Wireless Network Design: Optimization Models and Solution ...

3 Channel Models for Wireless Communication Systems 55
3.4.4 Finite Impulse Response Channel Model for Frequency
Selective Fading Channels
In most cases, the receiver receives multiple copies of attenuated and delayed copies
of the transmitted signal. At the baseband level, the channel response can be modeled
as a linear system where the transfer function is characterized by a Finite Impulse
Response (FIR) with L − 1 multipaths, given by
h(n) =
L−1
∑ αl δ(n − τl) (3.16)
l=0
where αl is modeled as a random co-efficient with a certain probability density
function and τl is the delay of the lth multipath, which need not be uniform.
Assuming that this FIR channel is ‘constant’ for a certain period of time, the
channel behaves like an FIR filter. The transfer function of this channel, H(z), is
a finite length polynomial. In the frequency domain, H( f ) will have a response
which will indicate the attenuation, the filter offers, to various frequencies. It implies
that some frequencies of the signal could suffer heavy attenuation, indicating the
frequency selective nature of the channel. If the zeros of H(z) are on the unit circle,
then the channel would null the frequency component in the signal, causing loss of
valuable information. In the case of flat fading channels, it is equivalent to a singletap
FIR channel and all frequencies of the signal suffer the same attenuation. The
following tables give the details about the impulse response coefficients for different
indoor scenarios. The Doppler spectrum is assumed to be the classic spectrum for
the outdoor scenario.
Table 3.2 Impulse response coefficients for two types of wireless indoor channels
Tap Channel A Channel A Channel B Channel B
Relative Relative Relative Relative
Delay(ns) Avg Pwr(dB) Delay (ns) Avg Pwr (dB)
1 0 0 0 0
2 50 -3.0 100 -3.6
3 110 -10.0 200 -7.2
4 170 -18.0 300 -10.8
5 290 -26.0 500 -18.0
6 310 -32.0 700 -25.2
3.4.5 Delay Spread Parameters
Average Delay: The average path delay is defined as τavg = ∑ L−1
l=0 |αl| 2 τl. The Root
Mean Square Delay (RMS Delay), τrms is given by