On gradient adaptation with unit-norm constraints

Douglas, S.C.; Амари, Шун-ичи; Kung, Sun Yuan

doi:10.1109/78.845952

Cited by 59 publications

(45 citation statements)

References 12 publications

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Section: Introductionmentioning

confidence: 99%

“…This approach is popular in subspace estimation and tracking problems with unitary constraints [28]- [31]. The gradient assisted cost function J (w) (with 1 w ∈ U(m, 1)) maximization (or minimization) problem is surveyed and investigated in [28]. For instance, using ideas from [28], the vector at time index n−1, w(n−1) ∈ U(m, 1) could be perturbed according tow(n) = w(n−1)+g(n−1) in Euclidean space C m×1 and projected as w(n) =w (n) w(n) .…”

Section: Introductionmentioning

confidence: 99%

“…The gradient assisted cost function J (w) (with 1 w ∈ U(m, 1)) maximization (or minimization) problem is surveyed and investigated in [28]. For instance, using ideas from [28], the vector at time index n−1, w(n−1) ∈ U(m, 1) could be perturbed according tow(n) = w(n−1)+g(n−1) in Euclidean space C m×1 and projected as w(n) =w (n) w(n) . The function g(n − 1) denotes the gradient vector defined by g(n − 1) = µ(n − 1)…”

Section: Introductionmentioning

confidence: 99%

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MIMO Systems with Limited Rate Differential Feedback in Slowly Varying Channels

Kim

Love

Clerckx³

2011

IEEE Trans. Commun.

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Abstract-In this paper, an adaptive limited feedback linear precoding technique for temporally correlated multiple-input multiple-output (MIMO) channels is proposed, where the receiver has perfect channel knowledge but the transmitter only receives a quantized channel direction. To perform adaptation to the time correlation structure, we employ a differential feedback, where the "amount" of the perturbation added to the previous precoder is determined by the statistics of the directional variation. Based on random matrix quantization analysis, we develop a spherical cap codebook approach, where the cap is centered at the previous precoder and the radius of the cap is determined proportional to the identified directional variation. If the channel is highly correlated in time, the proposed differential feedback scheme can achieve a throughput improvement in the large codebook size regime. The rest of the paper is devoted to developing a systematic spherical cap codebook generation method. The developed approach employs a feedback scheme that uses a differential rotation of the previously used precoder. Our codebook adaptation is based on generating a perturbation in Euclidean space and projecting the perturbation onto the unitary space. Simulation results show that the proposed adaptation scheme accurately tracks the channel using only a small rate of feedback.Index Terms-Multiple-input multiple-output (MIMO) channel, adaptive linear precoding, limited feedback, differential feedback, temporal correlation.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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MIMO Systems with Limited Rate Differential Feedback in Slowly Varying Channels

Kim

Love

Clerckx³

2011

IEEE Trans. Commun.

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“…is numerically-unstable for PSA and MSA, such that the rows of W(k) slowly diverge from orthonormality over time [29,32]. For this reason, modifications of the updates are required.…”

Section: General Implementation Issuesmentioning

confidence: 99%

“…where R xx is a symmetric positive-definite matrix, then (5) and (6) forms the framework for principal subspace analysis (PSA) or minor subspace analysis (MSA) [23][24][25][26][27][28][29][30][31][32]. Alternatively, if J (W) is a contrast function, then (5) and (6) forms the framework for contrast-based blind source separation of prewhitened instantaneous mixtures [33][34][35][36].…”

Section: Grassmann and Stiefel Manifoldsmentioning

confidence: 99%

Gradient Adaptive Paraunitary Filter Banks for Spatio-Temporal Subspace Analysis and Multichannel Blind Deconvolution

Douglas

Амари

Kung

2004

The Journal of VLSI Signal Processing-Systems for Signal, Image

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Abstract. Paraunitary filter banks are important for several signal processing tasks, including coding, multichannel deconvolution and equalization, adaptive beamforming, and subspace processing. In this paper, we consider the task of adapting the impulse response of a multichannel paraunitary filter bank via gradient ascent or descent on a chosen cost function. Our methods are spatio-temporal generalizations of gradient techniques on the Grassmann and Stiefel manifolds, and we prove that they inherently maintain the paraunitariness of the multichannel adaptive system over time. We then discuss the necessary practical approximations, modifications, and simplifications of the methods for solving two relevant signal processing tasks: (i) spatio-temporal subspace analysis and (ii) multichannel blind deconvolution. Simulations indicate that our methods can provide simple, useful solutions to these important problems.

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