Realizing complex beams via amplitude-phase digital coding metasurfaces and semidefinite relaxation optimization

Complex beams play important roles in wireless communications,radar,and satellites,and have attracted great interest in recent years.In light of this background,we present a fast and efficient approach to realize complex beams by using semidefinite relaxation(SDR)optimization and amplitude-phase digital coding metasurfaces.As the application examples of this approach,complex beam patterns with cosecant,flat-top,and double shapes are designed and verified using full-wave simulations and experimental measurements.The results show excellent main lobes and low-level side lobes and demonstrate the effectiveness of the approach.Compared with previous works,this approach can solve the complex beam-forming problem more rapidly and effectively.Therefore,the approach will be of great significance in the design of beam-forming systems in wireless applications.

Semidefinite Relaxation for Two Mixed Binary Quadratically Constrained Quadratic Programs:Algorithms and Approximation Bounds

This paper develops new semidefinite programming(SDP)relaxation techniques for two classes of mixed binary quadratically constrained quadratic programs and analyzes their approximation performance.The first class of problems finds two minimum norm vectors in N-dimensional real or complex Euclidean space,such that M out of 2M concave quadratic constraints are satisfied.By employing a special randomized rounding procedure,we show that the ratio between the norm of the optimal solution of this model and its SDP relaxation is upper bounded by 54πM2 in the real case and by 24√Mπin the complex case.The second class of problems finds a series of minimum norm vectors subject to a set of quadratic constraints and cardinality constraints with both binary and continuous variables.We show that in this case the approximation ratio is also bounded and independent of problem dimension for both the real and the complex cases.

Modified Exact Jacobian Semidefinite Programming Relaxation for Celis-Dennis-Tapia Problem

A modified exact Jacobian semidefinite programming(SDP)relaxation method is proposed in this paper to solve the Celis-Dennis-Tapia(CDT)problem using the Jacobian matrix of objective and constraining polynomials.In the modified relaxation problem,the number of introduced constraints and the lowest relaxation order decreases significantly.At the same time,the finite convergence property is guaranteed.In addition,the proposed method can be applied to the quadratically constrained problem with two quadratic constraints.Moreover,the efficiency of the proposed method is verified by numerical experiments.

Joint Beamforming Design for Dual-Functional Radar-Communication Systems Under Beampattern Gain Constraints

The joint beamforming design challenge for dual-functional radar-communication systems is addressed in this paper.The base station in these systems is tasked with simultaneously sending shared signals for both multi-user communication and target sensing.The primary objective is to maximize the sum rate of multi-user communication,while also ensuring sufficient beampattern gain at particular angles that are of interest for sensing,all within the constraints of the transmit power budget.To tackle this complex non-convex problem,an effective algorithm that iteratively optimizes the joint beamformers is developed.This algorithm leverages the techniques of fractional programming and semidefinite relaxation to achieve its goals.The numerical results confirm the effectiveness of the proposed algorithm.

Computing Geometric Measure of Entanglement for Symmetric Pure States via the Jacobian SDP Relaxation Technique

The problem of computing geometric measure of quantum entanglement for symmetric pure states can be regarded as the problem of finding the largest unitary symmetric eigenvalue(US-eigenvalue)for symmetric complex tensors,which can be taken as a multilinear optimization problem in complex number field.In this paper,we convert the problem of computing the geometric measure of entanglement for symmetric pure states to a real polynomial optimization problem.Then we use Jacobian semidefinite relaxation method to solve it.Some numerical examples are presented.

Rate optimization using low complex methods with reconfigurable intelligent surfaces

With the help of a developing technology called reconfigurable intelligent surfaces(RISs),it is possible to modify the propagation environment and boost the data rates of wireless communication networks.In this article,we optimized the phases of the RIS elements and performed a fair power allocation for each subcarrier over the full bandwidth in a single-input-single-output(SISO)wideband system where the user and the access point(AP)are provided with a single antenna.The data rate or its equivalent channel power is maximized by proposing different low-complex algorithms.The strongest tap maximization(STM)and power methods are compared with the semidefinite relaxation(SDR)method in terms of computational complexity and data rate performance.Runtime and complexity analysis of the suggested methods are computed and compared to reveal the actual time consumption and the required number of operations for each method.Simulation results show that with an optimized RIS,the sum rate is 2.5 times higher than with an unconfigured surface,demonstrating the RIS's tremendous advantages even in complex configurations.The data rate performance of the SDR method is higher than the power method and less than the STM method but with higher computational complexity,more than 6 million complex operations,and 50 min of runtime calculations compared with the other STM and power optimization methods.

An SDP randomized approximation algorithm for max hypergraph cut with limited unbalance

We consider the design of semidefinite programming （SDP） based approximation algorithm for the problem Max Hypergraph Cut with Limited Unbalance （MHC-LU）： Find a partition of the vertices of a weighted hypergraph H = （V, E） into two subsets V1, V2 with ｜｜V2｜ - ｜1/1 ｜｜ ≤ u for some given u and maximizing the total weight of the edges meeting both V1 and V2. The problem MHC-LU generalizes several other combinatorial optimization problems including Max Cut, Max Cut with Limited Unbalance （MC-LU）, Max Set Splitting, Max Ek-Set Splitting and Max Hypergraph Bisection. By generalizing several earlier ideas, we present an SDP randomized approximation algorithm for MHC-LU with guaranteed worst-case performance ratios for various unbalance parameters τ = u/｜V｜. We also give the worst-case performance ratio of the SDP-algorithm for approximating MHC-LU regardless of the value of τ. Our strengthened SDP relaxation and rounding method improve a result of Ageev and Sviridenko （2000） on Max Hypergraph Bisection （MHC-LU with u = 0）, and results of Andersson and Engebretsen （1999）, Gaur and Krishnamurti （2001） and Zhang et al. （2004） on Max Set Splitting （MHC-LU with u = ｜V｜）. Furthermore, our new formula for the performance ratio by a tighter analysis compared with that in Galbiati and Maffioli （2007） is responsible for the improvement of a result of Galbiati and Maffioli （2007） on MC-LU for some range of τ.