Beamforming Network Research Articles

Automatic Coupler Design Based on Artificial Neural Network With Self-Adaptive Local Surrogates

A new artificial neural network (ANN) inverse modeling method with self-adaptive local surrogates, called ANN-SALS, is presented in this article, for a large-scale beam-forming network (BFN). To get accurate dimensions of the huge number of directional couplers, constituting a large BFN could be computationally expensive. Here, we develop an automated and more efficient algorithm to design multiple couplers with different specifications simultaneously using shared data for local surrogate modeling. While the result predicted by ANN serves as the starting point, a Gaussian process (GP) local surrogate model is built around it for fine-tuning. Then, ANN database is updated by selected GP training samples as well as the fine-tuned solution. After carefully setting the design specification, GP training data can be shared among the design of multiple couplers despite different specifications so that the design of one coupler is improved by the other ones. What is more, the size of region where GP is built is corrected by a quasi-sensitivity analysis method to improve the local optimization success rate. To verify the algorithm, four different couplers with different design requirements are designed, showing the proposed technique could unravel various multiple coupler design problems automatically and is much more efficient compared with existing methods.

Air-Filled SIW Remote Antenna Unit With True Time Delay Optical Beamforming for mmWave-Over-Fiber Systems

A low-complexity and efficient mmWave-over-fiber remote antenna unit (RAU) is proposed for broadband transmission and wide-angle squint-free beam steering in the full [26.5–29.5] GHz n257 5G band. It leverages an optical beamforming network (OBFN), implemented on a silicon photonics integrated circuit, and a broadband optically enabled 1x4 uniform linear array (ULA). The antenna elements (AEs) of the ULA are implemented in air-filled substrate-integrated-waveguide technology. They adopt an improved aperture-coupled feeding scheme to achieve high efficiency, high isolation and minimal back radiation over a broad frequency band. Each AE is compactly integrated and co-optimized with a dedicated opto-electrical transmit chain, maximizing the RAU’s performance, including beamforming flexibility and energy efficiency, while minimizing its size. The separately packaged OBFN implements true-time-delay beamforming by means of four switchable optical delay lines that are capable of discretely tuning the delay difference between AEs with a resolution of 1.6 ps, up to a maximum delay of 49.6 ps to fully exploit the ULA’s full grating-lobe-free scan range. The measured AEs are excellently matched in the [25.1–30.75] GHz band, exhibit high isolation ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ &gt;$</tex-math></inline-formula> 15 dB) in the operating band, and feature a stable peak gain of 6.8 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\pm$</tex-math></inline-formula> 0.72 dBi with a beamwidth of at least 95 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^\circ$</tex-math></inline-formula> . Additionally, optical beamforming was successfully demonstrated by steering the RAU’s beam towards angles up to 51.8 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^\circ$</tex-math></inline-formula> without grating lobes. The optically enabled 1 × 4 ULA successfully establishes a 64-QAM wireless communication link at 2.2 Gbaud (13.2 Gbps) while beam steering up to 50 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ ^\circ$</tex-math></inline-formula> with an error vector magnitude below 7.6%.

Broadband 1×8 Optical Beamforming Network Based on Anti-resonant Microring Delay Lines

We demonstrate a 1×8 binary tree optical beamforming network (OBFN) chip for a microwave photonic phased array antenna. The OBFN is formed by cascading multiple microring resonators (MRRs) working at the anti-resonant wavelengths. The binary tree topology reduces the MRR amount by reusing the MRRs in the preceding stage, and the anti-resonant MRRs realize continuous delay tuning with a reduced in-band delay fluctuation. The delay adjustment is achieved by digitally tuned MRRs and one continuously tuned MRR in each stage with an improved operating bandwidth. The random initial states of the MRRs are calibrated to produce a flat delay response. Experimental results show that the maximum delay is 560 ps. The beamforming performance of the OBFN is evaluated in 20 ps and 45 ps delay increments. In an 8-GHz operating bandwidth, the maximum delay fluctuation is less than 7.6 ps. The capability of our delay lines to suppress the delay ripple encountered in conventional on-resonance delay lines opens exciting opportunities for the development of compact integrated broadband OBFNs demanded in broadband microwave phased array antennas.

