Butler Matrix Based on Substrate Integrated Waveguide Without Crossover and Phase Shifter for Millimeter Waves Applications

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The proposed 4 × 4 antenna Butler matrix comprises an inscribed structure, which makes it fundamentally different from traditional beam-forming networks in 5G 26-GHz applications. Method This novel Butler matrix comprises four hybrid couplers without crossovers or phase shifters. To reduce the size, magnitude, and phase difference, and to increase the bandwidth, interdigital and non-metallic vias are used in the coupler design. The performance of the proposed matrix was simulated using the CST software and implemented on a Rogers 8085 substrate. It was also interfaced with four substrate-integrated waveguide slot antennas to demonstrate its distinct beam scanning capability. Results The matrix yielded an error magnitude loss of 1 dB and a phase error of 1.7° with a broad operational bandwidth of 3 GHz. The measured coupling factor of the 4 × 4 Butler matrix at 26 GHz is -6 ±1 dB at the output. The measured results validate that four phase-scanning states at -14.3°, 14.88°, -32.21°, and 31.33° can be realized with return losses of less than -10 dB. Conclusions The proposed design achieves a compact, efficient, and low-loss beamforming solution suitable for 5G applications at 26 GHz, demonstrating distinct scanning features without the need for crossovers or phase shifters. " } { "@context": "http://schema.org", "@type": "BreadcrumbList", "itemListElement": [ { "@type": "ListItem", "position": "1", "item": { "@id": "https://f1000research.com/", "name": "Home" } }, { "@type": "ListItem", "position": "2", "item": { "@id": "https://f1000research.com/browse/articles", "name": "Browse" } }, { "@type": "ListItem", "position": "3", "item": { "@id": "https://f1000research.com/articles/14-969/v1", "name": "Butler Matrix Based on Substrate Integrated Waveguide Without Crossover..." } } ] } Home Browse Butler Matrix Based on Substrate Integrated Waveguide Without Crossover... ALL Metrics - Views Downloads Get PDF Get XML Cite How to cite this article Nayyef N, Tan KG, Keriee H et al. Butler Matrix Based on Substrate Integrated Waveguide Without Crossover and Phase Shifter for Millimeter Waves Applications [version 1; peer review: 1 approved with reservations, 1 not approved] . F1000Research 2025, 14 :969 ( https://doi.org/10.12688/f1000research.168318.1 ) NOTE: If applicable, it is important to ensure the information in square brackets after the title is included in all citations of this article. Close Copy Citation Details Export Export Citation Sciwheel EndNote Ref. Manager Bibtex ProCite Sente EXPORT Select a format first Track Share ▬ ✚ Research Article Butler Matrix Based on Substrate Integrated Waveguide Without Crossover and Phase Shifter for Millimeter Waves Applications [version 1; peer review: 1 approved with reservations, 1 not approved] Nawres Nayyef 1 , Kim Geok Tan 1,2 , Hussam Keriee 3 , Zahriladha Zakaria 4 , Chia Pao Liew https://orcid.org/0000-0002-9444-1987 5 , Chockalingam Aravind Vaithilingam https://orcid.org/0000-0002-2060-8748 6 Nawres Nayyef 1 , Kim Geok Tan 1,2 , [...] Hussam Keriee 3 , Zahriladha Zakaria 4 , Chia Pao Liew https://orcid.org/0000-0002-9444-1987 5 , Chockalingam Aravind Vaithilingam https://orcid.org/0000-0002-2060-8748 6 PUBLISHED 23 Sep 2025 Author details Author details 1 Multimedia University Faculty of Engineering and Technology, Ayer Keroh, Malacca, Malaysia 2 Centre for Advanced Analytics, CoE for Artificial intelligence, Multimedia University, Ayer Keroh, Malaysia 3 Ministry of Higher Education and Scientific Research, Baghdad, Iraq 4 Faculty of Electronics and Computer Engineering, Universiti Teknikal Malaysia Melaka, Durian Tunggal, Malacca, Malaysia 5 School of Energy and Chemical Engineering, Xiamen University Malaysia, Sepang, Selangor, Malaysia 6 Taylor's University School of Engineering, Subang Jaya, Selangor, Malaysia Nawres Nayyef Roles: Conceptualization, Investigation, Methodology, Software Kim Geok Tan Roles: Project Administration, Supervision Hussam Keriee Roles: Investigation Zahriladha Zakaria Roles: Supervision Chia Pao Liew Roles: Project Administration, Writing – Review & Editing Chockalingam Aravind Vaithilingam Roles: Writing – Review & Editing OPEN PEER REVIEW DETAILS REVIEWER STATUS Abstract Background A novel low-loss 4 × 4 Butler Matrix structure for 26 GHz operation is designed in this study. The proposed 4 × 4 antenna Butler matrix comprises an inscribed structure, which makes it fundamentally different from traditional beam-forming networks in 5G 26-GHz applications. Method This novel Butler matrix comprises four hybrid couplers without crossovers or phase shifters. To reduce the size, magnitude, and phase difference, and to increase the bandwidth, interdigital and non-metallic vias are used in the coupler design. The performance of the proposed matrix was simulated using the CST software and implemented on a Rogers 8085 substrate. It was also interfaced with four substrate-integrated waveguide slot antennas to demonstrate its distinct beam scanning capability. Results The matrix yielded an error magnitude loss of 1 dB and a phase error of 1.7° with a broad operational bandwidth of 3 GHz. The measured coupling factor of the 4 × 4 Butler matrix at 26 GHz is -6 ±1 dB at the output. The measured results validate that four phase-scanning states at -14.3°, 14.88°, -32.21°, and 31.33° can be realized with return losses of less than -10 dB. Conclusions The proposed design achieves a compact, efficient, and low-loss beamforming solution suitable for 5G applications at 26 GHz, demonstrating distinct scanning features without the need for crossovers or phase shifters. READ ALL READ LESS Keywords Butler matrix, Hybrid coupler, Vias, Substrate integrated waveguide, 5G Corresponding Author(s) Kim Geok Tan ( [email protected] ) Chia Pao Liew ( [email protected] ) Close Corresponding authors: Kim Geok Tan, Chia Pao Liew Competing interests: No competing interests were disclosed. Grant information: This research is under grant MMUE220012 from Telekom Research & Development Sdn. Bhd. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Copyright: © 2025 Nayyef N et al . This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. How to cite: Nayyef N, Tan KG, Keriee H et al. Butler Matrix Based on Substrate Integrated Waveguide Without Crossover and Phase Shifter for Millimeter Waves Applications [version 1; peer review: 1 approved with reservations, 1 not approved] . F1000Research 2025, 14 :969 ( https://doi.org/10.12688/f1000research.168318.1 ) First published: 23 Sep 2025, 14 :969 ( https://doi.org/10.12688/f1000research.168318.1 ) Latest published: 24 Apr 2026, 14 :969 ( https://doi.org/10.12688/f1000research.168318.2 )  There is a newer version of this article available. Suppress this message for one day. Introduction Over the past few years, phased arrays and beamforming have become essential elements in multiple fields, particularly in 5G wireless communication systems. An antenna array is typically controlled by a feeding network that controls the phase shift and amplitude of the respective antenna elements. 1 The antenna array is most easily articulated in these embodiments because the radiation beam is steered by the antenna array towards the selected position. This feature gives rise to three different types of feed networks for the control of antenna arrays: parallel-feed networks, series-feed networks, and matrix-based networks. 2 Wide-tuning phase shifters are required for both parallel and series feed networks, and they restrict the capability of the antenna array to simultaneously form more than one beam at the same time. However, this was not the case for matrix feed networks, which had hybrid couplers, crossover, and a phase shifter network. 3 In addition, matrix networks have the special property that multiple beams can be produced simultaneously. Different matrix feeding networks have been designed, such as the widely used Butler, Blass, and Nolen matrices. 4 – 6 The Butler matrix is well known for its symmetric design with an equal number of inputs and outputs. Equal-magnitude signals with progressive phase differences are emitted from the output ports 7 of each input port, and the simultaneous radiation of the two beams can be accomplished. The Butler matrix has been widely investigated for its low loss, 8 multiband, 9 wideband, 10 small size, 11 and millimeter-wave operating ranges. 12 Furthermore, studies on symmetric structures at two scales, including the 4× 4 13 and 8× 8 networks, have also been performed. 14 Later studies employed the Butler matrix for non-symmetric structures, such as the 2 × 4 network, 15 3 × 4 network, 16 and 4 × 8 network. 17 The Blass matrix is a cross-over free full-rank matrix with half as many input and output ports as the Butler matrix, but load terminations in the Blass matrix substitute for the crossovers of the Butler matrix. There are structural limitations of the Blass matrix that could lead to partial signal flow towards the termination loads, which causes the efficiency to be less than that of the Butler matrix. 5 To overcome this drawback, improvements in the Butler matrix have been suggested, focusing on a reduction in the number of components and element footprints. However, for lower 5G bands such as 26 GHz, beamforming components (e.g., couplers, phase shifters, and antenna elements) have limited flexibility and high signal loss. 18 An early beamforming network was introduced in Ref. 19 where it incorporated a Butler matrix algorithm in combination with a 90° coupler. Another development in beamforming networks was considered in Ref. 20 , which reports on a series-fed matrix design that suppresses sidelobes at 28 GHz. In Ref. 21, a microstrip beamforming system was presented for multiband operations at 26, 28, and 30 GHz. The coupler used in this configuration was H-type with a short slot. One recent example is in Ref. 22 , where the work is at 28 GHz with a 4 × 4 Butler matrix structure for a 2-D beamforming network that uses three couplers and three phase shifters. Another example of a compact form factor is the 4 × 4 beamforming network at 28 GHz, which was designed in Ref. 23 using lumped element couplers to alleviate the matrix size. In addition, a 4 × 4 beamforming network using 90-degree coupler was presented in Refs. 24 and 25 for 28 GHz, with four Substrate Integrated Waveguide (SIW) couplers, one crossover, and two phase shifters. Unfortunately, this structure is large in size with a very high IL and phase difference, which consequently results in size and phase error difficulties in these prior realizations at such increased 5G frequencies. In this paper, a novel 4 × 4 Butler matrix with low loss, compact size, small amplitude, and phase error across the band is presented, based on a normal and unequal separation vector structure along the waveguide walls. The remainder of this paper is organized as follows. First, the topology of the design and equations of the Butler matrix and its variants, as well as those of the design of couplers, are studied. Second, a comprehensive 4 × 4 Butler matrix approach is presented with flexible performance. Subsequently, the measurement results of the proposed 4 × 4 Butler matrix are systematically compared and discussed with respect to simulations and some works presented in the literature. Finally, the major findings are summarized. Taken together, this novel Butler matrix structure is promising for improving beamforming networks of 5G wireless communication systems. Method – Design of beamforming Figure 1 presents the structure of the 4 × 4 Butler matrix, where the four input ports are defined as (P1, P2, P3, and P4) and the four output ports are represented as (P5, P6, P7, and P8). The Butler matrix presented in Figure 1 contains only four hybrid couplers. All couplers have a single coupling constant that is distributed along the matrix equally between the lower and upper parts. To maintain edge-to-edge uniformity of signal levels (for the output of Butler matrix) and signal integrity of lines, the coupling ratios of (C1) and (C2) were selected. Hence, the coupling ratio of the couplers at the Butler matrix outputs can be expressed as Ref. 22 . Figure 1. The structure of 4 × 4 SIW Butler Matrix. The schematic structure of the two-section VAI hybrid coupler used for the speed demonstration with a center frequency of 26 GHz is illustrated in Figure 2 . The coupler is designed to have a symmetric four-port structure (P1–P4) and is based on a via-based internal coupler structure for coupling and phase modulation. The proposed power splitter is constructed using substrate-integrated waveguide (SIW) technology, the two power-dividing arms of which are synthesized by electromagnetic coupling and phase manipulations to achieve the desired characteristics. The design embodies 50 Ω quarter-wavelength transmission lines as the basic structure of the coupler arms. The arms are realized by a set of carefully optimized strip-line widths based on the microwave design equations found in Refs. 24 and 25 . Rows, which act as artificial magnetic conductors, are mainly utilized to confine electromagnetic fields but also affect impedance matching and phase response. This is evident in Figure 2 , which also shows the signal flow from port to port. The input power at port P1 is equally divided into ports P2 and P3, with-3 dB at each port. In addition, the coupler introduces a well-defined phase relationship, which provides 45° and constructive phase coupling at the central transmission axis, whereas the phase shift difference between the output ports is 135°. This phase shift is essential for many beamforming systems, such as the Butler matrix in 5G phased arrays. To widen the operating band, an arm-shaped structure was used for each coupling section. The modified arms act as impedance transformers to make the required impedance transitions (Z 1 , Z 2 , Z 3 ) over the band. The design equations are formulated in closed form as related to even- and odd-mode analyses to obtain low reflection and high isolation between ports. In general, the design exhibits good engineering accuracy, particularly with respect to impedance tuning, phase control, and coupling balance its due regard. These hybrid couplers are important in millimeter-wave transceivers, where the architecture, efficiency, and bandwidth require compactness, and wideband performance is achieved by providing degrees of freedom for phase control and power division in the physical layout. When a single is applied to port P1, the power is divided equally between ports P2 and P3, with a loss of approximately 3 dB. The signal path includes phase-adding means: in the vertical direction, it is a 45° phase adder, while the output ports P2 and P3 retain their 135° phase difference, which is essential for modern millimeter-wave beamforming systems where, for example, the Butler matrix is implemented. Figure 2. The structure of SIW Hybrid coupler with phase difference of 135 degree. The response of the coupler was characterized using numerical simulations based on full-wave electromagnetic equations. The obtained S-parameters indicate the operational bandwidth, matching properties, and isolation performance of the coupler and are depicted in Figure 3 . As shown in Figure 3(A) , a sharp dip below -30 dB in | S 11 | was observed at a center frequency