Fast Algorithms for Designing Unimodular Waveform(s) With Good Correlation Properties

We deal with the waveform design problem for the radar-communications coexistence (RCC) that ensures low levels of waveform correlations and meanwhile implements efficient information embedding (IE) via the fast-time waveform transmission. To tackle the problem, we propose two unimodular waveform designs, in which the integrated sidelobe level (ISL) is evaluated to find the optimal waveform correlations for the radar transmission and the attributes of waveform phases with large degrees of freedom are exploited to embed communication symbols. The first design is an offline strategy simply using the phase initialization for waveform generation to embed communication symbols. It requires only a predefined database that maps the waveform initialization to the emitted version of it, which gives the lowest ISL of the waveform. The second design serves as an online strategy employing the phase difference between any two waveform elements for the implementation of IE, and its accuracy to approaching desirable phases is elaborately transformed into a quadratic form and jointly designed with the minimization of ISL. We formulate this design as a nonconvex optimization problem, whose compound objective involves the outer product of the waveform vector that is to be designed. Moreover, we apply the majorization-minimization technique to solve the formulated problem, based on which we also devise an efficient algorithm that iterates with a closed-form solution. Simulation results verify the effectiveness of the proposed designs for the RCC.

In this paper, we focus on the multiple-waveform design for the joint multiple-input multiple-output radar and communications system, which aims to simultaneously attain low integrated sidelobe level (ISL) of waveforms and accurate fast-time modulation for information embedding (IE). We propose a novel strategy to exploit the attributes of waveform phases with extremely large degrees of freedom for embedding communication symbols, based on which we formulate the generalized waveform design into a nonconvex optimization problem. Our major contribution lies in converting both the ISL related objective and the fast-time modulation related constraints for IE into tractable quadratic forms. To achieve this, we introduce a novel diagonal matrix with Toeplitz blocks to reformulate and then relax the problem into a form that involves the outer product of the waveform vector in its objective. In order to solve this problem, we exploit the majorization-minimization technique to devise an algorithm that enables a closed-form solution at each iteration. Simulation results verify the effectiveness of our design.

A solution algorithm for non-convex mixed integer optimization problems with only few continuous variables

In this paper, the classical exact absolute value penalty function method is used for solving a new class of nonconvex nonsmooth optimization problems. Nonconvex nondifferentiable optimization problems with both inequality and equality constraints are considered here, in which not all functions constituting them have the fundamental property of convex functions and most classes of generalized convex functions—namely, a stationary point of such a function is its global minimum. It is proved for such nonconvex optimization problems that there exists a finite threshold of penalty parameters equal to the largest absolute value of a Lagrange multiplier such that, for every penalty parameter exceeding this lower bound, there is the equivalence between an optimal solution in the original constrained minimization problem with ‐invex functions and a minimizer in its associated penalized optimization problem with the exact l1 penalty function. Further, under nondifferentiable ‐invexity assumptions, a characterization of a saddle point of the Lagrange function, defined for the considered constrained optimization problem in terms of minimizers of its associated exact penalized optimization problem with the exact l1 penalty function, is presented.

Employing binary sequences with good autocorrelation properties leads to performance improvement for active sensing systems. Designing such sequences has been studied widely in the literature from optimization point of view. In this paper we consider the problem of designing binary sequences with good aperiodic/periodic auto-correlation functions in terms of Integrated Sidelobe Level (ISL) using machine learning method. Specifically, we propose a novel neural network structure which can learn an algorithm for designing binary sequences with small ISL. We also extend the resulting network, which we refer to as BiSCorN, by designing Low-Correlation Zone (LCZ) binary sequences. Numerical experiments show that our proposed method outperforms state-of-the-art algorithms in terms of ISL, and interestingly Peak Sidelobe Level (PSL).

A neurodynamic optimization technique based on overestimator and underestimator functions for solving a class of non-convex optimization problems

Waveform design is a critical technology for orthogonal time-frequency space (OTFS) integrated sens-ing and communication (ISAC) systems. Existing research mainly focuses on the design of multiple-input multiple-output (MIMO)-OTFS communication waveforms or the design of dual-functional OTFS waveforms for single-input single-output (SISO) systems, which results in degraded per-formance in dynamic, multi-user ISAC scenarios. To address these limitations, the paper mainly investigates waveform op-timization for MIMO-OTFS ISAC systems, which formulates the problem as minimizing the weighted integrated sidelobe level (WISL) under peak-to-average power ratio (PAPR) and multi-user interference (MUI) energy constraints. Due to its non-convex nature with multiple constraints, the problem is challenging to solve. To address the complicated optimization problem, an adaptive penalty analytic subproblem decompo-sition (APASD) method is proposed. First, auxiliary variables are introduced to decompose the original problem into several subproblems with analytic solutions. Then, leveraging the structure of the subproblems, we derive the corresponding analytic solutions. Finally, the penalty parameters are adap-tively updated based on the residuals, and the overall problem is iteratively refined until convergence. Simulation results demonstrate that the proposed method can achieve a lower sidelobe level while ensuring the achievable sum-rate, and shows better performance than existing methods.

