Applying characteristic mode analysis to systematically design of 5G logarithmic spiral MIMO patch antenna

The Theory of Characteristic Modes (TCM) provides a natural and systematic approach for designing Multiple-Input Multiple-Output (MIMO) antennas with high efficiency and uncorrelated antenna patterns. Recent progress in the growing field of MIMO antenna design, supported by TCM, is examined in this study. The challenge of designing MIMO antennas for 5G wireless communications is in particular highlighted. The results demonstrate that the characteristic modes play a key role in establishing the optimal positioning of antennas for optimal efficiency. Therefore, in this article, this theory is applied to a novel design of a logarithmic spiral patch antenna (LSPA) that is used to obtain a circular polarization with good performance more easily than the traditional shapes. The systematic design process starts by designing a single element with one logarithmic spiral arm and passing through adding another arm of this single element, also passing through a two-element array antenna, and ending in four configurations of two-port MIMO and selecting the configuration with best performance. The best configuration of the proposed MIMO provides a wide -10 dB measured impedance ranging from 27.3 GHz to 30.2 GHz covering the whole frequency band allocated for 5G communication systems with acceptable performance such as large bandwidth, high gain, high isolation, low envelope correlation coefficient, and low channel capacity loss. The isolation achieved for the operating bandwidth is better than -36 dB, demonstrating low mutual coupling. Moreover, the peak gain and total efficiency obtained are 9.9 dBi and 94%, respectively over the whole operating bandwidth. The proposed design is designed, analyzed, and simulated in the 3D electromagnetic full-wave software Computer Simulation Technology (CST). The design is fabricated using the photo-lithographic method and measured using R&SZNA67 vector network analyzer. The prototype achieved is extremely similar to the expected performance and consequently proves that the offered characteristics mode analysis method is applicable.


