A Kernel Adaptive Metropolis-Hastings algorithm is introduced, for the purpose of sampling from a target distribution with strongly nonlinear support. The algorithm embeds the trajectory of the Markov chain into a reproducing kernel Hilbert space (RKHS), such that the feature space covariance of the samples informs the choice of proposal. The procedure is computationally efficient and straightforward to implement, since the RKHS moves can be integrated out analytically: our proposal distribution in the original space is a normal distribution whose mean and covariance depend on where the current sample lies in the support of the target distribution, and adapts to its local covariance structure. Furthermore, the procedure requires neither gradients nor any other higher order information about the target, making it particularly attractive for contexts such as Pseudo-Marginal MCMC. Kernel Adaptive Metropolis-Hastings outperforms competing fixed and adaptive samplers on multivariate, highly nonlinear target distributions, arising in both real-world and synthetic examples.

In this paper we consider a non-coherent and coherent spectrum sensing scheme for OFDM signals. In addition to perfect symbol timing information we also assume full channel knowledge in the coherent case. For the non-coherent and the coherent scheme we derive analytical expressions for the detection error probability. In a comparison of these analytical and additional numerical results we find that the increased complexity of the coherent scheme does not necessarily result in a better performance. We thus provide an important insight in the complexity performance trade-off of spectrum sensing schemes.

The multilevel structure of the N-QAM modulation constellations is exploited to significantly reduce the complexity of the sequential Gaussian approximation (SGA) algorithm for near optimal symbol detection in spatial multiplexing multiple- input multiple-output (MIMO) system. We propose two multilevel SGA algorithms (MSGA) which are based on depth- first search (DFS) and breadth-first search (BFS) respectively. Additionally, an important methodological contribution to this multilevel technique is proposed where the mismatch between the pseudo symbols and the true symbols is taken into consideration for the computation of posterior probabilities of symbol combinations. We justify this from a theoretical perspective as well as with numerical results. Simulation results show that the performance of the two proposed multilevel algorithms can approach that of the optimal a posteriori probability (APP) detector while its total computation cost is at most 81% and 48% of that of the original SGA algorithm for 16QAM and 64QAM modulation MIMO systems with 4 transmit/receive antennas respectively.

Detection of spatially multiplexed data transmissions subject to frequency flat fading is considered. Optimal decoders require knowledge of the marginal posterior distributions of the transmitted symbols, but their exact computation is not feasible for practical systems. Hence sub-optimal approaches are generally sought. By recasting this problem into the graphical model framework, we investigate here a recently proposed suboptimal approach which relies on a tree-based reparameterization principle. For quasi-static fading channels, the resulting decoder complexity has an order which is at most quadratic in the number of transmit antennas. However, in its standard form, the algorithm often fails to converge, severely restricting its practical usability. We here develop a novel methodology to ensure systematic convergence of the algorithm in this communication scenario at the expense of the introduction of a minimal bias on the computation of the symbol marginal posterior probabilities. This bias is quantified theoretically and its innocuity for the problem at hand is ultimately demonstrated through numerical simulations. For a system using 16-QAM modulation with four transmit and receive antennas, the proposed detector achieves a bit-error rate of 10-4requiring only 3 dB greater SNR than the optimal method.

BCJR algorithm is an exact and efficient algorithm to compute the marginal posterior distributions of state variables and pairs of consecutive state variables of a trellis structure. Due to its overwhelming complexity, reduced complexity variations, such as the M-BCJR algorithm, have been developed. In this paper, we propose improvements upon the conventional M-BCJR algorithm based on modified active state selection criteria. We propose selecting the active states based on estimates of the fixed-lag smoothed distributions of the state variables. We also present Gaussian approximation techniques for the low-complexity estimation of these fixed-lag smoothed distributions. The improved performance over the M-BCJR algorithm is shown via computer simulations.

A novel Gaussian approximation based mixture reduction algorithm is proposed for semi-blind joint channel tracking and symbol detection for spatial multiplexing multiple-input multiple-output (MIMO) systems with frequency-flat time-selective channels. The proposed algorithm is based on a modified sequential Gaussian approximation detector (SGA) which takes into account channel uncertainty, and the first order generalized pseudo-Bayesian (GPB1) channel estimator. Simulation results show that the proposed algorithm performs better than the conventional and computationally expensive decision-directed method with Kalman filter based channel estimation and a posteriori probability (APP) symbol detection.

