Amplitude Constraints Research Articles

A Phase-Only Optimization Null Control Method for FDA-MIMO Based on ADMM

This paper investigates null control within the transmit–receive beampattern of Frequency Diverse Array-Multiple-Input and Multiple-Output (FDA-MIMO) systems, presenting a novel phase-only optimization approach for achieving null control in FDA-MIMO. We employ an alternating multiplier framework, which transforms the intricate and inherent constant modulus constraint and numerous amplitude constraints in optimization into more manageable projection problems. By employing a phase-only optimization strategy, the intricate hardware and computational burdens associated with null control in FDA-MIMO are effectively alleviated. The simulation results indicate that the algorithm proposed in this paper exhibits excellent null control ability while precisely maintaining constant modulus constraints, and it possesses an extremely high computational efficiency.

Single-shot dual-wavelength telecentric in-line-and-off-axis hybrid digital holography with non-prior reconstruction

Dual-wavelength in-line-and-off-axis hybrid digital holography (iohDH) can achieve high-resolution holographic dynamic imaging. However, it requires the prediction of the diffraction distance and the complex amplitude of the reference beam, which is time consuming and results in complications and accuracy limitations. While telecentric imaging technique can obtain nondiffractive images without predicting the diffraction distance, it also can even eliminate spherical aberration and astigmatic aberration. Therefore, a dual-wavelength telecentric iohDH is proposed to realize non-prior high-resolution reconstruction in a single shot. Employing the dual-wavelength telecentric iohDH, our approach acquires the focused in-line-and-off-axis hologram using a color camera in a single shot. In this case, we perform wavelength conversion on the phase and low-frequency information about the off-axis hologram as constraints for in-line iteration. Then, the in-line amplitude constraints are performed in the spatial and frequency domains until the algorithm converges. Compared to the state-of-the-art dual-wavelength iohDH, our approach can streamline the reconstructed processes without demanding a priori information of the diffraction distance and the complex amplitude of the reference beam. More importantly, our approach enables higher quality and efficient reconstruction under the telecentric system. We verified our approach using simulations and experiments, and the results indicate that our approach can allow the amplitude and phase reconstruction with high resolution in a single shot.

Array pattern synthesis with phase-only constraint based on scaled-ADMM algorithm

The utilization of constant modulus beamforming technology is prevalent in multiple-input multiple-output (MIMO) radar systems and MIMO wireless communication systems. This paper investigates the problem of phase-only pattern control and synthesis in linear antenna array systems. It imposes a fixed amplitude constraint on the excitation signal, which only involves a phase constraint. However, this constraint is NP-hard and non-convex. To effectively address this challenging problem, we propose an iterative solution based on the scaled form of ADMM. This solution provides a means to rapidly synthesize patterns and significantly contributes to mitigating interference in other directions. In addition, the convergence of the proposed method is proved theoretically, and it is further demonstrated that the algorithm converges to the KKT stationary point of the original problem. Finally, simulation results show that the proposed method is superior to the most advanced methods in terms of pattern synthesis and convergence speed.

Lensless Imaging Based on Dual‐Input Physics‐Driven Neural Network

Lensless imaging, as a novel computational imaging technique, has attracted great attention due to its simplicity, compactness, and flexibility. This technique analyzes and processes the diffraction of an object to obtain complex amplitude information. However, traditional algorithms such as Gerchberg‐Saxton (G–S) algorithm tend to exhibit significant errors in complex amplitude retrieval, particularly for edge information. Additional constraints have to be incorporated on top of amplitude constraints to enhance the accuracy. Recently, deep learning has shown promising results in optical imaging. However, it requires a large amount of training data. To address these issues, a novel approach called dual‐input physics‐driven network (DPNN) is proposed for lensless imaging. DPNN utilizes two diffractions recorded at different distances as inputs and uses an unsupervised approach that combines physical imaging model to reconstruct object information. DPNN adopts a U‐Net 3+ architecture with a loss function of mean absolute error (MAE) to better capture diffraction features. DPNN achieves highly accurate reconstruction without requiring extensive data and being immune to background noise. Based on different diffraction intervals, noise levels, and imaging models, DPNN exhibits superior capabilities in peak signal‐to‐noise ratio and structural similarity compared with conventional methods, effectively achieving accurate phase or amplitude information reconstruction.