Design of millimeter wave dual‐polarized multibeam antenna array with a boresight beam

A design of millimeter wave (mm-wave) dual-polarized multibeam antenna array (MAA) with a boresight beam is presented. In order to generate a boresight beam, a 5 × 6 Butler matrix based on three-way directional couplers is designed as the beamforming network, which achieves equal power division and −60°, +120°, 0°, −120°, +60° progressive phase differences among the output ports when the five input ports are excited, respectively. By four-layer design, the two 5 × 6 BMs for horizontal polarization (HP) and vertical polarization (VP) are constructed. The patch is used as radiator element, and the HP and VP wave are excited by aperture coupling and microstrip feed, respectively. A prototype is fabricated and measured to verify the design. The measured results show that the designed mm-wave dual-polarized MAA can generate five radiation beams including a boresight beam and the five beams with HP and VP cover the range of ±50° at 28 GHz. In addition, the designed mm-wave dual-polarized MAA can be a potential option for mm-wave multibeam application.

Photonic-assisted 2-D terahertz beam steering enabled by a LWA array monolithically integrated with a BFN.

A novel photonic-assisted 2-D Terahertz beam steering chip using only two tuning elements is presented. The chip is based on an array of three leaky wave antennas (LWAs) with a monolithically integrated beamforming network (BFN) on a 50 µm-thick indium phosphide substrate. The THz beam angle in elevation (E-plane) is controlled via optical frequency tuning using a tunable dual-wavelength laser. An optical delay line is used for azimuth (H-plane) beam control. The simulated beam scanning range is 92° in elevation for a frequency sweep from 0.23 THz to 0.33 THz and 69.18° in azimuth for a time delay of 3.6 ps. For the frequency range from 0.26 THz to 0.32 THz, it is confirmed experimentally that the THz beam scans from -12° to +33°, which is in good agreement with the numerical simulations. The beam direction in azimuth scans with a total angle of 39° when applying a delay difference of 1.68 ps. A good agreement is found between theoretically predicted and experimentally determined THz beam angles with a maximum angle deviation below 5°. The experimental scanning angles are limited due to the mechanical constraints of the on-wafer probes, the on-chip integrated transition and the bandwidth of the THz receiver LNA. The mechanical limitation will be overcome when using a packaged chip.

Robust Analog Beamforming for Periodic Broadcast V2V Communication

We generalize an existing low-cost analog signal processing concept that takes advantage of the periodicity of vehicle-to-vehicle broadcast service to the transmitter side. In particular, we propose to process multiple antennas using either an analog beamforming network (ABN) of phase shifters, or an antenna switching network (ASN) that periodically alternates between the available antennas, to transmit periodic messages to receivers that have an analog combining network (ACN) of phase shifters, which has been proposed in earlier work. To guarantee robustness, we aim to minimize the burst error probability for the worst receiving vehicular user, in a scenario of bad propagation condition that is modeled by a single dominant path between the communicating vehicles. In absence of any form of channel knowledge, we analytically derive the optimal parameters of both ABN and ASN. The ABN beamforming vector is found to be optimal for all users and not only for the worst receiving user. Further, we demonstrate that Alamouti scheme for the special case of two transmit antennas yields similar performance to ABN and ASN. At last, we show that the derived parameters of the two proposed transmission strategies are also optimal when hybrid ACN-maximal ratio combining is used at the receiver.

