Millimeter-wave Beam Research Articles

Security concerns on machine learning solutions for 6G networks in mmWave beam prediction

6G – sixth generation – is the latest cellular technology currently under development for wireless communication systems. In recent years, machine learning (ML) algorithms have been applied widely in various fields, such as healthcare, transportation, energy, autonomous cars, and many more. Those algorithms have also been used in communication technologies to improve the system performance in terms of frequency spectrum usage, latency, and security. With the rapid developments of ML techniques, especially deep learning (DL), it is critical to consider the security concern when applying the algorithms. While ML algorithms offer significant advantages for 6G networks, security concerns on artificial intelligence (AI) models are typically ignored by the scientific community so far. However, security is also a vital part of AI algorithms because attackers can poison the AI model itself. This paper proposes a mitigation method for adversarial attacks against proposed 6G ML models for the millimeter-wave (mmWave) beam prediction using adversarial training. The main idea behind generating adversarial attacks against ML models is to produce faulty results by manipulating trained DL models for 6G applications for mmWave beam prediction. We also present a proposed adversarial learning mitigation method’s performance for 6G security in mmWave beam prediction application a fast gradient sign method attack. The results show that the defended model under attack’s mean square errors (i.e., the prediction accuracy) are very close to the undefended model without attack.

Learning and Adaptation for Millimeter-Wave Beam Tracking and Training: A Dual Timescale Variational Framework

Millimeter-wave vehicular networks incur enormous beam-training overhead to enable narrow-beam communications. This paper proposes a learning and adaptation framework in which the dynamics of the communication beams are learned and then exploited to design adaptive beam-tracking and training with low overhead: on a long-timescale, a deep recurrent variational autoencoder (DR-VAE) uses noisy beam-training feedback to learn a probabilistic model of beam dynamics and enable predictive beam-tracking; on a short-timescale, an adaptive beam-training procedure is formulated as a partially observable (PO-) Markov decision process (MDP) and optimized via point-based value iteration (PBVI) by leveraging beam-training feedback and a probabilistic prediction of the strongest beam pair provided by the DR-VAE. In turn, beam-training feedback is used to refine the DR-VAE via stochastic gradient ascent in a continuous process of learning and adaptation. The proposed DR-VAE learning framework learns accurate beam dynamics: it reduces the Kullback-Leibler divergence between the ground truth and the learned model of beam dynamics by ~95% over the Baum-Welch algorithm and a naive learning approach that neglects feedback errors. Numerical results on a line-of-sight scenario with multipath and 3D beamforming reveal that the proposed dual timescale approach yields near-optimal spectral efficiency, and improves it by 130% over a policy that scans exhaustively over the dominant beam pairs, and by 20% over a state-of-the-art POMDP policy. Finally, a low-complexity policy is proposed by reducing the POMDP to an error-robust MDP, and is shown to perform well in regimes with infrequent feedback errors.

A Millimeter-Wave 2D Beam Steering Antenna Using Extended Hemispherical Dielectric Lens Antenna Subarrays

Recent work has proposed that millimeter-wave beam steering antennas consisting of lens antenna subarrays (LASs) reduce hardware complexity. This manuscript extends the concept to 2D beam steering with extended hemispherical dielectric lenses (EHDLs). To accomplish this, we introduce a design process to maximize scan range and side lobe level (SLL) performance. The design process first employs the solution of the geometric disk covering problem to identify the initial positions of the feed antennas such that the subarray size, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> , is minimized. This process is followed by systematic 3D full-wave simulation-based parametric sweeps of lens geometry and feed antenna positions to maximize scan range and minimize SLL. Finally, we demonstrate this process with a 38 GHz antenna consisting of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> = 7 LASs and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> = 17 feed antennas per LAS. The resulting antenna has a ±36° field of view, -9.5 dB SLL, 5° half-power beamwidth, and ~20 dBi maximum realized gain. Compared to the existing literature on subarray-based beam-steering antennas, this antenna performs with a more extensive scan range while offering a comparable SLL performance.