This paper investigates iterative channel estimation and symbol detection for spatial multiplexing multiple input multiple output (MIMO) systems with frequency flat block fading channels using the expectation-maximization (EM) algorithm. The maximum likelihood (ML) estimation of the MIMO channels via the EM algorithm requires the computation of the posterior mean and covariance of transmit symbol vectors which involve an exhaustive search of all possible symbol combinations and are computationally prohibitive for large systems. However, most of the symbol combinations contribute very little to the estimation. Therefore, we suggest that sequential Gaussian approximation (SGA) algorithm can be used to identify the M most significant symbol combinations and we can approximate the mean and covariance based on those symbol combinations. Simulation results are provided to illustrate the proposed algorithm.

This work investigates the performance of a new reduced-complexity trellis decoding algorithm (termed the EP-MBCJR algorithm) when employed for the task of equalization in an indoor multiple input multiple output wireless environment. The algorithm is a generic approximate reduced-state variation of the BCJR algorithm modeled after the conventional M-BCJR algorithm. Instead of choosing the active states based on the filtered distribution of states in the forward recursion, the EP-MBCJR algorithm selects the active states based on "beliefs" on the states. This can be seen as an application of the concept of "expectation propagation" and leads to identical forward and backward recursions which can be iterated to improve system performance. A receiver architecture comprising of channel estimation, sampling phase selection and turbo equalization is proposed and its performance evaluated through computer simulations. For the simulation of channels closely resembling the physical environment, we have used channels generated in accordance with the IEEE 802.11n TGn channel models

The inferential task of computing the marginal posterior probability mass functions of state variables and pairs of consecutive state variables of a hidden Markov model is considered. This can be exactly and efficiently performed using a message passing scheme such as the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm. We present a novel iterative reduced complexity variation of the BCJR algorithm that uses reduced support approximations for the forward and backward messages, as in the M-BCJR algorithm. Forward/backward message computation is based on the concept of expectation propagation, which results in an algorithm similar to the M-BCJR algorithm with the active state selection criterion being changed from the filtered distribution of state variables to beliefs of state variables. By allowing possibly different supports for the forward and backward messages, we derive identical forward and backward recursions that can be iterated. Simulation results of application for trellis-based equalization of a wireless communication system confirm the improved performance over the M-BCJR algorithm.

Particle methods are a set of powerful and versatile simulation-based methods to perform optimal state estimation in nonlinear non-Gaussian state-space models. The ability to compute the optimal filter is central to solving important problems in areas such as change detection, parameter estimation, and control. Much recent work has been done in these areas. The objective of this paper is to provide a detailed overview of them.

We present new online algorithms to estimate static parameters in nonlinear non-Gaussian state space models. These algorithms rely on online expectation-maximization (EM) type algorithms. Contrary to standard sequential Monte Carlo (SMC) methods recently proposed in the literature, these algorithms do not degenerate over time.

The paper considers a multiple-input multiple-output (MIMO) communication system, which uses space-time trellis coding (STTC). A novel method of decoding STTC without a need to transmit training sequences is developed. The technique uses only a single channel estimate to acquire a complete set of the channels' estimates while performing STTC detection. The method is akin to blind trellis search techniques (per-survivor processing - PSP) and adaptive Viterbi. Our solution consists of the deployment of a bank of Kalman filters. The bank of Kalman filters is coupled with Viterbi type decoders, which produce tentative decisions based on Kalman channel predictions. In return, the Kalman filters use the tentative decisions to update and track the MIMO channels corresponding to a number of tracked hypotheses. The proposed technique is particularly applicable to space-time systems operating in rapidly fading environments, where STTC can be decoded and MIMO channels efficiently tracked without relying on periodic pilot sequences.

