Confidence Levels For The Sample Mean And Standard Deviation Of A Rayleigh Process

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).

Optimal energy distribution applied to a least mean square error criterion for PCM transmission is discussed. Comparisons are drawn between the optimized scheme and standard scheme for: (1) White Noise Channel (2) White Noise and Rayleigh Fading Channel. It is concluded that for few bit samples only small energy savings are attained. (Author).

An equation for determination of the standard free energy of formation of a double oxide by means of a mass spectrometer has been derived. The quantities required by the equation are (1) the ratio of the intensities of an ion and (2) the ratio of the oxygen pressures at two equilibriums involving the double oxide and the constituent oxides. (Author).

Very narrow-band quenched filters used for studying VLF radio signals differ from conventional narrow-band circuits in that both signal and atmospheric noise impulses cause only brief quasi-sinusoidal outputs instead of a prolonged ringing. The random overlapping of these short noise and signal bursts can cause errors in phase measurements. It is shown that the distribution of phase errors can be calculated from the amplitude distribution of the output noise envelope. The properties of the phase distribution are discussed in detail, the computation required in the general case is illustrated by means of a numerical example. A simple 'time-sequential' method for experimentally obtaining typical amplitude distributions is suggested. (Author).