Modelos de propagacion

66 3 Radio Propagation and Propagation Path-Loss Models

3.9 Propagation Path-Loss ModelsPropagation path-loss models [20] play an important role in the design of cellular systems to specify key system parameters such as transmission power, frequency, antenna heights, and so on. Several models have been proposed for cellular systems operating in different environments (indoor, outdoor, urban, suburban, rural). Some of these models were derived in a statistical manner based on fi eld measure-ments and others were developed analytically based on diffraction effects. Each model uses specifi c parameters to achieve reasonable prediction accuracy. The long distance prediction models intended for macrocell systems use base station and mobile station antenna heights and frequency. On the other hand, the predic-tion models for short distance path-loss estimation use building heights, street width, street orientation, and so on. These models are used for microcell systems. When the cell size is quite small (in the range of 10 to 100 m), deterministic mod-els based on ray tracing methods are used. Thus, it is essential to select a proper path-loss model for design of the mobile system in the given environment.

Propagation models are used to determine the number of cell sites required to provide coverage for the network. Initial network design typically is based on coverage. Later growth is engineered for capacity. Some systems may need to start with wide area coverage and high capacity and therefore may start at a later stage of growth.

The coverage requirement along with the traffi c requirement relies on the propagation model to determine the traffi c distribution, and will offl oad from an existing cell site to new cell sites as part of a capacity relief program. The propagation model helps to determine where the cell sites should be placed to achieve an optimal location in the network. If the propagation model used is not effective in placing cell sites correctly, the probability of incorrectly deploying a cell site in the network is high.

The performance of the network is affected by the propagation model chosen because it is used for interference predictions. As an example, if the propagation model is inaccurate by 6 dB (provided S/I � 17 dB is the design requirement), then the signal-to-interference ratio, S/I, could be 23 dB or 11 dB. Based on traffi c con-ditions, designing for a high S/I could negatively affect fi nancial feasibility. On the other hand, designing for a low S/I would degrade the quality of service.

The propagation model is also used in other system performance aspects including handoff optimization, power level adjustments, and antenna placements. Although no propagation model can account for all variations experienced in real life, it is essential that one should use several models for determining the path losses in the network. Each of the propagation models being used in the industry has pros and cons. It is through a better understanding of the limitations of each of the models that a good RF engineering design can be achieved in a network.

We discuss two widely used empirical models: Okumura/Hata and COST 231 models. The Okumura/Hata model has been used extensively both in Europe and

North America for cellular systems. The COST 231 model has been recommended by the European Telecommunication Standard Institute (ETSI) for use in Personal Communication Network/Personal Communication System (PCN/PCS). In addi-tion, we also present the empirical models proposed by International Mobile Telecommunication-2000 (IMT-2000) for the indoor offi ce environment, outdoor to indoor pedestrian environment, and vehicular environment.

3.9.1 Okumura/Hata ModelOkumura analyzed path-loss characteristics based on a large amount of experimental data collected around Tokyo, Japan [6,11]. He selected propagation path conditions and obtained the average path-loss curves under fl at urban areas. Then he applied several correction factors for other propagation conditions, such as:

Antenna height and carrier frequency

Suburban, quasi-open space, open space, or hilly terrain areas

Diffraction loss due to mountains

Sea or lake areas

Road slope

Hata derived empirical formulas for the median path loss (L50) to fi t Okumura curves. Hata’s equations are classifi ed into three models:

1. Typical Urban

L50(urban) � 69.55 � 26.16 log fc � (44.9 � 6.55 log hb)log d

� 13.82 log hb � a(hm)(dB) (3.25)

where:

a(hm) � correction factor (dB) for mobile antenna height as given by:

For large cities

a(hm) � 8.29[log (1.54hm)]2 � 11 fc � 200 MHz (3.26)

a(hm) � 3.2[log (11.75hm)]2 � 4.97 fc � 400 MHz (3.27)

