Orthogonal Polynomials for Complex Gaussian Processes

Raich, Raviv; Zhou, G.T.

doi:10.1109/tsp.2004.834400

Cited by 108 publications

(100 citation statements)

References 14 publications

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“…In polynomial approximations, the basis functions ( ) x Φ are made of polynomials, or orthogonal polynomials [18] Fig 1(b) as described before, the coefficients may be computed from (12) and (15), or equivalently (19).…”

Section: A Polynomial Approximationmentioning

confidence: 99%

Constrained and Preconditioned Stochastic Gradient Method

Jiang¹,

Huang²,

Wilford³

et al. 2015

IEEE Trans. Signal Process.

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We consider stochastic approximations which arise from such applications as data communications and image processing. We demonstrate why constraints are needed in a stochastic approximation and how a constrained approximation can be incorporated into a preconditioning technique to derive the pre-conditioned stochastic gradient method (PSGM). We perform convergence analysis to show that the PSGM converges to the theoretical best approximation under some simple assumptions on the preconditioner and on the independence of samples drawn from a stochastic process. Simulation results are presented to demonstrate the effectiveness of the constrained and precondi-tioned stochastic gradient method.Comment: 14 pages, 8 figure

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Section: A Polynomial Approximationmentioning

confidence: 99%

Constrained and Preconditioned Stochastic Gradient Method

Jiang¹,

Huang²,

Wilford³

et al. 2015

IEEE Trans. Signal Process.

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“…For complex Gaussian baseband input signals, a derivation of orthogonal polynomials is found in [11].…”

Section: Baseband Power Seriesmentioning

confidence: 99%

Evolution of Black-Box Models Based on Volterra Series

Silveira

Coelho

Santos

2015

Journal of Applied Mathematics

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“…As pointed out in [6], choosing an adequate set of basis polynomials (such as Hermite or Chebyshev polynomials [7]), in the context of parameter estimation, the parameters hp can be estimated with higher numerical stability than the parameters ap in (1). The actual configuration of the basis is determined by the coefficients αp,i ∈ C. Introducing the basis vector ψ(u k ) = [ψ1 (u k ) , .…”

Section: Simplified Wiener Modelmentioning

confidence: 99%

Stability analysis of an adaptive Wiener structure

Dallinger

Rupp

2010

2010 IEEE International Conference on Acoustics, Speech and Signal Processing

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In the context of digital pre-distortion, a typical requirement is to identify the power amplifier with stringently low computational complexity. Accordingly, we consider a simple gradient method which is used to adaptively fit a simplified Wiener model, i.e., a cascade of a linear filter followed by a memoryless nonlinearity, to a dispersive and saturating reference system which represents the power amplifier. For adaptation, the gradient method only relies on the difference between the output of the reference system and the Wiener model. We show that such a structure can be formulated as a proportionate normalised least mean squares (PNLMS) algorithm. As a consequence, conditions for stability in the mean square sense can be deduced. Although not proven in a strict sense, simulation results allow to conjecture robustness.

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Orthogonal Polynomials for Complex Gaussian Processes

Cited by 108 publications

References 14 publications

Constrained and Preconditioned Stochastic Gradient Method

Constrained and Preconditioned Stochastic Gradient Method

Evolution of Black-Box Models Based on Volterra Series

Stability analysis of an adaptive Wiener structure

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