Spectral Efficiency Maximization for Mixed-Structure Cognitive Radio Hybrid Wideband Millimeter-Wave Transceivers in Relay-Assisted Multi-User Multiple-Input Multiple-Output Systems.

This paper proposes a cognitive radio network (CRN)-based hybrid wideband precoding for maximizing spectral efficiency in millimeter-wave relay-assisted multi-user (MU) multiple-input multiple-output (MIMO) systems. The underlying problem is NP-hard and non-convex due to the joint optimization of hybrid processing components and the constant amplitude constraint imposed by the analog beamformer in the radio frequency (RF) domain. Furthermore, the analog beamforming solution common to all sub-carriers adds another layer of design complexity. Two hybrid beamforming architectures, i.e., mixed and fully connected ones, are taken into account to tackle this problem, considering the decode-and-forward (DF) relay node. To reduce the complexity of the original optimization problem, an attempt is made to decompose it into sub-problems. Leveraging this, each sub-problem is addressed by following a decoupled design methodology. The phase-only beamforming solution is derived to maximize the sum of spectral efficiency, while digital baseband processing components are designed to keep interference within a predefined limit. Computer simulations are conducted by changing system parameters under different accuracy levels of channel-state information (CSI), and the obtained results demonstrate the effectiveness of the proposed technique. Additionally, the mixed structure shows better energy efficiency performance compared to its counterparts and outperforms benchmarks.

Active Flutter Suppression: Quantification of Performance Loss Due to Actuator Saturation

Active flutter suppression technologies have the potential to lead to major weight savings while keeping the envisaged flight envelope for the future generation of commercial aircraft. Since the stabilization of aeroelastic systems undergoing flutter instabilities is strongly affected by actuators’ characteristics and delays in the closed loop, the degradation of closed-loop performance due to actuators’ nonlinearities must be thoroughly understood. Comparisons between the region of attraction and the controllable region can support the quantification of performance loss due to common actuators’ nonlinearities, such as amplitude and rate limits. At first, this paper illustrates a numerically robust algorithm for the full characterization of the controllable region of a generic unstable system under input amplitude and rate constraints. Secondly, the concept of region of attraction is expanded to assess the boundedness of the closed-loop response in the presence of input saturation and atmospheric disturbances. These concepts are here employed to define two nonlinear performance measures that quantify the performance loss due to actuators’ saturation in an unstable aeroelastic system stabilized by a flutter suppression controller. The approach is demonstrated on a realistic aeroelastic system for which different H2 and H∞ output feedback controllers are synthesized to augment the damping of the critical flutter mode.

Interrupted-sampling multi-strategy forwarding jamming with amplitude constraints based on simultaneous transmission and reception technology

The interrupted-sampling repeater jamming (ISRJ) is a mainstream jamming method in electronic warfare, simple yet implemented. With the rapid development of anti-ISRJ, due to the defects of ISRJ and the difficulty in ensuring real-time response, there is an urgent need to propose a new ISRJ-based jamming method based on simultaneous transmission and reception (STAR) technology. An interrupted-sampling multi-strategy forwarding jamming (ISMSFJ) with amplitude constraints is proposed by utilizing the characteristics of interrupted sampling in this paper. By modulating different interrupted sampling pulses on the intercepted signal and accurately controlling the delay time and weighting coefficient, it not only destroys the space distribution law of false targets, shortens the response time of the jammer, but also enhances the jamming amplitude or broadens the jamming range. For radar receivers, the jamming overlaps with the time-frequency information of the radar echo signal, and the time-frequency analysis anti-jamming algorithm fails. It can effectively resist the Fractional Fourier Transform anti-jamming algorithm for interpulse and intrapulse frequency-agile signals. The validity of the jamming technology is verified by theoretical analysis and simulation.