For small and medium-sized cities

a(hm) � [1.1 log (fc) � 0.7]hm � [1.56 log (fc) � 0.8] (3.28)

•

•

•

•

•

•

•

3.9 Propagation Path-Loss Models 67


2. Typical Suburban

L50 � L50(urban) � 2 � � log � fc � 28

� 2 � � 5.4 � dB (3.29)

3. Rural

L50 � L50(urban) � 4.78(log fc)2 � 18.33 log fc � 40.94 dB (3.30)

where:

fc � carrier frequency (MHz)d � distance between base station and mobile (km)hb � base station antenna height (m)hm � mobile antenna height (m)

The range of parameters for which the Hata model is valid is:

150 � fc � 2200 MHz30 � hb � 200 m1 � hm � 10 m1 � d � 20 km

3.9.2 Cost 231 ModelThis model [19] is a combination of empirical and deterministic models for estimating the path loss in an urban area over the frequency range of 800 MHz to 2000 MHz. The model is used primarily in Europe for the GSM 1800 system.

L50 � Lf � Lrts � Lms dB (3.31)or

L50 � Lf when Lrts � Lms � 0 (3.32)

where: Lf � free space loss (dB)Lrts � roof top to street diffraction and scatter loss (dB)Lms � multiscreen loss (dB)

Free space loss is given as:

Lf � 32.4 � 20 log d � 20 log fc dB (3.33)

The roof top to street diffraction and scatter loss is given as:

Lrts � �16.9 �10 log W � 10 log fc � 20 log �hm � L0 dB (3.34)

where:W � street width (m)�hm � hr � hm mL0 � �10 � 0.354 0 � � 35°L0 � 2.5 � 0.075( � 35) dB 35° � � 55°L0 � 4 � 0.114( � 55) dB 55° � � 90°

where: � incident angle relative to the street

The multiscreen (multiscatter) loss is given as:

Lms � Lbsh � ka � kdlog d � kf log fc � 9 log b (3.35)

where:b � distance between building along radio path (m)d � separation between transmitter and receiver (km)

Lbsh � �18 log (11 � �hb) hb � hr

Lbsh � 0 hb hr

where: �hb � hb � hr, hr � average building height (m)

ka � 54 hb � hr

ka � 54 � 0.8hb d � 500m; hb � hr

ka � 54 � 0.8�hb(d/500) d 500m; hb � hr

Note: Both Lbsh and ka increase path loss with lower base station antenna heights.

kd � 18 hb hr

kd � 18 � 15�hb �

�hm hb � hr

kf � 4 � 0.7(fc / 925 � 1) for mid-size city and suburban area with moderate tree density

kf � 4 � 1.5 � fc �

925 � 1 � for metropolitan area

The range of parameters for which the COST 231 model is valid is:

800 � fc � 2000 MHz

4 � hb � 50 m



1 � hm � 3 m

0.02 � d � 5 km

The following default values may be used in the model:

b � 20–50 m

W � b/2

� 90°

Roof � 3 m for pitched roof and 0 m for fl at roof, and

hr � 3 (number of fl oors) � roof

Example 3.7Using the Okumura and COST 231 models, calculate the L50 path loss for a PCS system in an urban area at 1, 2, 3, 4 and 5 km distance (see Table 3.1). Assume hb � 30 m, hm � 2 m, and carrier frequency fc � 900 MHz. Use the following data for the COST 231 model:

W � 15 m, b � 30 m, � 90°, hr � 30 m

COST 231 Model

L50 � Lf � Lrts � Lms

Lf � 32.4 � 20 log d � 20 log fc � 32.4 � 20 log d � 20 log 900 dB

Lf � 91.48 � 20 log d dB

Lrts � �16.9 � 10 log W � 10 log fc � 20 log �hm � L0

�hm � hr � hm � 30 � 2 � 28 m

Table 3.1 Summary of path losses from COST 231 model.

d (km) Lf (dB) Lrts (dB) Lms (dB) L50 (dB)

1 91.49 29.82 9.72 131.03

2 97.50 29.82 15.14 142.46

3 101.03 29.82 18.31 149.16

4 103.55 29.82 20.56 153.91

5 105.47 29.82 22.30 157.59

Note: The table applies to this example only.

