedance matching of the antenna over the frequency range 3.4 ≤ f ≤ 70 GHz (covering the 5G microwave and mmwave bands), more specifically, to fulfill the condition |S11(x,f)| ≤ -10 dB for all f  F = [3.470.0] GHz, where x is a vector of adjustable parameters.Interactive manipulation of antenna geometry parameters using parameter sweeping or similar methods is not capable of identifying the optimum design, partly due to variable interactions, but also due to a very-broad range of operating frequencies to be controlled.In this paper, a rigorous numerical optimization was applied instead as outlined below.The designable parameters selected for the optimization process were gathered into a parameter vector x = [ay ax sl sw L2 sh] T , and all explained in Figure 1c.The search process was conducted over the design space X, demarked by the lower and upper bounds on the variables: 4 ≤ ax, ay ≤ 6

SWB Performance Optimization
The major objective of the design process was to ensure impedance matching of the antenna over the frequency range 3.4 ≤ f ≤ 70 GHz (covering the 5G microwave and mm-wave bands), more specifically, to fulfill the condition |S 11 (x,f )| ≤ -10 dB for all f ∈ F = [3.470.0] GHz, where x is a vector of adjustable parameters.Interactive manipulation of antenna geometry parameters using parameter sweeping or similar methods is not capable of identifying the optimum design, partly due to variable interactions, but also due to a very-broad range of operating frequencies to be controlled.In this paper, a rigorous numerical optimization was applied instead as outlined below.The designable parameters selected for the optimization process were gathered into a parameter vector x = [ay ax sl sw L 2 sh] T , and all explained in Figure 1c.The search process was conducted over the design space X, demarked by the lower and upper bounds on the variables: 4 ≤ ax, ay ≤ 6 mm, 9 ≤ sl ≤ 14 mm, 5 ≤ sw ≤ 7 mm, 2 ≤ L 2 ≤ 4 mm, and -3 ≤ sh ≤ 3 mm.Furthermore, the following geometry constraints were to be satisfied: ax < ay (to ensure that the major antenna axis was oriented towards the y-direction), sl > 2ax (to ensure that the radiator was beyond a trivial elliptical shape), sw < 2ay (to ensure that the radiator shape was not purely square), and -(ay − sw/2) < sh < (ay − sw/2).The reason for introducing the last constraint is as follows.The midpoint of the square coincides with the center of the elliptical shape and it can be vertically adjusted using sh.It should be noted that this movement does not exceed the y-axis dimension of the elliptical shape.There is also an additional constraint concerning the field properties of the antenna, namely, a requirement that the gain G(x,f ) ≥ 5 dB for f ∈ F. Given the primary objective and the constraints, the merit function undergoing minimization is formulated as follows where is the minimum in-band gain.The optimum solution x * is the identified by solving a nonlinear minimization task Reducing the value of U(x) corresponds to improving the impedance matching, as well as enforcing the condition imposed upon the antenna gain.The second term in ( 1) is proportional to a relative violation of the condition G(x,f ) ≥ 5 dB, with the proportionality coefficient β [25] set to 100.With this value, violations larger than a fraction of dB will result in considerable contribution of the penalty term to U, thereby fostering design relocation towards designs that satisfy that condition.At this point, it should be emphasized that implicit handling of the gain-related constraint [26] is recommended because it is a computationally-expensive one (requires EM simulation to be evaluated).The underpinning optimization engine is the trust-region (TR) algorithm [27].The Jacobian matrix of the antenna response is evaluated by means of finite differentiation [28].The TR algorithm produces a series x (i) , i = 0, 1, . .., of approximations to x * as In (4), U L (i) is the objective function defined as in (1) but computed based on the firstorder linear approximation model of antenna responses.For example, for the reflection response, we have where ∇S 11 (x (i) ,f ) is the gradient of the reflection response at design x (i) and frequency f.The linear model for the gain characteristics was defined in a similar manner.The size d (i) of the search region was set at the beginning of each algorithm iteration using standard TR rules [27].The optimization was concluded when converging in argument (||x (i+1) − x (i) || < ε; here, ε = 10 −3 ).The starting design x (0) = [5.5 4.5 11.0 6.0 2.8 0.0] T was established by means of interactive parametric studies.The final (optimized) design was found to be x * = [5.5994.186 10.917 6.363 3.501 1.499] T mm.It should be noted that the optimization algorithm was implemented as an external procedure written in Matlab (Matlab 9.0.0.341360 (R2016a)).Such an implementation was much more flexible than the built-in CST (CST Studio Suite 2019) algorithms and, in particular, it allowed for a straightforward and easy control over all components of the optimization process.This was especially pertinent to the constrained objective function (1), which cannot be implemented using the built-in optimization capabilities of the simulation software.The connection between Matlab and CST was realized using Visual Basic scripts, which were used to modify the values of design parameters (as requested by the optimization engine) within the antenna project, initiate batch-mode simulation, as well as acquire and post-process the results.Figure 2 (Step 2) and 3 show the antenna responses at the optimal and initial points.The optimized antenna exhibits an SWB spanning from 3.4 to 70 GHz and a gain exceeding 5 dB, cf. Figure 3.The radiation efficiency of the SWB antenna is depicted in Figure 3b, revealing that the average radiation efficiency of the examined antenna stood at 70.6%, with a peak efficiency reaching 86.2%.
Electronics 2023, 12, x FOR PEER REVIEW 6 of 16 built-in optimization capabilities of the simulation software.The connection between Matlab and CST was realized using Visual Basic scripts, which were used to modify the values of design parameters (as requested by the optimization engine) within the antenna project, initiate batch-mode simulation, as well as acquire and post-process the results.Figure 2 (Step 2) and 3 show the antenna responses at the optimal and initial points.The optimized antenna exhibits an SWB spanning from 3.4 to 70 GHz and a gain exceeding 5 dB, cf. Figure 3.The radiation efficiency of the SWB antenna is depicted in Figure 3b, revealing that the average radiation efficiency of the examined antenna stood at 70.6%, with a peak efficiency reaching 86.2%.