Optical Generation and Transmission of mmWave Signals in 5G ERA: Experimental Evaluation Paradigm

We demonstrate the generation, of a mmWave signal via the injection of an optical frequency comb (OFC) into an integrated tunable dual distributed Bragg reflector (DBR) laser as well as the fiber transmission and the processing of this signal by an optical beamforming network (OBFN). The dual DBR laser is based on a hybrid indium phosphide (InP) – polymer photonic integrated circuit (PIC). Two different cases have been examined in which the microwave signal is centered around 39 GHz and 60 GHz respectively, carrying quadrature amplitude modulation (QAM) formats at 0.5 Gbaud. In this proof-of-concept scenario, the OBFN consists of two optical paths, where the relative true time delay is induced by an optical delay line (ODL). Extensive comparison between the back-to-back (B2B) case and scenarios with transmission over 25 km of standard single-mode fiber (SSMF) has been made using the error-vector magnitude (EVM) and the bit-error ratio (BER) as evaluation criteria. In all cases, error-free transmission was suggested for all QPSK signals, whereas a worst-case EVM of 11.8% was observed for 16-QAM transmission, successfully showcasing the concept’s potential. The generated microwave signal’s frequency can be set arbitrarily high, provided that high-speed photodetection equipment is available for the detection and down-conversion of the signal. Extension to higher antenna elements (AEs) numbers is straight-forward, relying only on the number of available photodetectors.

Gain-enabled optical delay readout unit using CMOS-compatible avalanche photodetectors

A compact time delay unit is fundamental to integrated photonic circuits with applications in, for example, optical beam-forming networks, photonic equalization, and finite and infinite impulse response optical filtering. In this paper, we report a novel gain-enabled delay readout system using a tunable optical carrier, low-frequency RF signal and CMOS-compatible photodetectors, suitable for silicon photonic integration. The characterization method relies on direct phase measurement of an input RF signal and thereafter extraction of the delay profile. Both integrated silicon and germanium photodetectors coupled with low-bandwidth electronics are used to characterize a microring resonator-based, true-time delay unit under distinct ring–bus coupling formats. The detectors, used in both linear and avalanche mode, are shown to be successful as optical-to-electrical converters and RF amplifiers without introducing significant phase distortion. For a Si–Ge separate-absorption-charge-multiplication avalanche detector, an RF amplification of 10 dB is observed relative to a Ge PIN linear detector. An all-silicon defect-mediated avalanche photodetector is shown to have a 3 dB RF amplification compared to the same PIN detector. All ring delay measurement results are validated by full-wave simulation. Additionally, the impact of photodetector biasing and system linearity is analyzed.

"Conical" Frustum Multi-Beam Phased Arrays for Air Traffic Control Radars.

The design of conical frustum phased array antennas for air traffic control (ATC) radar systems is addressed. The array architecture, which is controlled by a fully digital beam-forming (DBF) network, is composed by a set of equal vertical modules. Each module consists of a linear sparse array that generates on receive multiple instantaneous beams pointing along different directions in elevation. To reach the best trade-off between the antenna complexity (i.e., minimum number of array elements and/or radio frequency components) and radiation performance (i.e., matching a set of reference patterns), the synthesis problem is formulated in the Compressive Sampling (CS) framework. Then, the positions of the array elements and the complex excitations for generating each single beam are jointly determined through a customized version of the Bayesian CS (BCS) tool. Representative numerical results, concerned with ideal as well as real antenna models, are reported both to validate the proposed design strategy and to assess the effectiveness of the synthesized modular sparse array architecture also in comparison with conventional arrays with uniformly-spaced elements.

Wideband Beam-Forming Networks Utilizing Planar Hybrid Couplers and Phase Shifters

In this article, a new approach to designing 6 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> 6 beamforming networks (BFNs) for producing five or six beams is presented. The configuration of the 6 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> 6 BFNs is designed utilizing planar wideband hybrid couplers and phase shifters. A new type of wideband hybrid coupler is built based on a slotline resonator and microstrip-to-slotline transitions. The proposed coupler design can achieve high level of isolation between the sum and difference ports. Two different formats of wideband 6 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> 6 BFNs are then developed, to generate five and six beams, respectively. A prototype is fabricated and tested, and the experimental results agree with the simulation ones very well, achieving a wide operating bandwidth of more than 30%. Finally, the BFN is verified by feeding a six-element array, and the realized patterns match the predicted ones very well, demonstrating the function of the BFN. The topology of an extended 12 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times12$ </tex-math></inline-formula> BFN is also given to demonstrate the possibility of creating higher-order BFNs using the presented approach.