A Novel Compact Magneto-Electric Dipole Antenna for Millimeter-Wave Beam Steering Applications

A novel compact magneto-electric (ME) dipole antenna with size of 0.31λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> ×0.31λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> ×0.12λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> (λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> is the wavelength at central frequency herein and after), gain of around 8 dBi, and bandwidth of 39.7% is presented for millimeter-wave beam steering applications with the combination of the fractal technique and reactive impedance surface (RIS) loading. In particular, a fractal ME dipole antenna with four modified second-order Minikowski structures is firstly designed, where an aperture size of 0.38λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> ×0.38λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> is achieved. Herein, the antenna gain is dropped with the size reduction. Then a capacitive RIS structure is designed and loaded to improve the antenna gain and further lower down the antenna operating frequency range. With the RIS structure, the antenna gain is increased by around 4 dB, and the operating center frequency is shifted to left side by 9.0 GHz, thus achieving a further size reduction. Simulation and measurement results are provided to demonstrate the excellent properties of the proposed antenna. Subsequently, the antenna is arranged into a 5 mm-spaced (half wavelength at 30 GHz) 16-element uniform linear array. The beam steering characteristics of the array are investigated with the influence of phase quantization errors into consideration.

Characterization of Orbital Angular Momentum Applying Single-Sensor Compressive Imaging Based on a Microwave Spatial Wave Modulator

In this work, a new technique to characterize a microwave orbital angular momentum (OAM) beam applying a single-sensor compressive imaging (SSCI) strategy is reported, which is much more time-efficient, cost-effective, and compact than traditional near-field scanning methods. A microwave spatial wave modulator (MSWM) realized by a programmable metasurface is applied to generate random mask patterns and modulate an OAM beam under test. The modulated fields are collected by a single-sensor detector. Two different algorithms can be used to reconstruct phase and magnitude profiles of the OAM beam, with the first one demands both amplitude and phase measurement while the second one only perceives the amplitude or intensity. Simulations are first carried out to investigate the effects of several parameters of the random mask patterns on the quality of reconstruction. Proof-of-concept experiments are then performed to characterize a microwave OAM beam, and obtained results show high-quality reconstructed phase and magnitude distributions of the OAM beam under test, which corroborates the effectiveness of the proposed SSCI technique. This work establishes an alternative paradigm for fast and economic measurement of microwave and millimeter-wave OAM beams. It may also facilitate OAM-based communication applications.

Millimeter-Wave Beam Selection in Time-Varying Channels With User Orientation Changes

The use of many narrow beams to overcome the adverse propagation conditions in millimeter-wave channels leads to large training durations and overheads in 5G systems. This causes the beam measurements to become outdated by different extents at the time the transmit and receive beams are selected. The rapid changes in user device orientation exacerbate this problem. We first present a novel modified bivariate Nakagami- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> (MBN) model to tractably and accurately characterize the joint, non-stationary statistics of the channel gains seen at the times of measurement and data transmission. We then derive a novel and optimal beam selection rule that maximizes the average rate of the system. We use the MBN model to propose a near-optimal, practically amenable bound-based selection (PABS) rule. Our approach captures several pertinent aspects about the spatial channel model and 5G, such as transmission of periodic bursts of reference signals, feedback from the user to enable the base station to select its transmit beam, and the faster pace of updating the data rate compared to the transmit-receive beam pair. The PABS rule markedly outperforms the widely used conventional power-based selection rule and is less sensitive to user orientation changes.

Millimeter-wave beam scattering and induced broadening by plasma turbulence in the TCV tokamak

The scattering of millimeter-wave beams from electron density fluctuations and the associated beam broadening are experimentally demonstrated. Using a dedicated setup, instantaneous deflection and (de-)focusing of the beam due to density blobs on the beam path are shown to agree with full-wave simulations. The detected time-averaged wave power transmitted through the turbulent plasma is reproduced by the radiative-transfer model implemented in the WKBeam code, which predicts a ∼50% turbulence-induced broadening of the beam cross-section. The role of core turbulence for the considered geometry is highlighted.