L0 � 4 � 0.114( � 55) � 4 � 0.114(90 � 55) � 0

Lrts � �16.9 � 10 log 15 � 10 log 900 � 20 log 28 � 0 � 29.82 dB

Lms � Lbsh � ka � kd log d � kf log fc � 9 log b

ka � 54 � 0.8hb � 54 � 0.8 � 30 � 30

�hb � hb � hr � 30 � 30 � 0 m

Lbsh � �18 log 11 � 0 � �18.75 dB

kd � 18 � 15�hb �

�hm � 18 � 15 � 0 �

28 � 18

kf � 4 � 0.7 � fc � 925

� 1 � � 4 � 0.7 � 900 � 925

� 1 � � 3.98 (for mid-sized city)

Lms � �18.75 � 30 � 18 log d � 3.98 log 900 � 9 log 30 � 9.72 � 18 log d dB

Okumura/Hata Model

L50 � 69.55 � 26.16 log fc � (44.9 � 6.55hb)log d � 13.82 log hb � a(hm) dB

a(hm) � (1.1 log fc � 0.7)hm � (1.56 log fc � 0.8)

� (1.1 log 1800 � 0.7)(2) � (1.56 log 900 � 0.8) � 1.29 dB

L50 � 69.55 � 26.16 log 900 � (44.9 � 6.55 log 30)log d � 13.82 log 30 � 1.29 dB

� 125.13 � 35.23 log d dB (refer to Table 3.2)

The results from the two models are given in Figure 3.9. Note that the calculated path loss with the COST 231 model is higher than the value obtained by the Okumura/Hata model.


Table 3.2 Summary of path losses from Okumura model.

d (km) L50 (dB)

1 125.13

2 135.74

3 141.94

4 142.34

5 145.76


3.9.3 IMT-2000 ModelsThe operating environments are identifi ed by appropriate subsets consisting of indoor offi ce environments, outdoor to indoor and pedestrian environments, and vehicular (moving vehicle) environments. For narrowband technologies (such as FDMA and TDMA), delay spread is characterized by its rms value alone. However, for wide band technologies (such as CDMA), the strength and relative time delay of the many signal components become important. In addition, for some technologies (e.g., those using power control) the path-loss models must include the coupling between all co-channel propagation links to provide accurate predictions. Also, in some cases, the shadow effect temporal variations of the environment must be modeled. The key parameters of the IMT-2000 propagation models are:

Delay spread, its structure, and its statistical variation

Geometrical path loss rule (e.g., d� , 2 � � 5)

Shadow fading margin

Multipath fading characteristics (e.g., Doppler spectrum, Rician vs. Rayleigh for envelope of channels)

Operating radio frequency

•

•

•

•

•

1 1.5 2 2.5 3 3.5 4 4.5 5Distance from transmitter in [km]

125

130

135

140

145

150

155

160

Pat

h lo

ss in

[dB

]

COST 231 modelHata model

Figure 3.9 Comparison of COST 231 and Hata-Okumura models.

Indoor Offi ce EnvironmentThis environment is characterized by small cells and low transmit powers. Both base stations and pedestrian users are located indoors. RMS delay spread ranges from around 35 nsec to 460 nsec. The path loss rule varies due to scatter and attenuation by walls, fl oors, and metallic structures such as partition and fi ling cabinets. These objects also produce shadowing effects. A lognormal shadowing with a standard deviation of 12 dB can be expected. Fading characteristic ranges from Rician to Rayleigh with Doppler frequency offsets are determined by walk-ing speeds. Path-loss model for this environment is:

