The structure of least-mean-square linear estimators for synchronous -ary signals (Corresp.)

Several authors have shown that the structure of the least-mean-square linear estimator of the sequence of random amplitudes in a synchronous pulse-amplitude-modulated signal that suffers intersymbol interference and additive noise is a matched filter whose output is periodically sampled and passed through a transversal filter (tapped delay line). It is our purpose in this paper to generalize this result to synchronous -ary signals (e.g., FSK, PSK, PPM signals). We prove that the structure of the least-mean-square linear estimator of the sequence of random parameters in a synchronous -ary signal, which suffers intersymbol interference and additive noise, is a parallel connection of matched filters followed by tapped delay lines. A similar structure is derived for the continuous waveform estimator of a synchronous -ary signal. Finally, we present a structure for estimation-decision detection of synchronous -ary signals, which is based on least-mean-suare linear estimates of a probabilities.