Bayesian techniques for deconvolution

A new deconvolution methodology that uses Bayesian techniques is introduced. Our method is based on writing the observations in a state-space form, and formulating deconvolution as a minimum mean-square-error (MMSE) problem and/or a maximum a posteriori (MAP) one, according to the filtering objective. Bayesian filtering algorithms are proposed which decouple both the filter lag and the channel length from the exponential complexity in these parameters and achieve suboptimal fixed-lag symbol-by-symbol demodulation for both known and unknown channels. Also, a scheme called the reduced-state Bayesian filtering algorithm is proposed to adaptively reduce computational complexity, according to estimation quality. Bayesian filters (BFs) and Bayesian decision feedback filters (BDFFs) which employ recursive MMSE and MAP estimation, respectively, are proposed for known channel deconvolution. The family of BFs interpolate between the optimum fixed lag linear filter and the optimum fixed lag MMSE filter in both performance and complexity. The family of BDFFs further reduce the complexity of the BFs, generalize the decision feedback equalizer (DFE) structure, and outperform common DFE algorithms. Extensions of the above two families, called extended Bayesian filters and extended Bayesian decision feedback filters, are applied to unknown channel deconvolution. These filters are conceptually superior to other blind deconvolution algorithms in several respects: they simultaneously estimate the channel and data; they handle severe intersymbol interference (ISI) channels; and they do not require a transfer from blind to decision-directed mode but smoothly handles all phases of demodulation. Extensive simulations characterizing the performance of the Bayesian filtering algorithms in severe ISI and nonminimum phase channels are presented. Their fast convergence and robust equalization proprieties improve error performance for linearly modulated signals transmitted over finite impulse response channels. Finally, preliminary ideas of an extension of the Bayesian filtering algorithms to infinite impulse response channel deconvolution and a variation of the Bayesian filtering structure using the MAP criterion are discussed. These preliminary results highlight the potential applications and variations of the Bayesian filtering algorithms