of 26 GHz, indicating a good impedance-matching Doppler radar. The isolation from port P1 to isolated port P4 ( S 41 ) follows a similar behavior, achieving values less than -30 dB at resonance and a minimum close to -40 dB. These findings verify the effective suppression of unwanted reflections and high isolation between noncoupled ports, which is an essential figure of merit for hybrid couplers. The coupling levels from input P1 to output ports P2 ( S 21 ) and P3 ( S 31 ) are well suppressed, as shown in Figure 3(B) . At 26 GHz, both S 21 and S 31 meet at about -3.1 dB, confirming the desired equal power splitting. Furthermore, making a power splitter at a power splitting range of -3 dB to -4.5 dB over a 5-GHz frequency range (from 24.5 to 29.5 GHz), that is, operation bandwidth is also realized. As shown in Figure 3(C) , the phase difference between ports P2 and P3 was 135°, not the standard 90°, which reflects a deliberate design choice. This enhancement of the phase difference enables the coupler to integrate both the coupling and phase-shifting functions into a single device, thereby combining the roles of a hybrid coupler and phase shifter. Figure 3. Simulated response for designed hybrid coupler. (A) Return loss and isolation, (B) Output power, (C) Phase difference vs standard coupler. As mentioned earlier, Figure 1 shows the implementation of a 4 × 4 Butler matrix design and the assembly of four couplers. A simulation using Computer Simulation Technology (CST) was carried out to prove the feasibility of the 4 × 4 Butler matrix. The S-parameters are linked to the return loss, isolation, and transmission coefficients, as shown in Figure 4(A) , 5(A) , 6(A) , and 7(A) , respectively. As shown in Figure 4 , the return loss of input port 1 shows acceptable results in all bands and is below -10 Db. More precisely, at 26 GHz, the measured return loss values were S 11 = −20:4 dB, S 21 = −18:7 dB, and S 31 = −22:9 dB, yielding a fractional bandwidth of 60% over all input ports. This demonstrates that good isolation was achieved for all the ports. Figure 4(B) also shows the transmission coefficients when port 1 is powered on, it produces S 51 = -5.8 dB, S 61 = -6.12 dB, S 71 = -6.12 dB > S 61 , and S 81 = -6.5 dB. These results indicate that the power is distributed equally in the outputs if Port 1 is excited. Thus, the calculated S-parameter results corresponded to the design specifications of the 4 × 4 Butler matrix. The input return loss at input port 2 is superior and less than -10 dB. At 26 GHz, for example, the return loss measurements read S 22 = -20.4 dB, S 12 = -18.7 dB and S 13 = -22.9 dB, which encompasses a fractional bandwidth of 60% for all of the input ports. This shows that the isolation between the ports is good. Figure also shows the behaviour of the transmission coefficients when Port 2 is on. As shown in Figure 5(B) The measured values are S 52 =-6.8 dB, S 62 = -6.35 dB, S 72 = -6.54 dB, and S 82 = -6.55 dB. This implies that equal power is distributed to the outputs with excitation at port 2. The return loss of input port 3 is shown in Figure 6(A) , with good performance below -10 dB. Return losses values of S 33 = -25.5 dB, S 23 = -20.7 dB, and S 43 = -24.7 dB at 26 GHz and a fractional bandwidth of 60% are obtained over all input ports This indicates that proper isolation was achieved at each port. The transmission coefficients upon the activation of port 3 are shown in Figure 6(B) . The measured values are S 53 = 6.2 dB, S 63 = 5.85 dB, S 73 = 6.22 dB and S 83 = 6.75 dB which implies that power equally distributes among the ports when port 3 is excited. Figure 7 shows the return loss behaviour at input port 4, where excellent performance is observed with a value of less than -10 dB. Remarkably, at 26 GHz, the return loss measurements are S 44 = -24.7 dB, S 43 = -22.8 dB, and S 42 =- 22.6 dB, respectively, which again constitute a 60% fractional bandwidth for all input ports. This means that strong isolation is reached at each port. The transmission coefficient responses upon the activation of port 4 are shown in Figure 7(B) . The measured S 53 = -6.8 dB, S 63 = -5.47 dB, S 73 = -6.65 dB, and S 83 = -6.52 dB, suggest that when port 4 is involved, the output power is evenly divided. Figure 4. Simulated Port 1 of BM. (A) Return loss and isolated ports, (B) Output ports. Figure 5. Simulated Port 2 of BM. (A) Return loss and isolated ports, (B) Output ports. Figure 6. Simulated Port 3 of BM. (A) Return loss and isolated ports, (B) Output ports. Figure 7. Simulated Port 4 of BM. (A) Return loss and isolated ports, (B) Output ports. The simulated phase shifts of the output ports with excitation from Port 1 are shown in Figure 8(A) . In particular, when port 1 is actuated, the phase dispersion of the outputs at ports 5, 6, 7, and 8 is 45.6°. By turning on port 2, a phase difference of 133.6° can be observed, as shown in Figure 8(B) . Note from the accompanying figure that all outputs (1, 2, and 3) have the correct phase of excitation when the signal from port 2 is set. The simulated phase shifts for the output ports under excitation at port 3 are shown in Figure 8(C) together with the phase differences for the four output ports of the 4 × 4 Butler matrix. It can also be found that when port 3 is excited, the simulated phase difference between the outputs (i.e., ports 5, 6, 7, and 8) is -133.23°, as shown in Figure 8(C) . -45.6° is the phase difference when port 4 is excited, as shown in Figure 8(D) . Figure 8. Simulated phase differences of proposed BM. (A) Port 1, (B) Port 2, (C) Port 3, (D) Port 4. Results and Discussion The suggested 4 × 4 Butler matrix design was realized on a Roger substrate with a thickness of h = 0.508 mm and relative permittivity of ε r = 2.2. Figure 9 shows the manufactured 4 × 4 Butler matrix. The S-parameter tests were performed using a Keysight (Agilent Technologies) field forecast vector network analyzer (VNA) (N9925A), two cables, and six referent dummy loads. The efficiency of the 4 × 4 Butler matrix hardware is demonstrated by its S -parameters, as seen in the simulation results shown in Figure 10 . Figure 9. Fabricated 4 × 4 SIW BM. Figure 10. Measured results of SIW BM. (A) Port 1, (B) Port 2, (C) Port 3 and (D) Port 4. The measured return loss and isolation from the port 1 excitation are plotted in Figure 10(A) . The measured S 11 is −20 dB at 26 GHz, and the wideband response has a 2 GHz percentage of 60 FBW of operation. The results of these simulations were compared with the measurements. Furthermore, the isolation of ports 2, 3, and 4 at all reconfigurable states is satisfactory and remains less than -10 dB over the desired band, as illustrated in Figure 10(A) . The measured transmission coefficients in Figure 10(A) are S 51 = −6.5 dB, S 61 = −6.69 dB, S 71 = −6.69 dB, S 81 = −7.2 dB, which shows an amplitude loss of −2.2 dB. Therefore, a low insertion loss was obtained for the port 1 excitation. The return loss and isolation of the port 2 excitation are shown in Figure 10 (B) . In particular, S 22 is measured at -15 dB and 26 GHz with a wideband of 2.4 GHz to maintain a 60% FBW, and is set for comparison with the simulated results. On the other hand, the remaining isolations (ports 1, 3, and 4) also perform well, with isolations in the range of −10 dB over the desired frequency band. The transmission coefficients of Figure 10(B) are given as S 52 = -7.5 dB, S 62 = -7.69 dB, S 72 = -6.49 dB, and S 82 = -6.2 dB, indicating amplitude attenuation of -1.5 db. Hence, for the port 2 drive, a low insertion loss is found. The simulated return loss and isolation at the port 3 excitation are shown in Figure 10(C) . The measured −18.6 dB S 33 at 26 GHz, together with the wideband characteristic (26 GHz, 55% FBW), is compared with the simulated results. The measured isolations from ports 1, 2, and 4 were well maintained at less than even -10 dB over the designed bandwidth, as depicted in Figure 10(C) . The measured transmission coefficients in Figure 10(C) are S 53 = -6.58 dB, S 63 = -6.49 dB, S 73 = -7.49 dB and S 83 = -7.3 dB with magnitude loss of –1.6 dB. Accordingly, in the port 3 excitation, a low insertion loss was attained. The measured return loss and isolation for the port 4 excitation are shown in Figure 10(D) . This measured S 44 = -19.7 dB at 26 GHz over a wideband characteristic of 4 GHz (60% FBW) is then compared to simulated results. In contrast, the measured isolation from ports 1, 2, and 3 exhibits a good performance of lower than -10 dB over the desired bandwidth, as illustrated in Figure 10(D) . From the Figure 10(D) , the measured transmission coefficients are -7.58 dB ( S 54 ), -6.87 dB ( S 64 ), -6.77 dB ( S 74 ) and –7.58 dB ( S 84 ), with a magnitude loss of -1.85 dB. Thus, the insertion loss at the port 4 excitation was also low. The measured phase difference of the outputs when all the input ports are active is shown in Figure 11 . When compared with the simulated phase differences, it was observed that the measured phase difference at the port 1 excitation was 131° with a phase error equal to 1°. When the excitation was performed from ports 2 and 3, the phase differences were 46.05° and -46.04° with phase errors of 1.05° and -1.04° respectively. The measured phase difference at port 4 was − -134° with a phase error of 2°. Therefore, the proposed Butler matrix has a tunable phase difference at the output ports, with an average phase error of 2° at the low-frequency stage. Figure 11. Measured vs simulated phase difference at 26 GHz. The prototype of the proposed antenna beamforming network with a Butler matrix network is shown in Figure 12 . The simulated return loss of the proposed beamforming network is illustrated in Figure 13 . At 26 GHz, the return loss for all excited ports is < −10 dB. This suggests that the beamforming feeding network performed well at the desired bandwidth. Nonetheless, at ports 2 and 3, a decay in the signal was detected because of the mismatch between the connectors and channels, as well as the losses of the cable. The bandwidth was approximately 2.8 GHz, which suggests that the performance of the beamformer is highly resonant at various frequencies. The measured and simulated radiation patterns for the designed BM in the SIW are shown in Figures 14(A) , 14(B) , 14(C) and 14(D) . Owing to ±31.23° for all ports, 9 dB beams were obtained at ±14.43° and ±11 dB at all ports. In summary, a low gain loss (within 3 dB) with a low phase error of 1.8° at port 2 was obtained. A comparison with other similar-frequency designs is presented in Table 1 . Therefore, the proposed beamforming network met the design specifications well and had a better performance than state-of-the-art devices with low loss and low profile and phase error at 26 GHz. Figure 12. The fabricated beamforming network. Figure 13. The measured vs simulated return loss of beamforming. Figure 14. The measured vs simulated RP at 26 GHz. (A) Port 1, (B) Port 2, (C) Port 3, (D) Port 4. Table 1. Comparison of this work with other related research work. Ref Technology Freq. Configuration Losses Phase error Size (mm 2 ) (L × W) 22 /2021 Waveguide 28 GHz 4 × 4 BM Standard 3.4 dB 4° 130 × 66 mm 2 23 /2022 Microstrip 28-32 GHz 6 × 6 BM Standard 8.5 dB 10° 130 × 38 mm 2 21 /2023 SIW 26 GHz 4 × 4 BM Standard 5.3 dB 6.7° 95 × 30 mm 2 24 /2024 SIW 28 GHz 4 × 4 BM Standard 6 dB 5° 93 × 42 mm 2 25 /2024 SIW 26 GHz 4 × 4 BM Standard 4.8 dB 7° 100 × 35 mm 2 This work/2025 SIW 26 GHz 4 × 4 BM couplers 1.4 dB 1.8° 74 × 28 mm 2 Conclusion A 4 × 4 Butler beamforming matrix with a low-loss wideband at 26 GHz for 5G mobile proposed to produce one type of 4 × 4 application is shown to produce a distinct sequential phase difference available in the output ports. The fabricated 4 × 4 Butler matrix was designed with four 3-dB couplers to achieve substantial size reduction. There is a good agreement between the measurement and simulation results to verify the final performance of the design. A high performance 1.4 dB low loss magnitude error, 1.8° phase error and a 2.8 GHz 1 dB bandwidth are achieved. The suggested 4 × 4 antenna Butler matrix has a novel method for BFN designs for 26 GHz 5G applications along with the presented properties. Data availability Zenodo. Experimental data for “Butler Matrix Based on Substrate Integrated Waveguide Without Crossover and Phase Shifter for Millimeter Waves Applications”. DOI: https://doi.org/10.5281/zenodo.17076167 . 26 This project contains the following underlying data: • Experimental Data (Nawras, Coupler and BM).xlsx Data are available under the terms of the Creative Commons Attribution 4.0 International license (CC-BY 4.0). Acknowledgements The authors would like to thank all those who contributed to the success of this study. References 1. Ojaroudiparchin N, Shen M, Zhang S, et al. : A Switchable 3-D-Coverage-Phased Array Antenna Package for 5G Mobile Terminals. IEEE Antennas Wirel. Propag. Lett. 2016; 15 (c): 1747–1750. Publisher Full Text 2. Moon SM, Yun S, Yom IB, et al. : Phased Array Shaped-Beam Satellite Antenna with Boosted-Beam Control. IEEE Trans. Antennas Propag. 2019; 67 (12): 7633–7636. Publisher Full Text 3. Vallappil AK, Rahim MKA, Khawaja BA, et al. : Butler Matrix Based Beamforming Net-works For Phased Array Antenna Systems: A Comprehensive Review and Future Directions For 5G Applications. IEEE Access. 2020; 9 : 3970–3987. Publisher Full Text 4. Dyab WM, Sakr AA, Wu K: Dually-Polarized Butler Matrix for Base Stations With Polarization Diversity. IEEE Trans. Microw. Theory Tech. 2018; 66 (12): 5543–5553. Publisher Full Text 5. Tsokos C, et al. : Analysis of a Multibeam Optical Beamforming Network Based on Blass Matrix Architecture. J. Lightwave Technol. 2018; 36 (16): 3354–3372. Publisher Full Text 6. Fonseca NJG: Printed S-band 4 × 4 nolen matrix for multiple beam antenna applications. IEEE Trans. Antennas Propag. 2009; 57 (6): 1673–1678. Publisher Full Text 7. Ren B, Arigong M, Zhou JD, et al. : A Novel Design of 4 × 4 Butler Matrix With Relatively Flexible Phase Differences. IEEE Antennas Wirel. Propag. Lett. 2016; 15 (c): 1277–1280. Publisher Full Text 8. Wang Y, Ma K, Jian Z: A low-loss butler matrix using patch element and honeycomb concept on SISL platform. IEEE Trans. Microw. Theory Tech. 2018; 66 (8): 3622–3631. Publisher Full Text 9. Rezvani M, Nikmehr S, Ghanbari L: A novel Butler matrix feeding system for BST multi-band antennas. IEICE Electron. Express. 2013; 10 (2): 1–6. Publisher Full Text 10. Ibrahim SZ, Bialkowski ME: Wideband butler matrix in microstrip-slot technology. APMC 2009 - Asia Pacific Microw. Conf. 2009. 2009; pp. 2104–2107. 11. Karimbu Vallappil A, Rahim MKA, Khawaja BA, et al. : Compact Metamaterial Based 4 × 4 Butler Matrix with Improved Bandwidth for 5G Applications. IEEE Access. 2020; 8 : 13573–13583. Publisher Full Text 12. Hsieh CH, Lin YT, Jhan HC, et al. : Application of a two-dimensional butler matrix antenna array for tile-based beamforming. IEICE Electron. Express. 2019; 16 (11): 1–6. Publisher Full Text 13. Tajik, Shafiei Alavijeh A, Fakharzadeh M: Asymmetrical 4×4 butler matrix and its application for single layer 8×8 butler matrix. IEEE Trans. Antennas Propag. 