Ultraminiaturized, Wideband and Flexible Square Ring-Shaped MIMO Antenna for Sub-6 GHz 5G (n77/n78/n79) Communications
Article information
Abstract
This investigation presents a wideband, flexible, and ultraminiaturized square ring multiple-input multiple-output (MIMO) antenna made for sub-6 GHz applications. The design incorporates a semicircular ground plane with a neutralization line and two orthogonally positioned feed ports, together with two square ring radiating elements connected by four short strips, to enhance isolation between the two ports. To enhance isolation and MIMO performance, a 50 Ω microstrip line positioned orthogonally feeds each ring. The antenna achieves a wideband resonant with a center frequency of 4.2 GHz, maintains the S11 under −10 dB, and achieves port isolation of up to 18 dB across the frequency span from 3.2 to 5.8 GHz and a fractional bandwidth of 61.9% with maximum peak gain of 3.21 dBi. Detailed evaluations of the radiation patterns, surface current distributions, and S-parameters of the antenna are provided. Built on a flexible PDMS substrate, the antenna’s observed findings closely match estimates, proving its efficiency. This design method consequently provides a dependable solution and has significant potential for 5G sub-6 GHz MIMO systems.
I. Introduction
With the arrival of 5G wireless communication, antenna configurations have gotten complicated due to the need to handle many frequency bands within the limited footprint of handheld devices. Developing multiple-input multiple-output (MIMO) antennas that perform well across a wide frequency range adds to the challenge. MIMO technology, a basis of modern wireless networks, employs multiple antennas at both the receiver and the transmitter ends which increase data rates and signal quality without increasing power or capacity [1–3]. This leads to increased spectral efficiency, greater throughput, and enhanced network dependability. MIMO antennas’ efficacy is determined by their ability to maintain spatial, polarization, or pattern diversity, which ensures independent signal routes. However, combining tiny MIMO antennas beside other device components in restricted locations poses a considerable design challenge, frequently mandating close antenna positioning.
Metamaterials, frequency selective surface (FSS), electromagnetic band gap (EBG) structures, metallic surfaces, and defected ground structures (DGS) are frequently implemented in MIMO antennas for enhancing isolation and reliability. These approaches limit reciprocal coupling by inhibiting or eliminating surface currents, which increases capacity of channels, efficiency, and diversity yield [4, 5]. A single-layer electromagnetic cloak can increase isolation bandwidth without adding complexity, whilst decoupling patch and carefully placed cutting pins enhance isolation between the components of an antenna. Furthermore, inserting a unique wheel-shaped metamaterial between closely spaced antennas in a small wideband MIMO array has been proven to considerably minimize coupling, increase gain, and improve overall system performance.
High isolation is required in MIMO systems to reduce interference between distant antenna elements. Parasite building materials, neutralization lines, and various decoupled approaches are common methods for improving isolation. The increased need for miniature and portable electronics stimulates the development of miniature MIMO antenna technologies [6]. Designers typically use meandering lines, fractal topologies, and multi-layered arrangements to reduce size while maintaining performance. Furthermore, such antennas must offer wideband or multiband functioning to support innovations such as 4G, 5G, and Wi-Fi, providing continuous connectivity across many frequency bands [7]. Diversity approaches are also important for improving signal integrity and reducing fades in MIMO systems.
Miniaturization is also a critical for incorporating antennas into small devices like phones and wearable electronics. However, reducing antenna size frequently results in less spacing between components, which may improve mutual coupling and reduce isolation [8–10]. Maintaining significant isolation is essential for retaining distinct signal channels in MIMO systems, ensuring good diversity and multiplexing. Techniques for improving isolation, such as decoupling structures, neutralization lines, and EBG materials, can raise antenna complexity or size. As consequently, striking an equilibrium between compact and high isolation necessitates accurate design optimization and novel methods to meet competing objectives while ensuring dependable, effective MIMO performance.
A number of MIMO and single-port antennas have recently been developed especially for wearable textile applications [11–15]. Flexible MIMO antennas are growing as intriguing options, particularly for wearable and conformal devices. These antennas provide high mechanical flexibility while maintaining electromagnetic execution, enabling them to adjust to a variety of designs that are suited for next-generation mobile and Internet of Things (IoT) applications. To satisfy 5G performance expectations, especially in the sub-6 GHz region, such antennas must have a large bandwidth, minimal mutual coupling, and excellent port isolation. Flexible MIMO antennas retain strong signal quality as well as effectiveness across a wide spectrum while preserving user convenience and device resilience, making them perfect for future 5G-enabled smart devices.
