A robust H2 filtering approach and its application to equalizer design for communication systems

In this paper, we aim at developing a robust H₂ filtering approach to the design of robust equalizers for communication systems. The contents of this paper mainly include two parts. First, we present a robust H₂ filter design method for general multi-input multioutput linear systems with norm-bounded uncertainties in the system matrices based on the linear matrix inequality technique. The characteristics of the equalization problem are taken into account in the filtering model considered here. The advantage of the proposed method is that we can find the optimal solution to robust H₂ filtering problem at a reasonable computational burden. Second, we apply the above method to the design of robust equalizers. Two generic examples are studied, one for a single transmit and receive antenna system and another for a multiple transmit and receive antenna system. Both analytical and simulation results show that robust H₂ equalizer outperforms the zero-forcing equalizer in both bit-error rate and mean-square errors in the whole simulated range of the signal-to-noise ratio (SNR) when the channel is perturbed from its nominal value, while for the nominal channel, the robust H₂ equalizer performs better than the zero-forcing equalizer when the SNR is lower, but it performs worse than the zero-forcing equalizer when the SNR is higher.