Integrated sidelobe level(ISL) criterion and the maximal sidelobe level(MSL) criterion are used to design frequency-hopping waveforms based on ambiguity functions respectively in this paper. Some simulation results are given and analyzed. The performance of the proposed algorithm is validated by numerical simulations. Frequency-hopping coding is a kind of orthogonal signals which can be used in radar and sonar systems. And frequency- hopping coding such as Costas arrays (1, 2) has good autocorrelation property. However, for radar and sonar systems, their properties of ambiguity function are mainly considered. In this paper, frequency-hopping waveforms are designed based on ambiguity functions. The results are achieved by minimizing two cost functions which measure the integrated sidelobe level(ISL) and the maximal sidelobe level(MSL) of the autocorrelation function respectively. In this paper, cost functions are defined based on ISL criterion and MSL criterion respectively, and some results are achieved based on genetic algorithm. The remainder of this paper is organized as follows. Section Ⅱ presents the ambiguity function of frequency-hopping waveforms and cost functions designed in this paper, and formulates the problem of designing frequency-hopping waveforms. In section Ⅲ, we introduce the genetic algorithm to optimize frequency-hopping waveforms sets. And design results and their curves of ambiguity functions are presented in Section Ⅳ. Finally, some conclusions are drawn in section Ⅴ.

Trajectory optimization for asteroid landing with two-phase free final time

On Nonconvex Optimization Problems with D.C. Equality and Inequality Constraints

Optimal insurance contract specification in the upstream sector of the oil and gas industry

Designing unimodular waveforms with good auto- and cross-correlation is one of the main problems for multiple-input multiple-output (MIMO) radar. Although long MIMO radar sequences improve long-range detection performance, it is difficult to design such long sequences owing to limitations of code theory and the cost of exhaustive searches. An autoencoder is a type of neural network that has had great success in designing long code sequences for wireless communication. This paper proposes a framework for designing long MIMO sequences with good auto- and cross-correlation properties using an autoencoder. Numerical results show that sequences designed using the proposed framework demonstrate better correlation properties than existing algorithms.

In radar systems, unimodular (or constant-modulus) waveform design plays an important role in achieving better clutter/interference rejection, as well as a more accurate estimation of the target parameters. The design of such sequences has been studied widely in the last few decades, with most design algorithms requiring sophisticated a priori knowledge of environmental parameters which may be difficult to obtain in real-time scenarios. In this paper, we propose a novel hybrid model-driven and data-driven architecture that adapts to the ever changing environment and allows for adaptive unimodular waveform design. In particular, the approach lays the groundwork for developing extremely low-cost waveform design and processing frameworks for radar systems deployed in autonomous vehicles. The proposed model-based deep architecture imitates a well-known unimodular signal design algorithm in its structure, and can quickly infer statistical information from the environment using the observed data. Our numerical experiments portray the advantages of using the proposed method for efficient radar waveform design in time-varying environments.

Polyphase sequences with low aperiodic autocorrelation sidelobes are well known to have extensive applications in communication and radar systems. In this paper, we present an effective algorithm named Majorization Minimization based Memetic Algorithm (MA-MM) to design such sequences. Compared with the previously proposed algorithms, this algorithm searches the solution space more efficiently to obtain a global solution with much better autocorrelation properties. It can be used to minimize the integrated sidelobe level (ISL) and peak sidelobe level (PSL), respectively. Numerical experiments are presented to illustrate the performance of the proposed algorithms. It is demonstrated that the proposed algorithms can generate sequences with much better autocorrelation properties compared with some well-known analytical sequences. In addition, the influence of some parameters on the performance of the designed sequences is investigated.

We consider minimizing a class of nonconvex composite stochastic optimization problems, and deterministic optimization problems whose objective function consists of an expectation function (or an average of finitely many smooth functions) and a weakly convex but potentially nonsmooth function. And in this paper, we focus on the theoretical properties of two types of stochastic splitting methods for solving these nonconvex optimization problems: stochastic alternating direction method of multipliers and stochastic proximal gradient descent. In particular, several inexact versions of these two types of splitting methods are studied. At each iteration, the proposed schemes inexactly solve their subproblems by using relative error criteria instead of exogenous and diminishing error rules, which allows our approaches to handle some complex regularized problems in statistics and machine learning. Under mild conditions, we obtain the convergence of the schemes and their computational complexity related to the evaluations on the component gradient of the smooth function, and find that some conclusions of their exact counterparts can be recovered.