Time-domain analysis is an effective method for assessing MIMO antenna performance. MIMO systems use spatial diversity for better efficiency and multiplexing to send and receive data via many pathways, enhancing efficiency and durability. Time-domain measurements reveal an antenna’s fluctuations and reaction time, which are particularly significant at high frequencies and in broadband applications [16]. Finding a balance between compact size, minimal envelope correlation coefficient (ECC), broad bandwidth, and strong isolation can be one of the most challenging parts of designing MIMO antennas. These difficulties are exacerbated when antennae are incorporated into metal-framed devices or atypical form factors. Key factors including gain, ECC, and efficiency must be properly adjusted. Maintaining minimal ECC is especially critical for ensuring uncorrelated signals from several antennas, which improves system reliability.
For 5G applications, a small two-element single-band MIMO antenna that targets the n77/n78 frequency bands has been created [17]. Its working bandwidth is constrained, though, and the antenna takes up a sizable amount of space. Furthermore, only 12 dB of isolation between the MIMO parts is achieved by the design technique [18]. A single-band fabric MIMO antenna operating in the ISM band (2.4 GHz), also it has been determined to have a gain of just 1.67 dBi and sufficient isolation of 12 dB [19]. Another wearable MIMO device shows moderate gain across its operational bands and offers a bigger footprint, excellent port isolation, and multiband operation [20]. Furthermore, a wearable ultrawideband antenna with a 7.2 dBi gain was unveiled; nevertheless, it is relatively bulkier and has poor port isolation [21].
In order to support 5G services at 4.8–5.0 GHz (in the n77 band), a self-neutralized MIMO antenna systems are being introduced with co-location [22]. This co-located architecture is appropriate for compact mobile platforms, as it reduces antenna size by 50% [23]. A ceramic substrate has been employed to make a dual-band MIMO antenna for 5G gadgets which measuring the size of 150 mm × 75 mm × 7 mm [24]. It is recommended to utilize a low-profile antenna that runs at 1.9 GHz for the 5G NR-n2 band and 5.9 GHz [25]. In order to increase bandwidth and attain a lower resonance frequency, slots and stubs are utilized. Another tiny four-element MIMO antenna system has been conceived and built, each of which is 26 mm × 26 mm × 0.8 mm in size [26]. A third, reconfigurable architecture that can handle any frequency is created by combining the first and second systems, which resonated at both 5G bands are 3.5 GHz and 5.2 GHz [27]. Another work implemented to use of cavity-backed construction and cross magnetic dipoles in a small wideband dual-polarized antenna for MIMO applications. This antenna measures 42.5 mm × 42.5 mm × 18 mm and operates at 3.4 GHz [8]. The compact mobile MIMO system, consisting of four elements placed in a sequential rotation and measuring 59.2 mm × 59.2 mm × 2.5 mm, covers the whole n77/n78/n79 5G bands with a bandwidth of 3.3–5.0 GHz [28]. There is another documentation of a textile antenna which implemented by denim-based MIMO antenna [29]. With a minimal dimension of 24 × 24 mm, it can function in two bands: 5.2 GHz (Wi-Fi) and supports for 5G sub-6 GHz, frequency of 3.5 GHz. There have been recent reports of 5G communication using several ultraminiaturized MIMO antennas [30–36].
This paper describes an extremely tiny, flexible, wideband interlinked square ring MIMO element optimized for 5G (n77/n78/n79) communications. To improve isolation, the design includes a neutralization line and two feed ports that are orthogonally positioned. The antenna provides more than 18 dB of port-to-port separation and works over a wide frequency band from 3.2 to 5.8 GHz, and reflection coefficients that maintain below −10 dB throughout the resonant band. Section III includes a comprehensive examination of S-parameters (both S11 and S21), radiation properties at both orientation, and surface current analysis for whole band. Additionally, timedomain MIMO measurements including channel capacity loss (CCL), total active reflection coefficient (TARC), diversity gain (DG), and ECC are used to confirm the diversity capability. According to these findings, this MIMO antenna design is well-suited for 5G MIMO communications in real time.
