In this paper, we investigate the problem of robust beamforming for multiple-input multiple-output (MIMO) dual-function radar-communication (DFRC) system, when there exist radar look direction ...mismatch and communication channel state information (CSI) error. To address these system imperfections, a region-of-interest (ROI) rather than a specific angle is considered for radar sensing, and the communication CSI is assumed to be available with a bounded unknown error. With these considerations, we design a robust dual-function beamformer through optimizing the radar sensing performance in terms of the energy radiated towards the ROI, while guaranteeing the communication quality-of-service (QoS) measured by the per-user signal-to-interference-plus-noise ratio (SINR) as required. For this robust design, a max-min optimization problem is formulated and a semidefinite programming (SDP) reformulation based on the S-procedure is presented. The popular semidefinite relaxation (SDR) technique is employed to solve the resulting non-convex problem, and the tightness of SDR is discussed. Further, we propose to incorporate an extra constraint of main beam control into the problem to achieve a flat magnitude response of the beampattern over the ROI. In addition, it is shown that the proposed approach is straightforwardly applicable to the scenario of multiple targets. Numerical examples are carried out to show the tightness, and demonstrate the effectiveness and robustness of the proposed MIMO-DFRC beamforming approach.
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bstract
We develop new tools for isolating CFTs using the numerical bootstrap. A “cutting surface” algorithm for scanning OPE coefficients makes it possible to find islands in high-dimensional ...spaces. Together with recent progress in large-scale semidefinite programming, this enables bootstrap studies of much larger systems of correlation functions than was previously practical. We apply these methods to correlation functions of charge-0, 1, and 2 scalars in the 3d O(2) model, computing new precise values for scaling dimensions and OPE coefficients in this theory. Our new determinations of scaling dimensions are consistent with and improve upon existing Monte Carlo simulations, sharpening the existing decades-old 8
σ
discrepancy between theory and experiment.
In this article, semidefinite programming (SDP) solutions are proposed for the elliptic localization problem in asynchronous radar networks, where the transmitters are subject to clock offsets. ...Relaxing the nonconvex problem into different convex forms, we design tight SDP (TSDP) and global SDP (GSDP) solutions for this problem. The TSDP solution includes several SDP cones to solve the problem, and the correlation is not considered. Hence, the TSDP solution performs poorly in the presence of correlated noise. We further put forward the GSDP solution to improve the performance by introducing a new GSDP form, which includes only one SDP cone to handle the correlated noise. We also theoretically prove that the GSDP problem is tight enough so that its performance is able to sufficiently approach the Cramér–Rao lower bound (CRLB) accuracy. The simulated results show that the TSDP solution can provide the comparable performance with the GSDP in the absence of related noise. The performance of the GSDP solution can almost attain the CRLB accuracy using less receivers.
This paper considers the set membership fusion estimation problem for the general multisensor dynamic systems with unknown but bounded noises. In order to achieve the ellipsoidal fusion formulae, we ...divide the set membership filter problem into two steps: the prediction step and the fusion update step. The proposed method has the following nice properties. First, each step can be converted into a semidefinite programming problem, which can be efficiently computed. Second, part-analytical formulae of the shape matrix and the center of the bounding ellipsoid can be derived by using a decoupled technique, which can significantly reduce the computational complexity. Moreover, the relationship between the fusion center and local sensors can be clearly revealed based on the ellipsoidal fusion formula. Finally, it is interesting that the ellipsoidal fusion formula is similar in form to the classic mean-squared error filter fusion, although they are of the different optimization frameworks. However, the fusion weights of the information matrix provided by the different sensors are different and the optimal fusion weights can be calculated by solving a convex optimization problem. A typical numerical example in target tracking demonstrates the effectiveness of the proposed centralized and distributed fusion formula.
This article develops distributed synchronous and asynchronous algorithms for the large-scale semidefinite programming with diagonal constraints, which has wide applications in combinatorial ...optimization, image processing, and community detection. The information of the semidefinite programming is allocated to multiple interconnected agents such that each agent aims to find a solution by communicating to its neighbors. Based on the low-rank property of solutions and the Burer-Monteiro factorization, we transform the original problem into a distributed optimization problem over unit spheres to reduce variable dimensions and ensure positive semidefiniteness without involving semidefinite projections, which are computationally expensive. For the distributed optimization problem, we propose distributed synchronous and asynchronous algorithms, both of which reduce computational burden and storage space compared with existing centralized algorithms. Specifically, the distributed synchronous algorithm almost surely escapes strict saddle points and converges to the set of optimal solutions to the optimization problem. In addition, the proposed distributed asynchronous algorithm allows communication delays and converges to critical points to the optimization problem under mild conditions. By applying the proposed algorithms to image segmentation, we illustrate the efficiency and convergence performance of the two proposed algorithms.
