Oktay Karakuş

Estimation of the nonlinearity degree for polynomial autoregressiv processes with RJMCMC

Despite the popularity of linear process models in signal and image processing, various real life phenomena exhibit nonlinear characteristics. Compromising between the realistic and computationally heavy nonlinear models and the simplicity of linear estimation methods, linear in the parameters nonlinear models such as polynomial autoregressive (PAR) models have been accessible analytical tools for modelling such phenomena. In this work, we aim to demonstrate the potentials of Reversible Jump Markov Chain Monte Carlo (RJMCMC) which is a successful statistical tool in model dimension estimation in nonlinear process identification. We explore the capability of RJMCMC in jumping not only between spaces with different dimensions, but also between different classes of models. In particular, we demonstrate the success of RJMCMC in sampling in linear and nonlinear spaces of varying dimensions for the estimation of PAR processes.

Bayesian estimation of polynomial moving average models with unknown degree of nonlinearity

Various real world phenomena such as optical communication channels, power amplifiers and movement of sea vessels exhibit nonlinear characteristics. The nonlinearity degree of such systems is assumed to be known as a general intention. In this paper, we contribute to the literature with a Bayesian estimation method based on reversible jump Markov chain Monte Carlo (RJMCMC) for polynomial moving average (PMA) models. Our use of RJMCMC is novel and unique in the way of estimating both model memory and the nonlinearity degree. This offers greater flexibility to characterize the models which reflect different nonlinear characters of the measured data. In this study, we aim to demonstrate the potentials of RJMCMC in the identification for PMA models due to its potential of exploring nonlinear spaces of different degrees by sampling.

Long term wind speed prediction with polynomial autoregressive model

Wind energy is one of the preferred energy generation methods because wind is an important renewable energy source. Prediction of wind speed in a time period, is important due to the one-to-one relationship between wind speed and wind power. Due to the nonlinear character of the wind speed data, nonlinear methods are known to produce better results compared to linear time series methods like Autoregressive (AR), Autoregressive Moving Average (ARMA) in predicting in a period longer than 12 hours. A method is proposed to apply a 48-hour ahead wind speed prediction by using the past wind speed measurements of the Çeşme Peninsula. We proposed to model wind speed data with a Polynomial AR (PAR) model. Coefficients of the models are estimated via linear Least Squares (LS) method and up to 48 hours ahead wind speed prediction is calculated for different models. In conclusion, a better performance is observed for higher than 12-hour ahead wind speed predictions of wind speed data which is modelled with PAR model, than AR and ARMA models.

Beyond trans-dimensional RJMCMC with a case study in impulsive data modeling

Abstract Reversible jump Markov chain Monte Carlo (RJMCMC) is a Bayesian model estimation method, which has been generally used for trans-dimensional sampling and model order selection studies in the literature. In this study, we draw attention to unexplored potentials of RJMCMC beyond trans-dimensional sampling. the proposed usage, which we call trans-space RJMCMC exploits the original formulation to explore spaces of different classes or structures. This provides flexibility in using different types of candidate classes in the combined model space such as spaces of linear and nonlinear models or of various distribution families. As an application, we looked into a special case of trans-space sampling, namely trans-distributional RJMCMC in impulsive data modeling. In many areas such as seismology, radar, image, using Gaussian models is a common practice due to analytical ease. However, many noise processes do not follow a Gaussian character and generally exhibit events too impulsive to be successfully described by the Gaussian model. We test the proposed usage of RJMCMC to choose between various impulsive distribution families to model both synthetically generated noise processes and real-life measurements on power line communications impulsive noises and 2-D discrete wavelet transform coefficients.

Nonlinear model selection for PARMA processes using RJMCMC

Many prediction studies using real life measurements such as wind speed, power, electricity load and rainfall utilize linear autoregressive moving average (ARMA) based models due to their simplicity and general character. However, most of the real life applications exhibit nonlinear character and modelling them with linear time series may become problematic. Among nonlinear ARMA models, polynomial ARMA (PARMA) models belong to the class of linear-in-the-parameters. In this paper, we propose a reversible jump Markov chain Monte Carlo (RJMCMC) based complete model estimation method which estimates PARMA models with all their parameters including the nonlinearity degree. The proposed method is unique in the manner of estimating the nonlinearity degree and all other model orders and model coefficients at the same time. Moreover, in this paper, RJMCMC has been examined in an anomalous way by performing transitions between linear and nonlinear model spaces.

Bayesian Volterra system identification using reversible jump MCMC algorithm

Abstract Volterra systems have had significant success in modelling nonlinear systems in various real-world applications. However, it is generally assumed that the nonlinearity degree of the system is known beforehand. In this paper, we contribute to the literature on Volterra system identification (VSI) with a numerical Bayesian approach which identifies model coefficients and the nonlinearity degree concurrently. Although this numerical Bayesian method, namely reversible jump Markov chain Monte Carlo (RJMCMC) algorithm has been used with success in various model selection problems, our use is in a novel context in the sense that both memory size and nonlinearity degree are estimated. The aforementioned study ensures an anomalous approach to RJMCMC and provides a new understanding on its flexible use which enables trans-structural transitions between different classes of models in addition to transdimensional transitions for which it is classically used. We study the performance of the method on synthetically generated data including OFDM communications over a nonlinear channel.

The effect of convolutional encoder memory on the sphere decoding search radius in MIMO systems

In the new generation communication systems Multiple-Input-Multiple-Output systems are frequently used. The processing load of the Maximum Likelihood (ML) Detector which is the optimum detector for these systems, increases exponentially as a function of system dimension and memory due to testing all possible points. Sphere Decoding (SD) method which tests only the probable points, decreases the processing load dramatically. System memory changes by system dimensions and length of the convolutional encoder. This, in turn, affects the radius of the hyper sphere centered at the observation in the observation space at which SD attains the performance of the ML detector. This effect is investigated via simulation studies. In these simulations, it is observed that the radius of the SD is relatively smaller than the one in ML, and the ratio between the radius values varies from 6,61 in the case of memoryless 2×2 MIMO system to 1,02 in the case of 8x8 MIMO system with memory K=10 according to increased antenna numbers and system memory. In addition to these, it is observed that the radius of the hyper sphere is directly proportional to the memory of the encoder.

The Performance Comparison of European DTTV Standards with LDPC-Encoded-DVB-T Standard under AWGN Channel

In this study, in addition to previous work which is a performance comparison of European DTTV Broadcasting standards which are known as DVB-T and DVB-T2, DVB-T2’s inner encoder/interleaver block which has LDPC Encoder/Bit Interleaver, is integrated into DVB-T instead of its own inner encoder/interleaver block. This Proposed System’s performance under AWGN channel is compared to the DVB-T/T2 standards. The Proposed System achieves better performance results according to DVB-T and very close results according to DVB-T2. It achieves nearly from 4 to 7 decibels SNR gain and up to 13 Mb/s data rate gain then DVB-T results according to different code rate and modulation parameters.