II. Proposed Antenna Geometry
1. Single Element Antenna Design
An ordinary square patch is connected to this antenna design via a 50 Ω stripline in order ensure appropriate impedance matching. The microstrip feed line has specifications of 2 mm width and 6.2 mm length. The antenna has been developed for a center frequency of 4.2 GHz and is constructed on a flexible polydimethylsiloxane (PDMS) substrate having a dielectric constant of 2.6 and a height of 1 mm. Two square ring radiating elements joined by four short strips make up the structure, together with a semicircular ground plane that has two perpendicular feed ports and a neutralization line. Each square ring patch measures 8 mm in side length, with 2 mm × 2 mm joining fragments among rings. In order to increase impedance matching and radiation performance, a semicircular shaped DGS is created in bottom layer. The semicircular ground plane has a diameter of 2.2 mm. A suitable impedance match is crucial for optimizing antenna resonant and overall efficiency. Fig. 1 depicts the whole design with ideal dimensions, while Table 1 contains the proposed antenna’s exact specifications. The simulated reflection coefficient of the single element antenna is plotted in Fig. 2. It has been shown that the antenna has a −10 dB bandwidth of 2.6 GHz obtained from 3.2 GHz to 5.8 GHz. The simulated gain is 3.1 dBi analyzed at 5.4 GHz. The simulated E-plane (xy-plane) and H-plane (xz-plane) radiation patterns of single element antenna at the resonant frequency of 5.4 GHz is shown in Fig. 2. The graph shows (black colored solid line) that the proposed antenna exhibits an omnidirectional pattern in H-plane and a bidirectional pattern in E-plane (red colored solid line) at 5.4 GHz.
2. Parametric Analysis
The proposed MIMO antenna is designed to enhance dependability for 5G applications operating in the sub-6 GHz band. By carefully designing the geometry, the antenna reduces mutual coupling between its parts while maintaining wideband performance. Its lightweight and effective design makes it ideal for smooth integration with current 5G devices.
Iteration 1
Eq. (1) provides the basic calculation for a square patch antenna having a complete ground plane, which forms the basis of the original design:
c is the velocity, S is the square patch’s sidelength, and ɛeff is the equivalent dielectric constant [37]. In order to attain a resonance frequency of 3.6 GHz, the side length is first established at 18.3 mm. Fig. 3(a) shows a design that serves a narrow band but is rather wide and has restricted bandwidth. The literature suggests changing this fundamental structure to boost bandwidth while decreasing size.
Iteration 2
As shown in Fig. 3(b), two square rings of varying sizes joined by tiny elements on all four sides were used in place of the square patch in order to increase performance. This improvement enhanced bandwidth and altered the resonance frequency to around 4 GHz.
Iteration 3
A partial ground plane which introduced at the beneath the PDMS substrate, has been employed in place of the entire ground plane due to size constraints. Furthermore, the feed and patch were placed farther apart to generate coupled resonant over a broader bandwidth. A rectangular resonator was installed near the feed to improve impedance matching. Fig. 3(c) shows a design that decreased the antenna footprint to 10 mm × 10 mm.
Iteration 4
To enable MIMO capabilities, a second feed element was added and positioned orthogonally to the first. Fig. 3(d) demonstrates how this orthogonal port layout improves element isolation. The antenna size has been reduced to around 22 mm × 22 mm.
Iteration 5
In the final cycle, the antenna’s general configuration, slot locations, and dimensions were modified to fulfil performance objectives such as radiation properties, perfect matching and isolation. To boost isolation even further, a unique neutralization line was added to the ground plane. Fig. 3(e) shows the finished design, which is highly compact (22 mm × 22 mm) and delivers good MIMO performance with great isolation. This makes it perfect for challenging 5G applications. The evolution of the proposed antenna has been analyzed to get a desired resonant frequency and respected simulated reflection coefficient (S11) curve is plotted in Fig. 4.
3. MIMO Antenna Design
Components were arranged appropriately through the MIMO development process to improve isolation, which improved overall performance. The study focused on a two-element MIMO antenna with a ground plane of neutralizing line. The design maintains the same dimensions as the previously stated single antenna by positioning two identical single antenna elements orthogonally to one another. Designing a two-port diversity antenna is difficult due to mutual interference between radiating parts that are near together. Isolation between elements and the ECC increase considerably with the number of components added, exacerbating the situation. To mitigate these effects, the current design includes an effective neutralizing line. Fig. 5 depicts a potential MIMO antenna arrangement.