SWB MIMO Antenna Design
As mentioned earlier, MIMO technology has the potential to enhance communication systems by improving the link quality and mitigating the effects of multipath fading.When combined with the SWB property, this technology can improve communication systems even further.In this section, we present a SWB MIMO antenna, which consists of four SWB elements arranged in an orthogonal configuration.This arrangement provides high isolation across the entire bandwidth and excellent diversity performance compared to a series arrangement or even an opposite orientation.It can mitigate the limitations of both the series and opposite orientations, where the spacing between the ground planes is sufficient to prevent high mutual coupling, and where the patches are adequately spaced to enhance the overall isolation of the system.The CST-Microwave Studio-2019 was used to simulate the SWB MIMO system with a hexahedral mesh accuracy of −40 dB. Figure 4 illustrates the proposed system configuration, which was implemented on a Rogers substrate with compact dimensions of 40 × 40 × 0.787 mm³. Figure 5 shows the simulated reflection and transmission coefficients, here, presented for S11, S21, S31, and S41 only due to the antenna symmetry.Although MIMO systems have multiple elements, their reflection coefficients behave similarly to that of a single-element antenna.As a result, MIMO systems can offer a wide range of frequencies, ranging from 3.4−70 GHz.On the other hand, the MIMO elements' orthogonal configuration improves their isolation, resulting in S21, S31, and S41 magnitudes of less than −20 dB across the entire frequency range,

