Trade-off between SNR and ISI in multi-channel zero-forcing equalizers

One of the primary objectives in linear equalizer design for communication systems, is to reduce inter-symbol interference (ISI) without enhancing the additive noise power. Indeed, ISI and noise power enhancement are competing impairments. A popular linear equalizer design technique is based on minimizing the mean-square error (MSE) between the output response of the equalizer and a desired response. While equalizer design based on minimum MSE (MMSE) provides joint minimization of ISI and noise power enhancement, it does not provide a direct trade-off between these two impairments. In this work we will show that performance gains are achievable, under certain conditions, by imposing a design technique which can more directly incorporate a tradeoff between ISI and additive noise power enhancement. We have developed a multi-channel equalizer design process based on the zero-forcing (ZF) criteria which ultimately permits us to maximize the signal-to-noise ratio at the output of the equalizer by deliberately permitting an error level in the ZF criteria. That is to say, our design method minimizes the noise power at the output of the equalizer under the constraint of a bound on the allowable equalization error. Our approach relies on numerical convex optimization based on linear matrix inequalities