Envelope probability density function of statistically variable fast fading and slow fading

In this paper a novel explicit analytical expression for the probability density function of the composite envelope in the presence of simultaneous changeable fast and slow fading is given. We use the term "changeable fast fading" to denote the fact that fast Nakagami fading, characterized by a given parameter m/sub i/, appears with probability p/sub i/. Analytical results are presented graphically for some characteristical values of parameters of fast and slow fading in the channel of mobile communications. This is a basic result, which opens possibilities to do explicit analytical treatment and analysis of the transmission quality in this channel. It is essentially a new contribution and quality in comparison with the present situation, where similar problems are solved using exclusively numerical integration methods or time-consuming simulation methods.