4. Isolation Enhancement
Isolation strategies have a significant impact on the performance of a MIMO antenna setup. In the absence of these improvements, mutual coupling between very adjacent antenna elements results in increased ECC, worse radiation efficiency, and less favorable isolation (typically less than −15 dB). This coupling generates signal interference and correlation, which reduces data throughput and dependability in the MIMO system. The suggested neutralization line, which consists of three interconnecting lines positioned on the ground plane, is intended to address this issue. Fig. 6 depicts the layout of the neutralization line, and Table 2 provides details on its specifications.
Isolation approaches improve MIMO antenna performance dramatically. The addition of a neutralization line enhances isolation by 3 dB, bringing it from −15 dB (without isolation) to −18 dB while keeping the same resonance frequency. The transmission (isolation) properties with and without the neutralizing line are compared in Fig. 7, which clearly demonstrates this improvement.
The radiation characteristics of the proposed antenna were investigated over the entire operational band. Fig. 8 presents the simulated patterns at the resonance frequencies of 3.75 GHz and 5.5 GHz for both the E- and H-planes. The results indicate that the antenna exhibits a nearly omnidirectional response in the E-plane and a bidirectional pattern in the H-plane, which are consistently maintained across the operating frequencies.
III. Result and Analysis
As displayed in Fig. 9(a), an antenna prototype has been built to ensure the real-time feasibility and reliability of the proposed antenna. The vector network analyzer (VNA) is utilized to determine the scattering parameters is shown in Fig. 9(b). In an anechoic environment, the antenna has been inspected and tested, as seen in Fig. 9(c). The Comparison graph of S-parameter of the proposed antenna in both simulation and measurement is shown in Fig. 10.
Photographs of the proposed antenna: (a) fabricated prototype, (b) S-parameter analysis with VNA, and (c) radiation pattern analysis with anechoic chamber.
1. Surface Current Analysis
The current density is displayed in Fig. 11(a) and 11(b) with the most significant flow of current locations highlighted when Ports 1 and 2 are activated, respectively. The surface current analysis requires substantial improvement to adequately demonstrate the antenna’s electromagnetic performance and MIMO functionality. Although the authors recognize current accumulation at the ring peripheries and feed structures, their examination omits essential details needed to comprehend the broadband behavior and port decoupling strategies. The study inadequately addresses how non-uniform current patterns emerge during individual port activation, which is fundamental for explaining the mechanism by which perpendicular feed positioning establishes isolated current pathways that enable the reported 18 dB port separation. A significant oversight involves neglecting the electromagnetic phenomena occurring at the ring’s open termination, where discontinuity-induced current crowding and associated charge buildup substantially affect field configurations and radiating properties throughout the entire 2.6 GHz operational spectrum. The frequency-limited current examination at 4.2 GHz center point overlooks the dynamic current behavior across the complete 3.2–5.8 GHz range, missing opportunities to identify resonant mode transitions and clarify the physical principles underlying the achieved bandwidth performance.
Essential quantitative characterization of the referenced standing wave phenomena should include amplitude distribution metrics, current ratio measurements along the radiating structure, and comprehensive evaluation of neutralization element current contributions to overall isolation improvement. Moreover, establishing direct relationships between surface current vector orientations and three-dimensional radiation characteristics would elucidate how current flow patterns influence both desired and undesired polarization components, which critically determines MIMO system effectiveness in terms of channel capacity and signal quality. Without incorporating these comprehensive electromagnetic insights spanning multiple frequencies and detailed inter-element coupling evaluation, the current distribution analysis remains inadequate for validating the antenna design’s performance claims and practical applicability in next-generation wireless communication systems.
2. Radiation Pattern
A well designed radiation analysis is necessary to minimize distortion and undesired side lobes whilst ensuring effective signal delivery and acquisition in the intended orientations. Fig. 12(a) and 12(b) show the measurements of the co- and cross-polarizations radiation characteristics of the designed flexible antenna at 3.55 GHz and 5.75 GHz in the E- and H-planes, accordingly. The E-plane belongs to the yoz plane in the electric field, while the H-plane goes along with the xoz plane in the magnetic field. At the measurement process, only Port 1 became agitated, and the other port is appropriately calibrated. The radiation patterns along both planes show that the antenna exhibits constant bidirectional and omnidirectional behavior across its operating range. From the radiation characteristics, it is observed that the co-polarization pattern is much greater than the cross-polarization pattern.
