Adaptive Multicarrier CDMA Space-Time Receivers - Adaptive Signal Processing in Wireless Communications - page 284

and CFO estimates provided by MC-STAR* [32]. The postcombined signal can be for-
mulated as

H H

d d

ˆ

d d d d d

s = WYs = + δ + δ + δ ISIkn + WN , (10. 30)

kn , kn , n k n , MAIkn , , ICIkn , , ,, kn , n

where δ d MAI , k , n , δ ICI , k , n , and δ ISI , k , n are the combining residuals of I d MAI, k , n , I ICI, k , n , and I ISI, k , n ,
respectively. We assume here that the interference rejection residuals δ d MAI , k , n , δ ICI , k , n , and
δ ISI , k , n are Gaussian random variables with zero mean. Hence, we only need to evaluate
their variances. Note that the residuals would be null (i.e., δ d MAI , k , n = δ ICI , k , n = δ ISI , k , n = 0)
if the reconstruction of the interference were perfect (i.e., Î k , n = I k , n ), and hence ˆ k , n =
s k,n + W d k,n N n would be corrupted only by the residual noise, which is Gaussian with zero
mean and variance:


 


  =κσ 2

H
,

d

Var WN
kn

, (10. 31)

n N

where

 

2

ML
ML

−
−

1
2

d
,

κ= E   W   = ,

kn

 

is a measure of the enhancement of the white noise compared to MRC (κ = 1 for MRC)
[45]. However, in practice the interference vector is reconstructed erroneously due to
wrong tentative data decisions and power control errors, and hence ˆ k , n is further cor-
rupted by non-null residual interference rejection components. Therefore, we introduce
the error indicating variables

= ∗

u u

bb

u

ξ kn

, kn , kn ,

and

2

ˆ ˆ

u u ∗ u u

λψψψ
kn

=

, kn , kn , kn ,

where (.) ∗ means complex conjugate. ξ k,n models the symbol estimation error provided
by MRC at the initial stage. λ k,n characterizes the power control error. ξ k,n and λ k,n equal 1
when the estimated data symbol and the power control are perfect; otherwise, they are
complex numbers. Since

u
Y

u u u

ˆ

u

ˆ

ˆ

, †

u u u u u u u u u

Y = s U = b ψ U =

kn

ξλ ψ b U = ′′ ′ ξλ

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

* Simulations will show little deviation from analysis in the operating BER region.
† Here we assume perfect time and frequency synchronization.