Design of Unimodular Sequences With Good Autocorrelation and Good Complementary Autocorrelation Properties

Arriaga-Trejo, Israel Alejandro; Orozco-Lugo, A.G.; Flores-Troncoso, Jorge

doi:10.1109/lsp.2017.2696950

Cited by 23 publications

(5 citation statements)

References 18 publications

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“…The gradient descent method based on phase-only derivative is exactly the basic tool used in research literatures [5], [8], [14]. We will not discuss this case in this paper further.…”

Section: Connection With Gradient-based Methodsmentioning

confidence: 99%

Fast Algorithms for Designing Complementary Sets of Sequences Under Multiple Constraints

Tian-liang

Zhou

et al. 2019

IEEE Access

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Complementary sets of sequences (CSSs) are widely used in many applications, such as active sensing and wireless communication. The construction of CSS has attracted considerable attention over the past few decades. In this paper, efficient and comprehensive computational algorithms for CSS design are proposed. We seek to minimize complementary integral sidelobe level (CISL) under multiple constraints, including unimodular, peak-to-average power ratio, discrete phase, and spectrum compatible constraint. The task of CSS design can be formulated as solving a nonconvex constraint optimization problem. As this problem is difficult to tackle directly, we resort to the general majorization-minimization (MM) method. By utilizing the inherent algebraic structure of the objective function, we construct the majorizing function via two consecutive applications of the MM method and obtain a closed-form solution by a couple of FFT operations at each iteration. The relationship between MM-based algorithms and derivative-based algorithms is revealed. Our algorithms are more flexible and widely applicable, and the numerical experiment results demonstrate the effectiveness and superiority over the existing state-of-art algorithms.

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“…The gradient descent method based on phase-only derivative is exactly the basic tool used in research literatures [5], [8], [14]. We will not discuss this case in this paper further.…”

Section: Connection With Gradient-based Methodsmentioning

confidence: 99%

Fast Algorithms for Designing Complementary Sets of Sequences Under Multiple Constraints

Tian-liang

Zhou

et al. 2019

IEEE Access

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“…Then, instead of minimizing nonconvex functions L Φ, {Φ k n , Λ k n , n ∈ T \0} and L n Φ k , Φ n , Λ k n directly, (22) can be relaxed to…”

Section: B Consensus-pdmm Algorithm Frameworkmentioning

confidence: 99%

“…In [19]- [21], the authors applied the majorization-minimization (MM) technique to minimize autocorrelation sidelobe levels, which can guarantee that its objective function value decreases in every iteration. The authors in [22] designed a strategy of minimizing the generalized weighted ISL measure to obtain the desired unimodular sequences.…”

Section: Introductionmentioning

confidence: 99%

Unimodular Sequences Design with Good Correlation Properties via Consensus-PDMM Algorithm

Wang

2019

ICC 2019 - 2019 IEEE International Conference on Communications (ICC)

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Unimodular sequences with good auto/crosscorrelation properties are favorable in wireless communication and radar applications. In this paper, we focus on designing these kinds of sequences. The main content is as follows: first, we formulate the designing problem as a quartic polynomial minimization problem with constant modulus constraints; second, by introducing auxiliary phase variables, the polynomial minimization problem is equivalent to a consensus nonconvex optimization problem; third, to achieve its good approximate solution efficiently, we propose two efficient algorithms based on alternating direction method of multipliers (ADMM) and parallel direction method of multipliers (PDMM); fourth, we prove that the consensus-ADMM algorithm can converge to some stationary point of the original nonconvex problem and consensus-PDMM's output is some stationary point of the original nonconvex problem if it is convergent. Moreover, we also analyze the nonconvex optimization model's local optimality and computational complexity of the proposed consensus-ADMM/PDMM approaches. Simulation results demonstrate that the proposed ADMM/PDMM approaches outperform state-ofthe-art ones in either computational cost or correlation properties of the designed unimodular sequences.

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“…The simple analysis described above indicates that to improve the autocorrelation property of a sequence it is necessary to optimize each code of the sequence, which means that the optimization problem is essentially andimensional optimization problem, and its optimal solution cannot be obtained directly. In order to solve this problem, the majority of scholars have proposed a number of algorithms to obtain the optimal solution [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Since thedimensional optimization problem may have multiple local optimal solutions, the simulated annealing [8] and stochastic optimization methods [9,10] were suggested to obtain the global optimal solution at the early stage.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

“…The work in [21] proposed a gradient-based algorithm named gradient-weighted correlation-SFW (Gra-WeCorr-SFW) to design unimodular sequences sets with both good aperiodic correlation and stopband properties. Furthermore, [22] proposed the design of unimodular sequences whose aperiodic autocorrelation and aperiodic complementary autocorrelation vanish for a given set of lags.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Optimal Unimodular Sequences Design Method for Active Sensing Systems

Hao

et al. 2018

Mathematical Problems in Engineering

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In active sensing systems, unimodular sequences with low autocorrelation sidelobes are widely adopted as modulation sequences to improve the distance resolution and antijamming performance. In this paper, in order to meet the requirements of specific practical engineering applications such as suppressing certain correlation coefficients and finite phase, we propose a new algorithm to design both continuous phase and finite phase unimodular sequences with a low periodic weighted integrated sidelobe level (WISL). With the help of the transformation matrix, such an algorithm decomposes the N-dimensional optimization problem into N one-dimensional optimization problems and then uses the iterative method to search the optimal solutions of the N one-dimensional optimization problems directly. Numerical experiments demonstrate the effectiveness and the convergence property of the proposed algorithm.

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Design of Unimodular Sequences With Good Autocorrelation and Good Complementary Autocorrelation Properties

Cited by 23 publications

References 18 publications

Fast Algorithms for Designing Complementary Sets of Sequences Under Multiple Constraints

Fast Algorithms for Designing Complementary Sets of Sequences Under Multiple Constraints

Unimodular Sequences Design with Good Correlation Properties via Consensus-PDMM Algorithm

Optimal Unimodular Sequences Design Method for Active Sensing Systems

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