Electromagnetohydrodynamic flow through a periodically grooved channel

This paper harnesses the spectral approach to study electromagnetohydrodynamics (EMHD) flow through an undulating 2D microchannel for a Newtonian fluid. The present study aims to investigate EMHD flow through a periodically patterned channel for large values of corrugation amplitude (surface roughness) relative to the channel height, Hartmann number and a wide range of wavelengths. A mathematical model is developed for the hydraulic permeability and the velocity field using the Fourier approach. By imposing a small pattern amplitude constraint, asymptotic analysis was employed to investigate the model presented in the literature. In the present study, hydraulic permeability is shown to strongly depend on the Hartmann number, pattern amplitude and wavelength. The spectral method predicts a monotonic decrease in hydraulic permeability irrespective of pattern amplitude at a small dimensionless wavelength (λ = 1) and Hartmann number (Ha < 1). At large wavelengths (λ > 3), the hydraulic permeability demonstrates an augmentation corresponding to the pattern amplitude. At intermediate wavelength ( 2.5<λ<3 ), the permeability of the channel firstly decreases and then increases with pattern amplitude. For large Hartmann numbers (Ha≫1) , the prediction from the spectral model exhibits a similar trend as a function of wavelength. Across a range of wavelengths, the spectral model captured the permeability minima for various large Hartmann number values. The spectral model is significantly faster than the finite-element-based numerical simulation, with computational efficiency ranging from 150 to 250 times higher. The existence of a limited pattern amplitude and Hartmann number for small-large wavelength patterns, at which the permeability of the channel is minimized, is one example of a prediction from the spectral model that is beyond the resolution of currently accessible asymptotic theories.

Dual-constrained physics-enhanced untrained neural network for lensless imaging.

An untrained neural network (UNN) paves a new way to realize lensless imaging from single-frame intensity data. Based on the physics engine, such methods utilize the smoothness property of a convolutional kernel and provide an iterative self-supervised learning framework to release the needs of an end-to-end training scheme with a large dataset. However, the intrinsic overfitting problem of UNN is a challenging issue for stable and robust reconstruction. To address it, we model the phase retrieval problem into a dual-constrained untrained network, in which a phase-amplitude alternating optimization framework is designed to split the intensity-to-phase problem into two tasks: phase and amplitude optimization. In the process of phase optimization, we combine a deep image prior with a total variation prior to retrain the loss function for the phase update. In the process of amplitude optimization, a total variation denoising-based Wirtinger gradient descent method is constructed to form an amplitude constraint. Alternative iterations of the two tasks result in high-performance wavefield reconstruction. Experimental results demonstrate the superiority of our method.

Controllers for Multiagent Systems With Input Amplitude and Rate Constraints and Their Application to Quadrotor Rendezvous

Controllers for Multiagent Systems With Input Amplitude and Rate Constraints and Their Application to Quadrotor Rendezvous

An improved algorithm for diffractive optical element with high imaging quality

An improved algorithm for diffractive optical element (DOE) with high imaging quality is proposed in this paper. The algorithm is designed based on amplitude division between signal and noise regions, further subdivides the noise region into two distinct parts. The image quality in the signal region will be effectively improved by employing a partition-constraint strategy, which imposes amplitude freedom on the first noise region while enforcing strict amplitude constraints on the second noise region. The principle of the algorithm, simulation analysis, and experimental results are presented. The simulation and experimental results demonstrate that the algorithm is feasible.