INTRODUCTION
The rapid proliferation of wireless devices, insufficient bandwidth, and restricted channel capacity in the modern era have significantly boosted attempts to establish improved communication network standards. This has subsequently fostered the development of communication systems in next-generation (5G) at the mm-wave frequency, with significantly improved channel capacity and data rates [1], [2]. The next 5G technology offers not just a significant improvement to the safety and reliability of the connected devices, high data rates and low power consumption, But additionally, it offers new potential for emerging technologies, such as virtual realities and intelligent cities [3]- [5]. Aspects of the mm-wave spectrum that are critical to consider include signal fading, atmospheric absorption, and path loss attenuations, which becomes more important when using a single antenna, [6], [7], that must nonetheless be addressed. Multiple-input multiple-output (MIMO) antenna has been identified as a key technology for existing and future wireless systems that demonstrates the simultaneous operations of multi-antennas and increases channel capacity with high data rates and Gigabits/sec throughput [8]- [12]. The MIMO antenna of the 5th generation demands a wide bandwidth to operate concurrently, whereas the high gain is needed in order to decrease air losses, absorptions, and compactness of structure for assimilation in MIMO systems is needed. In addition, there are challenges with the MIMO antenna design, including the design of antenna elements, placed close together and with low mutual coupling and strong isolation, which improves the antenna efficiency.
Patch antennas have garnered considerable interest due to their planar, compact, and resilient shapes in wireless systems and integrated circuits. The primary restrictions are lower gain and bandwidth that are greatly enhanced using various ways [13]- [15]. In contrast to the traditional methods mentioned previously for improving the defects of the patch antenna, we will use in this article a nontraditional form of the patch with high performance, which is the planar Spiral antenna.
A spiral antenna was first applied in the 1950s to obtain a frequency-independent antenna; it was defined in this context as an antenna that has an input impedance and gain that remain relatively constant throughout the bandwidth [16], [17]. This antenna has now become widely used in such sectors as military, satellite, telemetry, GPS, medical devices, wearable wireless communication and other wireless communication. A spiral antenna is noted for being adaptable in numerous applications, such as 5G wireless communications, which require large bandwidth, high gain and circular polarization. The Archimedean spiral, logarithmic spiral, square spiral, and star spiral are the numerous varieties of spiral antenna design. The most prevalent configurations are logarithmic spiral and Archimedean spiral.
There have lately been reports in literature on a variety of designs of MIMO antennas for 5G mm wave applications [18]- [24]. A circular polarized MIMO antenna with four ports was reported by references [18]. The antenna elements surround the metamaterial surface in order to obtain better radiation properties; nonetheless, the usage of the parasite parasitic elements the design of the MIMO difficult. A 5G MIMO antenna with a wide frequency range from 23 to 40 GHz with an overall dimension of 81 × 80 mm 2 has also been described [19]. Although the antenna has a high bandwidth and MIMO capabilities, they are expensive. The aforementioned [20] article offered an 8 × 8 MIMO antenna that measured 31.2 × 31.2 × 1.57 mm 3 in volume, and had a total gain of 8.732 dB with a center frequency of 25.2 GHz. This proposed antenna had an awful number of side and back lobes, which decreased its performance. An EBG-based MIMO antenna with a bandwidth of 0.8 GHz is reported in [21]. Reference [22] has a multi-element antenna design that directs the radiation in a direction that is suited for 5G communications. There is 1.5 GHz bandwidth ranging from 27.2 GHz to 28.7 GHz while the greatest gain achieved is 7.41 dB at 28 GHz. Another useful MIMO antenna option, designed for 5G, is a 4-element T-shaped antenna with total dimensions of 12 × 50.8 × 0.8 mm 3 [23]. The bottom layer partial ground is made up of iteratively inserted symmetrical split-ring slots. The proposed antenna design operates between 25.1 and 37.5 GHz and has a peak gain of 10.6 dBi. However, this study examines solely ECC as a MIMO performance measure. The work in point [24] also offers a high-gain fabrypert antenna for 5G MIMO applications, which includes a superstrate. The structure suggested spans the spectrum of mm-waves from 26-29.5 GHz and the highest gain value is 14.1 dBi. Additionally, ECC is studied to determine the MIMO performance of the antenna design.
Although the literature proposes numerous MIMO antenna designs, a lack of systematic design approach and the lack of understanding about performance constraints is still present. In this work, we have utilized the theory of characteristic mode (TCM) as a very effective analytical and systematic technique in the MIMO antenna design. The feature of a major contribution is that it may provide us access to the many characteristics that characterize the antenna without having to excite the antenna.
The theory of Characteristic modes is a modal analysis approach for antennas of any shape that was first established by Garbacz in 1968 [25] and then revised by Harrington in 1971 [26], [27]. Antenna designers may now extract the Eigen responses of an antenna using characteristic mode analysis (CMA), a rich set of information that was previously only available to closed waveguides and resonant cavities. The availability of these eigen responses might potentially provide fresh physical insights into antenna construction and analysis. characteristic modes or characteristic currents can be derived by the eigenfunctions of the following particular eigenvalue equation: Where λ n are the eigenvalues, are the eigenfuncions or eigen currents, and R and X are the real and imaginary parts of the impedance parameter Z. Another significant metric derived from eigenvalues is modal significance (MS n ), which is defined as MS n = |1/(1 + λ n )| Modal significance vividly demonstrates how each mode is near to resonance at each frequency. It reaches a maximum value of 1 at its resonant frequency (when λ n = 0 ) and then drops off as eigenvalues increase. One alternative to specifying the eigenvalues is to express them in terms of characteristic angle β n . Characteristic angle can be delineated according to the following equation [28]: Characteristic angle has the advantage that their value changes more quickly, making them ideal for analysis. Physically, the characteristic angle is a representation of the phase difference between the characteristic current J n , and the corresponding characteristic field E n . When λ n = 0 which is refer to the characteristic angle β n = 180°, a specific mode resonates. It is important to note that if the characteristic angle is equal to 180°, the excited mode radiates effectively. In cases when β n is close to 90° or 270°, the majority of energy is stored in the mode. Table. I summarizes the scenario with eigenvalues λ n , modal significance MS n and characteristic angles β n in the following manner: The novelty/contribution of this work boils down to the following: Instead of the traditional shapes of the patch such as the square, rectangular, triangle and circular shape previously used in some designs, but in this manuscript, a novel logarithmic spiral patch has been used to obtain the circular polarization with acceptable performance more easily than the traditional shapes used before. In this manuscript, a systematic design of four configurations of a two-port novel logarithmic spiral MIMO array patch antenna was presented based on the theory of characteristic modes, which gives a physical insight into how the design is done and how to improve its performance. The novelty of this work is to abolish the idea of trails and error, which wastes a lot of time in the design process without understanding the mechanism of the work of the antenna, and thus improving it will be more difficult and take a lot of time. Therefore, this paper gives a vision to the designers about how to design the MIMO antenna in four different configurations and get the required results based on the required application in a faster time and better performance than traditional methods. The design process begins with the support of characteristic mode analysis, starting with the design of a novel single element with one logarithmic spiral arm and then adding another arm to increase the bandwidth of the antenna, and then using the two element array to increase the gain of the antenna, and ending with the design of four configurations of a two-port MIMO antenna, and the best performance out of those four., and all this will be presented in Section II. While in Section III the fabricated antennas will be presented and comparing this proposed antenna with state-of-the-art works. Lastly, Section IV provides the conclusion.

