Fractionally-Spaced Equalization: An Improved Digital Transversal Equalizer

As is well known,1,2 high-speed (>4.8 kbit/s) voiceband modems must employ some sort of adaptive equalization to achieve reliable performance in the presence of linear distortion and additive noise. The equalizers are invariably implemented using transversal filters, but the question of how the taps should be spaced has been, and still is, of great theoretical as well as practical interest. Conventionally, the equalizer taps are spaced at the reciprocal of the signaling rate. While it has been known theoretically that this synchronous structure does not, by itself, realize the optimum linear filter, it has up to this time provided adequate performance. The continuing demand for improved 275 performance at 9.6 kbit/s has renewed interest in adaptive equalizers whose taps are spaced closer than the reciprocal of twice the highest frequency component in the baseband signal.3-7 As we shall demonstrate, such Fractionally-Spaced Equalizers (FSES) are able to compensate much more effectively for delay distortion than the conventional synchronous equalizers. Consequently, we will show that the performance of a FSE, with a sufficient number of taps, is almost independent of the channel delay distortion, and thus of the receiver sampling phase. More generally, the FSE is able to adaptively realize, in one device, the optimum linear receiver, which is known to be the cascade of a matched filter and a synchronously-spaced equalizer.8 The purpose of this paper is to report the results of an in-depth comparative analytical and simulation study of FSES and the conventional synchronous equalizer.