Worst-case Performance Optimization Research Articles

High-performance deep-sea long-range underwater acoustic communication: Deconvolved conventional beamforming based approach

To address the challenges posed by large propagation loss and severe multipath delay spread, while aiming to improve communication rates in long-range underwater acoustic (UWA) communication, this paper introduces a novel approach: multi-beam (MB) Orthogonal Frequency Division Multiplexing (OFDM) based on deconvolved conventional beamforming (dCv). The proposed method establishes a signal processing framework for UWA channel receivers, wherein received signals corresponding to each angle beam are isolated and concentrated using the dCv technique. Subsequently, the separated signals from each angle undergo maximal-ratio combining (MRC) channel equalization followed by demodulation. Compared to conventional single-beam (SB) processing methods, the proposed approach capitalizes on multipath diversity gain achieved by combining MB outputs originating from various arrival angles. Moreover, employing dCv processing demonstrates superior performance compared to popularly employed beamforming techniques, especially when dealing with paths arriving from closely aligned angles. Additionally, the array beamforming utilized significantly enhances the signal-to-noise ratio (SNR) of each beam output, mitigating the elevated error rates in channel estimation associated with combining low SNR signals received from individual elements. Simulation results utilizing BELLHOP and experimental data from the South China Sea showcase notably improved bit error rate (BER) performance for the proposed method compared to SB equalization, MB-MRC equalization based on conventional beamforming (CBF), minimum variance distortionless response (MVDR), and worst-case performance optimization (WCPO), as well as standard MRC equalization techniques. The proposed receiver achieves error-free decoding results at a communication distance of 80 km with a data rate of 247 bps.

On the 2D Beampattern Optimization of Sparse Group-Constrained Robust Capon Beamforming with Conformal Arrays

To overcome the problems of the high sidelobe levels and low computational efficiency of traditional Capon-based beamformers in optimizing the two-dimensional (elevation–azimuth) beampatterns of conformal arrays, in this paper, we propose a robust Capon beamforming method with sparse group constraints that is solved using the alternating-direction method of multipliers (ADMM). A robustness constraint based on worst-case performance optimization (WCPO) is imposed on the standard Capon beamformer (SCB) and then the sparse group constraints are applied to reduce the sidelobe level. The constraints are two sparsity constraints: the group one and the individual one. The former was developed to exploit the sparsity between groups based on the fact that the sidelobe can be divided into several different groups according to spatial regions in two-dimensional beampatterns, rather than different individual points in one-dimensional (azimuth-only) beampatterns. The latter is considered to emphasize the sparsity within groups. To solve the optimization problem, we introduce the ADMM to obtain the closed-form solution iteratively, which requires less computational complexity than the existing methods, such as second-order cone programming (SOCP). Numerical examples show that the proposed method can achieve flexible sidelobe-level control, and it is still effective in the case of steering vector mismatch.

Design of Robust Sparse Wideband Beamformers with Circular-Model Mismatches Based on Reweighted ℓ2,1 Optimization

Wideband beamformers have been widely studied in wireless communication, remote sensing and so on. Generally speaking, to improve the spatial filtering ability of beamformers, there usually needs more sensors, which implies increased computational complexity and hardware costs. Besides that, wideband beamformers are known to be exceedingly sensitive to sensor mismatches in practice. Nevertheless, there is still a gap in research on the design of robust sparse wideband beamformers. In this paper, a two-step design of this topic is proposed. Firstly, a robust design based on the worst-case performance optimization (WCPO) using circular-model (CM) sensor mismatches is reformulated to address shortcomings of constraint sensitivity. Secondly, inspired by the joint sparse technology in compressive sensing theory, we focus on the sparse design of wideband beamformer. The constraints for the response characteristics and robustness are set from first step, and an iterative algorithm based on reweighted ℓ2,1 optimization is adopted to achieve maximum sparsity of the sensor array. The mainly advantages of the work are that the proposed design exhibits accordant performance in terms of response and robustness, but few sensors compared with the counterpart with uniform array. Moreover, we surprisingly find that the optimized sparse array is also applicable to other design based on WCPO criterion. Simulation results are provided to verify the superior of the proposed methods compared to the existing counterparts.

