Distribution of the Complex Envelope for Signals Received from a Channel with a "Complex" Signal-Noise Environment

Relevance. In statistical analysis of complex envelopes of modulated signals received from a communication channel, the normal distribution density is generally assumed to be the probability density model. However, in a channel with deep fading and in the presence of interference, i.e. in the case of a "complex" signal-interference environment in the channel, distribution models with heavier tails may be of interest. The logistic distribution and the hyperbolic secant distribution are considered as such in the work. Expressions for the corresponding two-dimensional probability distribution densities are presented. The aim of the work is to show that, under certain conditions, models of the distribution of the complex envelope that other than normal one can be observed in a real communication channel. Taking this into account may allow to improve the characteristics of the communication system in the tasks of adaptation and evaluation of the reliability of demodulator solutions. Research methods: To check whether the complex envelope belongs to the corresponding distribution law, the Chi-square criterion is used. The implementation of the Chi-square criterion for the case of a two-dimensional distribution density is proposed in article. As results, the paper presents the analysis of statistical processing of signals received from a real communication channel under various conditions. The novelty lies in the experimental study of the fact that in real channels, in the case of deep fading and complex signal-interference conditions, the logistic distribution or the hyperbolic secant distribution may be more preferable. The practical significance lies in the fact that taking into account the distribution model makes it possible to obtain a more adequate estimate of the mean square deviation of the noise component and the signal-to-noise ratio, which is essential for the functioning of adaptive radio communication systems, as well as in the task of evaluating soft demodulation solutions.