Adaptive Multicarrier CDMA Space-Time Receivers - Adaptive Signal Processing in Wireless Communications - page 304

he interference I k,n is approximated as a Gaussian distributed random variable with
zero mean. Only its variance needs to be evaluated to derive the variance of the residual
interference in equation (10.59).

Derivation of the Interference Variance
for Band-Limited MC-CDMA

The chip waveform has been noted to be an important system parameter for DS-CDMA
and MC-DS-CDMA. Hence, the performances of DS-CDMA and MC-DS-CDMA with
various time-limited and band-limited chip waveforms have been investigated. How-
ever, for all the MT-CDMA systems found in the literature, a time-limited waveform
is generally employed [4, 18, 52, 53]. Since we consider a practical square-root raised
cosine pulse, the focus of this appendix is to derive the variance of the interference of
MC-CDMA (including MC-DS-CDMA and MT-CDMA) with a band-limited square-
root raised cosine waveform. Let G ( f ) be the Fourier transform of the raised cosine
filter:



≤≤ −

1
2

β

T , 0 f






c

T

c

 

 


 




 
 

 
 

T π

β

T

− −

1
2

β  1

2

− ≤≤ + β 1

2

β

() =

Gf

c

1 + cos

c

f , f . (10.63)

    

2 T T T






 

c c c

> +

1 β

0 , f

2 T c



Let - D = E [(ψ k d ) 2 ] be the average power of the k t h carrier of the desired user and - I be
the average power on each interfering carrier (assumed equal for all u and all k ). Using
the general results in [54], one has

2 ψ ςβ χβ,


 



  = ( ) () + ()

d

   

Var I C 1

I

(10.6 4)

MAIkn ,, k

L

where

1

∫

∞

ς () =

()

2

Gf df (10.65)

T

−∞

c

and

K

∑ ∫

1

∞

( )

() = () − ( )

χβ
k

GfGf f f df . (10.6 6)

k k ′

T

−∞

c
kK
kk

′=−
′≠