SWB MIMO Antenna Design
As mentioned earlier, MIMO technology has the potential to enhance communication systems by improving the link quality and mitigating the effects of multipath fading.When combined with the SWB property, this technology can improve communication systems even further.In this section, we present a SWB MIMO antenna, which consists of four SWB elements arranged in an orthogonal configuration.This arrangement provides high isolation across the entire bandwidth and excellent diversity performance compared to a series arrangement or even an opposite orientation.It can mitigate the limitations of both the series and opposite orientations, where the spacing between the ground planes is sufficient to prevent high mutual coupling, and where the patches are adequately spaced to enhance the overall isolation of the system.The CST-Microwave Studio-2019 was used to simulate the SWB MIMO system with a hexahedral mesh accuracy of −40 dB. Figure 4 illustrates the proposed system configuration, which was implemented on a Rogers substrate with compact dimensions of 40 × 40 × 0.787 mm 3 .Figure 5 shows the simulated reflection and transmission coefficients, here, presented for S 11 , S 21 , S 31 , and S 41 only due to the antenna symmetry.Although MIMO systems have multiple elements, their reflection coefficients behave similarly to that of a single-element antenna.As a result, MIMO systems can offer a wide range of frequencies, ranging from 3.4−70 GHz.On the other hand, the MIMO elements' orthogonal configuration improves their isolation, resulting in S 21 , S 31 , and S 41 magnitudes of less than −20 dB across the entire frequency range, as illustrated in Figure 5.The system achieved these properties without utilizing any decoupling techniques that could have increased its size and complexity.Through an analysis of the surface current distribution of the four SWB MIMO antenna elements, it was possible to explain their low mutual coupling.The system components are identified as Antenna 1, 2, 3, and 4. Figure 6 displays the simulated current distributions at 28 GHz, with the excitation at Port 1 and the remaining ports terminated by a 50-Ω load.It is noteworthy that mutual coupling among the antenna elements was low, with the current concentrated at Port 1 and negligible at the remaining ports.The analysis indicates that the antennas have minimum interaction with each other.
as illustrated in Figure 5.The system achieved these properties without utilizing any decoupling techniques that could have increased its size and complexity.Through an analysis of the surface current distribution of the four SWB MIMO antenna elements, it was possible to explain their low mutual coupling.The system components are identified as Antenna 1, 2, 3, and 4. Figure 6 displays the simulated current distributions at 28 GHz, with the excitation at Port 1 and the remaining ports terminated by a 50-Ω load.It is noteworthy that mutual coupling among the antenna elements was low, with the current concentrated at Port 1 and negligible at the remaining ports.The analysis indicates that the antennas have minimum interaction with each other.

Results
Ant. 1 as illustrated in Figure 5.The system achieved these properties without utilizing any decoupling techniques that could have increased its size and complexity.Through an analysis of the surface current distribution of the four SWB MIMO antenna elements, it was possible to explain their low mutual coupling.The system components are identified as Antenna 1, 2, 3, and 4. Figure 6 displays the simulated current distributions at 28 GHz, with the excitation at Port 1 and the remaining ports terminated by a 50-Ω load.It is noteworthy that mutual coupling among the antenna elements was low, with the current concentrated at Port 1 and negligible at the remaining ports.The analysis indicates that the antennas have minimum interaction with each other.

Results
Ant. 1 as illustrated in Figure 5.The system achieved these properties without utilizing any decoupling techniques that could have increased its size and complexity.Through an analysis of the surface current distribution of the four SWB MIMO antenna elements, it was possible to explain their low mutual coupling.The system components are identified as Antenna 1, 2, 3, and 4. Figure 6 displays the simulated current distributions at 28 GHz, with the excitation at Port 1 and the remaining ports terminated by a 50-Ω load.It is noteworthy that mutual coupling among the antenna elements was low, with the current concentrated at Port 1 and negligible at the remaining ports.The analysis indicates that the antennas have minimum interaction with each other.