3. Gain and Radiation Efficiency
The antenna depicted in Fig. 13 delivers strong performance at 5 GHz in both measurement and simulated gain and radiation efficiency. It’s boasting an average gain of 3.18 dBi and a radiation efficiency of 81% in simulation and 3.21 dBi gain has been evaluated in measurement. Its compact form factor, excellent efficiency, and straightforward construction make it exceptionally well-suited for 5G applications.
IV. Bending Analysis
The antenna’s flexibility is investigated by physically adjusting its overall electrical length. This assessment involves an examination of the scattering performance and radiation characteristics for both modelled and empirically measured at different bending situations. Once the optimum performance has been confirmed, the antenna surface is bent with curving radii of 10 mm and 20 mm. The developed prototype of the proposed antenna performs efficiently while bent along its x- and y-axes, as measured and evaluated to provide a better bending assessment. Fig. 14(a) and 14(b) show the simulated designs under x- and y-axis bending, respectively, while Fig. 14(c) shows the fabricated prototype bent over a cylindrical foam. A cylindrical foam support holds the antenna in place while it is being measured within the anechoic chamber. In order to prevent the antenna from spontaneously flattened thereby rendering bent-situation radiation pattern observations difficult, this support is necessary to keep the prototype at the appropriate bending level.
Bending analysis of the proposed antenna: (a) simulated x-axis, (b) simulated y-axis, and (c) fabricated prototype.
Fig. 15(a) and 15(b) show the simulated and measured scattering parameters under the bend level at 10 mm and 20 mm, respectively. The S-parameter results in both levels demonstrate that the proposed antenna maintains stable electromagnetic performance under bending conditions. The S11 responses for 10 mm and 20 mm bending radii show clear resonance with only slight shifts in resonant frequency, indicating that the change in curvature moderately alters the electrical length but does not compromise impedance matching. Impedance bandwidth from 3.62 GHz to 5.6 GHz along x-axis bending and slight shift from 4.56 GHz to 6.21 GHz along y-axis is observed, that agrees well with the computed results. In both cases, The S21 characteristics further highlight that isolation remains well below −15 dB throughout the working band, with only minor differences between simulation and measurement due to practical fabrication and setup factors.
Combined scattering analysis of the proposed antenna at bending conditions: (a) x-axis and (b) y-axis.
Fig. 16 illustrates the bending performance of the suggested flexible antenna and shows radiation behavior under curved configurations with radii of 10 mm and 20 mm. The structure was bent along perpendicular axes (x and y) with matching curvature values of 10 mm and 20 mm at the 4.5 GHz operating frequency in order to evaluate the pattern. Regardless of the bending position, the results show that the antenna maintains omnidirectional properties across both principal planes (E-plane and H-plane). The performance maintains constant and within allowable bounds during the whole flexure investigation carried out in both axial directions. The radiation profile has minor variations, which are mostly caused by the physical separation of the radiating components.
V. Time Domain Analysis
Studying the varying behavior of transmitters over time requires the use of a time-domain model. While frequency-domain research examines the response of antennas across different frequency ranges, time-domain analysis focuses on the temporal characteristics of antenna impulses. Researchers can acquire significant insights about the transient performance of an antenna system by examining how electromagnetic waves propagate across it in time. When assessing broadband or impulse- based antennas like those found in radar systems that are intended to send and receive brief signals, this technique is especially helpful. Additionally, time-domain analysis provides important details regarding the radiation analysis of the antenna in regular intervals. The directional behavior of the antenna can be better understood and optimized by designers by monitoring temporal fluctuations in the emitted electromagnetic fields.
Applications where antennas must dynamically modify their radiation patterns or guide energy beams require a certain level of temporal analysis. Furthermore, time-domain modeling aids in the assessment of features like as impedance matching and reflection behavior, allowing for an evaluation of an antenna’s time-varying susceptibility and energy transfer efficiency. This is especially important in wireless communication systems since signal fading and multipath propagation can have a main effect on antenna performance. Understanding the design’s transient behavior aids the development, and evaluation in a vast of real-time applications, like radar, wireless communication, and other time-critical systems.
