mohatta2015.pdf

MORE MATH 89
values of h k m (f) from all symbol periods, though practically the values in a window
around mo would be the most influential. Thus, the weights may depend on mo,
the symbol period, and fco, the PMC. For CDM, this means that there will be a
different weight solution for each symbol being detected. For OFDM, the values of
c k m(") are * ne same for different values of m and i. Thus, there will be a weight
vector for each subcarrier fc. This set of weight vectors can be reused for different
symbol periods m.
The MMSE weight solution is obtained by solving (4.77), which can be written
as
C(mo)w = (7£< io) (fco)) hltL- (4.114)
where
h (in)
fco."ID
[^:L(^T S )] T ... [h^rao (A J _ 1 T.)] T ] T . (4.115)
4.4.3 ML solution
The ML formulation for the general case is similar to the ML formulation for the
TDM case. As before, the end result is that C„ is replace with C„ in the weight
solution. Specifically, the ML weights are given by
C u (m n )w = (ν^'(mo) = p^R-V (4.118)
where
= E l Ä J ' W ^ ' W j ^ C - ^ , (4.119)
71=0
Î^\nT c ) = \A# 0) (M i[h ( ' r,) (AoT s - nT c )] T ... [h^(Aj^T s - nT c )] T ~\
(4.120)
and Ec ' (fco) = E¡¡ (ko)/N c is the energy per chip for code fco. Observe that
there is despreading being performed in (4.119). Also, there appears to be multiple
weight vectors, one for each chip period.
We can rewrite these equations as
^"»(mo) = y/Ep\ko) ¿ [c^J'W^W, (4-121)