Appendix 1. RANDOM PROCESSES IN THE SYSTEMS OF CELLULAR MOBILE COMMUNICATION. P. 1.1. Random variables and random processes.

P.1.1. Random variables and random processes.

The value characterizing the field strength in multipath propagation of radio waves is usually a random variable.
A random variable is one that can take any unknown value X of all its physically allowed continuous or discrete values.

Processes characterized by random variables are called random. When radio waves propagate in cellular mobile communication systems, the field strengths are unambiguously determined by the parameters of the propagation environment, however, these parameters themselves randomly vary in space and time, which causes the random nature of the spatial and temporal variations in the electric field E (r, t). In fig. Clause 1 shows the changes in E (t) and E (g) in the form of random changes in the value of E measured at certain points in time and at certain points in space.

In the statistical description of a random process, a random variable is characterized by the probability of the appearance of its various values. The statistical description of a random process can be based only on the analysis of a large number of individual random implementations of the process. Only under this condition do statistical laws acquire certainty and cease to depend on the individual characteristics of individual realizations. For example, by measuring the field strength during fading, each time the device registers different values ​​of E (t) {or £ (g)}, each of the short-term measurements does not provide specific information about the field strength, but the results of many measurements make it possible to statistically evaluate the changes the median level of the electric field strength ((E)).