**1. Introduction**

The additive and multiplicative noise exists forever in any wireless communication system. Quality and integrity of any wireless communication systems are defined and limited by statistical characteristics of the noise and interference, which are caused by an electromagnetic field of the environment. The main characteristics of any wireless communication system are deteriorated as a result of the effect of the additive and multiplicative noise. The effect of addition of noise and interference to the signal generates an appearance of false information in the case of the additive noise. For this reason, the parameters of the received signal, which is an additive mixture of the signal, noise, and interference, differ from the parameters of the transmitted signal. Stochastic distortions of parameters in the transmitted signal, attributable to unforeseen changes in instantaneous values of the signal phase and amplitude as a function of time, can be considered as multiplicative noise. Under stimulus of the multiplicative noise, false information is a consequence of changed parameters of transmitted signals, for example, the parameters of transmitted signals are corrupted by the noise and interference. Thus, the impact of the additive noise and interference may be lowered by an increase in the signal-to-noise ratio (SNR). However, in the case of the multiplicative noise and interference, an increase in SNR does not produce any positive effects.

The main functional characteristics of any wireless communication systems are defined by an application area and are often specific for distinctive types of these systems. In the majority of cases, the main performance of any wireless communication systems are defined by some initial characteristics describing a quality of signal processing in the presence of noise: the precision of signal parameter measurement, the definition of resolution intervals of the signal parameters, and the probability of error.

The main idea is to use the generalized approach to signal processing (GASP) in noise in wireless communication systems (Tuzlukov, 1998; Tuzlukov, 1998; Tuzlukov, 2001; Tuzlukov, 2002; Tuzlukov, 2005; Tuzlukov, 2012). The GASP is based on a seemingly abstract idea: the introduction of an additional noise source that does not carry any information about the signal and signal parameters in order to improve the qualitative performance of wireless communication systems. In other words, we compare statistical data defining the statistical parameters of the probability distribution densities (pdfs) of the observed input stochastic samples from two independent frequency-time regions – a "yes" signal is possible in the first region and it is known a priori that a "no" signal is obtained in the second region. The proposed GASP allows us to formulate a decision-making rule based on the determination of *the jointly sufficient statistics of the mean and variance* of the likelihood function (or functional). Classical and modern signal processing theories allow us to define *only the mean* of the likelihood function (or functional). Additional information about the statistical characteristics of the likelihood function (or functional) leads us to better quality signal detection and definition of signal parameters in compared with the optimal signal processing algorithms of classical or modern theories.

Thus, for any wireless communication systems, we have to consider two problems – analysis and synthesis. The first problem (analysis) – the problem to study a stimulus of the additive and multiplicative noise on the main principles and performance under the use of GASP – is an analysis of impact of the additive and multiplicative noise on the main characteristics of wireless communication systems, the receivers in which are constructed on the basis of GASP. This problem is very important in practice. This analysis allows us to define limitations on the use of wireless communication systems and to quantify the additive and multiplicative noise impact relative to other sources of interference present in these systems. If we are able to conclude that the presence of the additive and multiplicative noise is the main factor or one of the main factors limiting the performance of any wireless communication systems, then the second problem – the definition of structure and main parameters and characteristics of the generalized detector or receiver (GD or GR) under a dual stimulus of the additive and multiplicative noise – the problem of synthesis – arises.

GASP allows us to extend the well-known boundaries of the potential noise immunity set by classical and modern signal processing theories. Employment of wireless communication systems, the receivers of which are constructed on the basis of GASP, allows us to obtain high detection of signals and high accuracy of signal parameter definition with noise components present compared with that systems, the receivers of which are constructed on the basis of classical and modern signal processing theories. The optimal and asymptotic optimal signal processing algorithms of classical and modern theories, for signals with amplitudefrequency-phase structure characteristics that can be known and unknown a priori, are constituents of the signal processing algorithms that are designed on the basis of GASP.