2019; 67 (8): 5372–5379. Publisher Full Text 14. Shao Q, Chen FC, Chu QX, et al. : Novel Filtering 180° Hybrid Coupler and Its Application to 2 × 4 Filtering Butler Matrix. IEEE Trans. Microw. Theory Tech. 2018; 66 (7): 3288–3296. Publisher Full Text 15. Cao Y, Chin KS, Che W, et al. : A Compact 38 GHz Multibeam Antenna Array with Multifolded Butler Matrix for 5G Applications. IEEE Antennas Wirel. Propag. Lett. 2017; 16 (c): 2996–2999. Publisher Full Text 16. Lian JW, Ban YL, Xiao C, et al. : Compact Substrate-Integrated 4 × 8 Butler Matrix with Sidelobe Suppression for Millimeter-Wave Multibeam Application. IEEE Antennas Wirel. Propag. Lett. 2018; 17 (5): 928–932. Publisher Full Text 17. Rahimi R, Shahbazpanahi S: A Two-Way Network Beamforming Approach Based on Total Power Minimization with Symmetric Relay Beamforming Matrices. IEEE Access. 2017; 5 (c): 12458–12474. Publisher Full Text 18. Djerafi T, Fonseca NJG, Wu K: Architecture and implementation of planar 4 ×4 Ku-Band nolen matrix using SIW technology. Proc. 2008 Asia Pacific Microw. Conf. APMC 2008. 2008; pp. 4–7. 19. Fonseca NJG, Ferrando N: Nolen matrix with tapered amplitude law for linear arrays with reduced side lobe level. Proceedings of the Fourth European Conference on Antennas and Propagation. 2010; pp. 1–5. 20. Sivasundarapandian, Suriyakala CD: A new multi-band multiple beam forming nolen matrix antenna feeding network for cognitive radio. Int. J. Eng. Technol. 2014; 6 (5): 2061–2069. 21. Hussein YM, Rahim MKA, Murad NA, et al. : Low Loss Wideband 4×4 Butler Matrix Networks Based on Substrate Integrated Waveguide for 5G Applications. IEEE Access. 2024; 12 : 7896–7910. 22. Almeshehe MW, et al. : Low loss waveguide-based Butler matrix with iris coupling control method for millimeterwave applications. Waves Random Complex Media. Feb. 2021; 33 : 372–392. Publisher Full Text 23. Pezhman MM, Heidari A-A, Ghafoorzadeh-Yazdi A: A novel single layer SIW 6 × 6 beamforming network for 5G applications. AEU-Int. J. Electron. C. Oct. 2022; 155 : 154380. Publisher Full Text 24. Deng J-Y, Zhang Y, Lin W: Compact Multibeam Antenna Array Facilitated by Miniaturized Slow Wave Substrate Integrated Waveguide Butler Matrix. IEEE Trans. Antennas Propag. Jan. 2024; 72 : 9561–9564. Publisher Full Text 25. Idury SK, Delmonte N, Silvestri L, et al. : Design and realization of a compact substrate inte-grated coaxial line butler matrix for beamforming applications. Int. J. Microw. Wirel. Technol. Jan. 2024; 16 (5): 812–818. Publisher Full Text 26. Liew CP: Butler Matrix Based on Substrate Integrated Waveguide Without Crossover and Phase Shifter for Millimeter Waves Applications. Zenodo. Sept. 2025; 8 . Publisher Full Text Comments on this article Comments (0) Version 2 VERSION 2 PUBLISHED 23 Sep 2025 ADD YOUR COMMENT Comment Author details Author details 1 Multimedia University Faculty of Engineering and Technology, Ayer Keroh, Malacca, Malaysia 2 Centre for Advanced Analytics, CoE for Artificial intelligence, Multimedia University, Ayer Keroh, Malaysia 3 Ministry of Higher Education and Scientific Research, Baghdad, Iraq 4 Faculty of Electronics and Computer Engineering, Universiti Teknikal Malaysia Melaka, Durian Tunggal, Malacca, Malaysia 5 School of Energy and Chemical Engineering, Xiamen University Malaysia, Sepang, Selangor, Malaysia 6 Taylor's University School of Engineering, Subang Jaya, Selangor, Malaysia Nawres Nayyef Roles: Conceptualization, Investigation, Methodology, Software Kim Geok Tan Roles: Project Administration, Supervision Hussam Keriee Roles: Investigation Zahriladha Zakaria Roles: Supervision Chia Pao Liew Roles: Project Administration, Writing – Review & Editing Chockalingam Aravind Vaithilingam Roles: Writing – Review & Editing Competing interests No competing interests were disclosed. Grant information This research is under grant MMUE220012 from Telekom Research & Development Sdn. Bhd. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Article Versions (2) version 2 Revised Published: 24 Apr 2026, 14:969 https://doi.org/10.12688/f1000research.168318.2 version 1 Published: 23 Sep 2025, 14:969 https://doi.org/10.12688/f1000research.168318.1 Copyright © 2025 Nayyef N et al . This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Download Export To Sciwheel Bibtex EndNote ProCite Ref. Manager (RIS) Sente metrics Views Downloads F1000Research - - PubMed Central info_outline Data from PMC are received and updated monthly. - - Citations open_in_new 0 open_in_new 0 open_in_new SEE MORE DETAILS CITE how to cite this article Nayyef N, Tan KG, Keriee H et al. Butler Matrix Based on Substrate Integrated Waveguide Without Crossover and Phase Shifter for Millimeter Waves Applications [version 1; peer review: 1 approved with reservations, 1 not approved] . F1000Research 2025, 14 :969 ( https://doi.org/10.12688/f1000research.168318.1 ) NOTE: If applicable, it is important to ensure the information in square brackets after the title is included in all citations of this article. COPY CITATION DETAILS track receive updates on this article Track an article to receive email alerts on any updates to this article. TRACK THIS ARTICLE Share Open Peer Review Current Reviewer Status: ? Key to Reviewer Statuses VIEW HIDE Approved The paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. Not approved Fundamental flaws in the paper seriously undermine the findings and conclusions Version 1 VERSION 1 PUBLISHED 23 Sep 2025 Views 0 Cite How to cite this report: Lian JW. Reviewer Report For: Butler Matrix Based on Substrate Integrated Waveguide Without Crossover and Phase Shifter for Millimeter Waves Applications [version 1; peer review: 1 approved with reservations, 1 not approved] . F1000Research 2025, 14 :969 ( https://doi.org/10.5256/f1000research.185497.r442261 ) The direct URL for this report is: https://f1000research.com/articles/14-969/v1#referee-response-442261 NOTE: it is important to ensure the information in square brackets after the title is included in this citation. Close Copy Citation Details Reviewer Report 07 Jan 2026 Ji-Wei Lian , Nanjing University of Science and Technology, Nanjing, China Not Approved VIEWS 0 https://doi.org/10.5256/f1000research.185497.r442261 This paper presents a 4×4 Butler matrix implemented using Substrate Integrated Waveguide (SIW) technology operating at 26 GHz, targeting millimeter-wave 5G applications. The proposed design eliminates conventional crossovers and discrete phase shifters by employing only four hybrid couplers, enhanced ... Continue reading READ ALL This paper presents a 4×4 Butler matrix implemented using Substrate Integrated Waveguide (SIW) technology operating at 26 GHz, targeting millimeter-wave 5G applications. The proposed design eliminates conventional crossovers and discrete phase shifters by employing only four hybrid couplers, enhanced with interdigital structures and non-metalized vias to fine-tune performance. Both simulated and measured results are provided. There are several comments to address. The revised topology of the new 4x4 Butler matrix should be provided and compared with traditional topology The phase distribution of the revised topology should be thoroughly calculated and discussed to demonstrate the feasibility of this proposed Butler matrix. The bandwidth is quite narrow, which is not common for SIW butler matrix. Please discuss this issue. While the 4×4 case is demonstrated, it would be helpful to briefly discuss whether this architecture can be extended to larger Butler matrices (e.g., 8×8). Are there fundamental limitations in terms of layout or phase accumulation? The simulated and measured results should be plotted in the same figure for comparison. Fig. 11, it is not clear to see the simulated and measured results. The size in table 1 should be in wavelength. The gain and bandwidth should be added. Is the work clearly and accurately presented and does it cite the current literature? Partly Is the study design appropriate and is the work technically sound? Partly Are sufficient details of methods and analysis provided to allow replication by others? Partly If applicable, is the statistical analysis and its interpretation appropriate? Partly Are all the source data underlying the results available to ensure full reproducibility? Partly Are the conclusions drawn adequately supported by the results? Partly Competing Interests: No competing interests were disclosed. Reviewer Expertise: antenna I confirm that I have read this submission and believe that I have an appropriate level of expertise to state that I do not consider it to be of an acceptable scientific standard, for reasons outlined above. Close READ LESS CITE CITE HOW TO CITE THIS REPORT Lian JW. Reviewer Report For: Butler Matrix Based on Substrate Integrated Waveguide Without Crossover and Phase Shifter for Millimeter Waves Applications [version 1; peer review: 1 approved with reservations, 1 not approved] . F1000Research 2025, 14 :969 ( https://doi.org/10.5256/f1000research.185497.r442261 ) The direct URL for this report is: https://f1000research.com/articles/14-969/v1#referee-response-442261 NOTE: it is important to ensure the information in square brackets after the title is included in all citations of this article. COPY CITATION DETAILS Report a concern Author Response 11 Feb 2026 Chia Pao Liew , School of Energy and Chemical Engineering, Xiamen University Malaysia, Sepang, Malaysia 11 Feb 2026 Author Response Comment 1: highlighted in the design method Comment 2: the following is highlighted: In the revised crossover-free, phase-shifter-free topology, the required phase distribution is realized through the intrinsic phase ... Continue reading Comment 1: highlighted in the design method Comment 2: the following is highlighted: In the revised crossover-free, phase-shifter-free topology, the required phase distribution is realized through the intrinsic phase properties of the SIW hybrid couplers and path-length differences in the interconnecting SIW transmission sections. For an ideal 3-dB quadrature hybrid coupler: The two output signals have equal magnitude. The relative phase difference between the “through” and “coupled” ports is approximately ±90∘ \pm 90^\circ±90∘ (sign depends on port definition). Thus, the cumulative phase at each output port can be written as a sum of: hybrid-coupler phase terms, and propagation phase terms along SIW paths. (2) Where: N c = number of couplers on the signal route N p = number of SIW path segments L m = physical length of the m-th segment β g = guided propagation constant of SIW For SIW, the guided wavenumber can be approximated by: (3) where k₀= εᵣ is the substrate relative permittivity, and a eq is the equivalent SIW width determined from the via diameter and pitch. This expression allows computing the expected phase shift of any interconnect line: φ prop = β g L Comment 3: the following is highlighted: the operational bandwidth of the proposed Butler Matrix is relatively limited compared to some reported SIW-based implementations. This behaviour is primarily attributed to the cascaded hybrid-coupler topology employed to eliminate crossovers and discrete phase shifters. In such configurations, the overall bandwidth is governed by the intersection of the passbands of the individual couplers , resulting in a reduced effective bandwidth as the number of cascaded stages increases. Additionally, the bandwidth is influenced by the phase balance requirement intrinsic to Butler matrices. Even when acceptable impedance matching is maintained over a wider frequency range, stringent phase-error constraints impose a narrower usable bandwidth for accurate beamforming operation. Comment 4: the following is highlighted: Although this work demonstrates a 4×4 Butler Matrix as a proof of concept, the proposed SIW architecture is inherently scalable to higher-order matrices , such as 8×8 configurations. In principle, the extension follows the same hierarchical network structure used in conventional Butler matrices, where additional SIW hybrid couplers are cascaded to generate the required phase progression and output ports. No fundamental limitations prevent scaling the proposed crossover-free and phase-shifter-free topology to larger matrices. However, practical considerations arise as the matrix order increases. These include increased layout complexity, longer signal paths leading to higher cumulative insertion loss, and tighter control of phase balance due to phase accumulation across multiple cascaded couplers. At millimeter-wave frequencies, fabrication tolerances and via-placement accuracy may also impose constraints on achievable phase uniformity in large-scale implementations. Despite these practical challenges, SIW technology remains well suited for higher-order Butler matrices due to its low-loss waveguiding characteristics and planar layout flexibility. With careful layout optimization, symmetry preservation, and loss balancing, larger matrices such as 8×8 can be realized while maintaining acceptable broadband performance. Therefore, the proposed architecture provides a scalable foundation for higher-order beamforming networks, particularly in applications where compactness and integration are prioritized. Comment 5: modification was made on the figures to improve clarity with multiple lines in the Figures Comment 6: We have improved Fig 11. Comment 7: changed to wavelength Comment 1: highlighted in the design method Comment 2: the following is highlighted: In the revised crossover-free, phase-shifter-free topology, the required phase distribution is realized through the intrinsic phase properties of the SIW hybrid couplers and path-length differences in the interconnecting SIW transmission sections. For an ideal 3-dB quadrature hybrid coupler: The two output signals have equal magnitude. The relative phase difference between the “through” and “coupled” ports is approximately ±90∘ \pm 90^\circ±90∘ (sign depends on port definition). Thus, the cumulative phase at each output port can be written as a sum of: hybrid-coupler phase terms, and propagation phase terms along SIW paths. (2) Where: N c = number of couplers on the signal route N p = number of SIW path segments L m = physical length of the m-th segment β g = guided propagation constant of SIW For SIW, the guided wavenumber can be approximated by: (3) where k₀= εᵣ is the substrate relative permittivity, and a eq is the equivalent SIW width determined from the via diameter and pitch. This expression allows computing the expected phase shift of any interconnect line: φ prop = β g L Comment 3: the following is highlighted: the operational bandwidth of the proposed Butler Matrix is relatively limited compared to some reported SIW-based implementations. This behaviour is primarily attributed to the cascaded hybrid-coupler topology employed to eliminate crossovers and discrete phase shifters. In such configurations, the overall bandwidth is governed by the intersection of the passbands of the individual couplers , resulting in a reduced effective bandwidth as the number of cascaded stages increases. Additionally, the bandwidth is influenced by the phase balance requirement intrinsic to Butler matrices. Even when acceptable impedance matching is maintained over a wider frequency range, stringent phase-error constraints impose a narrower usable bandwidth for accurate beamforming operation. Comment 4: the following is highlighted: Although this work demonstrates a 4×4 Butler Matrix as a proof of concept, the proposed SIW architecture is inherently scalable to higher-order matrices , such as 8×8 configurations. In principle, the extension follows the same hierarchical network structure used in conventional Butler matrices, where additional SIW hybrid couplers are cascaded to generate the required phase progression and output ports. No fundamental limitations