Results
The optimal MIMO system was fabricated to confirm the numerical simulation outcomes, and to showcase its applicability for 5G systems.The fabricated prototype is shown in the inset of Figure 7. Measurements of the reflection and transmission coefficients were performed using the Anritsu vector network analyzer MS4644B (0-40 GHz).The radiation patterns were validated in the anechoic chamber, as depicted in Figure 7.It is important to note that the measurements of the reflection coefficient, mutual coupling, and gain were limited to 40 GHz, as the measurement range of the MS4644B VNA device used only extends up to 40 GHz.The optimal MIMO system was fabricated to confirm the numerical simulation outcomes, and to showcase its applicability for 5G systems.The fabricated prototype is shown in the inset of Figure 7. Measurements of the reflection and transmission coefficients were performed using the Anritsu vector network analyzer MS4644B (0-40 GHz).The radiation patterns were validated in the anechoic chamber, as depicted in Figure 7.It is important to note that the measurements of the reflection coefficient, mutual coupling, and gain were limited to 40 GHz, as the measurement range of the MS4644B VNA device used only extends up to 40 GHz.One can observe an acceptable match between both datasets using MS4644B VNA, which has a measurement range that extends up to 40 GHz.However, there is a noticeable difference between the measured and simulated data, particularly at higher frequencies.This is attributed to several factors, such as fabrication tolerances, cable loss, inaccuracies in assembly, and the utilization of large end-launch connectors.bands.One can observe an acceptable match between both datasets using MS4644B VNA, which has a measurement range that extends up to 40 GHz.However, there is a noticeable difference between the measured and simulated data, particularly at higher frequencies.This is attributed to several factors, such as fabrication tolerances, cable loss, inaccuracies in assembly, and the utilization of large end-launch connectors.
comes, and to showcase its applicability for 5G systems.The fabricated prototype i shown in the inset of Figure 7. Measurements of the reflection and transmission coeffi cients were performed using the Anritsu vector network analyzer MS4644B (0-40 GHz) The radiation patterns were validated in the anechoic chamber, as depicted in Figure 7.I is important to note that the measurements of the reflection coefficient, mutual coupling and gain were limited to 40 GHz, as the measurement range of the MS4644B VNA device used only extends up to 40 GHz.One can observe an acceptable match between both datasets using MS4644B VNA, which has a measurement range that extends up to 40 GHz.However, there is a noticeable dif ference between the measured and simulated data, particularly at higher frequencies.Thi is attributed to several factors, such as fabrication tolerances, cable loss, inaccuracies in assembly, and the utilization of large end-launch connectors.The measured isolation between the four ports, |S 21 |, |S 21 | , and |S 21 |, shows a strong resemblance to the simulation, thus validating that SWB MIMO offers an isolation of better than 20 dB across the entire range, cf.(Figure 9). Figure 10 displays the MIMO's simulated and measured maximum realized gain plots when exciting Port 1 and terminating the remaining ports with a 50-Ω load.As previously stated, the measurements were conducted up to 40 GHz using the VNA available in our laboratory.Nonetheless, the trends observed in the measured gain results suggest that the results beyond 40 GHz could also be favorable.The average gain of the n system was approximately 7 dB up to 44 GHz, and it exceeded 10 dB beyond 50 GHz.The measured isolation between the four ports, |S21|, |S21|, and |S21|, shows a strong resemblance to the simulation, thus validating that SWB MIMO offers an isolation of better than 20 dB across the entire range, cf.(Figure 9). Figure 10 displays the MIMO's simulated and measured maximum realized gain plots when exciting Port 1 and terminating the remaining ports with a 50-Ω load.As previously stated, the measurements were conducted up to 40 GHz using the VNA available in our laboratory.Nonetheless, the trends observed in the measured gain results suggest that the results beyond 40 GHz could also be favorable.The average gain of the n system was approximately 7 dB up to 44 GHz, and it exceeded 10 dB beyond 50 GHz.There is good matching between the two datasets, although a minor discrepancy is observed.This discrepancy may be explained, as previously, by inaccuracies pertaining to manufacturing; the other reasons may include imprecise assembly of the antenna or The measured isolation between the four ports, |S21|, |S21|, and |S21|, shows a strong resemblance to the simulation, thus validating that SWB MIMO offers an isolation of better than 20 dB across the entire range, cf.(Figure 9). Figure 10 displays the MIMO's simulated and measured maximum realized gain plots when exciting Port 1 and terminating the remaining ports with a 50-Ω load.As previously stated, the measurements were conducted up to 40 GHz using the VNA available in our laboratory.Nonetheless, the trends observed in the measured gain results suggest that the results beyond 40 GHz could also be favorable.The average gain of the n system was approximately 7 dB up to 44 GHz, and it exceeded 10 dB beyond 50 GHz.There is good matching between the two datasets, although a minor discrepancy is observed.This discrepancy may be explained, as previously, by inaccuracies pertaining to manufacturing; the other reasons may include imprecise assembly of the antenna or There is good matching between the two datasets, although a minor discrepancy is observed.This discrepancy may be explained, as previously, by inaccuracies pertaining to manufacturing; the other reasons may include imprecise assembly of the antenna or inaccurate angular placement of the antenna in the chamber.The E-plane and H-plane radiation patterns at 3.5 GHz, 10 GHz, 20 GHz, 28 GHz, 38 GHz, 45 GHz, and 65 GHz are shown in Figure 11a-g, where the measured and simulated results at Port 1are presented.The measured results are available for the initial five frequencies up to 40 GHz, as constrained by the mentioned measurement limitations.Conversely, simulated radiation results at 45 GHz and 65 GHz are provided to offer a more comprehensive perspective on radiation across the entire bandwidth.The radiation patterns at 3.5 GHz display bidirectional and omnidirectional characteristics in the E-plane and H-plane, respectively, with a low level of cross-polarized fields.At 10 GHz and 20 GHz, the MIMO system maintained low crosspolarization levels.However, at higher frequencies, both the E-plane and H-plane exhibit distorted omnidirectional patterns and high cross-polarization levels due to the excitation of higher order modes.