Design of Robust Polynomial Beamformers Using Worst Case Performance Optimization via Alternating Direction Method of Multipliers

This paper studies the design of robust polynomial beamformers (RPBs) for microphone arrays, which enable dynamic beam steering via simple online parameter tuning, under the criterion of worst-case performance optimization (WCPO). Although the WCPO criterion has been widely adopted in the design of various robust beamformers, conventional approaches using the WCPO criterion may not be applicable to the RPB design, due to the conservativeness problem resulting from the special structure of polynomial beamformers. In this paper, we propose to design the RPBs based on the semidefinite programming (SDP) using the WCPO criterion. Nevertheless, the resulting design optimization problems are highly computationally demanding. To overcome the computational difficulty, we then propose to solve the high-dimensional optimization problems for the RPB design using the alternating direction method of multipliers (ADMM) algorithm. By introducing auxiliary variables in the framework of ADMM, the original high-dimensional optimization problems are decomposed into several subproblems which are easier to handle. The algorithms to solve the corresponding subproblems are developed. Simulation and real-world experimental results show that the proposed SDP-based RPB design performs much better than its existing counterpart. Moreover, the computational efficiency can be significantly improved by using the proposed ADMM algorithm while the existing solution is very time-consuming and even fails.

Mainlobe maintenance for FDA-MIMO radar

During radar detection, the adaptive beamforming technique needs to create nulls to resist the interference. When the interference appears within the mainlobe, the main detection beam will become distorted. To solve this problem, a new method for the covariance matrix reconstruction is proposed for the mainlobe maintenance problem, and a worst-case performance optimization (WCPO) algorithm with enhanced waveform robustness is obtained. Its integration is performed over a known region without the target information to obtain the improved covariance matrix, which is then brought into the convex optimization equation to solve for the weight vector. Simulation results show that the output signal-to-noise ratio of this algorithm is higher than that of the conventional WCPO algorithm with a robust beam for the same signal-to-noise ratio. It can also effectively eliminate the primary lobe offset and secondary lobe elevation problems.

Statistically Robust Transceiver Design for Multi-RIS Assisted Multi-User MIMO Systems

In this letter, we investigate the robust transceiver design for a downlink multi-user multiple-input multiple-output (MIMO) system assisted by multiple reconfigurable intelligent surfaces (RISs), where the base station (BS) and multiple users are all equipped with multiple antennas. Different from most previous RIS related works focusing on worst-case performance optimization, which may lead to overly conservative transceiver designs, we assume stochastic channel estimation errors for the considered system, and aim to minimize the average sum mean square error (MSE) of the considered system by jointly optimizing the transmit precoders, the receive equalizers, and the RIS reflecting coefficients. To address the non-convexity of the formulated problem induced by strongly coupled optimization variables, we develop a low-complexity alternating optimization (AO) algorithm to find a locally optimal solution, where the unique optimal solution to each subproblem can be derived in closed-form. Numerical simulations demonstrate the robustness and excellent average sum MSE performance of the proposed AO algorithm compared to the adopted benchmark scheme.

Robust adaptive beamforming via improved worst-case performance optimization algorithm based on FDA-MIMO

Robust adaptive beamforming via improved worst-case performance optimization algorithm based on FDA-MIMO

Robust Widely Linear Beamforming With Multiple Uncertainty Sets

The widely linear minimum variance distortionless response (WL-MVDR) beamformer has a better performance than the conventional MVDR beamformer when the received signals are potentially noncircular. However, it is sensitive to the extended steering vector (ESV) mismatches which can be caused by direction of arrival (DOA) errors, noncircularity coefficient errors, array imperfections and so on. To improve the robustness against large ESV mismatches, a robust WL beamformer based on the worst-case performance optimization (WCPO) method with multiple uncertainty sets is proposed. The resultant beamformer has the mathematical form of a nonconvex optimization problem, which can be converted into a semidefinite programming (SDP) problem and solved iteratively. Simulation results show that, in comparison with several representative robust WL beamformers, the proposed method can achieve better performances, especially under large ESV mismatch conditions.

Optimal synthesis of reconfigurable planar arrays for monopulse radar applications: Use of subarrays and distributions with common aperture tail

An approach for the synthesis of sum and difference patterns in monopulse antennas is described. The proposed approach provides a significant reduction in the complexity of the beam-forming network that is fulfilled by reducing the number of array elements and keeping the elements at the edges of the array that share common excitations for both sum and difference modes. An iterative constrained optimisation method is used where the non-convex lower-bound constraints on the beam pattern are cast as an equivalent multi-convex optimisation problem while concurrently minimising a reweighted l1-norm of the magnitudes of the elements in the beam-forming weight vector. Thus, better radiation performance of beam pattern (e.g. narrower beamwidth, lower peak sidelobe level), a much narrower spatial aperture and a smaller number of elements can be achieved compared with the case of uniformly spaced arrays. To compensate for array imperfection in practice, robust beam pattern constraints are derived in the optimisation stage using a worst-case performance optimisation technique. Numerical examples show the effectiveness and advantages of the proposed synthesis approach.

