Instruction


FACTA UNIVERSITATIS   

Series: Electronics and Energetics Vol. 30, N
o
 4, December 2017, pp. 599 - 609 

DOI: 10.2298/FUEE1704599S 

PERFORMANCE OF MACRO DIVERSITY WIRELESS 

COMMUNICATION SYSTEM OPERATING IN WEIBULL 

MULTIPATH FADING ENVIRONMENT 

Suad N. Suljović
1
, Dejan Milić

1
, Zorica Nikolić

1
, Stefan R. Panić

2
, 

Mihajlo Stefanović
1
, Đoko Banđur

3 

1 
University of Niš, Faculty of Electronic Engineering, Niš, Serbia 

2 
Faculty of Natural Science and Mathematics, University of Priština, 

Kosovska Mitrovica, Serbia 
3
Faculty of Technical Sciences, University of Priština, Kosovska Mitrovica, Serbia    

Abstract. In this paper, we consider wireless mobile radio communication system with 

macro diversity reception. Signal is subject to Weibull small scale fading and Gamma 

large scale fading resulting in system performance degradation. Receiver uses macro 

diversity selection combining (SC) technique in order to reduce the impact of long term 

fading effects, and two micro diversity SC branches are used to mitigate Weibull short 

term fading effects on system performance. Probability density function (PDF), and 

cumulative distribution function (CDF), as well as level crossing rate (LCR) and average 

fade duration (AFD) of the SC receiver output signal envelope are evaluated. The 

obtained expressions converge rapidly for all considered values of Weibull fading 

parameter and Gamma shadowing severity parameter. Mathematical results are studied 

in order to analyze the influence of Weibull fading parameter and Gamma shadowing 

severity parameter on statistical properties of the SC receiver output signal. 

Key words: Weibull short term fading, probability density function, cumulative 

distribution function, level crossing rate, average fade duration. 

1. INTRODUCTION 

Long term fading and short term fading degrade outage probability and limit channel 

capacity of wireless communication systems in general, and different techniques can be used 

to lessen the impact of the fading effects. One of the strategies for mitigating both effects: 

long term fading (shadowing), as well as short term fading, is the use of macro diversity 

combining reception. In general, macro diversity receiver features two or more micro diversity 

combiners, and it then combines their outputs in order to avoid the possibility of deep fades. 

                                                           

 
Received December 3, 2016; received in revised form May 5, 2017 

Corresponding author: Suad N. Suljović  

Faculty of Electronic Engineering, University of Niš, Aleksandra Medvedeva 14, 18000 Niš, Serbia 

(E-mail: suadsara@gmail.com) 



600 S. SULJOVIĆ, D. MILIĆ, Z. NIKOLIĆ, S. PANIĆ, M. STEFANOVIĆ, Đ. BANĐUR 
 

Such system reduces the influence of simultaneously long term fading effects and short term 

fading effects on system performance. There are a number of statistical distributions that can 

be used to describe small scale signal envelope variation in multipath fading channels, 

depending on propagation environment and communication scenario. Rayleigh and Nakagami-

m distributions can be used to describe signal envelope in small scale non line-of-sight 

multipath fading environments, while Rician distribution can model signal envelope in line-of-

sight multipath fading environments. Signal envelope variation in nonlinear multipath fading 

environments can also be well described by using Weibull model [1]. 

Samples of a Weibull random process can easily be obtained by taking the samples of a 

Rayleigh random process and raising them to a power. Weibull distribution therefore has a 

parameter related to nonlinearity of environment. When this Weibull parameter tends to 

infinity, Weibull multipath fading channel becomes a channel without fading effects. When 

Weibull parameter goes to two, Weibull channel reduces to Rayleigh channel, and when 

Weibull parameter goes to one, Weibull channel becomes exponential fading channel. First 

order performance measures of a communication system include: outage probability, bit error 

probability and channel capacity. These performance measures can be calculated by using 

probability density function of receiver output signal. Second order performance measures of a 

wireless communication system usually encompass average level crossing rate and average fade 

duration. These performance measures can be evaluated by using joint probability density 

function of the receiver output signal and the first derivate of output signal. 

Log-normal distribution and Gamma distribution can be used to describe variations of 

signal average power in shadowed channels. When log-normal model is used to describe 

long term fading, the expression for probability density function and cumulative distribution 

function of received output signal cannot be evaluated in the closed form. Application of 

Gamma distribution enables tractable calculation of system performance of the wireless 

communications system in shadowing environment [2]. 