MIMO Performance
To evaluate the performance of a system, it is crucial to consider the correlation between MIMO ports.In this study, the four-element SWB MIMO system was analyzed using various parameters, including envelope correlation coefficient (ECC), diversity gain (DG), total active reflection coefficient (TARC), and channel capacity loss (CCL).These parameters were used to assess the system's reliability.ECC measures the correlation between MIMO elements, with an ideal value of zero, and a practical limit of below 0.5 [29,30].It can be determined from the S-parameters as [31] where ECC ij indicates the correlation between the ith and jth MIMO elements.The simulated and measured ECC plots of the developed SWB MIMO system are shown in Figure 12a.
The ECC is <3 × 10 −3 for the entire bandwidth, satisfying the wireless network requirement (ECC < 0.5) [32].The difference observed between the simulated and measured ECC can be attributed to the previously mentioned inconsistency in the simulation and measurement S-parameters.The DG, which shows the degree of transmission power reduction, constitutes an important performance metric.It is computed from the ECC as follows [33] Electronics 2023, 12, x FOR PEER REVIEW 12 of 16 To evaluate the performance of a system, it is crucial to consider the correlation between MIMO ports.In this study, the four-element SWB MIMO system was analyzed using various parameters, including envelope correlation coefficient (ECC), diversity gain (DG), total active reflection coefficient (TARC), and channel capacity loss (CCL).These parameters were used to assess the system's reliability.ECC measures the correlation between MIMO elements, with an ideal value of zero, and a practical limit of below 0.5 [29,30].It can be determined from the S-parameters as [31] where   indicates the correlation between the i th and j th MIMO elements.The simulated and measured ECC plots of the developed SWB MIMO system are shown in Figure 12a.The ECC is <3 × 10 −3 for the entire bandwidth, satisfying the wireless network requirement (ECC < 0.5) [32].The difference observed between the simulated and measured ECC can be attributed to the previously mentioned inconsistency in the simulation and measurement S-parameters.The DG, which shows the degree of transmission power reduction, constitutes an important performance metric.It is computed from the ECC as follows [33]  In general, higher DG values indicate better MIMO performance.Figure 12b presents the simulated and measured DG results, which show high DG values across the entire bandwidth, approaching the standard of 10 dB.Another crucial factor in evaluating the MIMO performance is TARC, which is defined as the ratio of the square root of the total reflected power to the square root of the total incident power.It is used to identify the operating bands of a MIMO antenna as well as radiation performance when modifying the phase of the input signal.The TARC can be calculated using the following expression [34]: In general, higher DG values indicate better MIMO performance.Figure 12b presents the simulated and measured DG results, which show high DG values across the entire bandwidth, approaching the standard of 10 dB.Another crucial factor in evaluating the MIMO performance is TARC, which is defined as the ratio of the square root of the total reflected power to the square root of the total incident power.It is used to identify the operating bands of a MIMO antenna as well as radiation performance when modifying the phase of the input signal.The TARC can be calculated using the following expression [34]: where θ i refers to excitation phase angle of the ith signal.Figure 13a depicts the simulated and measured TARC plots, indicating values of ≤−10 dB across the entire bandwidth [35].This provides additional evidence of the proposed system's SWB characteristic.The CCL is another essential parameter to assess the performance of MIMO systems, which quantifies channel capacity losses.The following equations can be used to calculate it [36]: where A is the correlation matrix, √ 4 where   refers to excitation phase angle of the ith signal.Figure 13a depicts the simulated and measured TARC plots, indicating values of ≤−10 dB across the entire bandwidth [35].This provides additional evidence of the proposed system's SWB characteristic.The CCL is another essential parameter to assess the performance of MIMO systems, which quantifies channel capacity losses.The following equations can be used to calculate it [36]: where A is the correlation matrix, Figure 13b shows the simulated and measured CCL results, which indicate values lower than the established standard of 0.4 bit/s/Hz.These values are lower than the practical standard of 0.4 bit/s/Hz [37].The proposed system demonstrates excellent diversity performance, as indicated by the low ECC (<3 × 10 −3 ), TARC (≤−10 dB), and CCL (<0.3 bit/s/Hz) values, as well as the high DG (≈10 dB) across the entire bandwidth.These results are indicative of the suitability of the system for transmission systems featuring a high data rate.
Table 1 presents a performance comparison between the proposed SWB MIMO and the state-of-the-art structures reported in the recent literature.In contrast to previous findings, the SWB MIMO antenna developed in this work demonstrates the highest isolation and bandwidth.Importantly, these properties are achieved without employing any decoupling techniques that could have increased the system's size and complexity.Additionally, it features a compact and low-profile design, high gain, and excellent diversity performance.
A compact self-decoupling MIMO on single-layer Rogers PCB with SWB, and high isolation and gain properties for 5G microwave and mm-wave applications, was developed.The proposed antenna design utilizes a simple elliptical-square structure that combines these two shapes to achieve SWB spanning from 3.4 GHz to 70 GHz.The antenna is capable of covering 5G frequency bands at 3.5, 26, 28, 38, 50, and 60 GHz.A gradientbased algorithm with numerical derivatives and design-goal regularization was utilized for antenna parameter refinement and simultaneously ensured SWB and high gain.Figure 13b shows the simulated and measured CCL results, which indicate values lower than the established standard of 0.4 bit/s/Hz.These values are lower than the practical standard of 0.4 bit/s/Hz [37].The proposed system demonstrates excellent diversity performance, as indicated by the low ECC (<3 × 10 −3 ), TARC (≤−10 dB), and CCL (<0.3 bit/s/Hz) values, as well as the high DG (≈10 dB) across the entire bandwidth.These results are indicative of the suitability of the system for transmission systems featuring a high data rate.
Table 1 presents a performance comparison between the proposed SWB MIMO and the state-of-the-art structures reported in the recent literature.In contrast to previous findings, the SWB MIMO antenna developed in this work demonstrates the highest isolation and bandwidth.Importantly, these properties are achieved without employing any decoupling techniques that could have increased the system's size and complexity.Additionally, it features a compact and low-profile design, high gain, and excellent diversity performance.Windmill shape [18] Yagi antenna (0.2 × 0.25) (FR-4) A compact self-decoupling MIMO on single-layer Rogers PCB with SWB, and high isolation and gain properties for 5G microwave and mm-wave applications, was developed.The proposed antenna design utilizes a simple elliptical-square structure that combines these two shapes to achieve SWB spanning from 3.4 GHz to 70 GHz.The antenna is capable of covering 5G frequency bands at 3.5, 26, 28, 38, 50, and 60 GHz.A gradientbased algorithm with numerical derivatives and design-goal regularization was utilized for antenna parameter refinement and simultaneously ensured SWB and high gain.

