The Internet Encyclopedia (Volume 3)

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130 PROPAGATIONCHARACTERISTICS OFWIRELESSCHANNELS

Transmitter Receiver

Building

Figure 7: The existence of multiple paths between the trans-

mitter and receiver.

(some times termedRayleigh fading) increases the uncer-

tainty in the received signal power, making it necessary

to develop methods to mitigate fading through diversity.

Second, the paths shown in Figure 7 take different times

leading to a broadening of the received pulse as shown in

Figure 8. Figure 8a shows a transmitted pulsep(t). This

pulse takes multiple paths and the received pulser(t) can

be expressed as

r(t)=

∑N

k= 1

akp(t−tk), (15)

whereakis the strength of the pulse andtkthe time taken by

thekthpulse. These delayed pulses of different strengths

overlap, broadening the pulse at the receiver seen in

Figure 8b. Note that the data rate is inversely propor-

tional to the pulse duration and any broadening of the

pulse will lead to overlapping of adjoining pulses resulting

in inter symbol interference (ISI). ISI increases the bit

error rate (BER). To prevent pulse broadening, it becomes

necessary to operate at a lower data rate when fading is

present. If pulse broadening leads to a reduction in data

rate or makes it necessary to put in place additional sig-

nal processing methods to mitigate the effects of pulse

broadening, the medium or channel in which this takes

place is referred to asa frequency selective fading chan-

nel. On the other hand, if the pulse broadening is negligi-

ble, the medium or channel is referred to as aflat fading

channel.

Regardless of whether the channel is flat or frequency

selective, the fluctuations of power are associated with

fading. The fluctuations in power cause an increase in the

BER, making it necessary to operate at higher powers.

This case is illustrated in Figure 9, which shows the BERs

when no fading is present and also when Rayleigh fading

time

amplitude

Resultant

broadened pulse

(a) (b)

Figure 8: Transmitted pulse (a) and the received pulse (b).

is present. To maintain a BER of 1 in 1,000 would require

an additional signal-to-noise ratio of approximately 17 dB

when fading is present, demonstrating the problems as-

sociated with fading.

Now consider a signal-to-noise ratio of 10 dB. The re-

sults shown in Figure 9 indicate that in the presence of

fading a signal-to-noise ratio of 10 dB is not sufficient

(Shankar, 2001) to have an acceptable level of perfor-

mance (say, 1 in 1,000). This leads to outage.

It is possible to have a direct path (LOS) between

the transmitter and the receiver in addition to the mul-

tiple paths. This condition is more ideal than a pure

multipath scenario because the LOS component pro-

vides a steady component to the signal. As the strength

of the steady component increases (over the multipath

components), the deleterious effects of fading decrease.

This fading channel is known as theRician channel.It

can be shown that as the strength of the LOS compo-

nent increases, the Rician channel starts approaching

the idealGaussian channel,thus reducing the severity of

fading.

Doppler Fading

Multipath fading does not take into account any relative

motion of the transmitter and receiver. If the wireless re-

ceiver (or transmitter) is mounted on a moving vehicle, the

motion introduces Doppler broadening. Motion-induced

fading is referred to asDoppler fadingand is responsible

for further degradation in the performance of the wireless

systems. If a pure tone of frequencyf 0 is transmitted, the

received signal spectrum will broaden (Doppler broaden-

ing) and contain spectral components raging fromf 0 −fd

tof 0 +fd, wherefdis the Doppler shift. If the bandwidth

occupied by the information is much greater than the

spectral broadening, Doppler spread does not lead to any

significant problems in transmission and reception. The

channel in this case is referred to as aslow channel.If

the bandwidth is smaller than the Doppler spread, motion

leads to channel varying rapidly within the duration of the

pulse. In this case, the channel is referred to as afast chan-

nel. Thus, multipath fading decides whether the channel

is flat or frequency selective, and Doppler fading decides

whether the channel slow or fast (Jakes, 1974; Parsons,

1996). Whereas multipath fading leads to pulse spreading

(time), Doppler fading leads to frequency spreading. The

different types of fading are summarized in Figure 10.

Long-Term Fading

As shown in Figure 3, power fluctuations have a longer pe-

riod in Figure 3b than the fluctuations in Figure 3c. These

fluctuations with larger periods are statistically described

in terms of lognormal fading (Jakes, 1974). Whereas

short-term fading is caused by the existence of multipath,

long-term fading is caused by the existence of multiple

reflections. This means that the signal in a single path

cannot reach the transmitter after a single reflection or

scattering process but must travel through several struc-

tures, causing a “shadowing effect” caused by the pres-

ence of many tall structures. The power expressed in deci-

bels in this case is normally distributed, and the power

in watts will therefore be lognormally distributed (Jakes,

1974; Rappaport, 2002; Steele & Hanzo, 1999). These