Abstract
Bayesian inference has been successfully applied in fields as varied as anti-spam filtering, DNA sequencing, war codebreaking and election forecasting. Founded on the apparently simple Bayes’ theorem, which relates the previous distribution of a parameter with its distribution after evidence is collected, Bayesian tools allow for incorporating all existing knowledge about the phenomenon under study in order to improve parameter estimation. Because of the stochastic nature of the wireless channel, Bayesian inference is particularly well suited to the problem of symbol detection in many modern digital communication systems. When combined with Markov Chain Monte Carlo (MCMC) techniques, Bayesian receivers are capable of achieving minimum Bit Error Rate (BER) while avoiding the prohibitively high computational complexity associated with standard Maximum Likelihood (ML) or Maximum A Posteriori (MAP) estimators. In addition, such receivers are capable of numerically integrating out channel coefficients and noise variance, thus avoiding the need to use sub-optimal estimates of these parameters. This tutorial presents the rudiments of Bayesian statistics and MCMC in general, and discusses their applications in wireless communications in particular. The paper also details the design of Bayesian MCMC receiver in a system employing BPSK and ubject frequency-selective fading and Gaussian noise. Afterwards, recent advances in Bayesian receivers are surveyed for several important practical wireless transmission schemes, including MIMO, CDMA and OFDM. In addition, the paper addresses the application of Bayesian tools in challenging channel conditions — namely, nonlinear, non-Gaussian, underwater and fast fading channels.
Highlights
From the most prosaic questions, as to whether bring an umbrella when going outside, to complex ones, such as which profession to choose, life requires the ability to make decisions in an uncertain world
XI we provide a survey of recent advances in Bayesian approaches in symbol detection for some modern communication systems, emphasizing the difficulties that typically arise in those systems in comparison to the simpler scenario of Sec
We start surveying a paper in which the convergence of three Markov Chain Monte Carlo (MCMC) algorithms is investigated, and we follow with an informal discussion regarding the comparison between Bayesian/MCMC receivers and a few alternative approaches for designing blind receivers
Summary
From the most prosaic questions, as to whether bring an umbrella when going outside, to complex ones, such as which profession to choose, life requires the ability to make decisions in an uncertain world. This paper presents the rudiments of Bayesian inference and the techniques of stochastic simulation that allow it to be applied to complex problems We will describe their application to the task of symbol detection and channel estimation in digital wireless communications systems, in which the frequency selective and noisy channel produce a problem that is adequate for Bayesian tools. The first sections of the tutorial introduce the foundations of Bayesian data analysis, and include an exposition of Bayes’ theorem, the formalization of the concept of prior distribution (in particular, the conjugate and the non-informative prior distributions), the Bayesian hierarchical model and parameter elimination In the latter sections, we turn on the numerical techniques for distribution simulation based on Markov Chain Monte Carlo (MCMC), which allow for the solution of inference problems that would be otherwise intractable. The remainder of the paper surveys possible Bayesian approaches to the problem of signal detection in a wireless communication system for important modern wireless communications systems
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