Bayesian techniques for blind deconvolution

This paper introduces extended Bayesian filters (EBFs), a new family of blind deconvolution filters for digital communications. The blind deconvolution problem is formulated as a nonlinear and non-Gaussian fixed-lag minimum mean square error filtering problem, and the EBF is derived as a suboptimal recursive estimator. The model-based setting makes extensive use of the transmitted symbol and noise distributions. A key feature of the EBF is that the filter lag can be chosen to be larger than the channel length, while the complexity is exponential in a parameter which is typically chosen to be smaller than both the channel length and the filter lag. Extensive simulations characterizing the performance of EBFs in severe intersymbol interference channels are presented. The fast convergence and robust equalization of the EBFs are demonstrated for uncoded linearly modulated signals [e.g., differentially encoded quaternary phase shift keying (QPSK)] transmitted over unknown channels. Comparisons are made to other blind symbol-by-symbol demodulation algorithms. The results show that the EBF provides much better performance (at increased complexity) compared to the constant modulus algorithm and the extended Kalman filter, and achieves a better performance-complexity trade-off than other Bayesian demodulation algorithms. The simulations also show that the EBF is applicable with large constellations and shaped modulations.