Polarised beampattern synthesis against array manifold mismatch

The problem of joint synthesis of spatial power pattern and mainlobe radiation polarisation using a vector antenna array is considered in the presence of array manifold errors. A general approach to the synthesis problem is to formulate the restriction on the power and radiation polarisation as a convex optimisation programing. However, for certain types of vector antennas like tripole and electromagnetic vector sensors, the optimal weights might be extremely large and the resultant beampattern could be very sensitive to the array manifold errors. An intuitive explanation on this phenomenon is given based on the subspace theory. A worst case performance optimisation technique- based scheme is presented to draw attention to the polarised beampattern synthesis against the large weights problem and array manifold errors. Numerical examples regarding different types of vector antennas used for one- and two-dimensional polarised beampattern synthesis are provided to validate the efficacy of the scheme.

Energy-efficient Power Allocation based on worst-case performance optimization under channel uncertainties

Energy-efficient Power Allocation based on worst-case performance optimization under channel uncertainties

Optimal synthesis of reconfigurable sparse arrays via multi‐convex programming

A new approach for the synthesis of one-dimensional (1D) and 2D reconfigurable sparse arrays generating sum and difference power patterns is presented in this study. In the case of 1D arrays, the design procedure provides solutions in which only one set of amplitude coefficients is required and the reconfigurability is obtained by modifying only the excitation phases. In the case of 2D arrays, the simplification of the antenna system is investigated by sharing some excitations for the sum and difference channels. An iterative scheme is used where the array response in the main lobe direction is cast as a multi-convex problem at each step that the non-convex lower bound constraint is relaxed while concurrently minimising a reweighted objective function based on the magnitudes of the element excitations. To ensure the robustness of the array, worst-case performance optimisation technique and white noise gain constraint are introduced in the array. Numerical tests and electromagnetic simulations, referred to known optimal solutions, show that the proposed design is able to obtain good radiation performance with a smaller number of elements.

Robust mismatched filtering algorithm for passive bistatic radar using worst-case performance optimization

Passive bistatic radar detects targets by exploiting available local broadcasters and communication transmissions as illuminators, which are not designed for radar. The signal usually contains a time-varying structure, which may result in high-level range ambiguity sidelobes. Because the mismatched filter is effective in suppressing sidelobes, it can be used in a passive bistatic radar. However, due to the low signal-to-noise ratio in the reference signal, the sidelobe suppression performance seriously degrades in a passive bistatic radar system. To solve this problem, a novel mismatched filtering algorithm is developed using worst-case performance optimization. In this algorithm, the influence of the low energy level in the reference signal is taken into consideration, and a new cost function is built based on worst-case performance optimization. With this optimization, the mismatched filter weights can be obtained by minimizing the total energy of the ambiguity range sidelobes. Quantitative evaluations and simulation results demonstrate that the proposed algorithm can realize sidelobe suppression when there is a low-energy reference signal. Its effectiveness is proved using real data.

Synthesis of pattern reconfigurable sparse arrays via sequential convex optimizations for monopulse radar applications

ABSTRACTIn this paper, a new array synthesis approach is developed for the design of reconfigurable sparse arrays radiating sum and difference patterns. The proposed approach provides a significant reduction in the complexity of the beam forming network, which is fulfilled by reducing the number of antenna elements in the array and sharing some excitation weights for the sum and difference channels. An iterative scheme is used where the prescribed pattern response in the mainlobe is cast as a multi-convex problem at each step that the nonconvex lower bound constraint is relaxed while including a reweighted -norm minimization based on the magnitudes of the elements. Thus a better performance of beam pattern (e.g. narrower 3-dB beamwidth, lower maximum sidelobe levels) and a smaller number of elements can be obtained compared with the case of uniformly spaced array. The practical array imperfections are also compensated in the optimization stage by using worst-case performance optimization technique. Numerical tests are presented and discussed to validate the versatility and effectiveness of the proposed approach.

Recursive Updating Algorithm for Robust Adaptive Beamforming in a Uniform Circular Array

When the phase-mode transformation technique is used in a uniform circular array, its output performance is known to degrade owing to the approximations applied to the formulation. In this paper, we develop a robust recursive updating algorithm based on the worst-case performance optimization and phase-mode transformation in the uniform circular array, which provides efficient robustness not only against the signal steering vector mismatches, but also against the transformation errors. The proposed algorithm belongs to the class of the diagonal loading technique and the transformation matrix belongs to a certain ellipsoid set. The weight vector is updated by the Lagrange multiplier method, in which the parameters are derived simply. The proposed algorithm has a closed-form solution, in which we analyse the reasonable ranges of two key parameters. The convergence performance and the output SINR performance are also analysed. In additional, the implementation complexity costs of the proposed algorithm and MVDR algorithm are presented in this paper. Our robust algorithm has a low implementation complexity cost and achieves the mean output array SINR consistently close to the optimal one. Simulation results are presented to compare the performances of our algorithm with the conventional algorithms.