L50 � 37 � 30 log d � 18.3 · n � � n � 2 � / � n � 1 � � 0.46 � dB (3.36)

where:d � separation between transmitter and receiver (m)n � number of fl oors in the path

Outdoor to Indoor and Pedestrian Environment This environment is characterized by small cells and low transmit power. Base stations with low antenna heights are located outdoors. Pedestrian users are located on streets and inside buildings. Coverage into buildings in high power sys-tems is included in the vehicular environment. RMS delay spread varies from 100 to 1800 nsec. A geometric path-loss rule of d�4 is applicable. If the path is a line-of-sight on a canyon-like street, the path loss follows a rule of d�2, where there is Fresnel zone clearance. For the region with longer Fresnel zone clearance, a path loss rule of d�4 is appropriate, but a range of up to d�6 may be encountered due to trees and other obstructions along the path. Lognormal shadow fading with a standard deviation of 10 dB is reasonable for outdoors and 12 dB for indoors. Average building penetration loss of 18 dB with a standard deviation of 10 dB is appropriate. Rayleigh and/or Rician fading rates are generally set by walking speeds, but faster fading due to refl ections from moving vehicles may occur some-times. The following path-loss model has been suggested for this environment:

L50 � 40 log d � 30 log fc � 49 dB (3.37)

This model is valid for non-line-of-sight (NLOS) cases only and describes the worst-case propagation. Lognormal shadow fading with a standard deviation equal to 10 dB is assumed. The average building penetration loss is 18 dB with a standard deviation of 10 dB.

Vehicular EnvironmentThis environment consists of larger cells and higher transmit power. RMS delay spread from 4 microseconds to about 12 microseconds on elevated roads in hilly or mountainous terrain may occur. A geometric path-loss rule of d�4 and lognormal



shadow fading with a standard deviation of 10 dB are used in the urban and suburban areas. Building penetration loss averages 18 dB with a 10 dB standard deviation.

In rural areas with fl at terrain the path loss is lower than that of urban and suburban areas. In mountainous terrain, if path blockages are avoided by selecting base station locations, the path-loss rule is closer to d�2. Rayleigh fad-ing rates are determined by vehicle speeds. Lower fading rates are appropriate for applications using stationary terminals. The following path-loss model is used in this environment:

L50 � 40(1 � 4 � 10�2�hb)log d � 18 log (�hb) � 21 log fc � 80 dB (3.38)

where: �hb � base station antenna height measured from average roof top level (m)

Delay SpreadA majority of the time rms delay spreads are relatively small, but occasionally, there are “worst case” multipath characteristics that lead to much larger rms delay spreads. Measurements in outdoor environments show that rms delay spread can vary over an order of magnitude within the same environment. Delay spreads can have a major impact on the system performance. To accurately evaluate the relative performance of radio transmission technologies, it is important to model the variability of delay spread as well as the “worst case” locations where delay spread is relatively large. For each environment IMT-2000 defi nes three multipath channels: low delay spread, median delay spread, and high delay spread. Channel “A” represents the low delay spread case that occurs frequently; channel “B” cor-responds to the median delay spread case that also occurs frequently; and channel “C” is the high delay spread case that occurs only rarely. Table 3.3 provides the rms values of delay spread for each channel and for each environment.

Channel “A” Channel “B” Channel “C”

Environment �rms (ns) % Occurrence �rms (ns) % Occurrence �rms (ns) % Occurrence

Indoor offi ce 35 50 100 45 460 5

Outdoor to indoor and pedestrian

100 40 750 55 1800 5

Vehicular (high antenna)

400 40 4000 55 12,000 5

Table 3.3 Rms delay spread (IMT-2000).

