Propagative Path Loss Models
FreeSpace Propagative Loss. When there is a LOS path between the transmitter and receiver, the freespace propagation model can be used to predict the signal strength. Such conditions occur in some satellite and terrestrial microwave communication links. Suppose that the distance between the transmitter and receiver is d meters, where d is in the far field. Then the freespace model (based on the Friis formula) gives
ing the propagative path loss (because the criteria for free – space propagation are not met). This topic has been very extensively studied. Detailed information can be found in Kefs. 7, 10, 12, and 16. Computation of path loss is of particular interest to communication systems designers. Because the actual KF communication environments encountered in practice are so numerous, a unified theoretical/analytical framework for estimating path loss is not feasible. Most system designers resort to empirical approaches and semianalytical methods, which have been validated by experimental/measured data, to estimate the path loss. The work of Okamura and Hata (13) is very widely used for path loss estimation. Okamura’s work is based purely on measured data, and Hata provided the empirical model to fit that data. The advantage of using empirical models and curve fitting to measured data is that it accounts for both known and unknown sources of path loss. On the other hand, the disadvantage is that the validity of the empirical model, derived from a set of data, is not guaranteed for a different environment.
Let d be the distance between the transmitter and receiver. Both theoretical and measurementbased models show that the average path loss [Lp(d)] increases directly proportional to dn, where n is called the path loss exponent. Typically n > 2, as summarized in the Table 1. By contrast, in free space, N = 2. The path loss Lp(d) is given by
Lp(d) a dn 
(44) (45) 
Lp(d) = Lp(d0) + 10ralog10 
The reference point d0 is chosen such that Lp(d0) can be computed using the freespace path loss model.
Hata and COST231 Models. This is one of the most widely used models for estimating path loss in KF communication channels. Based on extensive measured data, Okamura generated sets of curves that characterize the median attenuation (50th percentile) Lp50, for a wide range of environments (range of carrier frequency ( fc), effective height of transmitting antenna (ht, eff), and distance d from transmitter. Hata (12) provided an empirical formulation from Okamura’s data, which shows good agreement (between the model and the measured data) for fc < 1.5 GHz. An extension of Hata’s model for frequencies up to 2 GHz is provided in Kef. 14. The Hata model and COST231 models are given below: Hata Model
PtGtGrk2 (4 ж)2Ь 
1 d2 
Pr (d) = 
(41) 
where Pt and Pr are the transmitting and receiving power, respectively, with transmitting antenna gain Gt, receiving antenna gain Gr, and A is the wavelength of the carrier. The term L represents the losses in the system (L > 1). The path loss Lp is the difference between the transmitting and receiving power expressed in decibels.
(4tt)2L PtGtGTX2 
P Lp(dB) = 101og10 у = 10log 
+ 20 log d (42) 
Lp,50 = 69.55 + 26.16 log!0 fc — 13.82log!0 ht, eff — a(hr, eff) 
As the signal propagative distance d increases, the received power decreases at 20 dB/decade, as seen from Eq. (42). Another commonly used method to compute the signal power received Pr(d) is by measuring it relative to the received power Pr(d0) at a reference point (distance d0 from the transmitter) as given by 
+ (44.9 — 6.55 log10 ht, eff) log10 d 
(46) 
Environment 
Path Loss Exponent n 
Free space 
2 
Urban cellular 
2.74.0 
Inbuilding (nonLOS) 
3.06.0 
Shadowed urban cellular 
4.06.0 
(43) 
Table 1. Path Loss Exponents for Different Environments 
, d 2 PT(d)=PT(d0)[£j ,d>d, 
Outdoor Propagative Loss. In dealing with nonLOS environments, which is typical of most KF communication links, such as cellular/PCS, we need appropriate models for comput 
Lp (d) = 
(dB) (48) 
Pt 
Lognormal shadowing Rayleigh/ Ricean fading р i 
(49) 
COST231 Model
Lp,50 = 463 + 33 9log10 fc — 13*82 log10 ht, eff — a(hr, eff)
+ (44.9 — 6.55 lOg10 ht eff) log10 d + CM (47)
where hr, eff is the effective height of the receiving antenna, a(hreff), is a correction factor based on hreff and CM is a correction factor based on the propagative environment. The details regarding a(hreff), and CM are provided in Ref. 10. The range of values for which the Hata and COST231 models are valid are summarized in Table 2.
The Hata model has a correction factor for rural environments. In general, the Hata model and the COST231 model provide an example of the path loss computation in a outdoor, nonLOS environment. A variation, called the COST231Wal – fishIkegami model can be used for transmitting antennas above or below rooftops and is accurate for d > 20 m. A number of models similar to these discussed in this section are also used in practice. So, the choice of path loss models must take into account all aspects of the propagative environment, including transmission frequency, distance of transmission, polarization, antenna heights, surface refractivity, terrain irregularity, foliage, climate, ground conductivity, and ground dielectric constant (10).
Indoor Propagative Loss. An increasing number of wireless communications applications are designed for indoor environments. Hence, there is considerable interest in indoor propagation and in models for it. Although the characteristics of indoor propagation vary slowly [quasistatic behavior (15)] as compared with outdoor propagation, a key difference is that propagation within a building is strongly influenced by a number of factors, such as building type, layout, construction material (amount of metal used), types of partitions, and height and placement of antennas. As a result, the variability in signal propagation and hence the path loss is quite significant. The model best suited for characterizing path loss in indoor propagation is similar to that for lognormal shadowing. The path loss at a distance d from the transmitter is given by
Lp(d0) + 10ralog10 ( ^ ) + £2
where П is a normal RV with standard deviation a and n is the path loss exponent. It was reported in Ref. 15 that the typical range of n is 3 to 4. A comprehensive list of the typical values of n and a for a variety of indoor environments is provided in Ref. 10.
Table 2. Range of Validity of Hata and COST231 Models

Transmit power Path loss (Lp)
Shadow in margin (Ls)
Fast fading margin (Lf) Receiver sensitivity
Thermal noise floor
Figure 16. Different components of link budget:—propagative loss, shadowing margin, and fading margin.
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