Conclusions
Afterwards, the MIMO system was implemented with four radiators arranged orthogonally.This configuration helps to lower the mutual coupling to below −20 dB in the entire bandwidth.Further, it provides a high gain that exceeds 10 dB beyond 50 GHz and reaches a maximum of 12 dB at 70 GHz.The system displays excellent diversity performance, which is confirmed by the low ECC, TARC, and CCL metrics, along with the high DG values.The developed SWB MIMO system was experimentally validated.Good agreement between the simulated and measured data was observed.Overall, the proposed design provides a compact, low-cost, low-profile system of lower complexity featuring high isolation and gain, and a very-broad bandwidth in comparison to the state-of-the-art designs.

Figure 2 .
Figure 2. Reflection coefficients of the SWB antenna evaluation steps.Step 2 presents the S11 results before optimization.

Figure 2 .
Figure 2. Reflection coefficients of the SWB antenna evaluation steps.Step 2 presents the S11 results before optimization.

Figure 2 .
Figure 2. Reflection coefficients of the SWB antenna evaluation steps.Step 2 presents the S 11 results before optimization.

Figure 3 .
Figure 3.The SWB antenna performance, (a) the reflection coefficient and gain, and (b) the efficiency.

Figure 3 .
Figure 3.The SWB antenna performance, (a) the reflection coefficient and gain, and (b) the efficiency.

Figure 4 .
Figure 4. Configuration of the developed SWB MIMO system.