There are a number of papers in open technical literature considering outage probability, bit 

error probability and average level crossing rate of macro diversity system with two or more 

micro diversity receivers operating over shadowed multipath fading channels. In [3], [4], [5] 

macro diversity system with two micro diversity branches operating over Gamma shadowed 

Nakagami-m multipath fading channels is considered. Communication channel is described by 

the use of compound model [6].  

System performance of macro diversity system in the presence of log-normal 

shadowing and Rayleigh multipath fading are presented in [7]. Average level crossing rate 

and average fade duration of macro diversity system operating over Gamma shadowed 

multipath fading channel are evaluated in [8], where macro diversity reception in cellular 

system is considered and its outage probability is calculated. 

In this paper, we analyze macro diversity selection combining receiver, with two micro 

diversity SC branches, operating over Gamma shadowed Weibull multipath fading channel. 

Macro diversity SC receiver serves to reduce considered Gamma shadowing effects and 

micro diversity SC branches mitigate Weibull multipath fading effects on system performance. 

Analytical expressions can be obtained for calculation of important performance parameters 

such as outage probability and bit error probability. To the best author’s knowledge system 

performance of macro diversity system in Weibull fading channel is not reported in technical 

literature. 



 Performance of Macro Diversity Wireless Communication System… 601 

 

2. WEIBULL RANDOM VARIABLE 

Probability density function of Weibull random variable is [9]: 
1

1
( )

x

x
ex xp




 





                                                       (1) 

where α is Weibull fading parameter and Ω is average power of x. 

Cumulative distribution function of Weibull random variable is [10,11]: 
1

Ω

0

1( ) ( )
x

x

x x
F dtp ex t




                                                     (2) 

Weibull random variable x, and its first derivative x , are: 

2 2
1 1

2 2
2

, , ,
2

x y y x x y y y x x

 
 

 


   


 ,                                 (3) 

where y is Rayleigh random variable. 

Joint probability density function (JPDF) of x and x is [12]: 

1
/ 2 2, ,

2
( )

xx yy
x x p x x xp J





 

   
 

                                                 (4) 

where the Jacobian of the coordinate transform is: 

1
2

2
2

1
2

0
2

4
0

2

y y
x

x x
J x

y y
x

y x









  

 
  
  
 

                                     (5) 

Joint probability density function of Rayleigh random variable y and its first derivative 

y is [12]: 
2

2

2 22 22Ω( ) ( )
2 1

, ( ,
2

)

yy

yy m
p p y p y

y
y y e e f




   


 
 

,                 (6) 

where fm is maximal Doppler frequency, and y  is Gaussian random variable [13, 14], with 

variance β. 

After substituting (5) and (6) into (4), the expression for JPDF of Weibull random 

variable and its first derivative becomes:  

2
2 2

2

3 4
12 21
Ω/ 2 82( ) ( ), , ,

2 2 2 Ω

x x x

xx yy yy

x
x x J p y y J p x x x ep

 


  

 
  

      
       (7) 

The average level crossing rate of Weibull random processes is [15]: 

1

/ 2 Ω

0

2

Ω
( )

x

x xx m
N dxxp xx f x e





                                         (8) 

The selection combining diversity receiver with inputs operating over identical, 

independent Weibull multipath fading channel is considered next. Signal envelopes at 



602 S. SULJOVIĆ, D. MILIĆ, Z. NIKOLIĆ, S. PANIĆ, M. STEFANOVIĆ, Đ. BANĐUR 
 

inputs of a SC receiver are denoted with x1 and x2, and the SC receiver output signal 

envelope is denoted with x. PDF of SC receiver output signal envelope is [16]: 

 
1 2 2 1 1 2

1 1

1 Ω Ω( ) ( ) ( ) (
2

2 1
Ω

) ( ) ( ) ( )
x x

x x x x x x x
p x x x x x xp F p F F xp x e e

 
 


 

      
 

  (9) 

Cumulative distribution function of SC receiver output signal envelope is [17]: 

1 2

2
1

Ω( ) ( ) ( 1)
x

x x x
x x F xF F e


 

    
 

                                        (10) 

The JPDF of SC receiver output signal and its first derivative is [17]: 

 

2
2 2

2

1 1 2

3 4
1 12 2
Ω 8 Ω, 2 , 1

2
( ) ( ) (

Ω
)

x x x x

xx x x x

x
x x p x F e ep xx

 





  


 
      

    (11) 

where the SC receiver output signal envelope is denoted with  x. 

