Sufficient statistic and reduced-dimensionality equivalent symbol-space model for frequency-flat MIMO channel with spatially nonuniform delay

An equivalent symbol-space discrete channel model for a frequency-flat block-fading MIMO spatial diversity channel with spatially nonuniform path delays is derived. A general nonlinear modulation scheme is assumed by allowing channel symbols to be multidimensional per one antenna. The sufficient symbol-spaced statistic dimensionality is shown to be a product of transmit, receive and symbol dimensions unlike for a traditional frequency-flat MIMO model where the dimension is a product of receive and symbol dimensions. The traditional model is valid only for spatially uniform delays. It is shown that the spatially nonuniform path delays cause spatial interbranch interference (IBI). A reduced-dimensionality equivalent system is introduced. The spatial IBI can be reduced by using a linear minimum mean square error spatial-temporal preprocessor (equaliser). Numerical results show that this dimensionality-reducing preprocessing significantly lowers the residual self-noise mean square in comparison with the case of deliberately ignoring the higher dimensionality of the sufficient statistic. The spatial processing is found to be the essential one; additional temporal processing has only a small impact on the residual self-noise.