II. Antenna Design Procedure
A complete strong look at the design's growth based on the characteristic mode analysis starting from a single element, passing through a two-element array antenna, and ending in MIMO configuration is extensively detailed in the ensuing. Antenna modeling, analysis, and simulation are done in the CST microwave studio suite, which is a commercially accessible EM simulator.

A. Single element logarithmic spiral patch antenna
The 5G wireless communication requires high performance antennas such as high gain, large bandwidth and circular polarization. Therefore, in this article, we have chosen the logarithmic spiral patch antenna as shown in Figure1 because it gives the required specifications and performance for wireless 5G applications, as mentioned earlier in the introduction part. But at first, the characteristics of this logarithmic spiral patch must be studied using CMA to ensure its performance and what are the factors that must be improved in a systemic, easy and time-saving manner.

FIGURE 1. One arm logarithmic spiral patch antenna, (a) Top view, (b)
Bottom view (full metallic ground plane).
The one arm logarithmic spiral antenna was designed using the equations r 1 = r o e aθ and r 2 = r o e a(θ−θ o ) , where r 1 and r 2 are inner radius and outer radius of the spiral respectively, while r o is the initial radius, θ is the incremental angle, a is the progression factor, and θ o is the phase shift of the spiral. A fast optimization of the logarithmic spiral antenna with initial radius r o = 0.15 mm , incremental angle θ = 5, progression factor a = 0.35, and the phase shift θ o = 90̊ is verified by modal significance (MS) and characteristic angle (CA) as indicated in Figure 2. The modal significance and characteristic angle are the two parameters that dictate the radiation performance of each mode, notably the circular polarization radiation generated by two modes. As a result, the specifications for these two modes are as follows: (a) the modal significances of the two orthogonal modes are identical (the two modes' normalized amplitudes are identical), and (b) the characteristic angles of these modes are β1 = 135 ̊ and β2 = 225 , a difference of 45 ̊ from the operating angle mode of 180 . Figure 2 presents the MS and CA of the first five modes. In all CMA results, J 1 to J 5 denote to the first CM to the five CM. As can be seen, the magnitudes of modes J 1 and J 2 are almost the same and they present a phase difference of 87.5° in the desired operating frequency 28 GHz. Thus, it is possible to get a CP antenna after the proper feeding. The type of circular polarization, whether it is right-or lefthanded, may be determined quite easily by characteristics mode analysis. It is the phase difference's sign that determines the rotation's handedness Left-handed polarization with a phase shift of +90 o is achieved by rotating counterclockwise. Right-handed polarization is achieved by rotating clockwise with a -90° phase shift. As can be seen in Figure 2b, the phase shift between modes 2 and mode 1 is near to +90 degrees, and as a result, we can claim that this logarithmic spiral patch antenna has a lefthand circular polarization (LHCP). This was the motivation behind selecting a logarithmic spiral shape for the patch rather than the typical geometries described in the literature review, which made it easier to generate circular polarization.
(a) (b) After the proper quarter-wave impedance transformer feed as introduced in Figure1a, the proposed one arm logarithmic spiral patch is excited to resonate at the resonating frequency of 28 GHz with a bandwidth of about 1.7 GHz as shown in Figure 3. It is necessary to increase both impedance and axial ratio bandwidths of this antenna in a systematic way to meet the requirements of 5G wireless communication. Therefore, we will use an additional logarithmic spiral arm, as shown in Figure 4. Figure 4 depicts a spiral antenna with two equal arms, each with a 1.5 turn. These two spiral arms are connected to each other by a rectangular strip which has a length of 0.48 mm and a width of 0.15 mm. The simulated and measured of the reflection coefficient curve of the twoarm logarithmic spiral patch antenna is shown in Figure 5. It is evident from Figure 5, the bandwidth doubled to 3.07 GHz compared to the bandwidth of the one arm logarithmic spiral patch antenna.   Figure 6 shows a comparison of the simulated axial ratio between the one-arm and two-arm logarithmic spiral patch antenna. Comparing the two-arm logarithmic spiral patch antenna to the one-arm antenna, the gain in axial ratio bandwidth is up to 250 % more. The addition of a logarithmic spiral arm not only increased the bandwidth of the antenna, but it also increased its gain. When using only one arm, the gain of the logarithmic spiral patch antenna is reported to be 6.2 dB, which increases to 7 dB when using the patch antenna with two arms.

