herently combine virtually all of the current symbol's energy. The DFE also has a
feedback section, which removes energy remaining from previously detected sym-
bols [10.30-321. The basic idea behind the DFE is that once an information symbol
has been detected, the ISI that it induces on future symbols can be estimated and
subtracted before the detection of subsequent symbols. (See Section 3.4.3.2.)
A maximum-likelihood sequence estimation (MLSE) equalizer tests all pos-
sible data sequences (rather than detecting each received symbol by itself) and
chooses the data sequence that is the most probable of all the candidates. The
MLSE equalizer was first proposed by Forney [33) and implemented by using the
Viterbi decoding algorithm [34 The MLSE is optimal in the sense that it mini-
mizes the probability of a sequence error. Because the Viterbi decoding algorithm
is typically used in the implementation of the MLSE equalizer, this device is often
referred to as the Viterbi equalizer. Later in this chapter, we illustrate the adaptive
equalization performed in the Global System for Mobile (GSM) Communications
using the Viterbi equalizer.
Direct-sequence spread-spectrum (DS/SS) techniques can be used to mitigate
frequency-selective ISI distortion because the hallmark of spread-spectrum sys-
tems is their capability to reject interference, and ISI is a type of interference. Con-
sider a DS/SS binary phase-shift keying (PSK) communication channel comprising
one direct path and one reflected path. Assume that the propagation from trans-
mitter to receiver results in a multipath wave that is delayed by compared with
the direct wave. Neglecting noise. the received signal can be expressed as
r(t) = Ax(Op(t)cos(27rjet) + aAx(t — t)p(t — t)cos(27rft + 0) (15.35)
where x(r) is the data signal, p(t) is the pseudonoise (PN) spread code, and T is the
differential time delay between the two paths. The angle 0 is a random phase, as-
sumed to be uniformly distributed in the range (0. 2n). and a is the attenuation of
the multipath signal relative to the direct path signal. The receiver multiples the in-
coming r(t) by the code p(t). If the receiver is synchronized to the direct path sig-
nal, multiplication by the code signal yields
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