Joint Adaptive Transmission and Switched Diversity Reception - Adaptive Signal Processing in Wireless Communications - page 157

= ( )

L

SC

F () γ F () . γ (6.3)

γ γ c

Correspondingly, the PDF of the received SNR, p γ c (·), is given by



SC

 
 

p
p

(),
()

γ
γγγ

foroption1;

γ

p () γ =

c

foroption2,

(6.4)

(( ) +

γ

SC

F SC

c

U −

γ γδγ

()(),
2

γ T T

c 2

where U(·) is the Heaviside unit step function, δ(·) is the Dirac Delta function and p γ SC (·)
denotes the PDF of the combined SNR with L branch SC, which is given for the i.i.d.
fading environment by

= ( ) −1

L

SC

p () γ L F () γ p (). γ (6.5)

γ γ γ c

6.3.2 Performance and Efficiency Analysis

6.3.2.1 Average Spectral Efficiency
The average spectral efficiency of an adaptive modulation system can be calculated as
[2, equation (33)]

N

∑ np n
n

η= ,

= 2

where p n is the probability that the n th constellation is used. For the SC-based system
under consideration, it can be shown that p n is given by



( ) − () ≥
( +



SC SC

F γ F γ , n 3 ;

 
 

 

γ T γ T c n 1 c n

foroption1;

p =

SC

(6.6)

 F γ , n = 2

n γ T

c 3




( ) − (

γ ))

SC SC

F γ F , foroption2,



γ T γ T c n + 1 c n

Therefore, the average spectral efficiency of the SC-based scheme is given by



N

NF

− ()


 

SC

γ , foroption1;

γ T c n

η =

n = 3

(6.7)



N





∑ ,
n

(()

SC

NF − γ foroption2.

γ T

c n

 = 2