B. Two element array logarithmic spiral patch antenna
At mm-wave frequencies, the gain of the antenna must be sufficient to compensate for the increased attenuation and absorption caused by the atmosphere. Nevertheless, the single-element antenna yielded in this study offers insufficient gain. Therefore, as shown in Figure 8, with the addition of a corporate feed network, the design has been developed into a two-element array. The array's elements are connected by a T-junction-power divider feed network, where the network's feed line widths are intended to match at 50 Ω with the main feed but 100 Ω with the branching network. The array's two elements are spaced by a distance of 2 mm. which is approximately equal to 0.2λ at 28 GHz. The parameters for the optimal performance of the proposed antenna are obtainable in Table. II. The simulated and measured of the reflection coefficient curve of the twoelement array logarithmic spiral patch antenna is shown in Figure 9. It is apparent that the two-element array antenna operates in the 27.4-30.47 GHz mm-wave frequency range, with a bandwidth of 3.07 GHz. When a two-element array antenna is produced from a single-element antenna, the appearance of bandwidth gain is evident.
A comparison of the broadband gain between single element and two-element array logarithmic spiral patch antennas is shown in Figure 10. The simulated broadband gain increases from 7 dB to 10.2 dB when the single element antenna is turned into a two-element array antenna, as shown in Figure 10.     Figure 11 presents the radiation patterns of the two-element array logarithmic spiral patch antennas at 28 GHz for both the E-and H-planes. It could be observed that the twoelement array antenna exhibits the radiation patterns with left-hand CP (LHCP) radiation for both the E-and H-planes. The comparison of the simulated axial ratio for the singleelement and two-element array antennas are shown in Figure 12. It was observed that there was a modest increase in the axial ratio bandwidth when the single-element antenna was modified to become a two-element array antenna.