A 1-D Model for the Millimeter-Wave Absorption and Heating of Dielectric Materials in Power Beaming Applications

A heat exchanger, based on a millimeter-wave absorbing ceramic composite, is under development. This article describes a 1-D finite-difference model that is used in the design of the heat exchanger. The purpose of this model is to offer a design tool that can rapidly estimate the overall performance of the heat exchanger. This fast model allows for absorber performance to be evaluated over a wide parameter space as opposed to 3-D finite-difference time-domain methods, which provide accurate results but require substantially more computational resources. The model enables quick calculations by approximating the electric field such that the simulation runs on the slower thermal dynamics time scale without having to resolve the faster electromagnetic time scale. Example calculations were performed to illustrate the performance of a realistic absorber. These calculations used experimentally measured material properties for a molybdenum-loaded aluminum nitride (AlN:Mo) ceramic composite. Simulation results show dielectric tiles reaching equilibrium temperature in around 20 s and the samples absorbing up to 70% of the power from the millimeter-wave beam. Parameter studies over Mo loading percentage and boundary condition temperatures highlight the complexity of this coupled system. An AlN:Mo composite with 3% Mo (by volume) exhibits uniform power absorption across multiple boundary condition temperatures and suggests robustness to variety of possible experimental testing conditions.

KM Learning for Millimeter-Wave Beam Alignment and Tracking: Predictability and Interpretability

A data representation technique dubbed Kolmogorov model (KM), has been applied to the beam alignment problem in large-dimensional antenna systems. The previous learning-based beam alignment solely focused on utilizing the predictive power of KM, i.e., the capability of predicting the outcome of random variables that are outside the training set, to reduce the beam training overhead. However, a distinctive feature of KM, namely, the interpretability which enables the capability of extracting additional information hidden inside the data, has not yet been exploited. Moreover, the prohibitively high computational complexity of the existing KM learning algorithm offsets the benefits brought by KM and hampers its application to large-scale problems. In this paper, we propose a joint beam alignment and tracking framework by incorporating the predictability and interpretability of KM. Especially, our proposed scheme enables a novel interpretable beam tracking that reveals insights on relations among the sounded observations to alleviate the beam sounding overhead after the initial beam alignment. To reduce the computational complexity of KM learning, two enhancement approaches, based on discrete monotonic optimization (DMO) and dual optimization, respectively, are proffered. Numerical results demonstrate that the proposed methods can reduce the computational cost of the existing KM learning algorithm by up to three orders of magnitude. Furthermore, the proposed methods show superior beam alignment and tracking performance over other state-of-the-art techniques, notably in the low signal-to-noise ratio (SNR) regime.

A Compact Dual-Band and Dual-Polarized Millimeter-Wave Beam Scanning Antenna Array for 5G Mobile Terminals

This paper presents a compact dual-band and dual-polarized millimeter-wave patch antenna array with satisfactory performance on element mutual coupling and beam scanning capabilities. Using capacitive feed technique and stacked configuration with extra parasitic strips, the proposed antenna array is able to achieve a wide operating bandwidth in both the low- and high-bands. In order to reduce the array's footprint, and to enhance the beam scanning performance in both bands, the element spacing is shrunk to less than 0.36 wavelength at 26 GHz. To improve the isolation between array elements due to their small spacings, two effective decoupling approaches are adopted, which result in a 6-dB isolation enhancement. The overall size of the proposed antenna array is only 18.2 mm ×4.1 mm ×1.07 mm, which is smaller than some industrial mm-Wave antenna modules released recently. Our simulation shows that the antenna array can fully cover the 5G NR bands of n258~n261 simultaneously. The four-element array provides ±60° and ±45° beam scanning performance in the low- and high-bands, respectively. The experimental data of reflection coefficient, mutual coupling, and radiation patterns confirm with the simulated results, rendering the proposed array to be a good candidate for 5G mm-Wave communications.