We present a new quantum communication complexity protocol, the promise-quantum random access code, which allows us to introduce a new measure of unbiasedness for bases of Hilbert spaces. The ...proposed measure possesses a clear operational meaning and can be used to investigate whether a specific number of mutually unbiased bases exist in a given dimension by employing semidefinite programming techniques.
In this paper, we develop a dynamical system counterpart to the term sparsity sum-of-squares (TSSOS) algorithm proposed for static polynomial optimization. This allows for computational savings and ...improved scalability while preserving convergence guarantees when sum-of-squares methods are applied to problems from dynamical systems, including the problems of approximating region of attraction, the maximum positively invariant set, and the global attractor. At its core, the method exploits the algebraic structure of the data, thereby complementing existing methods that exploit causality relations among the states of the dynamical system. The procedure encompasses sign symmetries of the dynamical system as was already revealed for polynomial optimization. Numerical examples demonstrate the efficiency of the approach in the presence of this type of sparsity.
In a network of cooperating unmanned aerial vehicles (UAVs), individual UAVs usually need to localize themselves in a shared and generally global frame. This paper studies the localization problem ...for a group of UAVs navigating in three-dimensional space with limited shared information, viz., noisy distance measurements are the only type of interagent sensing that is available, and only one UAV knows its global coordinates, the others being GPS denied. Initially, for a two-agent problem, but easily generalized to some multiagent problems, this paper first establishes constraints on the minimum number of distance measurements required to achieve the localization. This paper then proposes a composite algorithm based on semidefinite programming (SDP) in a first step, followed by maximum likelihood estimation using gradient descent on a manifold initialized by the SDP calculation. The efficacy of the algorithm is verified with experimental noisy flight data.
Distribution system state estimation (DSSE) is one of the vital components in the next-generation distribution management system which allows operators to monitor the entire system's operating ...conditions. Due to the lack of real-time measurements, DSSE has to process measurements whose quality varies significantly across different sources, which causes a convergence issue to the Gauss-Newton solver. In this paper, a semidefinite programming (SDP) framework is proposed to reformulate the DSSE problem into a rank- constrained SDP problem. One challenge of this technique is the nonconvex rank-one constraint, which is generally relaxed. However, the relaxed SDP-DSSE problem cannot guarantee a rank-one solution and hence loses optimality. Therefore, we propose two solution approaches to obtain rank-one solutions for the SDP-DSSE problem: the rank reduction approach and the convex iteration approach. The model and the effectiveness of the proposed solution approaches are numerically demonstrated on the IEEE 13-bus, 34-bus, and 123-bus distribution systems.
Simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) is a promising technology that aids in achieving full-space coverage on both sides of the surface, by ...splitting the incident signal into transmitted and reflected signals. This paper investigates the resource allocation problem in a STAR-RIS-assisted multi-carrier communication networks. To maximize the system sum-rate, a joint optimization problem comprising of the channel assignment, power allocation, and transmission and reflection beamforming at the STAR-RIS for orthogonal multiple access (OMA) is first formulated. To solve this challenging problem, we first propose a channel assignment scheme utilizing matching theory and then invoke the alternating optimization-based method to optimize the resource allocation policy and beamforming vectors iteratively. Furthermore, the sum-rate maximization problem for non-orthogonal multiple access (NOMA) with flexible decoding orders is investigated. To efficiently solve it, we first propose a location-based matching algorithm to determine the sub-channel assignment, where a transmitted user and a reflected user are grouped on a sub-channel. Based on this transmission-and-reflection sub-channel assignment strategy, a three-step approach is proposed, which involves the optimization of decoding orders, beamforming-coefficient vectors, and power allocation, by employing semidefinite programming, convex upper bound approximation, and geometry programming, respectively. Numerical results unveil that: 1) For OMA, a general design that includes the same-side user-pairing for channel assignment is preferable, whereas for NOMA, the proposed transmission-and-reflection scheme can achieve comparable performance to the exhaustive search-based algorithm. 2) The STAR-RIS-aided NOMA network significantly outperforms networks employing conventional RISs and OMA.
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