Propagative Path Loss Models

Free-Space Propagative Loss. When there is a LOS path be­tween the transmitter and receiver, the free-space 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 free-space 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 measurement-based 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



Lp(d) = Lp(d0) + 10ralog10

The reference point d0 is chosen such that Lp(d0) can be com­puted using the free-space path loss model.

Hata and COST-231 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 COST-231 models are given below: Hata Model

PtGtGrk2 (4 ж)2Ь



Pr (d) =


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.




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



Path Loss Exponent n

Free space


Urban cellular


In-building (non-LOS)


Shadowed urban cellular



Table 1. Path Loss Exponents for Different Environments

, d 2

PT(d)=PT(d0)[-£j ,d>d,

Outdoor Propagative Loss. In dealing with non-LOS envi­ronments, which is typical of most KF communication links, such as cellular/PCS, we need appropriate models for comput-

Lp (d) =

(dB) (48)


Log-normal shadowing Rayleigh/ Ricean fading

р i


COST-231 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 COST-231 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 COST-231 model provide an example of the path loss computation in a outdoor, non-LOS environment. A variation, called the COST231-Wal – fish-Ikegami 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 [quasi-static 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 log-normal 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 COST-231 Models


Range of Validity



Carrier frequency fc

150-1500 MHz

1500-2000 MHz

Effective transmit height ht, efr

30-200 m

30-200 m

Effective receive height hr, eff

1-10 m

1-10 m

Distance d from transmitter

>1 km

1-20 km

Correction factors

a(hr, eff)

a(hr, eff), CM

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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