Using the previous expression (11), level crossing rate of the process x is [17]: 

2 2 1

1 1

/ 2 Ω Ω

0 0

( ) ( ) ( )
2

2 ( )2 2 1
x x

x xx x xx x x m
N dxxp xx F x dxxp xx F x N f x e e

  
 


 

        
   (12)                            

This expression can be used for calculation of average level crossing rate of wireless 

communication system with SC receiver operating over Weibull multipath fading channel. 

3. MACRO DIVERSITY SYSTEM WITH TWO MICRO DIVERSITY BRANCHES 

Macro diversity system with two micro diversity SC branches is considered next. Received 

signal experiences Gamma correlated long term fading and Weibull short term fading resulting 

in signal envelope and average power variation. Model of the system considered in this paper is 

shown in figure 1. Signal envelopes at inputs of the first micro diversity SC combiner are 

denoted with x11 and x12 and at input of the second micro diversity SC combiner with x21 and x22. 
Signal envelopes at the outputs of micro diversity SC combiners are denoted with x1 and x2, and 
ultimately, at the output of macro diversity SC combiner with x. 

 

Fig. 1 Model of a macro diversity system, featuring two front-end micro diversity combiners 



 Performance of Macro Diversity Wireless Communication System… 603 

 

Average signal powers at the inputs of micro diversity SC combiners are denoted with 
Ω1 and Ω2, and they follow correlated Gamma distribution [18]: 

 

1 2

2
0

1 2

1 2

2
0

1
Ω Ω

2
1/ 2 1/ 2Ω 11 2

Ω Ω 1 2 1 1 21 22 1
00

Ω Ω 1 12

(

Ω 1 1 2

2 2 2 2

)

0

( )

0

(Ω Ω ) 2
Ω Ω Ω Ω

Ω 1Γ( )(1 ) Ω

Ω Ω

Γ( ) Ω 1 !

( , )
( )

Γ( )

1

( )i

c

ccc

i c i ci

i c i c

e I
c

e
c i i

p

c









    


 





 
 


 

 



 

 

 

 (13) 

where Γ(a) denotes the well-known Gamma function [19, eq.(8.310)], ρ is correlation 

coefficient, Ω0 is the scaling factor proportional to mean value of Ω1 and Ω2, c  1/2 is Gamma 

shadowing parameter, and In () is the n-th order modified Bessel function of the first kind [19, 

eq. (8.406)]. Macro diversity SC receiver selects the branch with the highest signal power.  

Therefore, using the expression (9), probability density function of x can be written as 

[16]:   
1 2

1 1 2 2 1 2

Ω Ω

1 2 1 Ω Ω 1 2 2 1 2 Ω Ω 1 2

0 0 0 0

Ω Ω Ω Ω Ω Ω Ω( ) ( ) ( ) ( ) ( )Ω,
x x x

d d x p d d x pp x p p
 

         

  

1

1 1 2

1

2
1 0 1

Ω 1 2

1 2 1 Ω Ω 1 2 2
00 0 0

1 1

(1 )2 1
1 1 2

0 0

4
2 Ω Ω Ω Ω

( ) (1 ) ! (
( ) ( ,

)

1 ,

)

(1 )

i

x i c i
i

x x
i c

x
d d x p

c i i c

d e

p

e i c

 

  





   

    

 
   

    

    
         

       

 



 

1 2

1

2
2 1

1 2 1

2

1 2

1 2 1 2

2 2 2

2 2

1
1

0 0 2 2 2
2 2

0 1 1 1 1

1 2 2

2
2 2 1 2 2 12 2

0 0

8

Γ( )
Ω 1 !Γ( )( )(1 )

2
2 2 4

Ω 1 Ω 1

( )

( ) ( )

i i c

i

i
i ii i i c

i

i i c

i i c i i c

x

c
i i

K

c i c i c

x x
K

    

 

     

  

    







 
  

    

    
     

     
    



         (14) 

where γ(a, x) is incomplete lower Gamma function, (a)n is Pochhammer symbol [19] and 

Kν(·) is the second kind of the modified Bessel function of order ν [19, eq. (8.407)]. 