We address here the problem of developing efficient particle filtering techniques in order to estimate the state of Jump Markov Systems (JMS). These processes are often met in signal processing (target tracking, communication…). Our algorithm takes advantage of the structure of the process. We apply our algorithm to time varying autoregressive processes.

This paper addresses the general problem of estimating parameters in nuclear spectroscopy. We present a unified Bayesian formulation to tackle the various aspects of this problem. This includes deconvolution and modelling of both the peaks and background. The peaks are modelled with Gaussian or Lorentzian type functions and the background with cubic B-splines. The number of peaks and spline knots are treated as unknowns and as such are also estimated together with the model parameters. The Bayesian model allows us to define a posterior probability on the parameter space upon which all subsequent Bayesian inference is based. Direct evaluation of this distribution or its derived features such as the conditional expectation is, unfortunately, not possible on account of the need to evaluate high-dimension integrals. As such we resort to a stochastic numerical Bayesian technique, the reversible-jump Markov-chain Monte Carlo(RJMCMC) method.

This paper applies time-varying autoregressive (TVAR) models with stochastically evolving parameters to the problem of speech modeling and enhancement. The stochastic evolution models for the TVAR parameters are Markovian diffusion processes. The main aim of the paper is to perform on-line estimation of the clean speech and model parameters and to determine the adequacy of the chosen statistical models. Efficient particle methods are developed to solve the optimal filtering and fixed-lag smoothing problems. The algorithms combine sequential importance sampling (SIS), a selection step and Markov chain Monte Carlo (MCMC) methods. They employ several variance reduction strategies to make the best use of the statistical structure of the model. It is also shown how model adequacy may be determined by combining the particle filter with frequentist methods. The modeling and enhancement performance of the models and estimation algorithms are evaluated in simulation studies on both synthetic and real speech data sets.

EE Engineering University of Melbourne Parkville, Victoria 3052

We propose a hierarchical full Bayesian model for radial basis networks. This model treats the model dimension (number of neurons), model parameters, regularization parameters, and noise parameters as unknown random variables. We develop a reversible-jump Markov chain Monte Carlo (MCMC) method to perform the Bayesian computation. We find that the results obtained using this method are not only better than the ones reported previously, but also appear to be robust with respect to the prior specification. In addition, we propose a novel and computationally efficient reversible-jump MCMC simulated annealing algorithm to optimize neural networks. This algorithm enables us to maximize the joint posterior distribution of the network parameters and the number of basis function. It performs a global search in the joint space of the parameters and number of parameters, thereby surmounting the problem of local minima to a large extent. We show that by calibrating the full hierarchical Bayesian prior, we can obtain the classical Akaike information criterion, Bayesian information criterion, and minimum description length model selection criteria within a penalized likelihood framework. Finally, we present a geometric convergence theorem for the algorithm with homogeneous transition kernel and a convergence theorem for the reversible-jump MCMC simulated annealing method.

An efficient particle filtering algorithm is developed to solve the problem of demodulation of M-ary modulated signals under conditions of fading channels in the presence of non-Gaussian additive noise. Simulations for MDPSK signals are presented. The results show that the algorithm outperforms the current methods.

In this paper we address the problem of on-line source separation with sources modelled as mixtures of Gaussians which are linearly combined via a series of non-stationary mixing matrices. The online recovery of the sources from the observations is a non-linear statistical filtering problem that we address using state of the art particle filter methods. Simulations are presented and satisfactory results are obtained.

In this paper, we address the problem of on-line optimal estimation of signals modelled as the sum of sinusoids with time-varying amplitudes and phases. This is a complex optimal filtering problem. We present some efficient and original simulation-based methods to solve it. The posterior Cramer-Rao lower bound for this state estimation problem is also derived.

We address the complex problem of sequential Bayesian learning and model selection for neural networks. This problem does not usually admit any type of closed-form analytical solution and, as a result, one has to resort to numerical methods. We propose here an original sequential simulation-based strategy to perform the necessary computations. It combines sequential importance sampling, a selection procedure, variance reduction techniques and reversible jump Markov chain Monte Carlo (MCMC) moves. We demonstrate the effectiveness of the method by applying it to radial basis function networks. The approach can be easily extended to other interesting on-line model selection problems.

