Optimum Equalization and the Effect of Timing and Carrier Phase on Synchronous Data Systems

Abstract

The minimum mean-square error (M.M.S.E.) at the receiver output generally depends upon the sampling instant and demodulating carrier phase for synchronous data systems. In this study, it is shown that for certain single-sideband data systems with no excess bandwidth (e.g., class IV and class V partial-response systems), the M.M.S.E. is completely independent of the sampling instant and demodulating carrier phase if the receiver contains an infinitely long transversal filter equalizer. Practically speaking, computer calculations indicate that for a class IV system operating in the presence of typical received signal-to-noise ratios, a 19-tap equalizer is sufficient to make the M.M.S.E. relatively insensitive to the sampling instant and demodulating carrier phase. Thus, for such data systems, a significant reduction in the receiver complexity and possibly in the start-up time may be obtained, because no time is spent acquiring timing and carrier phase. The optimum infinite-length equalizer for synchronous data systems with a fixed channel is also calculated for two different conditions. The conditions are: (i) the minimization of the output noise plus mean-square intersymbol interference and (ii) the minimization of the output noise subject to the constraint that the equalizer forces the intersymbol interference to zero. Explicit expressions for the optimum equalizer and the M.M.S.E. are obtained. Satisfying condition (i) results in the lower value of M.M.S.E.; however, the M.M.S.E.s for these two criteria are almost equivalent for either large signal-to-noise ratios or small slope of the amplitude-frequency characteristics of the channel.