prevent scaling the proposed crossover-free and phase-shifter-free topology to larger matrices. However, practical considerations arise as the matrix order increases. These include increased layout complexity, longer signal paths leading to higher cumulative insertion loss, and tighter control of phase balance due to phase accumulation across multiple cascaded couplers. At millimeter-wave frequencies, fabrication tolerances and via-placement accuracy may also impose constraints on achievable phase uniformity in large-scale implementations. Despite these practical challenges, SIW technology remains well suited for higher-order Butler matrices due to its low-loss waveguiding characteristics and planar layout flexibility. With careful layout optimization, symmetry preservation, and loss balancing, larger matrices such as 8×8 can be realized while maintaining acceptable broadband performance. Therefore, the proposed architecture provides a scalable foundation for higher-order beamforming networks, particularly in applications where compactness and integration are prioritized. Comment 5: modification was made on the figures to improve clarity with multiple lines in the Figures Comment 6: We have improved Fig 11. Comment 7: changed to wavelength Competing Interests: None Close Report a concern Respond or Comment COMMENTS ON THIS REPORT Author Response 11 Feb 2026 Chia Pao Liew , School of Energy and Chemical Engineering, Xiamen University Malaysia, Sepang, Malaysia 11 Feb 2026 Author Response Comment 1: highlighted in the design method Comment 2: the following is highlighted: In the revised crossover-free, phase-shifter-free topology, the required phase distribution is realized through the intrinsic phase ... Continue reading Comment 1: highlighted in the design method Comment 2: the following is highlighted: In the revised crossover-free, phase-shifter-free topology, the required phase distribution is realized through the intrinsic phase properties of the SIW hybrid couplers and path-length differences in the interconnecting SIW transmission sections. For an ideal 3-dB quadrature hybrid coupler: The two output signals have equal magnitude. The relative phase difference between the “through” and “coupled” ports is approximately ±90∘ \pm 90^\circ±90∘ (sign depends on port definition). Thus, the cumulative phase at each output port can be written as a sum of: hybrid-coupler phase terms, and propagation phase terms along SIW paths. (2) Where: N c = number of couplers on the signal route N p = number of SIW path segments L m = physical length of the m-th segment β g = guided propagation constant of SIW For SIW, the guided wavenumber can be approximated by: (3) where k₀= εᵣ is the substrate relative permittivity, and a eq is the equivalent SIW width determined from the via diameter and pitch. This expression allows computing the expected phase shift of any interconnect line: φ prop = β g L Comment 3: the following is highlighted: the operational bandwidth of the proposed Butler Matrix is relatively limited compared to some reported SIW-based implementations. This behaviour is primarily attributed to the cascaded hybrid-coupler topology employed to eliminate crossovers and discrete phase shifters. In such configurations, the overall bandwidth is governed by the intersection of the passbands of the individual couplers , resulting in a reduced effective bandwidth as the number of cascaded stages increases. Additionally, the bandwidth is influenced by the phase balance requirement intrinsic to Butler matrices. Even when acceptable impedance matching is maintained over a wider frequency range, stringent phase-error constraints impose a narrower usable bandwidth for accurate beamforming operation. Comment 4: the following is highlighted: Although this work demonstrates a 4×4 Butler Matrix as a proof of concept, the proposed SIW architecture is inherently scalable to higher-order matrices , such as 8×8 configurations. In principle, the extension follows the same hierarchical network structure used in conventional Butler matrices, where additional SIW hybrid couplers are cascaded to generate the required phase progression and output ports. No fundamental limitations prevent scaling the proposed crossover-free and phase-shifter-free topology to larger matrices. However, practical considerations arise as the matrix order increases. These include increased layout complexity, longer signal paths leading to higher cumulative insertion loss, and tighter control of phase balance due to phase accumulation across multiple cascaded couplers. At millimeter-wave frequencies, fabrication tolerances and via-placement accuracy may also impose constraints on achievable phase uniformity in large-scale implementations. Despite these practical challenges, SIW technology remains well suited for higher-order Butler matrices due to its low-loss waveguiding characteristics and planar layout flexibility. With careful layout optimization, symmetry preservation, and loss balancing, larger matrices such as 8×8 can be realized while maintaining acceptable broadband performance. Therefore, the proposed architecture provides a scalable foundation for higher-order beamforming networks, particularly in applications where compactness and integration are prioritized. Comment 5: modification was made on the figures to improve clarity with multiple lines in the Figures Comment 6: We have improved Fig 11. Comment 7: changed to wavelength Comment 1: highlighted in the design method Comment 2: the following is highlighted: In the revised crossover-free, phase-shifter-free topology, the required phase distribution is realized through the intrinsic phase properties of the SIW hybrid couplers and path-length differences in the interconnecting SIW transmission sections. For an ideal 3-dB quadrature hybrid coupler: The two output signals have equal magnitude. The relative phase difference between the “through” and “coupled” ports is approximately ±90∘ \pm 90^\circ±90∘ (sign depends on port definition). Thus, the cumulative phase at each output port can be written as a sum of: hybrid-coupler phase terms, and propagation phase terms along SIW paths. (2) Where: N c = number of couplers on the signal route N p = number of SIW path segments L m = physical length of the m-th segment β g = guided propagation constant of SIW For SIW, the guided wavenumber can be approximated by: (3) where k₀= εᵣ is the substrate relative permittivity, and a eq is the equivalent SIW width determined from the via diameter and pitch. This expression allows computing the expected phase shift of any interconnect line: φ prop = β g L Comment 3: the following is highlighted: the operational bandwidth of the proposed Butler Matrix is relatively limited compared to some reported SIW-based implementations. This behaviour is primarily attributed to the cascaded hybrid-coupler topology employed to eliminate crossovers and discrete phase shifters. In such configurations, the overall bandwidth is governed by the intersection of the passbands of the individual couplers , resulting in a reduced effective bandwidth as the number of cascaded stages increases. Additionally, the bandwidth is influenced by the phase balance requirement intrinsic to Butler matrices. Even when acceptable impedance matching is maintained over a wider frequency range, stringent phase-error constraints impose a narrower usable bandwidth for accurate beamforming operation. Comment 4: the following is highlighted: Although this work demonstrates a 4×4 Butler Matrix as a proof of concept, the proposed SIW architecture is inherently scalable to higher-order matrices , such as 8×8 configurations. In principle, the extension follows the same hierarchical network structure used in conventional Butler matrices, where additional SIW hybrid couplers are cascaded to generate the required phase progression and output ports. No fundamental limitations prevent scaling the proposed crossover-free and phase-shifter-free topology to larger matrices. However, practical considerations arise as the matrix order increases. These include increased layout complexity, longer signal paths leading to higher cumulative insertion loss, and tighter control of phase balance due to phase accumulation across multiple cascaded couplers. At millimeter-wave frequencies, fabrication tolerances and via-placement accuracy may also impose constraints on achievable phase uniformity in large-scale implementations. Despite these practical challenges, SIW technology remains well suited for higher-order Butler matrices due to its low-loss waveguiding characteristics and planar layout flexibility. With careful layout optimization, symmetry preservation, and loss balancing, larger matrices such as 8×8 can be realized while maintaining acceptable broadband performance. Therefore, the proposed architecture provides a scalable foundation for higher-order beamforming networks, particularly in applications where compactness and integration are prioritized. Comment 5: modification was made on the figures to improve clarity with multiple lines in the Figures Comment 6: We have improved Fig 11. Comment 7: changed to wavelength Competing Interests: None Close Report a concern COMMENT ON THIS REPORT Views 0 Cite How to cite this report: Brunetti G. Reviewer Report For: Butler Matrix Based on Substrate Integrated Waveguide Without Crossover and Phase Shifter for Millimeter Waves Applications [version 1; peer review: 1 approved with reservations, 1 not approved] . F1000Research 2025, 14 :969 ( https://doi.org/10.5256/f1000research.185497.r421174 ) The direct URL for this report is: https://f1000research.com/articles/14-969/v1#referee-response-421174 NOTE: it is important to ensure the information in square brackets after the title is included in this citation. Close Copy Citation Details Reviewer Report 11 Nov 2025 Giuseppe Brunetti , Politecnico di Bari, Bari, Italy Approved with Reservations VIEWS 0 https://doi.org/10.5256/f1000research.185497.r421174 The proposed Substrate Integrated Waveguide (SIW) Butler Matrix can be contextualized within the broader framework of integrated switching and beamforming networks, which are conventionally categorized into broadband and narrowband architectures. Broadband switching matrices are typically realized using distributed transmission-line elements ... Continue reading READ ALL The proposed Substrate Integrated Waveguide (SIW) Butler Matrix can be contextualized within the broader framework of integrated switching and beamforming networks, which are conventionally categorized into broadband and narrowband architectures. Broadband switching matrices are typically realized using distributed transmission-line elements or waveguide-based implementations, optimized to sustain phase and amplitude uniformity over wide frequency ranges.Here, my comments: The manuscript lacks a clear contextualization of the proposed SIW Butler Matrix within the broader class of integrated switching matrices. A comparative discussion should be introduced early in the Introduction section, distinguishing between broadband and narrowband matrix architectures and highlighting the relevance of the proposed design in this framework. The classification between broadband and narrowband switching matrices should be explicitly articulated. Broadband matrices, typically based on distributed or waveguide structures, support wide frequency operation and are suited for multi-band applications such as 5G beamforming. Conversely, narrowband architectures, often resonant or lumped-element based, provide high selectivity and low insertion loss at the expense of operational bandwidth. (see, e.g., Butler Matrix-Based Beam Switching with Frequency-Tunable MIMO Array. In 2024 IEEE International Symposium on Antennas and Propagation and INC/USNC‐URSI Radio Science Meeting (AP-S/INC-USNC-URSI) (pp. 2475-2476). IEEE., 2024; Design of a large bandwidth 2× 2 interferometric switching cell based on a sub-wavelength grating. Journal of Optics, 23(8), 08580, 2021 ). The paper should include a concise review of integrated implementations of switching matrices, emphasizing microstrip, CPW, coaxial, and photonic platforms. Discussing their respective trade-offs, such as radiation losses, limited scalability, and fabrication complexity, would clarify the rationale for adopting an SIW-based solution. The originality of the proposed structure should be emphasized by contrasting it with existing 4×4 Butler Matrices that rely on crossovers and phase shifters. Quantitative comparisons of insertion loss, phase error, and physical dimensions with recent literature would reinforce the claim of superior broadband performance and compactness. The discussion of the SIW implementation should be expanded to underline its suitability for monolithic integration and compatibility with planar antenna arrays and photonic circuits. This aspect is particularly important for applications targeting compact, high-frequency front-end systems in 5G and beyond. Here, my minor comments: The abstract and introduction should better clarify the motivation behind eliminating crossovers and phase shifters, explaining how this contributes to both broadband performance and fabrication simplification. In Table 1, the comparison with previous works could be enriched by specifying whether each listed matrix operates in the broadband or narrowband regime. The terminology “wideband” and “broadband” should be used consistently throughout the text to avoid ambiguity. The introduction could benefit from one or two sentences connecting SIW-based microwave matrices with analogous developments in integrated photonics, where broadband beamforming networks are being explored using similar architectural concepts. Some of the numerical performance indicators (e.g., fractional bandwidth, insertion loss) should be explicitly defined or referenced to ensure clarity for readers from adjacent fields. Is the work clearly and accurately presented and does it cite the current literature? No Is the study design appropriate and is the work technically sound? Yes Are sufficient details of methods and analysis provided to allow replication by others? Yes If applicable, is the statistical analysis and its interpretation appropriate? Not applicable Are all the source data underlying the results available to ensure full reproducibility? No source data required Are the conclusions drawn adequately supported by the results? No Competing Interests: No competing interests were disclosed. Reviewer Expertise: Filter; photonics; beamforming I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above. Close READ LESS CITE CITE HOW TO CITE THIS REPORT Brunetti G. Reviewer Report For: Butler Matrix Based on Substrate Integrated Waveguide Without Crossover and Phase Shifter for Millimeter Waves Applications [version 1; peer review: 1 approved with reservations, 1 not approved] . F1000Research 2025, 14 :969 ( https://doi.org/10.5256/f1000research.185497.r421174 ) The direct URL for this report is: https://f1000research.com/articles/14-969/v1#referee-response-421174 NOTE: it is important to ensure the information in square brackets after the title is included in all citations of this article. COPY CITATION DETAILS Report a concern Author Response 11 Feb 2026 Chia Pao Liew , School of Energy and Chemical Engineering, Xiamen University Malaysia, Sepang, Malaysia 11 Feb 2026 Author Response Comment no. 1: the following is highlighted in the manuscript Beamforming networks and