Robust Adaptive Beam Tracking for Mobile Millimetre Wave Communications

Millimetre wave (mmWave) beam tracking is a challenging task because tracking algorithms are required to provide consistent high accuracy with low probability of loss of track and minimal overhead. To meet these requirements, we propose in this article a new cost-effective analog beam tracking framework namely Adaptive Tracking with Stochastic Control (ATSC). Under this framework, beam direction updates are made using a novel mechanism based on measurements taken from only two beam directions perturbed from the current data beam. To achieve high tracking accuracy and reliability, we provide a systematic approach to jointly optimise the algorithm parameters. The complete framework includes a method for adapting the tracking rate together with a criterion for realignment (perceived loss of track). ATSC adapts the amount of tracking overhead that matches well to the mobility level, without incurring frequent loss of track, as verified by an extensive set of experiments under both representative statistical channel models as well as realistic urban scenarios simulated by ray-tracing software. In particular, numerical results show that ATSC can track dominant channel directions with high accuracy for vehicles moving at 72 km/hour in complicated urban scenarios, with an overhead of less than 1%.

Urban Outdoor Measurement Study of Phased Antenna Array Impact on Millimeter-Wave Link Opportunities and Beam Misalignment

Exploiting multi-antenna technologies for robust beamsteering to overcome the effects of blockage and beam misalignment is the key to providing seamless multi-Gbps connectivity in millimeter-wave (mm-wave) networks. In this paper, we present the first large-scale outdoor mm-wave measurement study using a phased antenna array in a typical European town. We systematically collect fine-grained 3D angle-of-arrival (AoA) and angle-of-departure (AoD) data, totaling over 50,000 received signal strength measurements. We study the impact of phased antenna arrays in terms of number of link opportunities, achievable data rate and robustness under small-scale mobility, and compare this against reference horn antenna measurements. Our results show a limited number of 2–4 distinct spatial link opportunities per receiver location, indicating that the mm-wave multipath richness in a European town is surprisingly similar to that of dense urban metropolises. The results for the phased antenna array reveal that significant losses in estimated data rate occur for beam misalignments in the order of the half-power beamwidth, with significant and irregular variations for larger misalignments. By contrast, the loss for horn antennas is monotonically increasing with the misalignment. Our results strongly suggest that the effect of non-ideal phased antenna arrays must be explicitly considered in the design of agile beamsteering algorithms.

Millimeter-Wave Beam Search With Iterative Deactivation and Beam Shifting

Millimeter Wave (mmWave) communications rely on highly directional beams to combat severe propagation loss. In this paper, an adaptive beam search algorithm based on spatial scanning, called Iterative Deactivation and Beam Shifting (IDBS), is proposed for mmWave beam alignment. IDBS does not require advance information such as the Signal-to-Noise Ratio (SNR) and channel statistics, and matches the training overhead to the unknown SNR to achieve satisfactory performance. The algorithm works by gradually deactivating beams using a Bayesian probability criterion based on a uniform improper prior, where beam deactivation can be implemented with low-complexity operations that require computing a low-degree polynomial or a search through a look-up table. Numerical results confirm that IDBS adapts to different propagation scenarios such as line-of-sight and non-line-of-sight and to different SNRs. It can achieve better tradeoffs between training overhead and beam alignment accuracy than existing non-adaptive algorithms that have fixed training overheads.

Gyro-devices – natural sources of high-power high-order angular momentum millimeter-wave beams

