Matched Filter Systems in Rising Noise Spectrums

Abstract

It is common knowledge that the matched filters for signals in white noise have impulse responses whose time duration is exactly as long as that of the input signal. Nothing can be gained by extending the response of the matched filters to longer than one bit unless (1) the signal source is coded, or (2) the noise spectrum is rising or at least is other than white-Gaussian-ergodic. This paper discusses means of improving bit error rates without coding the source. There are essentially two ways of extending the integration time of the matched filters, each of which offers an improvement in signal-to-noise ratio. The first way is to extend the response directly to more than one bit but constrain the filter to give zero or some small pre-assigned intersymbol crosstalk. The second way is to build matched filters for multiple bits. Both techniques can be used simultaneously; i.e., matched filters can be constructed for bit patterns, and the responses can be extended to longer than the baud to which the filters are matched. Once again this extension is done under the constrain of zero or little crosstalk. In this paper, the matched filters for several examples are expanded in a rapidly converging series, each term of which is identifiable with a known network. For the cases where the shape of the noise is not known analytically, an experimental technique is given for determining sufficient statistics of the noise so that the optimum matched filters can be designed.