Exploiting symmetry in channel shortening equalizers

Time-domain equalization is crucial in reducing intercarrier and intersymbol interference in multicarrier systems. A channel shortening time-domain equalizer (TEQ), which is a finite impulse response (FIR) filter, placed in cascade with the channel, produces an effective impulse response that is shorter than the channel impulse response. We show that finite length minimum mean squared error (MMSE) and maximum shortening SNR (MSSNR) TEQs are approximately symmetric, and infinite length MSSNR TEQs with a unit norm TEQ (UNT) constraint are exactly symmetric. A symmetric TEQ halves FIR implementation complexity, enables the frequency-domain equalizer and TEQ to be trained in parallel, and exhibits only a small loss in bit rate over nonsymmetric TEQs. In addition, a symmetric MSSNR-UNT TEQ reduces training computational complexity by a factor of 4 and doubles the length of the TEQ that can be designed.