III. MIMO Antenna Configurations
After acquiring a two-element array, the design will be developed further, culminating in the creation of the four different configurations of the 2-port MIMO antenna system as indicated in Figure 13. Therefore, in this study, with the help of the characteristic mode analysis, we will make a comparison between these different configurations systems to select the best one in performance.  Figure 13 (a) depicts the geometry of the face-to-face 2-port MIMO logarithmic spiral patch antenna, which is also referred to as a system-1 antenna. The designed antenna's substrate is a Rogers RT5880 with a relative permittivity (ε r ) of 2.2, a loss tangent of 0.0009, and a thickness of 0.787 mm. The whole area of design was 32 × 43 mm 2 . The CMA approach has been applied to MIMO System-1, with its substrate included, as shown in Figure 13. In Figures 14  and 15, the modal significance MS and the modal current distribution curves at 28 GHz are depicted. As we can see in Figure 10, modes 1, 2, 3, 4, and 5 contribute to the radiating BW in the desired impedance BW of interest (MS ≥ 0.707), whereas mode 6 has no effect whatsoever. According to the current directions, we may note from Figure 11 that modes 1 and 2 do not contribute to the coupling between the two antennas, while modes 3,4, and 5 are cause the coupling between the two antennas, which in turn negatively affects the performance of this MIMO antenna system. According to our study, we are able to draw the conclusion that radiation is caused by either Mode 1 or Mode 2, or a combination of both.  The simulated s-parameters, including the S11 and S21 curves of the face-to-face 2-port MIMO antennas, are presented in Figure 16. The simulated impedance BW (VSWR < 2, -10 dB) of this system was 3.0341 GHz, ranging from 27.467 to 30.501 GHz, while a simulated isolation of -21.1 dB was accomplished between the System-1 antennas. This poor isolation was expected by the modal significance curve (Figure 14), and this was confirmed by the S-Parameters curve (Figure 16), which negatively affects the performance of this system.  Figure 13 (b) depicts the geometry of the Side by Side 2port MIMO logarithmic spiral patch antenna, which is also referred to as the System-2 antenna. As with the System-1 antenna, the System-2 antenna was designed using the same substrate properties. The total designed area was 65 × 25 mm 2 . Like the System-1 2-port MIMO antenna design, CMA was also applied to the Side by Side 2-port MIMO antenna, including the substrate. Figs. 17 and 18 present the 28 GHz modal significance and the modal current distribution curves. From Figure 17, it is interesting to note that modes 1, 2, 3, and 4 contribute to the radiating BW of interest (MS ≥ 0.707), while modes 5 and 6 have no effect on the required impedance BW. Figure 18 shows that modes 1 and 2 have a current null between the two antennas, but modes 3 and 4 have a current coupling between the antennas. There are two non-coupling modes, mode 1 and mode 2, as well as coupling modes 3 and 4. It is also clear from Figure 18 that this coupling is a horizontal coupling, which has less impact on the antenna performance than the vertical coupling occurring in the face-to-face 2-port MIMO antenna system. From the S-parameters plotted in Figure 19, the isolation is better between the side by side 2-port MIMO antenna system than between the face-to-face 2-port MIMO antennas. Therefore, it is expected that this system will give better and higher performance than System-1 antenna.

C. System-3 (Orthogonal) MIMO logarithmic spiral patch antenna
As shown in Figure 13 (c), the System-3 antenna is an orthogonal 2-port MIMO logarithmic spiral patch antenna. As with System-1 and System-2, the System-3 antenna was designed with the identical specifications of the substrate. The total design area was 53.5 × 33 mm 2 . CMA was also used on the orthogonal 2-port MIMO antenna, including the substrate, as it was on the face-to-face and side by side 2port MIMO systems. It is noteworthy to notice that modes 1, 2, 3, and 4 all contribute to the radiating BW of interest (MS ≥ 0.707), whereas modes 5 and 6 have no effect on the needed impedance BW, as shown in Figure 20. From Figure 21, we may conclude that modes 1 and 2 have no impact on the coupling between the two antennas, but modes 3, and 4 are responsible for the coupling between the two antennas, and the poor performance of this MIMO antenna system. According to the S-parameters plotted in Figure 22, the isolation between the orthogonal 2-port MIMO antenna system is better than the isolation between the antennas of System-1, but it has lower isolation than the antennas of System-2. As a result, it is anticipated that this system will provide better and greater performance than the competing System-1 antenna.

D. System-4 (Oppositely side by side) MIMO logarithmic spiral patch antenna
The geometry of the oppositely side by side 2-port MIMO logarithmic spiral patch antenna, also known as the System-4 antenna, is shown in Figure 13(d). As with the prior systems, the antenna was developed to the same specifications as the substrate, with a total design area of 65 × 25 mm 2 . CMA was also applied to the System-4 antenna, including the substrate, as was the case with earlier systems. Figure 23 shows that only modes 1, 2, and 3 are contributing to the target impedance BW (MS ≥ 0.707), but modes 4, 5, and 6 are entirely unnecessary. We can see from Figure 24 that modes 1 and 2 do not contribute to the coupling between the oppositely side by side MIMO antennas (As a result of the existence of current nulls). However, mode 3 is producing poor coupling between the oppositely side by side MIMO antennas. As it is clear from the CMA, only one mode (mode 3) causes a poor coupling between the antennas, and this system is expected to be the best in performance, and this is what was shown by the Sparameters curve in Figure 25.

