Adaptive Multicarrier CDMA Space-Time Receivers - Adaptive Signal Processing in Wireless Communications - page 286

K

∑ ,

− ( )

() =

χβ ϑ
k

kk (10. 37)

kK
kk

′=−
′≠

where

 

 



  


 


 




β x

L

3
4

β
π

π
β

x
L

β x

L

π
β

x
L

( )






 

1 −− + sin + −

 



cos , if 0 ≤≤ − xL min, ββ 1

22 4 4

x
L

1 − if β ≤ xxL ≤− 1 ββ and. < 0 5

sin  


 





 


 


 

3
444

β x

L

3
4

β
π

π
β

x
L

β x

L

π
β

x
L () =

−− + +− cos +

 

ϑ x



44






 

if β 1 − ≤≤ > xL β β and . 5

sin 


 


 


 


 


 

3
8

β
π

π
β

x
L

π
β

−− −

x
L

1 β π

β

x
L

π
β

− cos −

  8 8

 

 


 


 


 


 

3
44

β 3

4

x
LL

3
8

β π
β

x
L

π
β

−− −

x
L

1 β π

β

x
L

π
β

( )

+− + sin − cos − ifmax βββ ,1 −≤ ≤ xL 1

 



8 8

(10. 38)

for MT-CDMA (λ = L and f k = k / T Mc ). The expressions of

ξ =  

 

u u u ′∗ u ′∗

ρ E ξ λξλ

kn ′′ ′ ′ ′ , kn , kn , kn ′ ,

and


 


  −

λ = ( )

2

ρ E λ

u
,

1

kn

are derived for a Rayleigh fading channel with P paths to yield

( )

( )

2

=−− ( ) ρ 11 cos 2 π M S ,

ξ rec

(10. 39)

× ( )
−

2

2

4 π f

P

τ

DPC

ρ =

λ

1

where S rec is the symbol error rate in the previous MC-ISR stage, f D is the maximum
Doppler frequency, and τ PC is the power control feedback delay. The variances of the
residuals I d ICI, k , n and I d ISI, k , n can be written as