It is well known that in communicating over randomly time-varying channels, a receiver which performs a channel measurement can make a better decision than one that does not. It is shown that a channel-measuring system improves system performance even when the channel characteristics are fixed only during the present message interval. The randomly time-varying channel studied is that of a Rayleigh fading medium with independently fading mark and space channels whose fading is fixed over one baud interval but is independent from baud to baud. The transmission system is a modified frequency shift keying (FSK) system such that during a portion of a baud interval the mark and space frequencies are always transmitted so as to act as reference signals. For the above system, the following characteristics have been established: (a) Optimum receiver configuration, (b) Optimum ratio alpha of information energy to total signal energy as a function of total available signal-to-noise ratio for a single fading channel, (c) Asymptotic optimum alpha for an M-diversity channel, (d) Error probabilities for (b) and asymptotic error probabilities for (c) for alpha opt as a function of total signal-to-noise ratio. The asymptotic results show that by using reference techniques the order of diversity is effectively doubled. (Author).