Real-valued robust DOA estimation method for uniform circular acoustic vector sensor arrays based on worst-case performance optimization

The minimum variance distortionless response (MVDR) method suffers performance degradation when the considerable ambient noise and the steering vector mismatch exist. Therefore, this paper proposes a real-valued robust beamforming for the uniform circular acoustic vector sensor array (UCAVSA) based on worst-case performance optimization. The paper first extends the phase-mode transformation into the UCAVSA, and the relationship between the transformation matrices of the UCAVSA and the circular pressure sensor array is derived. The paper then utilizes the spatial correlation characteristic between the acoustic pressure and particle velocity to construct a cross-covariance matrix to eliminate the isotropic noise, and then transforms the cross-covariance matrix into a real-valued one by the unitary transformation. Finally, the paper derives the real-valued robust beamforming algorithm via optimizing the worst-case performance. Theoretical analyses and simulation results indicate that the proposed method is superior over previous methods under scenarios such as low signal-to-noise (SNR), steering vector mismatch and coherent sources. Moreover, the proposed method has a lower computational cost than the complex-valued operation in calculating the weight vector. The experiment results verify the effectiveness of the proposed method.

Robust adaptive beamforming with enhancing the interference suppression capability

AbstractThe steering vector mismatch causes signal self-nulling for adaptive beamforming when the training data contain the desired signal component. To prevent signal self-nulling, many beamformers use robust technology, which is usually equivalent to the diagonal loading approach. Unfortunately, the diagonal loading approach achieves better signal enhancement at the cost of losing its interference suppression capability, especially at high input signal-to-noise ratio. In this paper, a novel robust adaptive beamforming method is developed to improve the interference suppression capability. The proposed beamformer is based on the worst-case performance optimization technology with a new estimated steering vector and a special set parameter. Firstly, a subspace which is orthogonal to the interference's steering vector is obtained by using the interference-plus-noise covariance matrix; then a new steering vector which is orthogonal to each interference's steering vector is estimated; finally, the beamformer's weight is solved with the worst-case performance optimization technology with a special set parameter. Theoretical analysis of the interference suppression principle is analyzed in detail, and some simulation results are presented to evaluate the performance of the proposed beamformer.

Worst-Case Performance Optimization Beamformer with Embedded Array’s Active Pattern

This paper proposes an adaptive array beamforming method by embedding antennas’ active pattern in the worst-case performance optimization algorithm. This method can significantly reduce the beamformer’s performance degradation caused by inconsistency between hypothesized ideal array models and practical ones. Simulation and measured results consistently demonstrate the robustness and effectiveness of the proposed method in dealing with array manifold mismatches.

Robust adaptive beamforming against large steering vector mismatch using multiple uncertainty sets

Abstract Many efforts have been recently devoted to adaptive beamformers using one uncertainty set to achieve robustness against steering vector mismatch. However, these robust adaptive beamformers based on worst-case performance optimization suffer from difficulty in selecting an appropriate size of the uncertainty set. Besides, their performances degrade dramatically if large steering vector mismatch occurs. This motivates us to develop a robust beamforming approach to handle the large uncertainty set problem. In this paper, we utilize multiple small uncertainty sets, instead of using a single large set, to cover the whole large uncertainty region. Two efficient algorithms, iterative semidefinite programming-based robust adaptive beamforming (ISDP-RAB) and iterative linearization-based robust beamforming (IL-RAB), are developed to solve the nonconvex problem. Simulation results indicate that the proposed method offers a significant performance improvement in case of large steering vector mismatch.

An improved robust adaptive beamforming based on worst-case performance optimization

Generally, the adaptive beamformer has better spatial resolution and much better interference rejection capability than the conventional data-independent beamformer. But, in practice, the performance of the traditional adaptive beamformer will degrade greatly if some assumptions or information on the propagation model, array parameters, and signal model are imprecise. In this paper, a new approach to robust adaptive beamforming based on optimization of worst-case performance by parameter auto-adjust (PAWCO) is proposed, which can estimate the power of the signal using Newton-Raphson interactions. The method can confirm the upper bound of the mismatch vector neither overly nor under estimated. Theoretical analysis and simulation results are presented to show the proposed beamformer can estimate the power of signal precisely while achieving better spatial resolution. The robustness of the PAWCO algorithm to environment mismatch is also demonstrated by the acoustical experimental data.