switching matrices are fundamental components in modern multi-antenna systems, enabling signal routing, phase control, and spatial ... Continue reading Comment no. 1: the following is highlighted in the manuscript Beamforming networks and switching matrices are fundamental components in modern multi-antenna systems, enabling signal routing, phase control, and spatial beam steering in applications such as 5G millimeter-wave communications, radar, and satellite systems. Within this broad class, integrated switching matrices can be generally categorized into narrowband and broadband architectures, depending on their operational bandwidth, phase stability, and amplitude balance characteristics. Narrowband matrix architectures, including conventional waveguide and microstrip Butler matrices, are typically optimized for operation around a single center frequency. While these solutions offer compact layouts and relatively low insertion loss, their performance rapidly degrades outside the design band due to frequency-dependent phase errors and impedance mismatch. Such limitations restrict their suitability for emerging wideband and multi-carrier millimeter-wave systems. In contrast, broadband matrix architectures employ wideband couplers, phase shifters, or hybrid implementations to maintain stable phase progression and amplitude balance over an extended frequency range. These designs are particularly relevant for 5G and beyond systems, where wide instantaneous bandwidth, beam squint mitigation, and integration compatibility are critical design requirements. However, many reported broadband matrices rely on multilayer structures, complex transitions, or mixed technologies, which increase fabrication complexity and cost. In this context, Substrate Integrated Waveguide (SIW) technology provides an attractive platform for realizing broadband integrated switching matrices by combining the low-loss characteristics of conventional waveguides with the planar manufacturability of printed circuits. The proposed SIW Butler Matrix in this work is positioned within the broadband matrix architecture class , specifically targeting wideband operation with stable phase differences and reduced insertion loss while maintaining a fully planar and fabrication-friendly structure. By employing only SIW hybrid couplers without additional phase-shifting elements, the proposed design offers a simplified topology that directly addresses the bandwidth and integration challenges encountered in existing matrix implementations. Comment no. 2 - as highlighted in Comment no. 1 above Comment no. 3: the following is highlighted in the manuscript Various integrated platforms have been explored for the implementation of switching and beamforming matrices, including microstrip, coplanar waveguide (CPW), coaxial, and photonic technologies. Each platform offers distinct advantages, but also exhibits inherent limitations when applied to wideband millimeter-wave matrix architectures. Microstrip-based switching matrices are widely reported due to their low cost, planar form factor, and ease of integration with active components. However, at millimeter-wave frequencies, microstrip implementations suffer from increased radiation losses, surface-wave excitation, and dispersion effects, which limit achievable bandwidth and degrade phase accuracy in large matrix configurations. Coplanar waveguide (CPW) platforms alleviate some integration challenges and provide improved grounding flexibility, yet they remain susceptible to radiation leakage and conductor loss at high frequencies, particularly in dense multi-port networks. Coaxial and waveguide-based matrices offer superior isolation and low loss, making them attractive for high-performance systems. Nevertheless, their bulky three-dimensional structures, limited scalability, and high fabrication and assembly costs restrict their suitability for compact and highly integrated 5G and beyond applications. More recently, photonic switching matrices have been proposed to enable ultra-wide bandwidth and immunity to electromagnetic interference. Despite these advantages, photonic solutions typically require complex electro-optic conversion stages, precise alignment, and specialized fabrication processes, resulting in increased system complexity and cost. In comparison, Substrate Integrated Waveguide (SIW) technology combines the low-loss and high-isolation characteristics of conventional waveguides with the planar manufacturability of printed circuit technologies. This hybrid nature makes SIW particularly well suited for integrated broadband switching matrices, offering reduced radiation loss, improved phase stability, and excellent scalability while maintaining compatibility with standard PCB fabrication. Consequently, the SIW-based Butler Matrix proposed in this work provides a balanced solution that directly addresses the limitations of alternative integrated platforms. Comment no. 4: the following is highlighted in the manuscript The key contribution of this work lies in the original structural simplicity and performance advantages of the proposed SIW Butler Matrix compared to existing 4×4 matrix designs that rely on crossovers and discrete phase-shifter networks. Traditional implementations of 4×4 Butler Matrices in microstrip and CPW technologies often incorporate crossovers and fixed electrical-length phase shifters to achieve the required interconnections and phase progression. While functional, these elements introduce additional insertion loss , phase distortion , and size penalties , particularly at millimeter-wave frequencies, due to increased discontinuities, radiation effects, and dispersion. By contrast, the proposed SIW design employs only SIW hybrid couplers without separate crossovers or discrete phase shifters, leading to a reduction in cumulative junction loss and improved phase fidelity over a wide frequency band. Quantitatively, as shown in Table 1, the proposed matrix demonstrates a lower average insertion loss and reduced phase error across the operational band, while achieving a more compact footprint than representative matrices from recent literature. These performance improvements underscore the broadband performance and integration advantages of the proposed structure for millimeter-wave applications. Comment 5: the following is highlighted in the manuscript Beyond its electrical performance, the proposed SIW Butler Matrix is particularly well suited for monolithic integration and system-level co-design , which are essential requirements for compact millimeter-wave front-end architectures in 5G and beyond. The planar nature of SIW technology enables seamless integration with other passive and active components on a single substrate, including power dividers, filters, and transitions, while preserving low-loss wave-guiding behavior. A key advantage of the proposed structure is its direct compatibility with planar antenna arrays , such as SIW-fed slot arrays and substrate-integrated patch arrays. Since both the Butler Matrix and the antenna elements can be realized using the same fabrication process and substrate stack-up, the proposed design facilitates compact beamforming modules without the need for complex interconnects or vertical transitions. This compatibility significantly reduces assembly complexity, parasitic effects, and overall system footprint, which are critical constraints at millimeter-wave frequencies. Furthermore, SIW technology offers promising compatibility with photonic and electro-optic circuits , particularly in emerging hybrid microwave–photonic front-end systems. The well-defined electromagnetic confinement and planar interfaces of SIW structures simplify the integration of optoelectronic components, such as modulators and photodetectors, enabling efficient RF-to-photonic signal routing. This makes SIW-based beamforming networks attractive candidates for future high-frequency systems that combine electronic beamforming with photonic signal distribution to achieve wide bandwidth, low latency, and high integration density. Consequently, the proposed SIW Butler Matrix is not only a broadband and compact beamforming solution at the circuit level, but also a scalable building block for integrated, multi-functional front-end modules targeting advanced 5G and next-generation wireless systems. Minor comment no.1: the following is highlighted in the manuscript This paper presents a compact and broadband 4×4 Butler Matrix implemented using Substrate Integrated Waveguide (SIW) technology. In contrast to conventional Butler Matrices that rely on crossovers and discrete phase shifters, the proposed design employs only SIW hybrid couplers to realize the required phase progression and signal distribution. Eliminating crossovers and phase shifters significantly reduces structural discontinuities, junction losses, and frequency-dependent phase errors, thereby enhancing broadband performance. Moreover, the simplified topology minimizes fabrication complexity and improves suitability for planar and monolithic integration, making the proposed matrix well suited for compact millimeter-wave beamforming front ends in 5G and beyond systems. Minor comment no. 2: Considered Minor comment no. 3: corrected to just wideband Minor comment no. 4: Added as above Minor comment no. 5: Defined fractional bandwidth Comment no. 1: the following is highlighted in the manuscript Beamforming networks and switching matrices are fundamental components in modern multi-antenna systems, enabling signal routing, phase control, and spatial beam steering in applications such as 5G millimeter-wave communications, radar, and satellite systems. Within this broad class, integrated switching matrices can be generally categorized into narrowband and broadband architectures, depending on their operational bandwidth, phase stability, and amplitude balance characteristics. Narrowband matrix architectures, including conventional waveguide and microstrip Butler matrices, are typically optimized for operation around a single center frequency. While these solutions offer compact layouts and relatively low insertion loss, their performance rapidly degrades outside the design band due to frequency-dependent phase errors and impedance mismatch. Such limitations restrict their suitability for emerging wideband and multi-carrier millimeter-wave systems. In contrast, broadband matrix architectures employ wideband couplers, phase shifters, or hybrid implementations to maintain stable phase progression and amplitude balance over an extended frequency range. These designs are particularly relevant for 5G and beyond systems, where wide instantaneous bandwidth, beam squint mitigation, and integration compatibility are critical design requirements. However, many reported broadband matrices rely on multilayer structures, complex transitions, or mixed technologies, which increase fabrication complexity and cost. In this context, Substrate Integrated Waveguide (SIW) technology provides an attractive platform for realizing broadband integrated switching matrices by combining the low-loss characteristics of conventional waveguides with the planar manufacturability of printed circuits. The proposed SIW Butler Matrix in this work is positioned within the broadband matrix architecture class , specifically targeting wideband operation with stable phase differences and reduced insertion loss while maintaining a fully planar and fabrication-friendly structure. By employing only SIW hybrid couplers without additional phase-shifting elements, the proposed design offers a simplified topology that directly addresses the bandwidth and integration challenges encountered in existing matrix implementations. Comment no. 2 - as highlighted in Comment no. 1 above Comment no. 3: the following is highlighted in the manuscript Various integrated platforms have been explored for the implementation of switching and beamforming matrices, including microstrip, coplanar waveguide (CPW), coaxial, and photonic technologies. Each platform offers distinct advantages, but also exhibits inherent limitations when applied to wideband millimeter-wave matrix architectures. Microstrip-based switching matrices are widely reported due to their low cost, planar form factor, and ease of integration with active components. However, at millimeter-wave frequencies, microstrip implementations suffer from increased radiation losses, surface-wave excitation, and dispersion effects, which limit achievable bandwidth and degrade phase accuracy in large matrix configurations. Coplanar waveguide (CPW) platforms alleviate some integration challenges and provide improved grounding flexibility, yet they remain susceptible to radiation leakage and conductor loss at high frequencies, particularly in dense multi-port networks. Coaxial and waveguide-based matrices offer superior isolation and low loss, making them attractive for high-performance systems. Nevertheless, their bulky three-dimensional structures, limited scalability, and high fabrication and assembly costs restrict their suitability for compact and highly integrated 5G and beyond applications. More recently, photonic switching matrices have been proposed to enable ultra-wide bandwidth and immunity to electromagnetic interference. Despite these advantages, photonic solutions typically require complex electro-optic conversion stages, precise alignment, and specialized fabrication processes, resulting in increased system complexity and cost. In comparison, Substrate Integrated Waveguide (SIW) technology combines the low-loss and high-isolation characteristics of conventional waveguides with the planar manufacturability of printed circuit technologies. This hybrid nature makes SIW particularly well suited for integrated broadband switching matrices, offering reduced radiation loss, improved phase stability, and excellent scalability while maintaining compatibility with standard PCB fabrication. Consequently, the SIW-based Butler Matrix proposed in this work provides a balanced solution that directly addresses the limitations of alternative integrated platforms. Comment no. 4: the following is highlighted in the manuscript The key contribution of this work lies in the original structural simplicity and performance advantages of the proposed SIW Butler Matrix compared to existing 4×4 matrix designs that rely on crossovers and discrete phase-shifter networks. Traditional implementations of 4×4 Butler Matrices in microstrip and CPW technologies often incorporate crossovers and fixed electrical-length phase shifters to achieve the required interconnections and phase progression. While functional, these elements introduce additional insertion loss , phase distortion , and size penalties , particularly at millimeter-wave frequencies, due to increased discontinuities, radiation effects, and dispersion. By contrast, the proposed SIW design employs only SIW hybrid couplers without separate crossovers or discrete phase shifters, leading to a reduction in cumulative junction loss and improved phase fidelity over a wide frequency band. Quantitatively, as shown in Table 1, the proposed matrix demonstrates a lower average insertion loss and reduced phase error across the operational band, while achieving a more compact footprint than representative matrices from recent literature. These performance improvements underscore the broadband performance and integration advantages of the proposed structure for millimeter-wave applications. Comment 5: the following