E. Comparison between the different systems of antenna
This section deals with a brief comparison between the previous four different systems to determine the best performance system. This comparison is summarized in Table III, in terms of the number of modes that cause coupling between the MIMO ports, impedance BW, gain, envelope correlation coefficient (ECC), channel capacity loss (CCL), and axial ratio bandwidth. As it is evident from Table III, the MIMO antenna system that has the least mutual coupling has the best performance, and this is represented by the lowest ECC, the lowest channel capacity loss (CCL), and the highest gain. Therefore, system 4, which is namely the Oppositely side by side 2-port MIMO antenna, has only one mode that causes the lowest coupling between MIMO ports, unlike other systems that have more than two modes, which cause high coupling between MIMO ports, and this negatively affects the performance of these systems. System 4 exhibits the highest value of S21, indicating its high isolation, wider BW, and highest system in gain. Therefore, based on this study, which is completely based on characteristic mode analysis, system 4 is the best in performance.

F. The proposed 2-port MIMO antenna system
As it is clear from Figure 24, there is only one mode (mode 3) that causes coupling between the MIMO antenna ports, so we must block this mode without affecting the noncoupling modes (mode1 and mode 2), so we will use the connected five circular Ring Defected Ground structure to perform this task. The concept is easy to understand if we consider the desired bandwidth to have two modes, one that is coupling and one that is non-coupling, which can be completely blocked without causing the other to be hindered. When it comes to extra modes, though, it becomes much more difficult. For the concept to be proven and adapted to any design, a single ring DGS structure was not suitable. So instead, a DGS structure comprised of connected five rings with center-to-center distance d = 2.85 mm as shown in Figure 26 would be the best way to show the principle and generalize it to any design, regardless of antenna type. On the whole, DGS's inner and outer radiuses have been designed to optimize for the proposed operating frequency band. It will also save the designer time on optimization. As a result, the DGS was positioned in a central position on the ground plane between the two ports. The inner and outer radii are R i = 2.3 and R o = 2.5 , respectively. Discussing how the DGS influences the CM is essential before demonstrating the improvement in S-parameters. In Figures 27 and 28, the modal significance and current distribution plots at 28 GHz are displayed. Due to the fact that the DGS has been designed to be parallel to the current flow of the non-coupling modes, the modes 1 and 2 current distributions are not totally impacted, whereas the mode 3 current distribution is impacted and tuned out of the BW of interest (MS ≥ 0.707) because The DGS produces a current that flows in the opposite direction to the coupling mode's initial current flow. The S-parameters curve of the proposed oppositely side by side 2-port MIMO antenna with DGS is illustrated in Figure  29. We can see that a simulated isolation of -55 dB is obtained between the 2-port MIMO antenna. According to our estimates, the frequency BW has been reduced by 200 MHz, with the primary reason appearing to be the blocking of mode 3.

IV. Experimental Results
The proposed system prototype of the oppositely side by side 2-port MIMO logarithmic spiral patch antenna was fabricated using the photo-lithographic method, and measured using a vector network analyzer (VNA), R&S ZVA 67, in order to verify the simulation results. The Farfield measurement was performed using the VNA in twoport measurement mode by measuring the transmission coefficient |S21| between the antenna under test and the reference-standard gain horn antenna (LB-018400). Figures  30 and 31 depict the fabricated prototype of system as well as the measurement setup for the proposed antenna system. The following sections give a full description and comparative analysis of the measured results.  Figure 32 compares reflection S11 and transmission S21 coefficients based on simulated and measured values. It was found that the measured bandwidth was approximately 2.95 GHz (27.35-30.3 GHz), which is in excellent accord with the simulated result. It has been noted that the antenna has good isolation characteristics, with values ranging from -54.5 to -36 dB. It finds a minor disparity between the simulated and measured outcomes. This discrepancy is primarily the result of fabrication and measurement setup flaws.  Figure 33 depicts the proposed oppositely side by side 2port MIMO antenna system radiation patterns, which were simulated in both CST and HFSS software and measured at the resonating frequency of 28 GHz, in both principal planes of Phi = 0 and Phi = 90. Because of their oppositely side by side placement, the radiating elements of the proposed MIMO antenna exhibit pattern diversity, which is beneficial in reducing the multipath effect in communication systems. The directional radiation patterns of the MIMO antenna system are visible. The simulated and measured radiation patterns match up quite well with the antenna's suggested design. Figure 34 shows the simulated and measured gain and radiation efficiency of the proposed oppositely side by side 2-port MIMO antenna design. In the band of interest (27.3-30.3 GHz), the simulated gain fluctuates between 8.5 and 9.9 dBi, while the measured gain fluctuates between 8.2 and 9.5 dBi. The simulated radiation efficiency varies between 92 and 94 percent, while the measured radiation efficiency varies between 86 and 89 percent. As a result, the loss tangent of the Rogers dielectric material is 0.0009, which yields these highefficiency results. The proposed oppositely side by side 2-port MIMO CP antenna's simulated and measured axial ratio is shown in Figure 35. Figure 35 shows that the simulated (both with CST and HFSS) and measured axial ratio are roughly 0.66 dB at 28 GHz, suggesting that the resulting circular polarization is fairly satisfactory, while the ideal circular polarization has an axial ratio of 1 or 0 dB and is acceptable up to 3 dB [29].

