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We will provide statistical analysis of the square ratio of

Let

As a general probability distribution model, this model includes some classical distribution models as its particular cases, for example, Rician, and Nakagami-

Let

Multipath fading is physical phenomena that occurs as randomly delayed components of desired signal combine in constructive or destructive manner at the reception [

Observing interference-limited fading environment, where corruptive effects of thermal noise can be ignored, it is necessary to determine properties of signal-to-interference ratio (SIR) in order to carry out effective performance analysis of observed system. Indeed, SIR has been measured in base and mobile stations by using SIR estimators [

The paper is organized as follows. System model and closed-form of the PDF and CDF expressions are presented in Section

The desired signal follows

Now, we will observe random envelope statistics in observed interference-limited system. Here the novelty and significance of this model must be pointed out again. Namely, for the first time scenario is observed when desired signal envelope variations are caused by

After substituting (

Namely, with respect to well-known series representation of modified Bessel function (cf. [

Following [

After substituting (

Number of terms that should be added in expression (

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In this section we give an alternative approach for getting very high-precision approximation of the probability density function (PDF), as well as one of the cumulative distribution function (CDF). Our goal is to obtain fast convergence of quadrature sums,

As already mentioned PDF of this random process could be efficiently expressed by using Gaussian quadrature formulas, namely, starting from (

For calculating the weighted integral (

In fact, the nodes

In some special cases for calculating the weight coefficients

Elements in the Jacobi matrix (

The recursion coefficients in the three-term recurrence relation (

Knowing the first

It is known that if the integrand in the weighted integral (

Then the sequence of quadrature sums

For example, for some typical parameters

Approximation of PDF,

Relative errors

Relative errors in

According to (

As before, for approximating

The corresponding relative errors

Relative errors in the quadrature sums

As we can see, in the case when

Taking

Relative errors in the quadrature sums

Approximation of CDF,

One of standard performance criteria, used for managing CCI level in faded channel, and for meeting grade-of-service and quality-of-service requirements, is OP [

Diversity combining indicates a concept of upgrading reception system performances by combining replicas of information carrying signal [

At Figure

Outage probability versus normalized SIR.

In this paper the exact PDF and CDF expressions of the square ratio of

Contribution presented in this paper provides potentials for applying proposed efficient numerical methods in carrying out analysis of other important wireless telecommunication performance measures for observed propagation scenario, such as channel capacity (CC) and average bit error probability (ABER). Closed-form expressions for ABER values could be derived when both coherent and noncoherent modulation techniques are applied for wireless propagation over

The authors declare that they have no conflicts of interest.

This work is supported in part by the Serbian Academy of Sciences and Arts (Project no. Φ-96) and by the Serbian Ministry of Education, Science and Technological Development (Projects nos. OI 174015 and III 44006).