3.10 Indoor Path-Loss ModelsPicocells cover part of a building and span from 30 to 100 meters [13,15]. They are used for WLANs and PCSs operating in the indoor environment. The path-loss model for a picocell is given as:

Lp � �

L p(d0) � 10 log d � Lf(n) � X� dB (3.39)

where:

� L p(d0) � reference path loss at the fi rst meter (dB) � path-loss exponentd � distance between transmitter and receiver (m)X� � shadowing effect (dB)Lf (n) � signal attenuation through n fl oors

Indoor-radio measurements at 900 MHz and 1.7 GHz values of Lf per fl oor are 10 dB and 16 dB, respectively. Table 3.4 lists the values of � L p(d0), Lf (n), , and X�. Partition dependent losses for signal attenuation at 2.4 GHz are given in Table 3.5.

3.10 Indoor Path-Loss Models 75

Environment Residential Offi ce Commercial

� L p(d0) (dB) 38 38 38

2.8 3.0 2.2

Lf (n) (dB) 4n 15 � 4(n � 1) 6 � 3(n � 1)

X� (dB) 8 10 10

Table 3.4 Values of � L p(d0), �, Lf (n) and X� in Equation 3.39.

Signal attenuation through Loss (dB)

Window in brick wall 2

Metal frame, glass wall in building

6

Offi ce wall 6

Metal door in offi ce wall 6

Cinder wall 4

Metal door in brick wall 12.4

Brick wall next to metal door 3

Table 3.5 Partition dependent losses at 2.4 GHz.


Femtocellular systems span from a few meters to a few tens of meters. They exist in individual residences and use low-power devices using Bluetooth chips or Home RF equipment. The data rate is around 1 Mbps. Femtocellular systems use carrier frequencies in the unlicensed bands at 2.4 and 5 GHz. Table 3.6 lists the values of Lp(d0) and for LOS and NLOS conditions.

Example 3.8In a WLAN the minimum SNR required is 12 dB for an offi ce environment. The background noise at the operational frequency is �115 dBm. If the mobile terminal transmit power is 100 mW, what is the coverage radius of an access point if there are three fl oors between the mobile transmitter and the access point?

Solution

Transmit power of mobile terminal � 10 log 100 � 20 dBm

Receiver sensitivity � background noise � minimum SNR � �115 � 12 � �103 dB

Maximum allowable path loss � transmit power � receiver sensitivity � 20 � (�103) � 123 dB

� L p(d0) � 38 dB, Lf (n) � 15 � 4(3 � 1) � 23 dB, � 3, and X� � 10 dB (from Table 3.4)

Maximum allowable path loss � 123 � 38 � 23 � 10 � 30 log d

d � 54 m

3.11 Fade MarginAs we discussed earlier, the local mean signal strength in a given area at a fi xed radius, R, from a particular base station antenna is lognormally distributed [7]. The local mean (i.e., the average signal strength) in dB is expressed by a normal random variable with a mean Sm (measured in dBm) and standard deviation �s (dB). If Smin is the receiver sensitivity, we determine the fraction of the locations (at d � R) wherein a mobile would experience a received signal above the receiver sensitivity. The receiver sensitivity is the value that provides an acceptable signal under Rayleigh fading conditions. The probability distribution function for a log-normally distributed random variable is:

p(S) � 1 � �s �

�

2� e�[ (S � S m ) 2 /(2 � s 2 )] (3.40)

•

•

•

•

The probability for signal strength exceeding receiver sensitivity P S min (R) is

given as

P S min (R) � P[S � Smin] � �

Smin

�

p(S)dS � 1 � 2 � 1 �

2 erf � Smin � Sm �

�s ��

2 � (3.41)

Note: See Appendix D for erf, erfc and Q functions.

Example 3.9If the mean signal strength and receiver sensitivity are �100 dBm and �110 dBm, respectively and the standard deviation is 10 dB, calculate the probability for exceeding signal strength beyond the receiver sensitivity.

Solution

P S min (R) � 1 �

2 � 1 �

2 erf � �110 � 100 ��

10 ��

2 � � 0.5 � 0.5 erf(0.707) � 0.84

3.11 Fade Margin 77

Table 3.6 Values of A and � for femtocellular systems.