is highlighted in the manuscript Beyond its electrical performance, the proposed SIW Butler Matrix is particularly well suited for monolithic integration and system-level co-design , which are essential requirements for compact millimeter-wave front-end architectures in 5G and beyond. The planar nature of SIW technology enables seamless integration with other passive and active components on a single substrate, including power dividers, filters, and transitions, while preserving low-loss wave-guiding behavior. A key advantage of the proposed structure is its direct compatibility with planar antenna arrays , such as SIW-fed slot arrays and substrate-integrated patch arrays. Since both the Butler Matrix and the antenna elements can be realized using the same fabrication process and substrate stack-up, the proposed design facilitates compact beamforming modules without the need for complex interconnects or vertical transitions. This compatibility significantly reduces assembly complexity, parasitic effects, and overall system footprint, which are critical constraints at millimeter-wave frequencies. Furthermore, SIW technology offers promising compatibility with photonic and electro-optic circuits , particularly in emerging hybrid microwave–photonic front-end systems. The well-defined electromagnetic confinement and planar interfaces of SIW structures simplify the integration of optoelectronic components, such as modulators and photodetectors, enabling efficient RF-to-photonic signal routing. This makes SIW-based beamforming networks attractive candidates for future high-frequency systems that combine electronic beamforming with photonic signal distribution to achieve wide bandwidth, low latency, and high integration density. Consequently, the proposed SIW Butler Matrix is not only a broadband and compact beamforming solution at the circuit level, but also a scalable building block for integrated, multi-functional front-end modules targeting advanced 5G and next-generation wireless systems. Minor comment no.1: the following is highlighted in the manuscript This paper presents a compact and broadband 4×4 Butler Matrix implemented using Substrate Integrated Waveguide (SIW) technology. In contrast to conventional Butler Matrices that rely on crossovers and discrete phase shifters, the proposed design employs only SIW hybrid couplers to realize the required phase progression and signal distribution. Eliminating crossovers and phase shifters significantly reduces structural discontinuities, junction losses, and frequency-dependent phase errors, thereby enhancing broadband performance. Moreover, the simplified topology minimizes fabrication complexity and improves suitability for planar and monolithic integration, making the proposed matrix well suited for compact millimeter-wave beamforming front ends in 5G and beyond systems. Minor comment no. 2: Considered Minor comment no. 3: corrected to just wideband Minor comment no. 4: Added as above Minor comment no. 5: Defined fractional bandwidth Competing Interests: None Close Report a concern Respond or Comment COMMENTS ON THIS REPORT Author Response 11 Feb 2026 Chia Pao Liew , School of Energy and Chemical Engineering, Xiamen University Malaysia, Sepang, Malaysia 11 Feb 2026 Author Response Comment no. 1: the following is highlighted in the manuscript Beamforming networks and switching matrices are fundamental components in modern multi-antenna systems, enabling signal routing, phase control, and spatial ... Continue reading Comment no. 1: the following is highlighted in the manuscript Beamforming networks and switching matrices are fundamental components in modern multi-antenna systems, enabling signal routing, phase control, and spatial beam steering in applications such as 5G millimeter-wave communications, radar, and satellite systems. Within this broad class, integrated switching matrices can be generally categorized into narrowband and broadband architectures, depending on their operational bandwidth, phase stability, and amplitude balance characteristics. Narrowband matrix architectures, including conventional waveguide and microstrip Butler matrices, are typically optimized for operation around a single center frequency. While these solutions offer compact layouts and relatively low insertion loss, their performance rapidly degrades outside the design band due to frequency-dependent phase errors and impedance mismatch. Such limitations restrict their suitability for emerging wideband and multi-carrier millimeter-wave systems. In contrast, broadband matrix architectures employ wideband couplers, phase shifters, or hybrid implementations to maintain stable phase progression and amplitude balance over an extended frequency range. These designs are particularly relevant for 5G and beyond systems, where wide instantaneous bandwidth, beam squint mitigation, and integration compatibility are critical design requirements. However, many reported broadband matrices rely on multilayer structures, complex transitions, or mixed technologies, which increase fabrication complexity and cost. In this context, Substrate Integrated Waveguide (SIW) technology provides an attractive platform for realizing broadband integrated switching matrices by combining the low-loss characteristics of conventional waveguides with the planar manufacturability of printed circuits. The proposed SIW Butler Matrix in this work is positioned within the broadband matrix architecture class , specifically targeting wideband operation with stable phase differences and reduced insertion loss while maintaining a fully planar and fabrication-friendly structure. By employing only SIW hybrid couplers without additional phase-shifting elements, the proposed design offers a simplified topology that directly addresses the bandwidth and integration challenges encountered in existing matrix implementations. Comment no. 2 - as highlighted in Comment no. 1 above Comment no. 3: the following is highlighted in the manuscript Various integrated platforms have been explored for the implementation of switching and beamforming matrices, including microstrip, coplanar waveguide (CPW), coaxial, and photonic technologies. Each platform offers distinct advantages, but also exhibits inherent limitations when applied to wideband millimeter-wave matrix architectures. Microstrip-based switching matrices are widely reported due to their low cost, planar form factor, and ease of integration with active components. However, at millimeter-wave frequencies, microstrip implementations suffer from increased radiation losses, surface-wave excitation, and dispersion effects, which limit achievable bandwidth and degrade phase accuracy in large matrix configurations. Coplanar waveguide (CPW) platforms alleviate some integration challenges and provide improved grounding flexibility, yet they remain susceptible to radiation leakage and conductor loss at high frequencies, particularly in dense multi-port networks. Coaxial and waveguide-based matrices offer superior isolation and low loss, making them attractive for high-performance systems. Nevertheless, their bulky three-dimensional structures, limited scalability, and high fabrication and assembly costs restrict their suitability for compact and highly integrated 5G and beyond applications. More recently, photonic switching matrices have been proposed to enable ultra-wide bandwidth and immunity to electromagnetic interference. Despite these advantages, photonic solutions typically require complex electro-optic conversion stages, precise alignment, and specialized fabrication processes, resulting in increased system complexity and cost. In comparison, Substrate Integrated Waveguide (SIW) technology combines the low-loss and high-isolation characteristics of conventional waveguides with the planar manufacturability of printed circuit technologies. This hybrid nature makes SIW particularly well suited for integrated broadband switching matrices, offering reduced radiation loss, improved phase stability, and excellent scalability while maintaining compatibility with standard PCB fabrication. Consequently, the SIW-based Butler Matrix proposed in this work provides a balanced solution that directly addresses the limitations of alternative integrated platforms. Comment no. 4: the following is highlighted in the manuscript The key contribution of this work lies in the original structural simplicity and performance advantages of the proposed SIW Butler Matrix compared to existing 4×4 matrix designs that rely on crossovers and discrete phase-shifter networks. Traditional implementations of 4×4 Butler Matrices in microstrip and CPW technologies often incorporate crossovers and fixed electrical-length phase shifters to achieve the required interconnections and phase progression. While functional, these elements introduce additional insertion loss , phase distortion , and size penalties , particularly at millimeter-wave frequencies, due to increased discontinuities, radiation effects, and dispersion. By contrast, the proposed SIW design employs only SIW hybrid couplers without separate crossovers or discrete phase shifters, leading to a reduction in cumulative junction loss and improved phase fidelity over a wide frequency band. Quantitatively, as shown in Table 1, the proposed matrix demonstrates a lower average insertion loss and reduced phase error across the operational band, while achieving a more compact footprint than representative matrices from recent literature. These performance improvements underscore the broadband performance and integration advantages of the proposed structure for millimeter-wave applications. Comment 5: the following is highlighted in the manuscript Beyond its electrical performance, the proposed SIW Butler Matrix is particularly well suited for monolithic integration and system-level co-design , which are essential requirements for compact millimeter-wave front-end architectures in 5G and beyond. The planar nature of SIW technology enables seamless integration with other passive and active components on a single substrate, including power dividers, filters, and transitions, while preserving low-loss wave-guiding behavior. A key advantage of the proposed structure is its direct compatibility with planar antenna arrays , such as SIW-fed slot arrays and substrate-integrated patch arrays. Since both the Butler Matrix and the antenna elements can be realized using the same fabrication process and substrate stack-up, the proposed design facilitates compact beamforming modules without the need for complex interconnects or vertical transitions. This compatibility significantly reduces assembly complexity, parasitic effects, and overall system footprint, which are critical constraints at millimeter-wave frequencies. Furthermore, SIW technology offers promising compatibility with photonic and electro-optic circuits , particularly in emerging hybrid microwave–photonic front-end systems. The well-defined electromagnetic confinement and planar interfaces of SIW structures simplify the integration of optoelectronic components, such as modulators and photodetectors, enabling efficient RF-to-photonic signal routing. This makes SIW-based beamforming networks attractive candidates for future high-frequency systems that combine electronic beamforming with photonic signal distribution to achieve wide bandwidth, low latency, and high integration density. Consequently, the proposed SIW Butler Matrix is not only a broadband and compact beamforming solution at the circuit level, but also a scalable building block for integrated, multi-functional front-end modules targeting advanced 5G and next-generation wireless systems. Minor comment no.1: the following is highlighted in the manuscript This paper presents a compact and broadband 4×4 Butler Matrix implemented using Substrate Integrated Waveguide (SIW) technology. In contrast to conventional Butler Matrices that rely on crossovers and discrete phase shifters, the proposed design employs only SIW hybrid couplers to realize the required phase progression and signal distribution. Eliminating crossovers and phase shifters significantly reduces structural discontinuities, junction losses, and frequency-dependent phase errors, thereby enhancing broadband performance. Moreover, the simplified topology minimizes fabrication complexity and improves suitability for planar and monolithic integration, making the proposed matrix well suited for compact millimeter-wave beamforming front ends in 5G and beyond systems. Minor comment no. 2: Considered Minor comment no. 3: corrected to just wideband Minor comment no. 4: Added as above Minor comment no. 5: Defined fractional bandwidth Comment no. 1: the following is highlighted in the manuscript Beamforming networks and switching matrices are fundamental components in modern multi-antenna systems, enabling signal routing, phase control, and spatial beam steering in applications such as 5G millimeter-wave communications, radar, and satellite systems. Within this broad class, integrated switching matrices can be generally categorized into narrowband and broadband architectures, depending on their operational bandwidth, phase stability, and amplitude balance characteristics. Narrowband matrix architectures, including conventional waveguide and microstrip Butler matrices, are typically optimized for operation around a single center frequency. While these solutions offer compact layouts and relatively low insertion loss, their performance rapidly degrades outside the design band due to frequency-dependent phase errors and impedance mismatch. Such limitations restrict their suitability for emerging wideband and multi-carrier millimeter-wave systems. In contrast, broadband matrix architectures employ wideband couplers, phase shifters, or hybrid implementations to maintain stable phase progression and amplitude balance over an extended frequency range. These designs are particularly relevant for 5G and beyond systems, where wide instantaneous bandwidth, beam squint mitigation, and integration compatibility are critical design requirements. However, many reported broadband matrices rely on multilayer structures, complex transitions, or mixed technologies, which increase fabrication complexity and cost. In this context, Substrate Integrated Waveguide (SIW) technology provides an attractive platform for realizing broadband integrated switching matrices by combining the low-loss characteristics of conventional waveguides with the planar manufacturability of printed circuits. The proposed SIW Butler Matrix in this work is positioned within the broadband matrix architecture class , specifically targeting wideband operation with stable phase differences and reduced insertion loss while maintaining a fully planar and fabrication-friendly structure. By employing only SIW hybrid couplers without additional phase-shifting elements, the proposed design offers a simplified topology that directly addresses the bandwidth and integration challenges encountered in existing matrix implementations. Comment no. 2 - as highlighted in Comment no. 1 above Comment no. 3: the following is highlighted in the manuscript Various integrated platforms have been explored for the implementation of switching and beamforming matrices, including microstrip, coplanar waveguide (CPW), coaxial, and photonic technologies. Each platform offers distinct advantages, but also exhibits inherent limitations when applied to wideband millimeter-wave matrix