W-Band Binary Phase-Controlled Multibeam Antenna Array Based on Gap Waveguide Magic-Tee

In this article, a compact 94 GHz multibeam antenna array based on the binary phase-controlled concept is proposed. The feeding network is composed of four unconnected layers, and the ridge or groove gap waveguides are adopted as the guided wave structures. A key planar gap waveguide Magic-Tee is designed to obtain 0° and 180° phase states and then integrates with an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$8\,\times \,8$ </tex-math></inline-formula> slot antenna array to achieve multibeam operation for the first time. Compared with the traditional phased array and passive beamforming networks (BFNs), the feeding design is simple in construction, consisting of only Magic-Tees and cascaded power dividers without any phase shifters. Benefiting from the gap waveguide technology, the antenna array does not require electrical contact among the metal layers, so it is simple and low cost to manufacture. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$8\times8$ </tex-math></inline-formula> slot antenna array can easily switch among one-beam and three different dual-beam states that point to ±7°, ±17°, and ±38°. The measurement results of 6.6% bandwidth from 91.7 to 98 GHz for both reflection coefficients <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$&lt; -10$ </tex-math></inline-formula> dB and isolations >25 dB are achieved. The proposed multibeam antenna array would be an attractive candidate for millimeter-wave multiuser communication where it requires multiple beams simultaneously.

Low-Profile Dual-Polarized Multi-Beam Antenna Based on Pillbox Reflector and 3D-Printed Ridged Waveguide

In this article, a dual-polarized multibeam antenna is proposed. Two orthogonally polarized slotted waveguide antennas (SWAs) are cross-placed as the main radiator, which is designed based on ridged waveguides (RGWs) to reduce the width of the waveguides and obtain a wider steering range. The two SWAs are fed by two pillbox reflector beamforming networks (BFNs), and a special impedance transition is designed to reduce the reflection between the quasi-TEM wave in the parallel-plate waveguide (PPW) to the TE10 wave. By exciting different feeding patches in the focal planes of the pillbox reflectors, the SWA achieves different beams. In order to further increase the crossover level, the single-port excitation (SPE) and the dual-port excitation (DPE) method are used together to increase the equivalent source number in the compact area of the focal plane. Besides, the DPE method can also reduce the sidelobe level (SLL) of the beams excited by the side ports. A prototype is designed at the operating frequency of 10 GHz and fabricated by the 3-D-printed technology and computer numerical control (CNC) technology. The measured results show that the proposed antenna achieves ± 36° beam scanning in the multibeam plane with the minimum crossover level of −2.1 dB. The cross polarizations are below −20.0 and −15.9 dB for the horizontal polarization (H-P) and the vertical polarization (V-P), respectively. The advantages of dual polarization, high aperture efficiency, low cross polarization, wide beam scanning range, and low crossover level make this antenna a very appropriate choice in multibeam radars and communication systems.

A General Approach for Synthesizing Multibeam Antenna Arrays Employing Generalized Joined Coupler Matrix

Despite the rapidly increasing interest in analog multibeam antennas, there has been a lack of systematic theoretical approaches to synthesizing circuit-type multiple beamforming networks, such as the Blass matrix and the Nolen matrix. To address the issue, this article presents a new concept, the generalized joined coupler (GJC) matrix, which encapsulates both the Blass matrix and the Nolen matrix, as well as their variants, and presents a novel theoretical framework for generating individually and independently controllable multiple beams using the GJC matrix. A GJC matrix has <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N $ </tex-math></inline-formula> columns to feed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N $ </tex-math></inline-formula> antenna elements and <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> rows to feed <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> beams, and the direction of each individual beam can be controlled by tuning the phase shifters in the associated row of the GJC matrix. In this article, a matrix theory is developed, and an optimization algorithm is proposed to provide a mathematical tool for synthesizing such matrices and, consequently, the multiple beams. Using a particle swarm optimization algorithm, numerical results demonstrate that multibeams with independent control of individual beam directions and sidelobes can, indeed, be synthesized in a systematic manner. Specifically, two GJC matrix variants, the Blass-like matrix and the Nolen-like matrix, are investigated.

