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

12.1 Linear Distortions of Wireless Multipath Channels 669
Once again, we can define a baseband (complex) impulse response
K
q(t) = L cti exp(JwcTi)p(t - kT - r;)
i=O
(12.6a)
and the baseband complex noise
n e (I) = n,(t) +jn, (I)
(12.6b)
The receiver demodulator output signal at the baseband can be then written simply as
y(t) = L Skq(t - kT) + n e (t)
k
(12.7)
in which all variables are complex-valued. Clearly, the original pulse p(t) that was designed to
be free of ISi has been transformed by the multipath channel route into q(t). In the frequency
domain, we can see that
K
Q(f) = L a; exp [-j (2n f - co, ) rd • P(f) ( 12.8)
i=O
This means that the original frequency response P(f) encounters a frequency-dependent
transfer function because of multipath response
K
L a; exp(Jwcri) exp [-j2nf r;]
i=O
Therefore, the channel distortion is a function of the frequency f. Communication channels
that introduce frequency-dependent distortions are known as frequency-selective channels.
Frequency-selective channels can exhibit substantial ISI, which can lead to significant increase
of detection errors.
Wire-Line ISi
Although we have just demonstrated how multipath in wireless communications can lead to
ISi and linear channel distortions, wire-line systems are not entirely immune to such problems.
Indeed, wire-line systems do not have a multipath environment because all signals are transmitted
by dedicated cables. However, when the cables have multiple unused open terminals,
impedance mismatch at these open terminals can also generate reflective signals that will arrive
as delayed copies at the receiver terminals. Therefore, ISi due to linear channel distortion can
also be a problem in wire-line systems. Cable internet service is one example.
Equalization and OFDM
Because ISI channels lead to serious signal degradation and poor detection performance,
their effects must be compensated either at the transmitter or at the receiver. In most cases,
transmitters in an uncertain environment are not aware of the actual conditions of propagation.
Thus, it is up to the receivers to identify the unknown multipath channel q(t) and to find
effective means to combat the ISi. The two most common and effective tools against ISi
channels are channel equalization and OFDM.