Environment

Center

frequency (GHz) Scenario �

L p(d0)(dB) �

Indoor offi ce 2.4 LOS 41.5 2.0

NLOS 37.7 3.3

Meeting room 5.1 LOS 46.6 2.22

NLOS 61.6 2.22

Suburban residence

5.2 LOS (same fl oor)

47 2 to 3

NLOS (same fl oor)

4 to 5

NLOS & room in higher fl oor directly above Tx

4 to 6

NLOS & room in higher fl oor not directly above Tx

6 to 7


Next, we determine the fraction of the coverage within an area in which the received signal strength from a radiating base station antenna exceeds Smin. We defi ne the fraction of the useful service area Fu as that area, within an area for which the signal strength received by a mobile antenna exceeds Smin. If P S min

is the probability that the received signal exceeds Smin in an incremental area dA, then

Fu � 1 � �R2 �P S min

dA (3.42)

Using the power law we express mean signal strength Sm as

Sm � � � 10 log d � R

(3.43)

where � accounts for the transmitter effective radiated power (ERP), receiver antenna gain, feed line losses, etc.

Substituting Equation 3.43 into 3.41 we get:

P S min � 1 �

2 � 1 �

2 erf � Smin � � � 10 log(d ⁄ R)

�� s �

� 2 � (3.44)

Let a � (Smin � �)/(�s ��

2 ) and b � (10 log (d/R))/(�s ��

2 )

Substituting Equation 3.44 into 3.42, we get

�Fu � 1 � 2 � 1 �

R2 � 0 R

x {erf[a � b log (x/R)]}dx (3.45)

Let t � a � b log (x/R), then

∴Fu � 1 � 2 � 1 �

b e(�2a)/b �

��

a

e(2t)/b erf(t)dt (3.46)

or

Fu � 1 � 2 � 1 � erf(a) � e (1 � 2ab)/b2 � 1 � erf � 1 � ab �

b � � � (3.47)

If we choose � such that Sm � Smin at d � R, then a � 0 and

Fu � 1 � 2 1 � e 1/b

2 [1 � erf(1/b)] (3.48)

Figure 3.10 shows the relation in terms of the parameter �s � .

3.12 Link MarginTo consider the losses incurred in transmitting a signal from point A to point B, we start by adding all the gains and losses in the link to estimate the total overall link performance margin [4].

The receiver power Pr is given as:

Pr � PtGtGr �

Lp (3.49)

where:Pt is the transmitter powerGt and Gr are the gains of transmitter and receiverLp is the path loss between the transmitter and receiver.

In addition, there are also the effects due to receiver thermal noise, which is generated due to random noise inherent within a receiver’s electronics. This

3.12 Link Margin 79

PSmin (R ) 0.95

0.9

1.0

0.9

0.8

0.7

0.6

0.50 1 2 3 4 5 6 7 8

0.850.8

0.75

0.7

0.65

0.6

0.55

0.5σm STANDARD DEVIATIONdB; PATH LOSS VARIES AS1 r r, PSmin

(R) COVERAGEPROBABILITY ON AREABOUNDARY (d R)

s

FRA

CTI

ON

OF

TOTA

L A

RE

AW

ITH

SIG

NA

L A

BO

VE

TH

RE

SH

OLD

, Fu

Figure 3.10 Fraction of total area with average power above threshold.

(After: W. C. Jakes, Jr., (editor), Microwave Mobile Communications. New York: John Wiley & Sons, 1974, p. 127)


increases with temperature. We account for this thermal noise effect with the following:

N � kTBw (3.50)

where:k � Boltzmann’s constant (1.38 � 10�23 W/Kelvin-Hz)T � temperature in KelvinBw � receiver bandwidth(Hz).