Hybrid Wideband Beamforming for Sum Spectral Efficiency Maximization in Millimeter-Wave Relay-Assisted Multiuser MIMO Cognitive Radio Networks

Relay-assisted hybrid beamforming plays an inevitable role in enhancing network coverage, transmission range, and spectral efficiency while simultaneously reducing hardware cost, power consumption, and hardware implementation complexity. This study investigates a cognitive radio network (CRN)-based hybrid wideband transceiver for millimeter-wave (mm-wave) decode-and-forward (DF) relay-assisted multiuser (MU) multiple-input multiple-output (MIMO) systems. It is worth mentioning that the underlying problem has not been addressed so far, which is a real motivation behind the proposed algorithm. The joint optimization of hybrid processing components and the constant amplitude constraints imposed by the analog beamforming solution make this problem non-convex and NP-hard. Furthermore, the analog beamformer common to all sub-carriers is another challenging aspect of the underlying problem. To derive the frequency-flat analog processing component in the radio frequency (RF) domain and frequency-dependent baseband processing matrices in the baseband domain, the original complicated problem is reformulated as two single-hop sum-rate maximization sub-problems. Taking advantage of this decomposition, the sum spectral efficiency is maximized through RF precoding and combining. On the other hand, the impact of interference among transmitted data streams and inter-user interference (IUI) is minimized via baseband processing matrices. Finally, computer simulations are conducted by changing system parameters, considering both perfect and imperfect channel state information (CSI). Simulation results demonstrate that the proposed algorithm achieves performance close to full-complexity precoding and outperforms other well-known hybrid beamforming techniques. Specifically, more than 95% efficiency is achieved with perfect CSI, and more than 90% efficiency is attained under the assumption of 30% error in the estimated channels.

Amplitude-Constrained Constellation and Reflection Pattern Designs for Directional Backscatter Communications Using Programmable Metasurface

The large scale reflector array of programmable metasurfaces is capable of increasing the power efficiency of backscatter communications via passive beamforming and thus has the potential to revolutionize the low-data-rate nature of backscatter communications. In this paper, we propose to design the power-efficient higher-order constellation and reflection pattern under the amplitude constraint brought by backscatter communications. For the constellation design, we adopt the amplitude and phase-shift keying (APSK) constellation and optimize the parameters of APSK such as ring number, ring radius, and inter-ring phase difference. Specifically, we derive closed-form solutions to the optimal ring radius and inter-ring phase difference for an arbitrary modulation order in the decomposed subproblems. For the reflection pattern design, we propose to optimize the passive beamforming vector by solving a multi-objective optimization problem that maximizes reflection power and guarantees beam homogenization within the interested angle range. To solve the problem, we propose a constant-modulus power iteration method, which is proven to be monotonically increasing, to maximize the objective function in each iteration. Numerical results show that the proposed APSK constellation design and reflection pattern design outperform the existing modulation and beam pattern designs in programmable metasurface enabled backscatter communications.

A revised BDS Klobuchar model with a non-symmetrical processing strategy and a high-latitude amplitude constraint