A progressively dual reconstruction network for plane wave beamforming with both paired and unpaired training data

High-frame-rate plane wave (PW) imaging suffers from unsatisfactory image quality due to the absence of focus in transmission. Although coherent compounding from tens of PWs can improve PW image quality, it in turn results in a decreased frame rate, which is limited for tracking fast moving tissues. To overcome the trade-off between frame rate and image quality, we propose a progressively dual reconstruction network (PDRN) to achieve adaptive beamforming and enhance the image quality via both supervised and transfer learning in the condition of single or a few PWs transmission. Specifically, the proposed model contains a progressive network and a dual network to form a close loop and provide collaborative supervision for model optimization. The progressive network takes the channel delay of each spatial point as input and progressively learns coherent compounding beamformed data with increased numbers of steered PWs step by step. The dual network learns the downsampling process and reconstructs the beamformed data with decreased numbers of steered PWs, which reduces the space of the possible learning functions and improves the model’s discriminative ability. In addition, the dual network is leveraged to perform transfer learning for the training data without sufficient steered PWs. The simulated, in vivo, vocal cords (VCs), and public available CUBDL dataset are collected for model evaluation.

Analysis and design of ultra-wideband PRGW hybrid coupler using PEC/PMC waveguide model

In this paper, a new method to facilitate the design of Printed Ridge Gap Waveguide (PRGW) structures is introduced. One of the main difficulties in designing such structures is related to their simulation process which is really time and energy-consuming. Therefore, a suitable boundary condition is considered to bring about the primary structure without involving the bed of nails or mushroom unit cells. Using this technique, a wideband PRGW 3 dB hybrid double-box coupler is designed to serve in mm-wave frequencies at a center frequency of 30 GHz, which can be deployed for the next generation of mobile communication. The designed coupler provides a wide matching and isolation bandwidth with low output amplitude imbalance, which is unique in comparison with current couplers. The prototype of the proposed coupler is fabricated and measured where the simulation and measurement results show a good agreement indicating the strength of the proposed method in PRGW structure design as well. The measured results show the couplers achieve better than 10-dB return loss and isolation over the frequency range from 25 to 40 GHz (46% BW) with the power-split unbalance and phase error within ± 1 dB and ± 5°, respectively. In addition, square mushrooms are chosen here to satisfy the high impedance surface. Not only do they bring about larger stop bandwidth, but also their configuration facilitates the arrangement of them around the coupler. The proposed design has superb characteristics such as low profile, low loss, and easy integration with microwave circuits and systems that can be suitable for designing mm-wave beamforming networks.

A novel single layer SIW 6 × 6 beamforming network for 5G applications

A novel single layer 6 × 6 beamforming network (BFN) based on substrate integrated waveguide (SIW) is proposed for 5G applications. The proposed BFN is realized by 3 × 3 multi-aperture couplers (MACs), hybrid couplers, phase shifters, and crossovers. The BFN is designed for equal power division and ± 30°, ± 90°, ± 150° phase difference between output signals in the 28–32 GHz frequency band. By feeding a 6 × 2 SIW slot antenna array with proposed BFN, a six-beam antenna is implemented that generates six symmetrical beams in the ± 11°, ± 31°, and ± 52° directions. To confirm the simulation results, the proposed six-beam antenna is fabricated and measured. The simulation and measurement results show that the six-beam antenna has good radiation patterns, −10 dB impedance bandwidth from 28 GHz to 32 GHz, and a 3-dB wide-angle coverage of about 150°. The size of the antenna is 106 × 31.8 × 0.787 mm3, which is suitable for 5G applications.