Spectral noise density, N0, is the ratio of thermal noise to receiver band-width

N0 � N/Bw � kT (3.51)

Finally, there is an effect on signal-to-noise (SNR) ratio due to the quality of the components used in the receiver’s amplifi ers, local oscillators (LOs), mixers, etc. The most basic description of a component’s quality is its noise fi gure, Nf, which is the ratio of the SNR at the input of the device versus the SNR at its out-put. The overall composite effect of several amplifi ers’ noise fi gures is cumulative, and can be obtained as:

Nf,total � Nf1 � (Nf2 � 1)/G1 � (Nf3 � 1)/(G1G2) � . . . (3.52)

where:Nfk is the noise fi gure in stage kGk � gain of the kth stage.

By combining all the factors, we can develop a relation that allows us to calculate the overall link margin

M � PtGtGrAg

��

Nf, totalTkLpLfL0Fmargin R � Eb � N0

� reqd (3.53)

where:Ag � gain of receiver amplifi er in dBR � data rate in dBFmargin � fade margin in dBTk � noise temperature in Kelvin(Eb / N0)reqd � required value in dBLp � path losses in dBLf � antenna feed line loss in dBL0 � other losses in dB

Expressing Equation 3.53 in dB, we obtain

M � Pt � Gt � Gr � Ag � Nf, total � Tk � Lp � Lf � L0 � Fmargin

� R � (Eb /N0)reqd dB (3.54)

Example 3.10Given a fl at rural environment with a path loss of 140 dB, a frequency of 900 MHz, 8 dB transmit antenna gain and 0 dB receive antenna gain, data rate of 9.6 kbps, 12 dB in antenna feed line loss, 20 dB in other losses, a fade margin of 8 dB, a required Eb /N0 of 10 dB, receiver amplifi er gain of 24 dB, noise fi gure total of 6 dB, and a noise temperature of 290 K, fi nd the total transmit power required of the transmitter in watts for a link margin of 8 dB.

k � 10 log (1.38 � 10�23) � �228.6 dBW

Lp � 140 dB; Ag � 24 dB; Nf � 6 dB; Fmargin � 8 dB; Gt � 8 dB; Gr � 0 dB;

L0 � 20 dB; Lfeed � 12 dB; T � 24.6 dB; R � 39.8 dB; (Eb /N0)reqd � 10 dB; and M � 8 dB

From Equation (3.54)

Pt � M � Gt � Gr � Ag � Nf, total � T � k � Lp � Lf � L0 � Fmargin � R

� (Eb /N0)reqd

Pt � 8 � 8 � 0 � 24 � 6 � (24.6 � 228.6) � 140 � 12 � 20 � 8 � 39.8 � 10

� 7.8 dBW

∴Pt � 100.78 ≈ 6 W

3.13 SummaryIn this chapter we discussed propagation and multipath characteristics of a radio channel. The concepts of delay spread that causes channel dispersion and inter-symbol interference were also presented. Since the mathematical modeling of the propagation of radio waves in a real world environment is complicated, empiri-cal models were developed by several authors. We presented these empirical and semi-empirical models used for calculating the path losses in urban, suburban, and rural environments and compared the results obtained with each model. Dop-pler spread, coherence bandwidth, and time dispersion were also discussed. The

3.13 Summary 81


forward error correcting algorithms [3] for improving radio channel performances are given in Chapter 8.

Problems 3.1 Defi ne slow and fast fading.

3.2 What is a frequency selective channel?

3.3 Defi ne receiver sensitivity.

3.4 A vehicle travels at a speed of 30 m/s and uses a carrier frequency of 1 GHz. What is the maximum Doppler shift? What is the approximate fade duration?

3.5 A mobile station traveling at 30 km per hour receives a fl at Rayleigh fading signal at 800 MHz. Determine the number of fades per second above the rms level. What is the average duration of fade below the rms level? What is the average duration of fade at a level 20 dB below the rms level?

3.6 Find the received power for the link from a synchronous satellite to a terrestrial antenna. Use the following data: height � 60,000 km; satellite transmit power � 4 W; transmit antenna gain � 18 dBi; receive antenna gain � 50 dBi; and transmit frequency � 12 GHz.

