Adaptive Multicarrier CDMA Space-Time Receivers - Adaptive Signal Processing in Wireless Communications - page 285

we can rewrite equation (10.23) as

C K n + 1

∑ ∑ ∑

u

d

ˆ

u u

YY = + ξλ Y

n nkn ,, kn ′′ ′ , kn , nkn ′ ′ ,,

u
ud

= 1

kK ′=− nn ′= − 1

-

(10. 32)

∑

K

∑

n + 1

∑

n + 1

d
Y

d

ˆ ˆ

d d d d

+ ξλ

′′=−

+ ξλ

,

Y +

N

.

kn ′′ ′ , kn , nkn ′ ′ ,, kn ′ kn , nkn ′ ,,

kK
kk

′=−
′≠

nn
nn

′′=−
′≠

1

nn 1

The signal after MC-ISR combining is then

∑

C

∑

K

∑

n + 1

H H

ˆ

u

d d

d u u

WY s =+ ξλ W Y

kn , n k n , kn ′′ ′ , kn , kn , nkn ′ ′ ,,

u
ud

=
≠

1

kK ′=− nn ′= − 1

∑

K

∑

n + 1

∑

n + 1

H
,

d

H

d

d

ˆ ′′

d

ˆ

d d d d

+ ξλ WWY

kn

+ ξ n λ , WY (10. 33)

kn ′′ ′ , kn , nkn ,, k , ′ kn kn , nkn ′ ,,

kK
kk

′=−
′≠

nn
nn

′= −
′≠

1

nn ′= − 1

H

d

+ W N .

k , n n

The MC-ISR combiner W k,n satisfies the optimization property in equation (10.25),
and thus


 


  =0


 


 

H H

d d d d

I

d

ˆ

d

ˆ ˆ ˆ

WI =⇒ 0 ar WI + I + . (10. 34)

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

This result allows the derivation of the variance of the interference rejection residuals,
as shown in the appendix. Let - 2 = E [( - k d ) 2 ] be the average power of the k t h carrier of the
desired user and - I 2 be the average interference power on each interfering carrier. The
variances of the residual I d MAI, k , n can be written as

2

ψ ςβ χβ ρ

    = ( ) () + ()     +

( ) ,

d

Var δ C 1

I

1

λ ξ ρκ

(10. 35)

MAIkn ,, k

L

where ς(β) = 1 - β/4 and



β

, if kKK =− or ,

 

8

() =

χβ  (10. 36)

k




β

, if kK =− + 1 , …− , K 1 ,



4

for MC-DS-CDMA (λ = L and f k = k / T c ) and