mohatta2015.pdf

MORE MATH 47
10" 1
Odeg
90 deg X
180 deg X
REF -Θ-
IQ" 2
10" 3 -2 0 2 4 6 8 10 12 14
Eb/NO (dB)
Figure 2.5 BER vs. E b /N 0 for QPSK, root-raised-cosine pulse shaping (0.22 rolloff),
static, two-tap, half-symbol-spaced ehaimel, with relative path strengths 0 and —1 dB, and
path angles 0 and 0/90/180 degrees.
2.4 MORE MATH
In this section, the more general system model is considered. We introduce the
notions of chip-level and despread-level matched filtering, depending on the order
of the matching operations. While this terminology is more commonly used for
CDM systems, we will also use it for OFDM systems for consistency, even though
time-domain and frequency-domain matched filtering may be more appropriate
terms. Partial MF and the matched filter bound are revisited. Finally, we consider
matched filtering in colored (nonwhite) noise and the notion of group matched
filtering.
The derivation of the matched filter is similar in the more general case, only now
the problem is in terms of a vector of filters. Also, the filter vector may be different
for each symbol period, so that (2.46) becomes
4:;W= Γ^Ι,ΜΓΦ)^ (2.70)
where ¿o, fco T and m ( > are indices for a particular symbol. SNR is maximized when
f£n« = h £nM· (2·71 )