Using the expression (12), the level crossing rate of macro-diversity SC receiver output 

signal envelope of x can be written in the form [20]: 
1 2

1 1 2 2 1 2

1 1

1 1 2

1 2 2

Ω Ω

1 2 1 Ω Ω 1 2 2 1 2 Ω Ω 1 2

0 0 0 0

Ω 2

1 1 1 Ω Ω 1 2
0 0 1 1 1 10 0

( ) ( ) ( , ) ( ) ( , )

2
( ) (

Ω Ω Ω Ω Ω Ω Ω Ω

8
2 Ω Ω Ω Ω

Γ( ) !Γ( )( )
, )

(1 )

x x x

i

m
x

i i i

N d d N x p d d N x p

f
d d N x p

c i i c i c i c

x
 

  

 

    


   

  





   

 

     

2
1

2
1

1 2 1 2

12
4 2

1 12 2 2
2 2 2 2

0 0 02 2

1

4 2
2 2 4

Ω 1 Ω( ) ( )1 1( )Ω

i
i i

i c

i i c i i c

c

x x x
KK

  
  

     

        
      

            

  (15)                    



604 S. SULJOVIĆ, D. MILIĆ, Z. NIKOLIĆ, S. PANIĆ, M. STEFANOVIĆ, Đ. BANĐUR 
 

Using the expression (10), cumulative distribution function of macro diversity SC 

receiver can be written in the form [21]: 

1 1

1 1 2 2 1 2

Ω Ω

1 2 1 Ω Ω 1 2 2 1 2 Ω Ω 1 2

0 0 0 0

Ω Ω Ω Ω Ω Ω( ) ( ) ( , ) ( ) ( , )Ω Ω
x x x

F d d F x d d F xx p p
 

         

 

1 1

1 1 2 1 2 1 2

1 2

2
1 2 1

2

1 2

Ω 2

1 2 1 Ω Ω 1 2 2 2 22
0 00 0 0 1 1

2 2
2 2

0 0
1 2

1 1

2 2

0

2

2
2 Ω Ω Ω Ω

Γ( ) Ω 1 !Γ( )

Ω 1 Ω 11
Γ(2 2 ) 4

( )

( ) ( , )
( )

( ) (

(1 ) 2 2

2
2

Ω

)

(1

i

x i i c i i c
i i

i
i i c i

i i c

c

i

i

i

d d F x p
c i c

x
i i c

c i c

x
K

  

   
 

 




 

 


   

 


    

             




 

2
1

1 2

2

0 2 22 2

0

22( Ω 1 ) 4(
) ( )Ω

)
1

i
i c

i i c

x
x K


 


 

   
    

        

 (16) 

Using expressions (16) and (15), we can easily obtain AFD. The AFD is defined as 

the average time over which the signal envelope ratio remains below the specified level 

after crossing that level in a downward direction, and is determined as [12,15]: 

 

1

2
1

1 2

2

2
1

1

1 2 2

2

0 0 2 2
1 1 1 1 0

1
2 4

2
0 0 1 1 1 1 0

2

!Γ( )( )(1 ) Ω 1( )
( )

( )

4 2
!Γ( )( )

( ( ))

( )(1 ) Ω 1

i

i
ii i

i

x

x j
c

m
j j

x

j
j

j

i i c i c i cF x
T x

N x
x

f x
j c c jj j c

 

 

 
 



 



    
  

 
  

     



 

     

2
1 2 21

1

4 2

11 2

1 2 1 21 2

2
1

1 2 1 2

2 2
20 1 2

2 2 2 22 2 2 2

0 0

1 12
2 2 2 2

02 2

Ω 1 Γ(2 2 ) 2
2 2 2 4

Ω 1 Ω 12

2
2 2 4

Ω 1

( ( ))

( ) ( )

( )

i
i c

j
j c

i
i c i

i c

i i c i i ci i c

j j c j j c

i i c x x
x K K

x x
K K













        
 

    

 

     

     
    

 
 
 


    
   


 
 
 







2

0
(Ω 1 )

 
 
 
 

 (17) 

4. NUMERICAL RESULTS 

Numerically obtained results are presented graphically in order to examine the influence 

of shadowing and fading severity on the concerned quantities. Probability density function of 

macro diversity SC receiver output signal is given in Fig. 2. It is evident that the probability 

density function shifts to the right due to the increase of α, while the change of correlation 

coefficient ρ causes only slight changes of general PDF behavior. 

