Adaptive Multicarrier CDMA Space-Time Receivers - Adaptive Signal Processing in Wireless Communications - page 302


 


  =

∑∑

N N

∑

N

∑

N

t t t t

    +    

Var ξ x Var ξ x E ξξ xx

αα αα α αααα ′ ′

α = 1 α = 1 α = 1 ααα ′= ′≠ 1

∑

N

∑

N

∑

N

t t t

           

= Vx Var + E ξ αα E xx (10. 5 4)

ξ α ′ αα ′

α = 1 α = 1 ααα ′= ′≠ 1

∑

N

∑ 1

N t

∑

N t t

    +    

= VVx Var ρ E xx .

ξ α ξ α α ′

α = 1 α = ααα ′= ′≠ 1

From Var[ Σ N α=1 x α ] = 0 we have

 

N N N N t t t t

∑∑ ∑ ααα ∑




     +    =

Var x

 =

Var x E xx 0



α α αα ′

 

α = 1 α = 1 α = 1 ′= ′≠ 1

(10. 55)

N N N

t t t

∑ ∑ ∑

       

⇒ E xx =− Var x .

αα ′ α

α = 1 ααα ′= ′≠ 1 α = 1

Then, by substituting equation (10.55) in equation (10.54) we obtain






N N

t t

∑ .

 = ( )






   

Var ξ x V ρ Var x (10. 56)

αα ξ ξ α



α = 1 α = 1

Now we apply the same procedure to derive the variance of δ d MAI,k,n + δ ICI,k,n + δ ISI,k,n .
We substitute ξ α with ξ k ′, n ′ λ k ′, n and x α with W d k,n Ŷ n ′, k ′ n . The MC-ISR combiner W k,n satis-
fies the optimization property in equation (10.25); thus,


 


  =0


 


 

H H

ˆ

d

ˆ

d

ˆ

d

ˆ

d

d d

WI =⇒ 0 ar WI + I + I . (10. 57)

kn , kn , kn , MAI, ,, kn ICI, ,, kn ISI, ,, kn

hen,


 


 

∑ ≠

C

∑

K

∑ Var WY

n + 1

H
,

    = ( ))

u

d

ˆ

d d d

Var δ + δ + δ V ξ ξ

MAIkn ,, ICIkn ,, ISIkn ,, kn nkn ′′ ,,

u
ud

1

kK ′=− nn ′= − 1


 



∑

K

∑

n + 1

H

d

+ ( )

ˆ

d

V ρ Var W (10. 58)

 

ξ ξ kn , nkn ′′ ,,

kK
kk

′=−
′≠

nn ′= − 1


 


 

∑ 1

n + 1

+ ( )

H

d

d

ˆ

V ρ Var W Y nkn .

ξ ξ ′ ,,

kn ,

n nn ′= −

′≠