Design of Multi-channel Equalizers via Linear Matrix Inequalities: Trade-off between Snr and Isi

Multi-channel linear equalizers are commonly employed in digital communication systems to mitigate channel distortions and thereby reduce inter-symbol interference (ISI). Traditional multichannel linear equalizer design for linear time-invariant channels requires synthesis of equalizing filters such that the frequency response of the overall system has unit magnitude and linear phase. In this work, we investigate the efficacy of deliberately allowing equalization errors, i.e., allowing deviations from unit magnitude and linear phase of the overall frequency response, with the goal of increasing the signal-to-noise ratio (SNR) in the symbol decision statistics. Our approach relies on numerical convex optimization based on linear matrix inequalities. Our investigations reveal that as the allowable equalization error is increased, the mean-square error (MSE) of the post-equalizer signal constellation decreases despite the attendant increase in ISI. This implies that the trade-off between SNR and ISI in the symbol decision statistic weighs more heavily in favor of SNR improvement for a surprisingly large range of allowable Figure 1: Multi-Channel communication model. equalization error. having a square-root raised cosine spectrum with excess band