Figure 6 .
Figure 6.The simulated current distribution of SWB MIMO system at.

Figure 4 .
Figure 4. Configuration of the developed SWB MIMO system.

Figure 4 .
Figure 4. Configuration of the developed SWB MIMO system.

Figure 6 .
Figure 6.The simulated current distribution of SWB MIMO system at.

Figure 4 .
Figure 4. Configuration of the developed SWB MIMO system.

Figure 6 .
Figure 6.The simulated current distribution of SWB MIMO system at.

Figure 6 .
Figure 6.The simulated current distribution of SWB MIMO system at.

Figure 7 .
Figure 7.The MIMO antenna in the anechoic chamber.The inset shows a magnified picture of the fabricated prototype.

Figures 8
Figures 8 and 9 illustrate the comparison between the simulated, measured |S11|, and mutual couplings |S21|, |S21|, and |S21|.The developed SWB MIMO provided a wide impedance bandwidth ranging from 3.4 to 70 GHz, effectively covering the all 5G bands.One can observe an acceptable match between both datasets using MS4644B VNA, which has a measurement range that extends up to 40 GHz.However, there is a noticeable difference between the measured and simulated data, particularly at higher frequencies.This is attributed to several factors, such as fabrication tolerances, cable loss, inaccuracies in assembly, and the utilization of large end-launch connectors.

Figure 8 .
Figure 8. Simulated and measured reflection coefficients at Port 1.

Figure 7 .
Figure 7.The MIMO antenna in the anechoic chamber.The inset shows a magnified picture of the fabricated prototype.

Figures 8
Figures 8 and 9 illustrate the comparison between the simulated, measured |S 11 |, and mutual couplings |S 21 |, |S 21 |, and |S 21 |.The developed SWB MIMO provided a wide impedance bandwidth ranging from 3.4 to 70 GHz, effectively covering the all 5Gbands.One can observe an acceptable match between both datasets using MS4644B VNA, which has a measurement range that extends up to 40 GHz.However, there is a noticeable difference between the measured and simulated data, particularly at higher frequencies.This is attributed to several factors, such as fabrication tolerances, cable loss, inaccuracies in assembly, and the utilization of large end-launch connectors.

Figure 7 .
Figure 7.The MIMO antenna in the anechoic chamber.The inset shows a magnified picture of th fabricated prototype.

Figures 8
Figures 8 and 9 illustrate the comparison between the simulated, measured |S11|, and mutual couplings |S21|, |S21|, and |S21|.The developed SWB MIMO provided a wide im pedance bandwidth ranging from 3.4 to 70 GHz, effectively covering the all 5G bandsOne can observe an acceptable match between both datasets using MS4644B VNA, which has a measurement range that extends up to 40 GHz.However, there is a noticeable dif ference between the measured and simulated data, particularly at higher frequencies.Thi is attributed to several factors, such as fabrication tolerances, cable loss, inaccuracies in assembly, and the utilization of large end-launch connectors.

Figure 8 .
Figure 8. Simulated and measured reflection coefficients at Port 1.

Figure 10 .
Figure 10.Simulated and measured realized gain at Port 1.

Figure 10 .
Figure 10.Simulated and measured realized gain at Port 1.

Figure 10 .
Figure 10.Simulated and measured realized gain at Port 1.

Figure 12 .
Figure 12.The diversity performance of the MIMO system; simulated and measured (a) ECC and (b) DG.

Figure 12 .
Figure 12.The diversity performance of the MIMO system; simulated and measured (a) ECC and (b) DG.

Figure 13 .
Figure 13.The simulated and measured (a) TARC and (b) CCL of the SWB MIMO system.

Figure 13 .
Figure 13.The simulated and measured (a) TARC and (b) CCL of the SWB MIMO system.

λ
max refers to free space wavelength corresponding to the minimum frequency of the band.

Table 1 .
Comparison between the developed SWB MIMO system and state-of-the-art structures.Ref. Single Antenna Structure (Size λ 2 max) (Substrate) BW Range (GHz) BW Enhance Method Max.(Min.)Gain (dB) Isolation (dB) Cross-Polarization Level ECC DG (dB) CCL (bits/s/H) Decoupling Structure Bow tie Using CPW

Table 1 .
Comparison between the developed SWB MIMO system and state-of-the-art structures.