The design of MIMO antenna systems relies heavily on diversity techniques to maximize performance. To effectively tackle wireless communication challenges, diversity considerations must be integrated into MIMO antenna design. Key metrics like DG and ECC reveal how well closely placed antenna elements interact. As shown in Fig. 17(a) and 17(b), the proposed architecture achieves an impressively low ECC of 0.004 and a DG of 9.99 dBi, highlighting excellent diversity performance and minimal mutual coupling.
The temporal properties of the shorter pulses used by wideband antennas to convey information become crucial. As a result, group delay becomes an important metric for measuring pulse distortion. To guarantee that there is as little distortion as possible during signal transmission, high phase linearity must be maintained. The phase sensitivity of the system is assessed using group delay of the signal, which is the rate at which the total phase changes in relation to angular frequency. Both ports consistently display a group delay of roughly 0.19 ns in simulation and measurement at 5 GHz, as seen in Fig. 18, demonstrating good phase linearity and low signal distortion.
The TARC is a crucial performance metric for MIMO antenna systems. When several ports are open at once, this statistic evaluates the effective bandwidth and reflection behavior. It is computed using scattering characteristics and aids in assessing the phase stability and reflection loss of the antenna. For consistent phase behavior and to minimize reflection loss, a TARC value below −10 dB is generally preferred across the operating spectrum. The suggested antenna confirms its superior performance with a mean TARC of less than -30 dB across the resonant band, as shown in Fig. 19(a). This indicates excellent phase stability and little reflection. CCL is another important parameter for MIMO antennas. Generally, a CCL value of less than 0.4-bit/s/Hz is considered appropriate. As shown in Fig. 19(b), the recommended antenna maintains the CCL below 0.25-bit/s/Hz over the entire operating frequency range, demonstrating exceptional channel performance efficiency and reliability.
VI. Performance Comparison
Table 3 provides a thorough comparison with current designs to further emphasize the superior design and performance of the suggested work. According to a thorough research, examination, and assessment, the suggested design is thought to have a high potential for being a successful MIMO system.
VII. Conclusion
A compact, wideband MIMO antenna designed for sub-6 GHz 5G (n77/n78/n79) applications is presented in this paper. It has enhanced isolation between two MIMO elements, realized gain, and efficiency. The design achieves 84.7% miniaturization in a small 22 mm × 22 mm size, a unique combination of good isolation and a small footprint. It is perfect for integration into effective MIMO systems because it offers great efficiency, enhanced gain, and wideband operation. Notably, the suggested structure is well suited for lower 5G bands and provides excellent isolation of over 18 dB, suggesting low mutual coupling despite the smaller size. Key performance metrics like DG and ECC are outstanding; they beat many current designs with a DG of 9.99 dBi and an ultra-low ECC of about 0.004. Strong agreement was found when the experimental results were used to validate the simulated MIMO properties. For 5G massive MIMO applications, the suggested antenna is a good option due to its straightforward, scalable, and high-performance design. Future developments might concentrate on optimizing its geometry and dimensions in order to further reduce size.
References
Biography
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J. Karthi, https://orcid.org/0000-0001-5174-8682 received his B.E. degree in Electronics and Communication Engineering in 2011 from Pallavan College of Engineering, Kanchipuram, India and M.E. degree in Communication Systems from Rajalakshmi Engineering College, Chennai, India in 2013. He is working as assistant professor & pursuing his Ph.D. in the Department of Electronics and Communication Engineering, Rajalakshmi Engineering College, Chennai, Tamilnadu, India. His areas of interests are MIMO antennas, UWB antennas and wireless communication. textile MIMO antenna for 5G and WiFi wearable applications,”
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M. Palanivelan, https://orcid.org/0000-0001-8278-9348 completed his Ph.D. at Anna University, Chennai in 2015. He received his M.E. degree from College of Engineering (CEG), Anna University, Chennai and BE degree from MS University, Tirunelveli. He is working as professor in the Department of Electronics and Communication Engineering, Rajalakshmi Engineering College, Chennai, Tamilnadu, India. He has published several research papers in International Journals and Conferences. He is a senior member of IEEE and a life member of ISTE. His research interest includes multicarrier modulation systems, wireless communication systems, optical communication, Internet of Things, and signal processing.
