The free space path loss equation is not accurate to model the path loss in terrestrial
wireless communications with multipaths from the transmitter to the receiver. In
general, the path loss model can be represented by the equation:
PL(dB) = PL(d0) + 10nloglo(d/do)
where n is the path loss exponent which depends on the environment. Table 1.1
illustrates the values of path loss exponents under various environment.
Table 1.1 Path loss exponents.
| Environment | Path Loss Exponent |
| In building line-of-sight Free space Obstructed in factories Urban area cellular Shadowed urban cellular Obstructed in building | 1.6-1.8 2 2-3 2.7-3.5 3-5 4-6 |
The higher the path loss exponent is, the faster the signal strength drops with respect
to the increase in distance. For example, a commonly assumed path loss exponent in
non line-of-sight environment is n = 4. In this case, doubling the distance separation
between the transmitter and the receiver will result in 16 times reduction in received
signal strength.
In some more complicated propagation environments such as irregular terrain and
cities, there is no simple analytical path loss model. Empirical models based on
extensive channel measurements are used to model the path loss versus distance in
such complex environments. Examples are the Okumura model [261], Hata model
and COST 231 extension to the Hata model [316] for cellular systems simulations
and link budget analysis.
1.3 SHADOWING EFFECTS
In the shadowing model, we are interested to study the medium term variation in
received signal strength when the distance between the transmitter and receiver is
fixed. For example, image a mobile station is circling around a base station with radius
T . As the mobile moves, one expects some medium term fluctuations in the received
signal strength but the variation is not due to the path loss component because the
distance between the transmitter and the receiver is not changed. This signal variation
is due to the variations in terrain profile such as variation in the blockage due to trees,
buildings, hills, etc. This effect is called shadowing. Consider a signal undergoing
multiple reflections (each with an attenuation factor ai) and multiple diffractions (each
with an attenuation factor bi) as illustrated in Figure 1.3
Figure 1.3
hills, etc.
Shadowing model-variations in path loss predication due to buildings, trees,
The received signal strength is given by:
where N, and Nt denote the number of obstacles with reflecting and diffracting the
signal respectively. Expressing the received power in dB, we have:
where ơ~i is the attenuation coefficient due to reflections or diffractions. Each of
the term ơ!i (dB) represents a random and statistically independent attenuation. As
the number of reflectors and diffractors increase, by central limit theorem, the sum
S(dB)= ∑I a;i (dB)a pproaches a Gaussian random variable. Hence, the received
signal power can be expressed as:
where S(dB) N ( ṵ s , 02) and X ( d B ) N(0, 02). The mean shadowing ps is usually
included into the path loss model and that is why the path loss exponent can be larger
than 2. Hence, without loss of generality, we move the term ps(dB) to the path
loss model and consider only the shadowing effect X ( d B ) . Expressing the received
power in linear scale, we have:
where A, =10 ˣ̷¹º is the power attenuation due to shadowing and is modeled by
the log-normal distribution with standard derivation o (in dB).
Combining the path loss model and the shadowing model, the overall path loss is
given by:
where PL,, is the path loss component obtained from the large scale path loss model
and X ( d B ) is the shadowing component which is modeled as a zero-mean Guassian
random variable with standard derivation 0 in dB.
to be continue...