Model of deep fading

Introduction: Fading, i. e. random changes in the level of a radio signal, is one of the main problems in signal processing, as the result strongly depends on the fading depth. The distribution of the received signal envelope is sometimes left-shifted relative to the Rayleigh law. A radio propagation channel with such a sub-Rayleigh fading^ may be considered a "critical" one. Purpose: Synthesizing a model of a narrow-band random process with an envelope distribution left-shifted relative to the Rayleigh law. Results: The synthesis of a model is based on representing the process as a reaction of a stable dynamic system to white Gaussian noise excitation. We have obtained nonlinear stochastic second-order differential equations to simulate the fading of a radio signal having an envelope with Nakagami or Weibull distribution. The envelope is considered a Markov continuous process. An analytical expression for the envelope correlation function is obtained. It is shown that, at least, for Nakagami fading, the correlation interval of the envelope almost does not depend on its depth. Practical relevance: In various applications, including indoor radio communication, the level of the received signal can be critically low during long time intervals. The proposed model used as a simulator core for such a propagation channel provides the opportunity to evaluate the performance quality of a communication system at the stage of its development.