Rodrigo Carvajal

EM-Based Maximum-Likelihood Channel Estimation in Multicarrier Systems With Phase Distortion

In this paper, we address channel-impulse response (CIR) estimation in multicarrier systems with phase distortion, namely, phase noise (PHN) and carrier frequency offset (CFO). The estimation problem also considers the joint estimation of the channel noise variance, CFO, and PHN bandwidth. We develop a general state-space model for multicarrier systems, separating the complex signals into their real and imaginary parts. This provides a valid framework for any modulation scheme (proper or improper). We use the expectation-maximization (EM) algorithm to solve the maximum-likelihood (ML) estimation problem. Our approach exploits the linear and Gaussian structure associated with the transmitted signal. Due to the nonlinear nature of the PHN, sequential Monte Carlo (MC) techniques are considered. Our analysis includes general expressions under different training scenarios. We show, via simulation, the impact of PHN bandwidth estimation on overall parameter estimation, and we study the impact of different training levels. In addition, we consider the accuracy of the parameter estimates, providing expressions for the Fisher information matrix (FIM) and focusing on the estimation accuracy of the PHN bandwidth.

Identification of sparse FIR systems using a general quantisation scheme

This paper presents an identification scheme for sparse FIR systems with quantised data. We consider a general quantisation scheme, which includes the commonly deployed static quantiser as a special case. To tackle the sparsity issue, we utilise a Bayesian approach, where an ℓ1 a priori distribution for the parameters is used as a mechanism to promote sparsity. The general framework used to solve the problem is maximum likelihood (ML). The ML problem is solved by using a generalised expectation maximisation algorithm.

A novel approach to model error modelling using the expectation-maximization algorithm

In this paper we develop a novel approach to model error modelling. There are natural links to others recently developed ideas. However, here we make several key departures, namely (i) we focus on relative errors; (ii) we use a broad class of model error description which includes, inter alia, the earlier idea of stochastic embedding; (iii) we estimate both, the nominal model and undermodelling simultaneously using the Expectation-Maximization (EM) algorithm. Simulation studies illustrate the performance of the proposed technique.

A map approach for ℓ q -norm regularized sparse parameter estimation using the EM algorithm

In this paper, Bayesian parameter estimation through the consideration of the Maximum A Posteriori (MAP) criterion is revisited under the prism of the Expectation-Maximization (EM) algorithm. By incorporating a sparsity-promoting penalty term in the cost function of the estimation problem through the use of an appropriate prior distribution, we show how the EM algorithm can be used to efficiently solve the corresponding optimization problem. To this end, we rely on variance-mean Gaussian mixtures (VMGM) to describe the prior distribution, while we incorporate many nice features of these mixtures to our estimation problem. The corresponding MAP estimation problem is completely expressed in terms of the EM algorithm, which allows for handling nonlinearities and hidden variables that cannot be easily handled with traditional methods. For comparison purposes, we also develop a Coordinate Descent algorithm for the ℓq-norm penalized problem and present the performance results via simulations.

On the accuracy of phase noise bandwidth estimation in OFDM systems

Phase noise is of importance in OFDM systems, since it generates intercarrier interference and general system performance degradation. In this paper we analyse the accuracy of maximum likelihood estimation of the phase noise bandwidth for OFDM systems. We utilize the auxiliary functions used in the EM algorithm to obtain an expression for the Fisher information matrix. Our key conclusion is that it is difficult to obtain accurate estimates of the phase noise bandwidth for practical cases when the number of subcarriers is limited.

EM-Based Channel Estimation in OFDM Systems with Phase Noise

In this paper we address the joint estimation of phase noise (PHN) and channel impulse response (CIR) in orthogonal frequency division multiplexing (OFDM) systems. We solve the estimation problem utilizing an algorithm based on a Monte Carlo (MC) implementation of the Expectation-Maximization (EM) algorithm. Our approach exploits the linear and Gaussian structure associated with the transmitted signal. We also focus on the impact that inaccurate estimation of PHN bandwidth has on the accuracy of the channel estimates. We show the benefits of the proposed algorithm via simulation studies.

Minimum variance control for mitigation of vibrations in adaptive optics systems

In this paper, we address the design of a minimum variance controller (MVC) for the mitigation of vibrations in modern telescope adaptive optics (AO) systems. It is widely accepted that a main source of non-turbulent perturbations is the mechanical resonance induced by the wind or the instrumentation systems, such as fans and cooling pumps. To adequately mitigate vibrations, the application of frequency-based controllers has been considered in the past decade. In this work, we express the system model in terms of the tracking of a zero-input signal via the MVC. We show that the MVC is an equivalent representation of the linear quadratic Gaussian (LQG) controller for the AO system. We also show that by developing the MVC, we can obtain different expressions, in terms of transfer functions, that offer insights into the behavior and expected performance of the controller in the frequency domain. In addition, we analyze the impact of the accuracy of the system and perturbations model on the mitigation of vibrations.

EM-based identification of sparse FIR systems having quantized data1

Abstract In this paper, we explore the identification of sparse FIR systems having quantized output data. Our approach is based on the use of regularization. We explore several aspects concerning the implementation of the Expectation-Maximization (EM) algorithm, including: i) a general framework, based on mean-variance Gaussian mixtures, for incorporating a regularization term that forces sparsity, ii) utilization of Markov Chain Monte Carlo techniques (namely a Gibbs sampler) and scenarios to implement the EM algorithm for multiple input multiple output systems. We show that for single input single output systems, it is possible to obtain closed form expressions for solving the EM algorithm.

An identification method for Errors-in-Variables systems using incomplete data

Abstract In this paper we develop a novel identification algorithm for Errors-in-Variables systems (represented in transfer function form) using incomplete data. We propose a Maximum Likelihood formulation in the frequency domain that considers a restricted frequency range from the available measurements. We compare the proposed technique with the traditional frequency domain system identification technique applied to Errors-in-Variables systems.

EM-based ML channel estimation in OFDM systems with phase distortion using RB-EKF

In this paper we address the joint estimation of the channel impulse response in orthogonal frequency division multiplexing systems with phase distortion, namely phase noise and carrier frequency offset, phase noise bandwidth and the additive noise variance. The estimation algorithm is based on an implementation of the Extended Kalman Filter within the general framework of the Expectation-Maximization algorithm. We focus on the partial training case, where the transmitted signal is not fully known. To tackle this problem, we utilize a Rao-Blackwellized Extended Kalman Filter. We also compare our results with another nonlinear filtering technique, namely Rao-Blackwellized Particle Filtering, applied to this joint estimation problem. The performance of the two filtering techniques considered in this paper is evaluated in terms of the mean square error of the channel estimates and the numerical complexity introduced by each of these techniques.