Adaptive linear predictors in cascade for blind deconvolution of non-stationary and non-minimum-phase channels

Brotto, Renan; Filho, Kenji Nose; Attux, Romis; Romano, João Marcos Travassos

doi:10.14209/sbrt.2019.1570558960

Cited by 1 publication

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“…where is the learning rate. For simplicity, we considered real signals in the derivation of (10) but these adaptation rules can be easily extended for complex signals [9].…”

Section: Proposed Structure and Algorithmsmentioning

confidence: 99%

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Cascade of Linear Predictors for Deconvolution of Non-Stationary Channels in Sparse and Antisparse Scenarios

Brotto

Nose-Filho²,

Attux³

et al. 2021

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This work deals with adaptive predictive deconvolution of non-stationary channels. In particular, we investigate the use of a cascade of linear predictors in the recovering of sparse and antisparse signals. To do so, we first discuss the behavior of the ℓ Prediction Error Filter (PEF), with ≠ 2, showing that it can better attenuate the effects of non-minimum phase channels in comparison with the classical ℓ 2 PEF, although the ℓ PEF, with ≠ 2, still presents intrinsic limitations in compensating the channel distortions, due to its direct forward structure. Hence, the cascade of linear predictors, i.e., one forward filter followed by a backward one, emerges as a possible solution to circumvent the structure limitation addressed. We apply the proposed cascade structure in the deconvolution of nonstationary channels, with minimum, maximum-, mixedand variable-phase responses, and also in noisy scenarios. From the simulation results we observed that, besides the duality relation between the ℓ 1 and ℓ ∞ norms, they present different algorithmic behavior: a cascade adjusted by minimizing the ℓ 1 norm of the error attains a fast convergence, enhancing the cascade tracking capacity, but is more sensitive to noise. Adjusting the cascade by minimizing the ℓ 4 norm of the error (a smooth approximation of the ℓ ∞ norm), on the other hand, leads to a filter more robust to noise, but presents slower convergence and tracking capability.

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“…where is the learning rate. For simplicity, we considered real signals in the derivation of (10) but these adaptation rules can be easily extended for complex signals [9].…”

Section: Proposed Structure and Algorithmsmentioning

confidence: 99%

“…One possible way to circumvent this limitation is using a cascade of linear predictors: a forward linear predictor followed by a backward one, as we did in [9]. The use of a series of deconvolution filters has been addressed in previous works as [10], [11], [12] and [13].…”

Section: Introductionmentioning

confidence: 99%