arXiv subjects

Eva Arias-de-Reyna

Publications and source records attributed to Eva Arias-de-Reyna.

5 recordsLinked to original sources

arXiv2019

Equalization with Expectation Propagation at Smoothing Level

In this paper we propose a smoothing turbo equalizer based on the expectation propagation (EP) algorithm with quite improved performance compared to the Kalman smoother, at similar complexity. In scenarios where high-order modulations or/and large memory channels are employed, the optimal BCJR algorithm is computationally unfeasible. In this situation, low-cost but suboptimal solutions, such as the linear minimum mean square error (LMMSE), are commonly used. Recently, EP has been proposed as a tool to improve the Kalman smoothing performance. In this paper we review these solutions to apply the EP at the smoothing level, rather than at the forward and backwards stages. Also, we better exploit the information coming from the channel decoder in the turbo equalization schemes. With these improvements we reduce the computational complexity, speed up convergence and outperform previous approaches. We included some simulation results to show the robust behavior of the proposed method regardless of the scenario, and its improvement in terms of performance in comparison with other EP-based solutions in the literature.

eess.SP↗

arXiv2019

A double EP-based proposal for turbo equalization

This letter deals with the application of the expectation propagation (EP) algorithm to turbo equalization. The EP has been successfully applied to obtain either a better approximation at the output of the equalizer or at the output of the channel decoder to better initialize the Gaussian prior used by the equalizer. In this letter we combine both trends to propose a novel double EP-based equalizer that is able to decrease the number of iterations needed, reducing the computational complexity to twice that of the linear MMSE. This novel equalizer is developed in three different implementations: a block design that exploits the whole vector of observations, a Wiener filter-type approach that just uses the observations within a predefined window and a Kalman smoothing filter-type approach that emulates the BCJR behavior. Finally, we include some experimental results to compare the three different implementations and to detail their improvements with respect to other EP-based proposals in the literature.

eess.SP↗

arXiv2018

Turbo EP-based Equalization: a Filter-Type Implementation

This manuscript has been submitted to Transactions on Communications on September 7, 2017; revised on January 10, 2018 and March 27, 2018; and accepted on April 25, 2018 We propose a novel filter-type equalizer to improve the solution of the linear minimum-mean squared-error (LMMSE) turbo equalizer, with computational complexity constrained to be quadratic in the filter length. When high-order modulations and/or large memory channels are used the optimal BCJR equalizer is unavailable, due to its computational complexity. In this scenario, the filter-type LMMSE turbo equalization exhibits a good performance compared to other approximations. In this paper, we show that this solution can be significantly improved by using expectation propagation (EP) in the estimation of the a posteriori probabilities. First, it yields a more accurate estimation of the extrinsic distribution to be sent to the channel decoder. Second, compared to other solutions based on EP the computational complexity of the proposed solution is constrained to be quadratic in the length of the finite impulse response (FIR). In addition, we review previous EP-based turbo equalization implementations. Instead of considering default uniform priors we exploit the outputs of the decoder. Some simulation results are included to show that this new EP-based filter remarkably outperforms the turbo approach of previous versions of the EP algorithm and also improves the LMMSE solution, with and without turbo equalization.

eess.SP↗

arXiv2018

Complex-Valued Gaussian Processes for Regression

In this paper we propose a novel Bayesian solution for nonlinear regression in complex fields. Previous solutions for kernels methods usually assume a complexification approach, where the real-valued kernel is replaced by a complex-valued one. This approach is limited. Based on results in complex-valued linear theory and Gaussian random processes we show that a pseudo-kernel must be included. This is the starting point to develop the new complex-valued formulation for Gaussian process for regression (CGPR). We face the design of the covariance and pseudo-covariance based on a convolution approach and for several scenarios. Just in the particular case where the outputs are proper, the pseudo-kernel cancels. Also, the hyperparameters of the covariance {can be learnt} maximizing the marginal likelihood using Wirtinger's calculus and patterned complex-valued matrix derivatives. In the experiments included, we show how CGPR successfully solve systems where real and imaginary parts are correlated. Besides, we successfully solve the nonlinear channel equalization problem by developing a recursive solution with basis removal. We report remarkable improvements compared to previous solutions: a 2-4 dB reduction of the MSE with {just a quarter} of the training samples used by previous approaches.

cs.LG↗

arXiv2015

Proper Complex Gaussian Processes for Regression

Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process is uncorrelated with its complex conjugate. This assumption is a good model of the underlying physics in many problems, and simplifies the computations. While linear processing and neural networks have been widely studied for these signals, the development of complex-valued nonlinear kernel approaches remains an open problem. In this paper we propose Gaussian processes for regression as a framework to develop 1) a solution for proper complex-valued kernel regression and 2) the design of the reproducing kernel for complex-valued inputs, using the convolutional approach for cross-covariances. In this design we pay attention to preserve, in the complex domain, the measure of similarity between near inputs. The hyperparameters of the kernel are learned maximizing the marginal likelihood using Wirtinger derivatives. Besides, the approach is connected to the multiple output learning scenario. In the experiments included, we first solve a proper complex Gaussian process where the cross-covariance does not cancel, a challenging scenario when dealing with proper complex signals. Then we successfully use these novel results to solve some problems previously proposed in the literature as benchmarks, reporting a remarkable improvement in the estimation error.

cs.LG↗