Level crossing rate values normalized by maximal Doppler shift frequency fm, versus SC 

receiver output signal, are presented in Fig. 3, for several values of Weibull fading parameter 

α, Gamma shadowing severity parameter c and correlation coefficient. In Fig. 3, abscissa 

represents arbitrary crossing level, relative to scaling factor 0. 

http://jwcn.eurasipjournals.springeropen.com/articles/10.1186/1687-1499-2011-151#Fig1


 Performance of Macro Diversity Wireless Communication System… 605 

 

0 2 4 6 8

0,0

0,5

1,0

p
(x

)

x

 =1, 

=1, =0.2, c=1

 =1.5, 

=1, =0.2, c=1

 =2, 

=1, =0.2, c=1

 =2.5, 

=1, =0.2, c=1

 =3, 

=1, =0.2, c=1

 =1, 

=1, =0.4, c=1

 =1, 

=1, =0.6, c=1

 =1, 

=1, =0.8, c=1

 

Fig. 2 PDF of macro diversity SC receiver output signal 

-10 -5 0 5 10 15 20

1E-3

0,01

0,1

1

N
x
[x

]/
fm

x[dB]

 =1, 

=1, =0.2, c=1

 =1.5, 

=1, =0.2, c=1

 =2, 

=1, =0.2, c=1

 =2.5, 

=1, =0.2, c=1

 =3, 

=1, =0.2, c=1

 =1, 

=1, =0.4, c=1

 =1, 

=1, =0.6, c=1

 =1, 

=1, =0.8, c=1

 

Fig. 3 LCR for different fading severity and correlation parameter 

-10 -5 0 5 10 15 20

1E-4

1E-3

0,01

0,1

1

N
x
[x

]/
fm

x[dB]

 =1, 

=1, =0.2, c=1

 =1.5, 

=1, =0.,2 c=1

 =2, 

=1, =0.2, c=1

 =2.5, 

=1, =0.2, c=1

 =3, 

=1, =0.2, c=1

 =1, 

=1, =0.2, c=1.5

 =1, 

=1, =0.2, c=2

 =1, 

=1, =0.2, c=2.5

 =1, 

=1, =0.2, c=3

 

Fig. 4 LCR for different fading and shadowing severity 



606 S. SULJOVIĆ, D. MILIĆ, Z. NIKOLIĆ, S. PANIĆ, M. STEFANOVIĆ, Đ. BANĐUR 
 

Average level crossing rate increases as the crossing level increases towards the mean 

signal level. Close to mean signal level, LCR achieves its maximum and then decreases 

again with increasing the crossing level. Sharpness of the peak near the maximum is closely 

related to Weibull fading severity parameter. While the higher values of Weibull parameter 

α correspond to less severe fading conditions, increasing of correlation parameter slightly 

worsens the effectiveness of diversity reception. 

It is evident from Fig. 3. that, for severe fading conditions, higher correlation increases 

probabilities that signal passes lower threshold levels. General influence of correlation is the 

same for lower fading severity, but this is not shown in figures. When correlation coefficient 

tends to one, the same signal is present simultaneously on both antenna ports and system will 

not be able to achieve any diversity gain. 

Fig. 4 shows LCR when shadowing severity parameter increases. This increases the 

mean signal level, identified by the peak LCR, and it is the consequence of normalization by 

the scaling factor 0, which we chose previously. Going back to (13), we see that averaging 

over 1, mean value of 2 is c0, and vice versa. This higher mean value is clearly seen as 

LCR curves shift to the right in Fig. 4. By increasing parameter c, shadowing severity 

decreases, which is analogous to behavior due to Weibull parameter . 

Cumulative distribution function of macro diversity SC receiver output signal for different 

system parameters is presented in Fig. 5. From the figure, we can conclude that changes of the 

parameter α show significant influence on the outage probability. Due to an increase in the 

parameter α, the outage probability becomes lower, and the system is more stable at lower 

threshold levels. Cumulative distribution clearly shows that probability of signal staying below 

the threshold level is lower. An increase of parameter ρ affects the stability of the system also. If 

ρ rises, the outage probability is greater and the system operation becomes less stable. 