architectures. Microstrip-based switching matrices are widely reported due to their low cost, planar form factor, and ease of integration with active components. However, at millimeter-wave frequencies, microstrip implementations suffer from increased radiation losses, surface-wave excitation, and dispersion effects, which limit achievable bandwidth and degrade phase accuracy in large matrix configurations. Coplanar waveguide (CPW) platforms alleviate some integration challenges and provide improved grounding flexibility, yet they remain susceptible to radiation leakage and conductor loss at high frequencies, particularly in dense multi-port networks. Coaxial and waveguide-based matrices offer superior isolation and low loss, making them attractive for high-performance systems. Nevertheless, their bulky three-dimensional structures, limited scalability, and high fabrication and assembly costs restrict their suitability for compact and highly integrated 5G and beyond applications. More recently, photonic switching matrices have been proposed to enable ultra-wide bandwidth and immunity to electromagnetic interference. Despite these advantages, photonic solutions typically require complex electro-optic conversion stages, precise alignment, and specialized fabrication processes, resulting in increased system complexity and cost. In comparison, Substrate Integrated Waveguide (SIW) technology combines the low-loss and high-isolation characteristics of conventional waveguides with the planar manufacturability of printed circuit technologies. This hybrid nature makes SIW particularly well suited for integrated broadband switching matrices, offering reduced radiation loss, improved phase stability, and excellent scalability while maintaining compatibility with standard PCB fabrication. Consequently, the SIW-based Butler Matrix proposed in this work provides a balanced solution that directly addresses the limitations of alternative integrated platforms. Comment no. 4: the following is highlighted in the manuscript The key contribution of this work lies in the original structural simplicity and performance advantages of the proposed SIW Butler Matrix compared to existing 4×4 matrix designs that rely on crossovers and discrete phase-shifter networks. Traditional implementations of 4×4 Butler Matrices in microstrip and CPW technologies often incorporate crossovers and fixed electrical-length phase shifters to achieve the required interconnections and phase progression. While functional, these elements introduce additional insertion loss , phase distortion , and size penalties , particularly at millimeter-wave frequencies, due to increased discontinuities, radiation effects, and dispersion. By contrast, the proposed SIW design employs only SIW hybrid couplers without separate crossovers or discrete phase shifters, leading to a reduction in cumulative junction loss and improved phase fidelity over a wide frequency band. Quantitatively, as shown in Table 1, the proposed matrix demonstrates a lower average insertion loss and reduced phase error across the operational band, while achieving a more compact footprint than representative matrices from recent literature. These performance improvements underscore the broadband performance and integration advantages of the proposed structure for millimeter-wave applications. Comment 5: the following is highlighted in the manuscript Beyond its electrical performance, the proposed SIW Butler Matrix is particularly well suited for monolithic integration and system-level co-design , which are essential requirements for compact millimeter-wave front-end architectures in 5G and beyond. The planar nature of SIW technology enables seamless integration with other passive and active components on a single substrate, including power dividers, filters, and transitions, while preserving low-loss wave-guiding behavior. A key advantage of the proposed structure is its direct compatibility with planar antenna arrays , such as SIW-fed slot arrays and substrate-integrated patch arrays. Since both the Butler Matrix and the antenna elements can be realized using the same fabrication process and substrate stack-up, the proposed design facilitates compact beamforming modules without the need for complex interconnects or vertical transitions. This compatibility significantly reduces assembly complexity, parasitic effects, and overall system footprint, which are critical constraints at millimeter-wave frequencies. Furthermore, SIW technology offers promising compatibility with photonic and electro-optic circuits , particularly in emerging hybrid microwave–photonic front-end systems. The well-defined electromagnetic confinement and planar interfaces of SIW structures simplify the integration of optoelectronic components, such as modulators and photodetectors, enabling efficient RF-to-photonic signal routing. This makes SIW-based beamforming networks attractive candidates for future high-frequency systems that combine electronic beamforming with photonic signal distribution to achieve wide bandwidth, low latency, and high integration density. Consequently, the proposed SIW Butler Matrix is not only a broadband and compact beamforming solution at the circuit level, but also a scalable building block for integrated, multi-functional front-end modules targeting advanced 5G and next-generation wireless systems. Minor comment no.1: the following is highlighted in the manuscript This paper presents a compact and broadband 4×4 Butler Matrix implemented using Substrate Integrated Waveguide (SIW) technology. In contrast to conventional Butler Matrices that rely on crossovers and discrete phase shifters, the proposed design employs only SIW hybrid couplers to realize the required phase progression and signal distribution. Eliminating crossovers and phase shifters significantly reduces structural discontinuities, junction losses, and frequency-dependent phase errors, thereby enhancing broadband performance. Moreover, the simplified topology minimizes fabrication complexity and improves suitability for planar and monolithic integration, making the proposed matrix well suited for compact millimeter-wave beamforming front ends in 5G and beyond systems. Minor comment no. 2: Considered Minor comment no. 3: corrected to just wideband Minor comment no. 4: Added as above Minor comment no. 5: Defined fractional bandwidth Competing Interests: None Close Report a concern COMMENT ON THIS REPORT Comments on this article Comments (0) Version 2 VERSION 2 PUBLISHED 23 Sep 2025 ADD YOUR COMMENT Comment keyboard_arrow_left keyboard_arrow_right Open Peer Review Reviewer Status info_outline Alongside their report, reviewers assign a status to the article: Approved The paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. Not approved Fundamental flaws in the paper seriously undermine the findings and conclusions Reviewer Reports Invited Reviewers 1 2 Version 2 (revision) 24 Apr 26 read Version 1 23 Sep 25 read read Giuseppe Brunetti , Politecnico di Bari, Bari, Italy Ji-Wei Lian , Nanjing University of Science and Technology, Nanjing, China Comments on this article All Comments (0) Add a comment Sign up for content alerts Sign Up You are now signed up to receive this alert Browse by related subjects keyboard_arrow_left Back to all reports Reviewer Report 0 Views copyright © 2026 Lian J. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 21 May 2026 | for Version 2 Ji-Wei Lian , Nanjing University of Science and Technology, Nanjing, China 0 Views copyright © 2026 Lian J. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. format_quote Cite this report speaker_notes Responses (0) Approved info_outline Alongside their report, reviewers assign a status to the article: Approved The paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. Not approved Fundamental flaws in the paper seriously undermine the findings and conclusions All my comments are addressed properly. I approve of this article. Competing Interests No competing interests were disclosed. Reviewer Expertise antenna I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. reply Respond to this report Responses (0) Lian JW. Peer Review Report For: Butler Matrix Based on Substrate Integrated Waveguide Without Crossover and Phase Shifter for Millimeter Waves Applications [version 1; peer review: 1 approved with reservations, 1 not approved] . F1000Research 2025, 14 :969 ( https://doi.org/10.5256/f1000research.196449.r478745) NOTE: it is important to ensure the information in square brackets after the title is included in this citation. The direct URL for this report is: https://f1000research.com/articles/14-969/v2#referee-response-478745 keyboard_arrow_left Back to all reports Reviewer Report 0 Views copyright © 2026 Lian J. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 07 Jan 2026 | for Version 1 Ji-Wei Lian , Nanjing University of Science and Technology, Nanjing, China 0 Views copyright © 2026 Lian J. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. format_quote Cite this report speaker_notes Responses (1) Not Approved info_outline Alongside their report, reviewers assign a status to the article: Approved The paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. Not approved Fundamental flaws in the paper seriously undermine the findings and conclusions This paper presents a 4×4 Butler matrix implemented using Substrate Integrated Waveguide (SIW) technology operating at 26 GHz, targeting millimeter-wave 5G applications. The proposed design eliminates conventional crossovers and discrete phase shifters by employing only four hybrid couplers, enhanced with interdigital structures and non-metalized vias to fine-tune performance. Both simulated and measured results are provided. There are several comments to address. The revised topology of the new 4x4 Butler matrix should be provided and compared with traditional topology The phase distribution of the revised topology should be thoroughly calculated and discussed to demonstrate the feasibility of this proposed Butler matrix. The bandwidth is quite narrow, which is not common for SIW butler matrix. Please discuss this issue. While the 4×4 case is demonstrated, it would be helpful to briefly discuss whether this architecture can be extended to larger Butler matrices (e.g., 8×8). Are there fundamental limitations in terms of layout or phase accumulation? The simulated and measured results should be plotted in the same figure for comparison. Fig. 11, it is not clear to see the simulated and measured results. The size in table 1 should be in wavelength. The gain and bandwidth should be added. Is the work clearly and accurately presented and does it cite the current literature? Partly Is the study design appropriate and is the work technically sound? Partly Are sufficient details of methods and analysis provided to allow replication by others? Partly If applicable, is the statistical analysis and its interpretation appropriate? Partly Are all the source data underlying the results available to ensure full reproducibility? Partly Are the conclusions drawn adequately supported by the results? Partly Competing Interests No competing interests were disclosed. Reviewer Expertise antenna I confirm that I have read this submission and believe that I have an appropriate level of expertise to state that I do not consider it to be of an acceptable scientific standard, for reasons outlined above. reply Respond to this report Responses (1) Author Response 11 Feb 2026 Chia Pao Liew, School of Energy and Chemical Engineering, Xiamen University Malaysia, Sepang, Malaysia Comment 1: highlighted in the design method Comment 2: the following is highlighted: In the revised crossover-free, phase-shifter-free topology, the required phase distribution is realized through the intrinsic phase properties of the SIW hybrid couplers and path-length differences in the interconnecting SIW transmission sections. For an ideal 3-dB quadrature hybrid coupler: The two output signals have equal magnitude. The relative phase difference between the “through” and “coupled” ports is approximately ±90∘ \pm 90^\circ±90∘ (sign depends on port definition). Thus, the cumulative phase at each output port can be written as a sum of: hybrid-coupler phase terms, and propagation phase terms along SIW paths. (2) Where: N c = number of couplers on the signal route N p = number of SIW path segments L m = physical length of the m-th segment β g = guided propagation constant of SIW For SIW, the guided wavenumber can be approximated by: (3) where k₀= εᵣ is the substrate relative permittivity, and a eq is the equivalent SIW width determined from the via diameter and pitch. This expression allows computing the expected phase shift of any interconnect line: φ prop = β g L Comment 3: the following is highlighted: the operational bandwidth of the proposed Butler Matrix is relatively limited compared to some reported SIW-based implementations. This behaviour is primarily attributed to the cascaded hybrid-coupler topology employed to eliminate crossovers and discrete phase shifters. In such configurations, the overall bandwidth is governed by the intersection of the passbands of the individual couplers , resulting in a reduced effective bandwidth as the number of cascaded stages increases. Additionally, the bandwidth is influenced by the phase balance requirement intrinsic to Butler matrices. Even when acceptable impedance matching is maintained over a wider frequency range, stringent phase-error constraints impose a narrower usable bandwidth for accurate beamforming operation. Comment 4: the following is highlighted: Although this work demonstrates a 4×4 Butler Matrix as a proof of concept, the proposed SIW architecture is inherently scalable to higher-order matrices , such as 8×8 configurations. In principle, the extension follows the same hierarchical network structure used in conventional Butler matrices, where additional SIW hybrid couplers are cascaded to generate the required phase progression and output ports. No fundamental limitations prevent scaling the proposed crossover-free and phase-shifter-free topology to larger matrices. However, practical considerations arise as the matrix order increases. These include increased layout complexity, longer signal paths leading to higher cumulative insertion loss, and tighter control of phase balance due to phase accumulation across multiple cascaded couplers. At millimeter-wave frequencies, fabrication tolerances and via-placement accuracy may also impose constraints on achievable phase uniformity in large-scale implementations. Despite these practical challenges, SIW technology remains well suited for higher-order Butler matrices due to its low-loss waveguiding characteristics and planar layout flexibility. With careful layout optimization, symmetry preservation, and loss balancing, larger matrices such as 8×8 can be realized while maintaining acceptable broadband performance. Therefore, the proposed architecture provides a scalable foundation for higher-order beamforming networks, particularly in applications where compactness and integration are prioritized. Comment 5: modification was made on the figures to improve clarity with multiple lines in the Figures Comment 6: We have improved Fig 11. Comment 7: changed to wavelength View more View less Competing Interests None reply Respond Report a concern Lian JW. Peer Review Report For: Butler Matrix Based on Substrate Integrated Waveguide Without Crossover and Phase Shifter for Millimeter Waves Applications [version 1; peer review: 1 approved with reservations, 1 not approved] . F1000Research 2025, 14 :969 ( https://doi.org/10.5256/f1000research.185497.r442261) NOTE: it is important to ensure the information in square brackets after the title is included in this citation. The direct URL for this report is: https://f1000research.com/articles/14-969/v1#referee-response-442261 keyboard_arrow_left Back to all reports Reviewer Report 0 Views copyright © 2025 Brunetti G. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 11 Nov 2025 | for Version 1 Giuseppe Brunetti , Politecnico di Bari, Bari, Italy 0 Views copyright © 2025 Brunetti G. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. format_quote Cite this report speaker_notes Responses (1) Approved With Reservations info_outline Alongside their report, reviewers assign a status to the article: Approved The paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. Not approved Fundamental flaws in the paper seriously undermine the findings and conclusions The proposed Substrate Integrated Waveguide (SIW) Butler Matrix can be contextualized within the broader framework of integrated switching and beamforming networks, which are conventionally categorized into broadband and narrowband architectures. Broadband switching matrices are typically realized using distributed transmission-line elements or waveguide-based implementations, optimized to sustain phase and amplitude uniformity over wide frequency ranges.Here, my comments: The manuscript lacks a clear contextualization of the proposed SIW Butler Matrix within the broader class of integrated switching matrices. A comparative discussion should be introduced early in the Introduction section, distinguishing between broadband and narrowband matrix architectures and highlighting the relevance of the proposed design in this framework. The classification between broadband and narrowband switching matrices should be explicitly articulated. Broadband matrices, typically based on distributed or waveguide structures, support wide frequency operation and are suited for multi-band applications such as 5G beamforming. Conversely, narrowband architectures, often resonant or lumped-element based, provide high selectivity and low insertion loss at the expense of operational bandwidth. (see, e.g., Butler Matrix-Based Beam Switching with Frequency-Tunable MIMO Array. In 2024 IEEE International Symposium on Antennas and Propagation and INC/USNC‐URSI Radio Science Meeting (AP-S/INC-USNC-URSI) (pp. 2475-2476). IEEE., 2024; Design of a large bandwidth 2× 2 interferometric switching cell based on a sub-wavelength grating. Journal of Optics, 23(8), 08580, 2021 ). The paper should include a concise review of integrated implementations of switching matrices, emphasizing microstrip, CPW, coaxial, and photonic platforms. Discussing their respective trade-offs, such as radiation losses, limited scalability, and fabrication complexity, would clarify the rationale for adopting an SIW-based solution. The originality of the proposed structure should be emphasized by contrasting it with existing 4×4 Butler Matrices that rely on crossovers and phase shifters. Quantitative comparisons of insertion loss, phase error, and physical dimensions with recent literature would reinforce the claim of superior broadband performance and compactness. The discussion of the SIW implementation should be expanded to underline its suitability for monolithic integration and compatibility with planar antenna arrays and photonic circuits. This aspect is particularly important for applications targeting compact, high-frequency front-end systems in 5G and beyond. Here, my minor comments: The abstract and introduction should better clarify the motivation behind eliminating crossovers and phase shifters, explaining how this contributes to both broadband performance and fabrication simplification. In Table 1, the comparison with previous works could be enriched by specifying whether each listed matrix operates in the broadband or narrowband regime. The terminology “wideband” and “broadband” should be used consistently throughout the text to avoid ambiguity. The introduction could benefit from one or two sentences connecting SIW-based microwave matrices with analogous developments in integrated photonics, where broadband beamforming networks are being explored using similar architectural concepts. Some of the numerical performance indicators (e.g., fractional bandwidth, insertion loss) should be explicitly defined or referenced to ensure clarity for readers from adjacent fields. Is the work clearly and accurately presented and does it cite the current literature? No Is the study design appropriate and is the work technically sound? Yes Are sufficient details of methods and analysis provided to allow replication by others? Yes If applicable, is the statistical analysis and its interpretation appropriate? Not applicable Are all the source data underlying the results available to ensure full reproducibility? No source data required Are the conclusions drawn adequately supported by the results? No Competing Interests No competing interests were disclosed. Reviewer Expertise Filter; photonics; beamforming I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above. reply Respond to this report Responses (1) Author Response 11 Feb 2026 Chia Pao Liew, School of Energy and Chemical Engineering, Xiamen University Malaysia, Sepang, Malaysia Comment no. 1: the following is highlighted in the manuscript Beamforming networks and switching matrices are fundamental components in modern multi-antenna systems, enabling signal routing, phase control, and spatial beam steering in applications such as 5G millimeter-wave communications, radar, and satellite systems. Within this broad class, integrated switching matrices can be generally categorized into narrowband and broadband architectures, depending on their operational bandwidth, phase stability, and amplitude balance characteristics. Narrowband matrix architectures, including conventional waveguide and microstrip Butler matrices, are typically optimized for operation around a single center frequency. While these solutions offer compact layouts and relatively low insertion loss, their performance rapidly degrades outside the design band due to frequency-dependent phase errors and impedance mismatch. Such limitations restrict their suitability for emerging wideband and multi-carrier millimeter-wave systems. In contrast, broadband matrix architectures employ wideband couplers, phase shifters, or hybrid implementations to maintain stable phase progression and amplitude balance over an extended frequency range. These designs are particularly relevant for 5G and beyond systems, where wide instantaneous bandwidth, beam squint mitigation, and integration compatibility are critical design requirements. However, many reported broadband matrices rely on multilayer structures, complex transitions, or mixed technologies, which increase fabrication complexity and cost. In this context, Substrate Integrated Waveguide (SIW) technology provides an attractive platform for realizing broadband integrated switching matrices by combining the low-loss characteristics of conventional waveguides with the planar manufacturability of printed circuits. The proposed SIW Butler Matrix in this work is positioned within the broadband matrix architecture class , specifically targeting wideband operation with stable phase differences and reduced insertion loss while maintaining a fully planar and fabrication-friendly structure. By employing only SIW hybrid couplers without additional phase-shifting elements, the proposed design offers a simplified topology that directly addresses the bandwidth and integration challenges encountered in existing matrix implementations. Comment no. 2 - as highlighted in Comment no. 1 above Comment no. 3: the following is highlighted in the manuscript Various integrated platforms have been explored for the implementation of switching and beamforming matrices, including microstrip, coplanar waveguide (CPW), coaxial, and photonic technologies. Each platform offers distinct advantages, but also exhibits inherent limitations when applied to wideband millimeter-wave matrix architectures. Microstrip-based switching matrices are widely reported due to their low cost, planar form factor, and ease of integration with active components. However, at millimeter-wave frequencies, microstrip implementations suffer from increased radiation losses, surface-wave excitation, and dispersion effects, which limit achievable bandwidth and degrade phase accuracy in large matrix configurations. Coplanar waveguide (CPW) platforms alleviate some integration challenges and provide improved grounding flexibility, yet they remain susceptible to radiation leakage and conductor loss at high frequencies, particularly in dense multi-port networks. Coaxial and waveguide-based matrices offer superior isolation and low loss, making them attractive for high-performance systems. Nevertheless, their bulky three-dimensional structures, limited scalability, and high fabrication and assembly costs restrict their suitability for compact and highly integrated 5G and beyond applications. More recently, photonic switching matrices have been proposed to enable ultra-wide bandwidth and immunity to electromagnetic interference. Despite these advantages, photonic solutions typically require complex electro-optic conversion stages, precise alignment, and specialized fabrication processes, resulting in increased system complexity and cost. In comparison, Substrate Integrated Waveguide (SIW) technology combines the low-loss and high-isolation characteristics of conventional waveguides with the planar manufacturability of printed circuit technologies. This hybrid nature makes SIW particularly well suited for integrated broadband switching matrices, offering reduced radiation loss, improved phase stability, and excellent scalability while maintaining compatibility with standard PCB fabrication. Consequently, the SIW-based Butler Matrix proposed in this work provides a balanced solution that directly addresses the limitations of alternative integrated platforms. Comment no. 4: the following is highlighted in the manuscript The key contribution of this work lies in the original structural simplicity and performance advantages of the proposed SIW Butler Matrix compared to existing 4×4 matrix designs that rely on crossovers and discrete phase-shifter networks. Traditional implementations of 4×4 Butler Matrices in microstrip and CPW technologies often incorporate crossovers and fixed electrical-length phase shifters to achieve the required interconnections and phase progression. While functional, these elements introduce additional insertion loss , phase distortion , and size penalties , particularly at millimeter-wave frequencies, due to increased discontinuities, radiation effects, and dispersion. By contrast, the proposed SIW design employs only SIW hybrid couplers without separate crossovers or discrete phase shifters, leading to a reduction in cumulative junction loss and improved phase fidelity over a wide frequency band. Quantitatively, as shown in Table 1, the proposed matrix demonstrates a lower average insertion loss and reduced phase error across the operational band, while achieving a more compact footprint than representative matrices from recent literature. These performance improvements underscore the broadband performance and integration advantages of the proposed structure for millimeter-wave applications. Comment 5: the following is highlighted in the manuscript Beyond its electrical performance, the proposed SIW Butler Matrix is particularly well suited for monolithic integration and system-level co-design , which are essential requirements for compact millimeter-wave front-end architectures in 5G and beyond. The planar nature of SIW technology enables seamless integration with other passive and active components on a single substrate, including power dividers, filters, and transitions, while preserving low-loss wave-guiding behavior. A key advantage of the proposed structure is its direct compatibility with planar antenna arrays , such as SIW-fed slot arrays and substrate-integrated patch arrays. Since both the Butler Matrix and the antenna elements can be realized using the same fabrication process and substrate stack-up, the proposed design facilitates compact beamforming modules without the need for complex interconnects or vertical transitions. This compatibility significantly reduces assembly complexity, parasitic effects, and overall system footprint, which are critical constraints at millimeter-wave frequencies. Furthermore, SIW technology offers promising compatibility with photonic and electro-optic circuits , particularly in emerging hybrid microwave–photonic front-end systems. The well-defined electromagnetic confinement and planar interfaces of SIW structures simplify the integration of optoelectronic components, such as modulators and photodetectors, enabling efficient RF-to-photonic signal routing. This makes SIW-based beamforming networks attractive candidates for future high-frequency systems that combine electronic beamforming with photonic signal distribution to achieve wide bandwidth, low latency, and high integration density. Consequently, the proposed SIW Butler Matrix is not only a broadband and compact beamforming solution at the circuit level, but also a scalable building block for integrated, multi-functional front-end modules targeting advanced 5G and next-generation wireless systems. Minor comment no.1: the following is highlighted in the manuscript This paper presents a compact and broadband 4×4 Butler Matrix implemented using Substrate Integrated Waveguide (SIW) technology. In contrast to conventional Butler Matrices that rely on crossovers and discrete phase shifters, the proposed design employs only SIW hybrid couplers to realize the required phase progression and signal distribution. Eliminating crossovers and phase shifters significantly reduces structural discontinuities, junction losses, and frequency-dependent phase errors, thereby enhancing broadband performance. Moreover, the simplified topology minimizes fabrication complexity and improves suitability for planar and monolithic integration, making the proposed matrix well suited for compact millimeter-wave beamforming front ends in 5G and beyond systems. Minor comment no. 2: Considered Minor comment no. 3: corrected to just wideband Minor comment no. 4: Added as above Minor comment no. 5: Defined fractional bandwidth View more View less Competing Interests None reply Respond Report a concern Brunetti G. Peer Review Report For: Butler Matrix Based on Substrate Integrated Waveguide Without Crossover and Phase Shifter for Millimeter Waves Applications [version 1; peer review: 1 approved with reservations, 1 not approved] . F1000Research 2025, 14 :969 ( https://doi.org/10.5256/f1000research.185497.r421174) NOTE: it is important to ensure the information in square brackets after the title is included in this citation. The direct URL for this report is: https://f1000research.com/articles/14-969/v1#referee-response-421174 Alongside their report, reviewers assign a status to the article: Approved - the paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations - A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. 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