Simultaneous multichannel time domain equalizer design based on the maximum composite shortening SNR

A time domain equalizer (TEQ) is a finite impulse response filter that shortens the channel impulse response (CIR) to mitigate intersymbol interference (ISI). P. Melsa et al. (see IEEE Trans. on Commun., vol.44, p.1662-72, 1996) minimized ISI in the time domain by maximizing the shortening signal-to-noise ratio (SSNR) of the energy in a target window to the energy outside the target window in the shortened CIR. Infinite SSNR means zero ISI. Melsa et al. also developed a joint channel shortening method to design a single TEQ to shorten a channel and a near-end echo impulse response. We extend the joint SSNR method to design a single TEQ to shorten multiple channels by maximizing the composite SSNR. The composite SSNR is a weighted sum of normalized channel SSNRs. The normalized SSNR is the ratio of the energy in the target window samples to the energy of all samples in the shortened CIR and has a range of [0, 1] so that it is better suited for numerical stability and fixed-point implementation. Our proposed method outperforms the joint channel shortening method. because it achieves higher weighted sum of SSNRs of the used channels.