The Orbital Angular Momentum (OAM) carried by light beams with helical phasefront (vortex beams) has been widely employed in many applications such as optical tweezers, optical drives of micro-machines, atom trapping, and optical communication. OAM provides an additional dimension (diversity) to multiplexing techniques, which can be utilized in addition to conventional multiplexing methods to achieve higher data rates in wireless communication. OAM beams have been thoroughly studied and used in the optical regime but in the mm-wave and THz-wave region, they are still under investigation. In these frequency bands, there are difficulties associated with beam-splitting and beam-combining processes as well as with the use of spiral phase plates and other methods for OAM generation, since the wavelength is much larger compared to those at optical frequencies, leading to higher diffraction losses. The present paper describes the natural generation of high-power OAM modes by gyro-type vacuum electron devices with cylindrical interaction circuit and axial output of the generated rotating higher-order transverse electric mode TEm,n, where m &gt; 1 and n are the azimuthal and radial mode index, respectively. The ratio between the total angular momentum (TAM) JN and total energy WN of N photons is given by m/ω, where ω is the angular frequency of the operating mode, which in a gyrotron oscillator is close to the TEm,n-mode cutoff frequency in the cavity. Therefore, m/ω = Rc/c, where Rc is the caustic radius and c the velocity of light in vacuum. This means that the OAM is proportional to the caustic radius and at a given frequency the same for all modes with the same azimuthal index m. Right-hand rotation (co-rotation with the electrons) corresponds to a positive value of m and left-hand rotation to negative m. The corresponding OAM mode number (topological charge) is l = m – 1. Circularly polarized TE1n modes only possess a Spin Angular Momentum (SAM: s = ±1). TE0n modes have neither SAM nor OAM. This is the result of the photonic (quasi-optical) approach to derive the TAM of modes generated in gyrotrons. The same result follows from the electromagnetic (EM) wave approach for the TAM within a given waveguide volume per total energy of the EM wave in the same volume. Such high-power output beams with very pure higher-order OAM, generated by gyrotron oscillators or amplifiers (broadband) could be used for multiplexing in long-range wireless communications. The corresponding mode and helical wavefront sensitive detectors for selective OAM-mode sorting are available and described in the present paper.

Fingerprint-based Millimeter-Wave Beam Selection for Interference Mitigation in Beamspace Multi-User MIMO Communications

Millimeter-wave communications are suitable for application to massive multiple-input multiple-output systems in order to satisfy the ever-growing data traffic demands of the next-generation wireless communication. However, their practical deployment is hindered by the high cost of complex hardware, such as radio frequency (RF) chains. To this end, operation in the beamspace domain, through beam selection, is a viable solution. Generally, the conventional beam selection schemes focus on the feedback and exhaustive search techniques. In addition, since the same beam in the beamspace may be assigned to a different user, conventional beam selection schemes suffer serious multi-user interference. In addition, some RF chains may be wasted, since they do not contribute to the sum-rate performance. Thus, a fingerprint-based beam selection scheme is proposed to solve these problems. The proposed scheme conducts offline group-based fingerprint database construction and online beam selection to mitigate multi-user interference. In the offline phase, the contributing users with the same best beam are grouped. After grouping, a fingerprint database is created for each group. In the online phase, beam selection is performed for purposes of interference mitigation using the information contained in the group-based fingerprint database. The simulation results confirm that the proposed beam selection scheme can achieve a signal-to-interference-plus-noise ratio and sum-rate performance which is close to those of a fully digital system, and having much higher energy efficiency.

Explore and Eliminate: Optimized Two-Stage Search for Millimeter-Wave Beam Alignment

Swift and accurate alignment of transmitter (Tx) and receiver (Rx) beams is a fundamental design challenge to enable reliable outdoor millimeter-wave communications. In this paper, we propose a new Optimized Two-Stage Search (OTSS) algorithm for Tx-Rx beam alignment via spatial scanning. In contrast to one-shot exhaustive search, OTSS judiciously divides the training energy budget into two stages. In the first stage, OTSS explores and trains all candidate beam pairs and then eliminates a set of less favorable pairs learned from the received signal profile. In the second stage, OTSS takes an extra measurement for each of the survived pairs and combines with the previous measurement to determine the best one. For OTSS, we derive an upper bound on its misalignment probability, under a single-path channel model with training codebooks having an ideal beam pattern. We also characterize the decay rate function of the upper bound with respect to the training budget and further derive the optimal design parameters of OTSS that maximize the decay rate. OTSS is proved to asymptotically outperform state-of-the-art beam alignment algorithms, and is numerically shown to achieve better performance with limited training budget and practically synthesized beams.

