This paper introduces a new family of deconvolution filters for digital communications subject to severe intersymbol interference. These fixed lag smoothing filters for known channel demodulation are called Bayesian filters. Bayesian filters are derived using a new approach to suboptimal recursive minimum mean square error estimation for non-Gaussian processes. The family of Bayesian filters interpolates between the optimum fixed lag linear filter (i.e., the Kalman filter) and the optimum fixed lag symbol-by-symbol demodulator in both performance and complexity. The complexity of the Bayesian filter is exponential in a parameter, typically chosen smaller than the channel length and the filter lag. Hence, the Bayesian filter decouples the channel length and the filter lag from the exponential complexity in these parameters found in many other high performance demodulation algorithms. Simulations characterize the performance and compare the Bayesian filter to both optimal and reduced complexity demodulation algorithms.

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.

There has been great interest in reduced complexity suboptimal MAP symbol-by-symbol estimation for digital communications. We propose a new suboptimal estimator suitable for both known and unknown channels. In the known channel case, the MAP estimator is simplified using a form of conditional decision feedback, resulting in a family of Bayesian conditional decision feedback estimators (BCDFEs); in the unknown channel case, recursive channel estimation is combined with the BCDFE. The BCDFEs are indexed by two parameters: a "chip" length and an estimation lag. These algorithms can be used with estimation lags greater than the equivalent channel length and have a complexity exponential in the chip length but only linear in the estimation lags. The BCDFEs are derived from simple assumptions in a model-based setting that takes into account discrete signalling and channel noise. Extensive simulations characterize the performance of the BCDFE and BCDPE for uncoded linear modulations over both known and unknown (nonminimum phase) channels with severe ISI. The results clearly demonstrate the significant advantages of the proposed BCDFE over the BCDFE in achieving a desirable performance/complexity tradeoff. Also, a simple adaptive complexity reduction scheme can be combined with the BCDFE resulting in further substantial reductions in complexity, especially for large constellations. Using this scheme, we demonstrate the feasibility of blind 16QAM demodulation with 10/sup -4/ bit error probability at E/sub b//N/sub 0//spl ap/ 18.5 dB on a channel with a deep spectral null.>

This paper applies the Bayesian conditional decision feedback estimator (BCDFE) to rapidly fading frequency selective channels. The BCDFE is a model-based deconvolution algorithm which jointly estimates the transmitted data and channel parameters. The BCDFE applies joint symbol-by-symbol MAP demodulation and channel estimation to equalize channels, and consequently provides robust performance in rapidly fading channels. We provide a brief derivation of the BCDFE and characterize the performance on the land mobile radio channel. We assess the BCDFE's principle design characteristics and the resulting performance in both transient and steady-state operation. The effects of delay spread, Doppler spread, and co-channel interference on the BEP performance are also presented. The BCDFE demonstrates many of the desirable characteristics of an equalizer for mobile radio.>