C. MIMO Performance Parameters
In this part, we will discuss the essential performance parameters of a MIMO system. These characteristics are crucial to a MIMO system: the Envelope Correlation Coefficient (ECC), Diversity Gain (DG), and Channel Capacity Loss (CCL). The envelope correlation coefficient (ECC) describes the degree to which one antenna's performance is independent of the performance of another antenna. In ideal conditions, the value of ECC should be 0; nonetheless, it is acceptable to have an ECC < 0.5 for practical purposes. The proposed oppositely side by side 2port MIMO antenna's ECC can be computed using following expression [30]: As shown in Figure 36.a, the ECC values for the proposed work were calculated using simulation and measurement data. As can be seen, the measured ECC is substantially smaller than 0.002, which is owing to the high degree of isolation between the MIMO radiating elements. Diversity Gain (DG) is the loss in transmission power that happens when diversity methods are implemented in a MIMO antenna system. DG is also considered to be an essential characteristic for evaluating the performance of MIMO antenna systems. The formula in [30] can be used to calculate the DG value: As shown in Figure 36.b, all of the antenna ports have a diversity gain more than 9.995 dB, which is extremely close to the ideal value of 10 dB. Channel Capacity Loss (CCL) is one of the most significant MIMO system metrics. CCL describes a potential loss of channel capacity due to correlation between the MIMO links. One method of calculating the CCL is provided in equation (6) as reported in [30].
where a = [ σ 11 σ 12 σ 21 σ 22 ] , σ ii = 1 − (|S ii | 2 − |S ij | 2 ) , and σ ij = −(S ii * S ij + S ji S jj * ) Figure 36.C depicts the measured and simulated CCL of the proposed system. We found that CCL over the entire operational bandwidth was less than 0.1 bps/Hz.  Table. IV summarizes the full comparison of the proposed and recent published mm-wave MIMO antennas. It can be inferred that when the proposed antenna is compared to [10], [21], [32], [33] and [34], it has the best isolation, gain, impedance bandwidth, and ECC values. In contrast, [11], [18], [23], [29] and [36] reported greater gain and impedance bandwidth values than our suggested antenna, but with a lower ECC and CCL. The presented antenna design demonstrates superior MIMO performance to that of the other antennas discussed above. Despite the large size of this antenna, it is perfectly suitable for the proposed application, which is device-to-device (D2D) communication in smart cities such as cars, automobiles, and smart devices in smart homes.

VI. Conclusion
It is presented in this paper how to apply the TCM to the design of a multi-antenna system for 5G wireless communication systems in a systematic manner. Therefore, in this article, this theory was applied to the novel design of 2-port MIMO logarithmic spiral patch antenna in order to systematically place the antenna ports with low correlation. The systematic design method was implemented with the idea of starting with a single element that has a single logarithmic spiral arm, moving through an array that has two logarithmic spiral arms, and coming to a conclusion with four configurations, including 2-port MIMO and the best performance out of those four. The four different 2port MIMO configurations, namely face-to-face, side by side, oppositely side by side, and orthogonal 2-port MIMO logarithmic spiral patch antennas, are designed and analyzed using characteristic mode analysis to select the best one in performance. There is a high correlation between experimental and simulated outcomes. Because of its considerable return loss, wide bandwidth, high gain, low ECC, low CCL, and strong element isolation characteristics, the suggested oppositely side by side 2-port MIMO antenna could be a good choice for 5G wireless communication systems.