Integrated Millimeter-Wave Wideband End-Fire 5G Beam Steerable Array and Low-Frequency 4G LTE Antenna in Mobile Terminals

In this paper, a novel technique of collocating a millimeter-wave end-fire 5G beam steerable array antenna with a low-frequency planar inverted-F antenna (PIFA) is presented. In this technique, the low-frequency antenna can be transparent by using some grating strips between the low- and high-frequency antennas. A quad-element mm-wave array with end-fire radiation patterns operating in 22–31 GHz is integrated with a dual-band low-frequency PIFA in a mobile terminal. The novelty of this paper is the collocation of a high-frequency end-fire 5G antenna array with an old-generation low-frequency antenna, such as 4G in small space in the mobile terminal, without interfering with the radiation pattern and impedance matching of both low- and high-frequency antennas. The proposed 5G antenna covers 22–31 GHz and can scan ±50° with the scan loss of better than 3 dB. The coverage efficiency of the proposed mm-wave 5G antenna is better than 50% and 80% for a minimum gain of 4 and 0 dBi in 22–31 GHz, respectively. The gain of the high-frequency antenna array is better than 9.5 dBi at 28 GHz. The low-frequency antenna covers some practical 4G LTE bands from 740–960 MHz and 1.7–2.2 GHz bands. The measured results in both low and high frequencies agree well with the simulations.

Voltage-Controlled, Nonreciprocal Millimeter-Wave Propagation From Magnetoelastic Membranes Infused With Aligned Nickel Microparticles

Differential Faraday rotation of the linear polarization of millimeter-wave (mmW) Gaussian beams has been observed from a magnetoelastic material system consisting of a silicone membrane that was infused with aligned nickel microparticles, mounted to a piezoelectric annulus, and immersed in a static magnetic field. The piezoelectric crystal was driven near its radial mode of resonance by an ac voltage signal so as to periodically stretch the membrane about the axis of mmW propagation. The stretching modulated the distribution of nickel microparticles and resulted in a change in magnetic properties of the material, specifically the effective Verdet constant. A customized, quasi-optical apparatus was phase locked with the ac driving signal to determine the difference in Faraday rotation due to the stretched and un-stretched states of the membrane.

Instantaneous measurement of high-power millimeter-wave beam for 28 GHz gyrotron.

An instantaneous measurement system of high-power millimeter-wave was proposed and demonstrated with a 28 GHz gyrotron at the Plasma Research Center, University of Tsukuba. The high-power detector consists of an attenuator and a linear polarized microstrip antenna with an F-class load rectifier, which is a commonly used system for radio-frequency wireless power transmission. The detector obtained the power distribution of the gyrotron output beam which showed good agreement with the infrared camera image. The rectenna array detector received 45 W RF input power with a 0.4 ms response time. The results revealed that the proposed narrow band detector is useful as an imaging sensor and power meter for high-power millimeter-wave beam output with a wide wavelength range.

Design evolution of the diamond window unit for the ITER EC H&CD upper launcher

The torus window unit is a very particular component of the ITER EC H&CD upper launcher aiming to provide the primary vacuum and confinement boundary between the vacuum vessel and the transmission lines (TLs). The high power 170 GHz millimeter-wave beams generated by the gyrotrons travel along the TLs and pass through the window units, before being quasi-optically guided into the plasma via the upper launchers. The design of the window unit shall thus meet stringent requirements to guarantee the safety function, the millimeter-wave beam transmission and the structural integrity during normal operation and off-normal events. The unit consists of an ultra-low loss CVD diamond disk brazed to two copper cuffs; this structure is then integrated into a metallic housing by welding. The compliance with the requirements shall be assured by applying the ASME Section III – Subsection NC code and a dedicated experimental qualification program. This paper reports the way in which the design of the unit, already optimized by FEM analyses against the ITER loading conditions, was further improved by the application of the ASME III-NC code, leading to a more feasible and simpler manufacturing and assembling sequence. In addition, the impact of the ITER project decision to change the inner diameter of the waveguide from 63.5 to 50 mm, to improve the beams’ mode purity, was assessed and it is also discussed. Different materials for the metallic housing and in particular for the millimeter-wave inserts of the unit were compared using appropriate engineering criteria to mitigate the significant increase of the millimeter-wave thermal loads on the waveguides when the diameter is decreased.