B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

12.3 Linear T-Spaced Equalization (TSE) 677
where u is a fixed delay in the equalizer output. Because both the channel and the equalizer
must be causal, the inclusion of a possible delay u provides opportunities for simpler and better
equalizer designs.
To better understand the design of the TSE filter F(z), we can divide the TSE output into
different terms
00
d [nl = L CiSn-i + Lf [i]w[n - i]
i=O i=O
00
00
= Cu Sn-u + L CiSn-i + Lf [i]wln - i]
i=O, if-u
'-...-'
ISi term
00
i=O
________ _,,
noise term
(12.30)
The equalizer filter output d [n l consists of the desired signal component with the right delay,
plus the ISi and noise tem1s. If both the ISi and noise terms are zero, then the QAM decision
device will always make correct detections without any error. Therefore, the design of this
linear equalizer filter F(z) should aim to minimize effect of the ISI and the noise terms. In
practice, there are two very popular types of linear equalizer: zero-forcing (ZF) design and
minimum mean square error (MMSE) design.
12.3.1 Zero-Forcing TSE
The principle of zero-forcing equalizer design is to eliminate the ISi term without considering
the noise effect. In principle, a perfect ZF equalizer F(z) should force
In other words, all ISi terms are eliminated
00
L CiSn-i = 0
i=O, if-u
C. , - { 1 i = u
0 if= u
Equivalently in frequency domain, the ZF equalizer requires
(12.31b)
C(z) = F ( z) H ( z ) = z -u (12.31 a)
Notice that the linear equalizer F(z) is basically an inverse filter of the discrete ISI channel
H (z) with appropriate delay u
F ( ) - z-u
z - H ( z)
(12.31c)
If the ZF filter of Eq. (12.3 lc) is causal and can be implemented, then the ISi is completely
eliminated from z [n]. This appears to be an excellent solution, since the only decision that the
decision device now must make is based on
z [n] = Sn-u + F ( z) w[n]