6 GHz Altı 5G Kablosuz Haberleşme Uygulamalarında Butler Matris Besleme Hattı İçin Küçük Boyutlu Atlama Tasarımı

The butler matrix is one of the passive feeding networks used with array antennas to form beams. There are several advantages to using this beamforming network. One of them is that it is easy to manufacture, and the other is that it is low in cost. Butler matrix structure consists of three passive microwave components. These are directional hybrid couplers, phase shifters, and crossovers. A crossover is a passive microwave component used to cross between two lines with high isolation between them. This article presents microstrip crossover for use in Butler matrix feeding networks designed for 5G applications. The crossover has been presented in the article was designed and simulated. The proposed crossover operates at 4.5 GHz and it is designed for use in mostly butler matrix applications. The crossover has been proposed in the article has been designed using the FR-4 substrate. The dielectric constant of the used substrate is 4.3 and the thickness is 1.57 mm. The size of the designed crossover is 62.8 x 27.8 mm^2. The reflection coefficient and isolation level are in the permissible level in order for the proposed crossover to be utilized in the Butler matrix beamforming network for 5G the application. The return loss value of the designed crossover is 26.09 dB at 4.5 GHz. Same time the isolation value is 22.78 dB.

A Pillbox Based Dual Circularly-Polarized Millimeter-Wave Multi-Beam Antenna for Future Vehicular Radar Applications

In this paper, a dual circularly-polarized (CP) multi-beam antenna is proposed for future vehicular radar applications. The antenna is composed of two pillbox reflector beamforming networks (BFNs) and a series-fed microstrip line based dual CP leaky-wave antenna (LWA) array, which has a symmetrical structure and can obtain both left hand circular polarization (LHCP) and right hand circular polarization (RHCP) by switching the exciting current direction of the microstrip line. Besides, a shorted stub is loaded in the LWA to suppress the open-stop band (OSB), and thus achieve the broadside radiation and good impedance matching of the LWA. To realize the dual-polarized radiation characteristic with low-cost passive beam scanning capability, two pillbox BFNs are connected at both sides of the LWA to share the LWA aperture. The two different BFNs can excite different CP radiation patterns. A prototype of the proposed antenna is fabricated in the frequency band 23.5–24.5 GHz, and the measured results approve that the proposed antenna can realize ±36° beam scanning range with −4.0 dB crossover level, and the gain is higher than 17.7 dBi in the operating band. The advantages of the proposed antenna, including low-profile, low-cost, passive beam scanning ability, and dual circular polarization, make it an attractive choice for low-cost millimeter-wave radar applications.

Hybrid Beamforming Based on an Unsupervised Deep Learning Network for Downlink Channels With Imperfect CSI

Hybrid beamforming can provide rapid data transmission rates while reducing the complexity and cost of massive multiple-input multiple-output (MIMO) systems. However, channel state information (CSI) is imperfect in realistic downlink channels, introducing challenges to hybrid beamforming (HBF) design. This letter proposes an unsupervised deep learning neural network (USDNN) for hybrid beamforming to prevent the labeling overhead of supervised learning and improve the achievable sum rate based on imperfect CSI. The simulation results show that our proposed method is 74% better than MO and 120% better than orthogonal match pursuit (OMP) systems; our proposed USDNN can achieve near-optimal performance.

Synthesis Method of an Orthogonal Beamforming Network With Arbitrary Ports for Shaped Beams

This article proposes a synthesis method of orthogonal beamforming networks (BFNs) with arbitrary ports. The proposed method is based on matrix decomposition theory and breakthrough the synthesized BFN number to arbitrary. It has been theoretically demonstrated that the BFN with cascading 180° hybrid couplers can synthesize shaped beams. Therefore, a BFN synthesis method that combines the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">QR</i> decomposition theory and the optimization algorithm is introduced. With the help of an optimization program, a specific power ratio of each 180° hybrid coupler in the BFN is determined. The proposed synthesis method is verified by experiments with an orthogonal <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$6\times2$ </tex-math></inline-formula> BFN with flat-topped radiation patterns. Through optimization, five 180° hybrid couplers with different power ratios synthesize the proposed BFN. Results show that two flat-topped beams with a beamwidth of (32° ± 0.3°), gain ripples less than 2.5 dB, and a sidelobe level less than 12 dB are achieved. The proposed method has the advantages of high accuracy and efficiency and a simple structure, which makes it convenient for multi-beam antenna arrays in multiple-input–multiple-output (MIMO) systems.