We address the problem of demodulation of M-ary modulated signals under conditions of noisy fading channels. The transmitted signal is corrupted in a random manner by a variety of possible mechanisms, and our aim is to recover the original message from the observations. This is a challenging non-linear filtering problem, and in order to solve it an efficient simulation-based algorithm, based on particle filters, is developed. The method combines sequential importance sampling, a selection scheme, Markov chain Monte Carlo (MCMC) methods and variance reduction techniques. Optimal fixed-lag smoothing is also considered. An application to the problem of demodulation of digital M-ary differential phase shift keyed (MDPSK) signals is presented and an extensive simulation study is carried out. The results show that the algorithm outperforms the current methods that are routinely used in most communication applications.

This paper applies time-varying autoregressive (TVAR) models with stochastically evolving parameters to the problem of speech modelling and enhancement. The stochastic evolution models for the TVAR parameters are Markovian diusion processes. The main aim of the paper is to perform on-line estimation of the clean speech and the model parameters, and to determine the adequacy of the chosen statistical models. An ecient simulation-based method is developed to solve the optimal ltering problem. The algorithm combines sequential importance sampling and a selection step, and employs several variance reduction strategies to make the best use of the statistical structure of the model. The modelling and enhancement performance of the model and algorithm are evaluated in simulation studies on real speech data sets. 1. INTRODUCTION For enhancement purposes, speech is commonly modelled as the output of an autoregressive (AR) process observed in additive white Gaussian noise (AWGN). The main sh...

Hidden Markov models are mixture models in which the populations from one observation to the next are selected according to an unobserved finite state-space Markov chain. Given a realization of the observation process, our aim is to estimate both the parameters of the Markov chain and of the mixture model in a Bayesian framework. We present an original simulated annealing algorithm which, in the same way as the EM (expectation-maximization) algorithm, relies on data augmentation, and is based on stochastic simulation of the hidden Markov chain. This algorithm is shown to converge toward the set of maximum a posteriori (MAP) parameters under suitable regularity conditions.

Jump Markov linear systems (JMLS) are linear systems whose parameters evolve with time according to a finite state Markov chain. We present three original deterministic and stochastic iterative algorithms for optimal state estimation of JMLS whose computational complexity at each iteration is linear in the data length. The first algorithm yields conditional mean estimates. The second algorithm is an algorithm that yields the marginal maximum a posteriori (MMAP) sequence estimate of the finite state Markov chain. The third algorithm is an algorithm that yields the MMAP sequence estimate of the continuous state of the JMLS. Convergence results for these three algorithms are obtained. Computer simulations are carried out to evaluate their performance.

In this paper we address the problem of the separation and recovery of convolutively mixed autoregressive processes in a Bayesian framework. Solving this problem requires the ability to solve integration and/or optimization problems of complicated posterior distributions. We thus propose efficient stochastic algorithms based on Markov chain Monte Carlo (MCMC) methods. We present three algorithms. The first one is a classical Gibbs sampler that generates samples from the posterior distribution. The two other algorithms are stochastic optimization algorithms that allow to optimize either the marginal distribution of the sources, or the marginal distribution of the parameters of the sources and mixing filters, conditional upon the observation. Simulations are presented.

An improvement over the Beadle-Djuric (see ibid., vol.4, p.259-61, 1997) method to simulate the parameters of stable invertible autoregressive moving average (ARMA) (p,q) processes is presented. It is computationally efficient and is especially suitable for simulation of high-order models.

In this paper we address the problem of the joint detection and estimation of sinusoids embedded in noise, from a Bayesian point of view. We first propose an original Bayesian model. A large number of parameters has to be estimated, including the number of sinusoids. No analytical developments can be performed. This leads us to design a new stochastic algorithm relying on reversible jump MCMC (Markov chain Monte Carlo). We obtain very satisfactory results.

We propose an original algorithm for the Bayesian joint estimation and detection of shot noise processes. The solution we propose relies on Markov chain Monte Carlo methods and provides the a posteriori probability density of the unknown parameters conditionally to the observations. The solution we propose provides many degrees of freedom for the inclusion of any a priori knowledge.