The BeiDou Navigation Satellite System (BDS) broadcasts the BDS Klobuchar model (BDSK) for ionospheric delay correction in both BDS-2 regional service phase and BDS-3 global service phase. Unlike the GPS Klobuchar model, the BDSK model adopts a simple “symmetrical strategy” due to the limited ionospheric input data within China, which results in inaccurate total electron content (TEC) estimation in the southern hemisphere. Besides, the “high latitude anomaly” occurs in the BDSK model due to the lack of latitude limitation strategy, which deteriorates the accuracy of the BDSK model in the southern hemisphere further. To solve this problem, we propose a revised BDS Klobuchar model (RBDK), in which the “non-symmetrical strategy” is adopted in the southern hemisphere and an amplitude constraint is introduced at high latitudes. For comparison, the fitted BDS Klobuchar model (BDFK) that is estimated using the same ionospheric input data and constraint algorithm for the RBDK model but with the “symmetrical strategy” is also included. First, we conduct a comparative analysis of the time series of the eight parameters for the BDSK, BDFK and RBDK models in 2021. The parameters of the BDFK and RBDK models are more stable, and there will be no abnormal jumping phenomenon that occurs in the BDSK model. Then, the performance of the broadcast BDSK model, the fitted BDFK model and the proposed RBDK model during the whole year of 2021 are evaluated by comparing them with the high-precision global ionospheric map (GIM) of the International GNSS Service (IGS). In the southern hemisphere, the root mean square (RMS) values of the BDSK and BDFK are 6.5 and 5.8 TEC unit (TECU), respectively, while that of the RBDK is 4.6 TECU, showing improvements of 29% and 21%, respectively. At high latitudes in the northern hemisphere, the RMS value of the BDSK is 7.6 TECU, while they are only 3.7 TECU for the RBDK and BDFK when the amplitude constraint is introduced. Final, we select 16 IGS stations to validate the performance of the BDSK, BDFK and RBDK models in the standard point positioning (SPP) domain in 2021. The average SPP accuracy of the BDSK is 8.88 m at 6 high-latitude stations, while they are 5.48 m for the RBDK and BDFK, showing significant improvement of 38%. Excluding the high-latitude stations, the SPP accuracy of the RBDK outperforms the BDFK and BDSK by 14% and 18%, respectively, at stations in the southern hemisphere. As expected, the proposed RBDK model shows significantly better performance in the southern hemisphere and at high latitudes in contrast to the broadcast BDSK model.

Sum and difference patterns synthesis with common excitation amplitude

This paper focuses on the joint optimization problem of sum and difference patterns with common excitation amplitudes and separate excitation phases. The objective is to reduce the complexity of the antenna system while still maintaining a certain degree-of-freedom (DoF) in synthesizing dual-patterns. The problem is formulated with angular response and common excitation amplitude constraints, making it a nonconvex optimization problem. To address this, we introduce two groups of auxiliary variables to decouple the excitation vector from the complex nonconvex constraints. This allows the original problem to be effectively solved via alternately determining the closed-form solutions for several single-variable optimization subproblems. Additionally, our approach is extended to scenarios involving dynamic range ratio (DRR) reduction, aiming to lower the cost and difficulty of hardware implementation. Theoretical analysis and simulation results are provided to demonstrate that the proposed algorithm can converge to the Karush-Kuhn-Tucker points of the original problem. It is also observed that our approach is capable of generating desired dual-patterns with common excitation amplitudes, regardless of the presence or absence of DRR control.

Camouflaged cryptosystem based on optical diffractive imaging

A camouflaged cryptosystem based on optical diffractive imaging is proposed in this paper. During the encryption process, a camouflaged image is first encoded into an intensity image by optical diffractive imaging, which is stored and transmitted as a fake ciphertext. Then a secret image is encoded into two generated phase masks(GPMs) with the fake ciphertext as the amplitude constraint by cascading phase encoding. The ciphertext and random phase masks(RPMs) used in the optical diffractive imaging are transmitted to the receivers via a common channel, while GPMs are transmitted via a private channel. The common channel can be accessed by both authorized receivers and potential illegal intruders. Therefore, illegal intruders can just obtain the camouflaged image by the fake ciphertext and RPMs, while only authorized receivers with the fake ciphertext and GPMs can retrieve the secret image. The decoded camouflaged image would confuse the illegal users and provide additional security protection for the secret image. The feasibility and security of this cryptosystem would by verified by several simulation experiments.