-10 -5 0 5 10 15 20

1E-4

1E-3

0,01

0,1

1

F
x
[x

]

x[dB]

 =1, 

=1, =0.2, c=1

 =1.5 

=1 =0.2, c=1

 =2, 

=1, =0.2, c=1

 =2.5, 

=1, =0.2, c=1

 =3, 

=1, =0.2, c=1

 =1, 

=1, =0.4, c=1

 =1, 

=1, =0.6, c=1

 =1, 

=1, =0.8, c=1

 

Fig. 5 CDF for different system parameters 

 

Table 1 represents the table of convergence for the expression (16) in reliance on the 

variable x. The table shows number of terms needed to be included in (16), in order for 

the accuracy of the resulting expression to achieve 6 accurate decimal positions, for the 



 Performance of Macro Diversity Wireless Communication System… 607 

 

given parameter values. It is evident that the expression converges rapidly for the given 

parameters. We can conclude from the table 1 that due to increase of the coefficient α, the 

number of terms that have to be summed is slightly lower, while for the greater values of 

correlation coefficient ρ, the required number of terms increase.  

 

Table 1 Number of terms that should be added in expression (16) in order  

to reach 6 accurate decimal positions, when parameters α and ρ change. 

 

 x= -10 dB x=0 dB x=10 dB 

α=1,  Ω0=1, ρ=0.2, c=1 8 13 19 

α =1.5, Ω0 =1, ρ =0.2, c=1 6 13 19 

α =2,  Ω0 =1, ρ =0.2, c=1 5 13 19 

α =2.5,  Ω0 =1, ρ =0.2, c=1 5 13 19 

α =3,  Ω0=1, ρ =0.2, c=1 5 13 19 

α =1,  Ω0 =1, ρ =0.4, c=1 9 15 19 

α =1,  Ω0 =1, ρ =0.6, c=1 9 15 21 

α =1,  Ω0 =1, ρ =0.8, c=1 13 20 29 

-10 -5 0 5 10 15 20

0,01

0,1

1

10

T
x
[x

]/
fm

x[dB]

 =1, 

=1, =0.2, c=1

 =1.5, 

=1, =0.2, c=1

 =2, 

=1, =0.2, c=1

 =2.5, 

=1, =0.2, c=1

 =3, 

=1, =0.2, c=1

 =1, 

=1, =0.4, c=1

 =1, 

=1, =0.6, c=1

 =1, 

=1, =0.8, c=1

 

Fig. 6 AFD for different system parameters 

Fig. 6 presents normalized values for average fade duration for various system 

parameters. When the crossing threshold level x is below the average signal level, AFD 

stays low, and it is the main mode in which the system is operates normally. Better 

performance is expected in cases where the value of Weibull parameter α is higher, and 

correlation coefficient ρ is lower, resulting in lower AFD. 



608 S. SULJOVIĆ, D. MILIĆ, Z. NIKOLIĆ, S. PANIĆ, M. STEFANOVIĆ, Đ. BANĐUR 
 

4. CONCLUSION 

Macro diversity receiver with macro diversity SC combiner and two micro diversity 

SC combiners operating over Gamma shadowed multipath fading environment is considered 

in this paper. Received signal experiences combined effects of Gamma long term fading and 

Weibull short term fading resulting in system performance degradation. When shadowing 

severity parameter tends to infinity the composite channel approaches a simple Weibull 

multipath channel, and when Weibull fading parameter tends to infinity the channel tends to 

a Gamma shadowing channel. When Weibull fading parameter equals two, the composite 

fading channel reduces to Gamma shadowed Rayleigh multipath channel. 

Closed form expressions for probability density function, cumulative distribution 

function and average level crossing rate of macro diversity SC receiver output signal 

envelope are calculated. For special case when Weibull parameter is equal to two, we can 

easily evaluate PDF, CDF and average level crossing rate for the resulting Rayleigh signal 

envelope. Infinity series expressions converge for any values of Gamma shadowing severity 

parameter, Weibull fading parameter, and shadowing correlation coefficient. Number of terms 

that need to be summed in order to achieve desired accuracy depends on Gamma severity 

parameter, Weibull fading parameter and correlation coefficient. The number of terms increases 

as Gamma severity parameter and Weibull parameter deceases, and correlation coefficient 

increases. 

Level crossing rate and average fade duration are presented graphically to show the 

influence of Gamma severity parameter, Weibull fading parameter, and correlation coefficient. 

on average level crossing rate of SC receiver output signal. As expected, system performance is 

better when the fading and shadowing severity is lower, and correlation between the 

diversity branches is relatively low. When the correlation of shadowing effects on the two 

macro branches is substantial, macro diversity system gains are minimal, and the receiver 

performance reduces to performance of a micro diversity receiver. 

Acknowledgement: The paper is supported in part by the projects III44006 and TR32051 funded 

by Ministry of Education, Science and Technological Development of Republic of Serbia. 

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