Approximation methods for complex polynomial optimization

Jiang, Bo; Li, Zhening; Zhang, Shuzhong

doi:10.1007/s10589-014-9640-5

Cited by 18 publications

(30 citation statements)

References 25 publications

(54 reference statements)

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“…The objective (31a) is to minimize the VIP of baseband CPS-OFDM signals so as to reduce the impact from PA nonlinearity. However, the VIP functionσ 2 x (p) is a fourthorder polynomial of p as given by (28), which generally makes the problem NP-hard and difficult to be analyzed [43]. We will overcome this difficulty later in this section.…”

Section: Optimization Of Prototype Shaping Vector Via Majorizatiomentioning

confidence: 99%

Circularly Pulse-Shaped Precoding for OFDM: A New Waveform and Its Optimization Design for 5G New Radio

Huang

2018

IEEE Access

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A new circularly pulse-shaped (CPS) precoding orthogonal frequency division multiplexing (OFDM) waveform, or CPS-OFDM for short, is proposed in this paper. CPS-OFDM, characterized by user-specific precoder flexibility, possesses the advantages of both low out-of-subband emission (OSBE) and low peak-to-average power ratio (PAPR), which are two major desired physical layer signal properties for various scenarios in 5G New Radio (NR), including fragmented spectrum access, new types of user equipments (UEs), and communications at high carrier frequencies. As opposed to most of existing waveform candidates using windowing or filtering techniques, CPS-OFDM prevents block extension that causes extra interblock interference (IBI) and envelope fluctuation unfriendly to signal reception and power amplifier (PA) efficiency, respectively. An optimization problem of the prototype shaping vector built in the CPS precoder is formulated to minimize the variance of instantaneous power (VIP) with controllable OSBE power (OSBEP) and noise enhancement penalty (NEP). In order to solve the optimization problem involving a quartic objective function, the majorization-minimization (MM) algorithmic framework is exploited. By proving the convexity of the proposed problem, the globally optimal solution invariant of coming data is guaranteed to be attained via numbers of iterations. Simulation results demonstrate the advantages of the proposed scheme in terms of detection reliability and spectral efficiency for practical 5G cases such as asynchronous transmissions and mixed numerologies.Index Terms-5G, New Radio (NR), new waveform, OFDM, DFT-S-OFDM, circularly pulse-shaped (CPS) precoding, low outof-subband emission (OSBE), low peak-to-average power ratio (PAPR), variance of instantaneous power (VIP), majorizationminimization (MM), convex optimization, transceiver design.Y. Huang and B. Su are 3GPP standardization delegates

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Section: Optimization Of Prototype Shaping Vector Via Majorizatiomentioning

confidence: 99%

Circularly Pulse-Shaped Precoding for OFDM: A New Waveform and Its Optimization Design for 5G New Radio

Huang

2018

IEEE Access

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“…Huang and Zhang [13] also discussed bilinear complex polynomial optimization models. Beyond quadratics, Jiang et al [14] studied approximation algorithms for various high-degree complex polynomial optimization under the m-th roots of unity constraints, the complex unit circle constraints, and complex spherical constraints.…”

Section: Introductionmentioning

confidence: 99%

“…The emphasis is to propose polynomial-time approximation algorithms and analyze their performances. Originated from previous researches in probability estimation of random sampling [18,8], tensor relaxation and polarization formula [9] and feasible solution reconstruction [14], we develop some new techniques and results on that line, which enable us to study a new and much more general class of complex polynomial optimization models that covers and improves many existing researches in the literature. The main contributions of the paper are as follows:…”

Section: Introductionmentioning

confidence: 99%

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Approximation algorithms for optimization of real-valued general conjugate complex forms

Jiang

2017

J Glob Optim

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Complex polynomial optimization has recently gained more and more attention in both theory and practice. In this paper, we study the optimization of a real-valued general conjugate complex form over various popular constraint sets including the m-th roots of complex unity, the complex unit circle, and the complex unit sphere. A real-valued general conjugate complex form is a homogenous polynomial function of complex variables as well as their conjugates, and always takes real values. General conjugate form optimization is a wide class of complex polynomial optimization models, which include many homogenous polynomial optimization in the real domain with either discrete or continuous variables, and Hermitian quadratic form optimization as well as its higher degree extensions. All the problems under consideration are NP-hard in general and we focus on polynomial-time approximation algorithms with worst-case performance ratios. These approximation ratios improve previous results when restricting our problems to some special classes of complex polynomial optimization, and improve or equate previous results when restricting our problems to some special classes of polynomial optimization in the real domain. These algorithms are based on tensor relaxation and random sampling. Our novel technical contributions are to establish the first set of probability lower bounds for random sampling over the m-th root of unity, the complex unit circle, and the complex unit sphere, and propose the first polarization formula linking general conjugate forms and complex multilinear forms.

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“…[8] provided approximation methods for complex polynomial optimization. In [8], the objective function takes three forms: multilinear, homogenous polynomial and a conjugate symmeric form. The constraint belongs to three sets: the mth roots of complex unity, the complex unity and the Euclidean sphere.…”

Section: Introductionmentioning

confidence: 99%

Global optimality conditions and optimization methods for constrained polynomial programming problems

Tian

Ugon

et al. 2015

Applied Mathematics and Computation

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a b s t r a c tThe general constrained polynomial programming problem (GPP) is considered in this paper. Problem (GPP) has a broad range of applications and is proved to be NP-hard. Necessary global optimality conditions for problem (GPP) are established. Then, a new local optimization method for this problem is proposed by exploiting these necessary global optimality conditions. A global optimization method is proposed for this problem by combining this local optimization method together with an auxiliary function. Some numerical examples are also given to illustrate that these approaches are very efficient.

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Approximation methods for complex polynomial optimization

Cited by 18 publications

References 25 publications

Circularly Pulse-Shaped Precoding for OFDM: A New Waveform and Its Optimization Design for 5G New Radio

Circularly Pulse-Shaped Precoding for OFDM: A New Waveform and Its Optimization Design for 5G New Radio

Approximation algorithms for optimization of real-valued general conjugate complex forms

Global optimality conditions and optimization methods for constrained polynomial programming problems

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