On Optimally Shaped Signals for Nonlinear Frequency Division Multiplexed Fiber Systems

An approximated channel model is proposed for direct signaling on the continuous spectrum of a nonlinear frequency division multiplexed (NFDM) communication system, describing the effect of noise and nonlinearity at the receiver. The optimal input distribution that maximizes the mutual information of the proposed approximated channel under the peak amplitude constraint is then studied. We present that, considering the input-dependency of the noise, the conventional amplitude-constrained constellation designs can be geometrically shaped to provide significant mutual information gains. However, it is observed that further probabilistic shaping and constellation size optimization can provide only limited additional gains beyond the best geometrically shaped benchmark scheme, i.e., 64 Amplitude Phase Shift Keying. Then, an approximated channel model that neglects the correlation between subcarriers is proposed for the matched filtered signaling system, based on which the input constellation is geometrically shaped. We demonstrate that although the inter-subcarrier interference in the filtered case is neglected in the channel model, the shaping of the matched filtered case can provide promising gains in mismatch capacity over the unfiltered scenario.

Multiplane full-color phase-only holograms generation based on iterative algorithm with a modified amplitude constraint

Depth-division multiplexing (DDM) is distinguished for generating full-color holograms. However, this method is confronted with such issues as poor quality and severe crosstalk when reconstructing multiplane color images. In this paper, we propose an improved iterative method based on Gerchberg-Saxton (GS) algorithm to generate multiplane full-color phase-only holograms (POHs), and the information of red (R), green (G), and blue (B) channels of images is recorded in three POHs, respectively. In the iterative process, we introduce an improved hologram plane constraint that consists of modified amplitudes given a static weighting factor, and display the reconstruction results for three-layer images, which ultimately improve the quality of the reconstructed images and effectively avoid the crosstalk among different color channels. And compared with GS algorithm, our method can effectively balance the reconstruction quality of three-color channels of each image. The feasibility of the method is verified by numerical simulations and optical experiments.

Ptychographical iterative engine based on pixel binning for improving the computational efficiency

Ptychographical iterative engine (PIE) is an attractive modality of phase retrieval that can provide the quantitative phase of the sample and extend the field of view. For a large sample, a great deal of images with a large dataset are recorded, which will result in high requirements for the computing power and increase the calculation burden. Here, we propose a pixel binning strategy to improve the computational efficiency and reduce the calculation time of PIE. In this method, the recorded image chosen as the amplitude constraint in reconstruction algorithm is compressed by merging the amplitude values of the adjacent positions into one value by the linear superposition, and the compressed pattern is set as a new amplitude constraint to reconstruct the compressed object and probe with fewer pixel number and larger grid size compared to the uncompressed results. Then, the compressed values are extended by the interpolation method. The improvement in the computational efficiency at the point lies in the fact that it takes less time to do the free-space diffraction propagation calculation for images with fewer pixel number. Experiments demonstrate that the proposed method behaves good performance with high computational efficiency. The proposed approach would be helpful for large-scale imaging with high computational efficiency.

Quantum Goemans-Williamson Algorithm with the Hadamard Test and Approximate Amplitude Constraints

Semidefinite programs are optimization methods with a wide array of applications, such as approximating difficult combinatorial problems. One such semidefinite program is the Goemans-Williamson algorithm, a popular integer relaxation technique. We introduce a variational quantum algorithm for the Goemans-Williamson algorithm that uses only n+1 qubits, a constant number of circuit preparations, and poly(n) expectation values in order to approximately solve semidefinite programs with up to N=2n variables and M&amp;#x223C;O(N) constraints. Efficient optimization is achieved by encoding the objective matrix as a properly parameterized unitary conditioned on an auxilary qubit, a technique known as the Hadamard Test. The Hadamard Test enables us to optimize the objective function by estimating only a single expectation value of the ancilla qubit, rather than separately estimating exponentially many expectation values. Similarly, we illustrate that the semidefinite programming constraints can be effectively enforced by implementing a second Hadamard Test, as well as imposing a polynomial number of Pauli string amplitude constraints. We demonstrate the effectiveness of our protocol by devising an efficient quantum implementation of the Goemans-Williamson algorithm for various NP-hard problems, including MaxCut. Our method exceeds the performance of analogous classical methods on a diverse subset of well-studied MaxCut problems from the GSet library.