3.7 Determine the SNR for the spacecraft that uses a transmitter power of 16 W at a frequency of 2.4 GHz. The transmitter and receiver antenna gain are 28 dBi and 60 dBi, respectively. The distance from the space-craft to ground is 2 � 1010 m, the effective noise temperature of antenna plus receiver is 14 degrees Kelvin, and a bit rate of 120 kbps. Assume the bandwidth of the system to be half of the bit rate, 60 kHz.

3.8 A base station transmits a power of 10 W into a feeder cable with a loss of cable 10 dB. The transmit antenna has a gain of 12 dBi in the direction of the mobile receiver with a gain of 0 dBi and feeder loss of 2 dB. The mobile receiver has a sensitivity of �104 dBm. (a) Determine the effec-tive isotropic radiated power, and (b) maximum acceptable path loss.

3.9 A receiver in a digital mobile communication system has a noise band-width of 200 kHz and requires that its input signal-to-noise ratio should be at least 10 dB when the input signal is �104 dBm. (a) What is the maximum permitted value of the receiver noise fi gure, and (b) What is the equivalent input noise temperature?

3.10 Calculate the maximum range of the communication system in Problem 8, assuming a mobile antenna height (hm) of 1.5 m, a base station antenna height (hb) of 30 m, a frequency equal to 900 MHz and propagation that

takes place over a plane earth. Assume base station and mobile station antenna gains to be 12 dBi and 0 dBi, respectively. How will this range change if the base station antenna height is doubled?

3.11 A mobile station traveling at a speed of 60 km/h transmits at 900 MHz. If it receives or transmits data at a rate of 64 kbps, is the channel fading slow or fast?

3.12 The power received at a mobile station is lognormal with a standard deviation of 8 dB. Calculate the outage probability assuming the average received power is �96 dBm and the threshold power is �100 dBm.

3.13 Determine the minimum signal power for an acceptable voice quality at the base station receiver of a GSM system (bandwidth 200 kHz, data rate 271 kbps). Assume the following data: Receiver noise fi gure � 5 dB, Boltzmann’s constant � 1.38 � 10�23 Joules/K, mobile radiated power � 30 dBm, transmitter cable losses � 3 dB, base station antenna gain � 16 dBi, mobile antenna gain � 0 dBi, fade margin � 10.5 dB, and required Eb /N0 � 13.5 dB. What is the maximum allowable path loss? What is the maximum cell radius in an urban area where a 1 km inter-cept is 108 dB and the path-loss exponent is 4.2?

3.14 Develop a MATLAB program and obtain a curve for maximum path loss versus cell radius. Test your program using the following data: base station transmit power � 10 W, base station cable loss � 10 dB, base station antenna gain � 8 dBi, base station antenna height � 15 m, mobile station antenna gain � 0 dBi, mobile station antenna height � 1 m, body and matching loss � 6 dB, receiver noise bandwidth � 200 kHz, receiver noise fi gure � 7 dB, noise density ��174 dBm/Hz, required SNR � 9 dB, building penetration loss � 12 dB, and fade margin � 10 dB.

3.15 In the Bluetooth device with NLOS, S /N required is 10 dB in an indoor offi ce environment. The background noise at the operating frequency is �80 dBm. If the transmit power of the device is 20 dBm, what is its coverage?

References1. Bertoni, H. L. Radio Propagation for Modern Wireless Systems. Upper Saddle River, NJ:

Prentice Hall, 2000.

2. Clarke, R. H. “A Statistical Theory of Mobile Radio Reception.” Bell System Technical Journal 47 (July–August 1968): 957–1000.

3. Forney, G. D. “The Viterbi Algorithm.” Proceedings of IEEE, vol. 61, no. 3, March 1978, pp. 268–278.

4. Garg, V. K., and Wilkes, J. E. Wireless and Personal Communications Systems. Upper Saddle River, NJ: Prentice Hall, 1996.

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