Considerations of SNR improvement characteristics of the optimum linear filter of systems with signal-dependent noises

A new expression model for such signal-dependent noises as shot noise and multiplicative noise which involves the introduction of a signal-dependent index, n, is proposed. The optimum linear filter with respect to the signal-to-noise (SNR) criterion is derived for transmission systems containing additive noise, some signal-dependent noise, and intersymbol-interference. By assuming Gaussian input signal waveforms, SNR improvements by the optimum filter are obtained by way of numerical calculation. It is shown that the SNR improvement increases as the signal-dependent index, n, of the dominant noise of the system increases; the improvement in intersymbol-interference here is large, and the optimum filter operates in such a way as to eliminate the dominant noise of the system first. In addition, it is shown that the SNR of the optimum filter varies according to the value of the standard deviation of a signal waveform and has a certain maximum value when the standard deviation varies under the constant signal energy. The advantages conferred by this filter are given quantitatively by comparing the SNR improvement characteristics with this filter with those of the full cosine roll-off filter.