Spatial-temporal fractionally spaced decision-feedback equalisation for fading channels with dispersive interference

The authors study the spatial-temporal minimum mean square error decision-feedback equaliser (ST-DFE) to combat dispersive interference over fading channels. The proposed ST-DFE consists of an anticausal fractionally spaced feedforward filter (FFF) on each antenna branch to perform co-channel interference (CCI) and precursor intersymbol interference (ISI) cancellation, followed by a symbol-spaced feedback filter to remove postcursor ISI. An optimum ST-DFE with a double-sided symbol-spaced FFF demonstrates excellent CCI/ISI cancellation ability, but occupies wider time span and is too complicated to implement in practice. Several ST-DFE schemes using the anticausal symbol-spaced FFF were proposed, but the simulation reveals that such an approach is unable to eliminate dispersive CCI efficiently and even performs substantially worse than spatial-temporal linear equalisers, when the continuous transmitted pulse shape is considered. The performance might become worse owing to the error propagation. The proposed ST-DFE is capable of improving the performance significantly, and even outperforms the double-sided symbol-spaced ST-DFE. The algorithm for computing the fractionally spaced coefficients is presented and then applied to the fast error probability calculation using the Gauss quadrature rule which can approximate the probability of the density function of the residual ISI and CCI. Such an approach avoids the interference characteristic of the inaccurate Gaussian method.