Modelos de propagacion


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Modelos de propagacion

  1. 1. 66 3 Radio Propagation and Propagation Path-Loss Models3.9 Propagation Path-Loss ModelsPropagation path-loss models [20] play an important role in the design of cellularsystems to specify key system parameters such as transmission power, frequency,antenna heights, and so on. Several models have been proposed for cellular systemsoperating in different environments (indoor, outdoor, urban, suburban, rural).Some of these models were derived in a statistical manner based on field measure-ments and others were developed analytically based on diffraction effects. Eachmodel uses specific parameters to achieve reasonable prediction accuracy. Thelong distance prediction models intended for macrocell systems use base stationand mobile station antenna heights and frequency. On the other hand, the predic-tion models for short distance path-loss estimation use building heights, streetwidth, 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 properpath-loss model for design of the mobile system in the given environment. Propagation models are used to determine the number of cell sites requiredto provide coverage for the network. Initial network design typically is based oncoverage. Later growth is engineered for capacity. Some systems may need to startwith wide area coverage and high capacity and therefore may start at a later stageof growth. The coverage requirement along with the traffic requirement relies on thepropagation model to determine the traffic distribution, and will offload froman existing cell site to new cell sites as part of a capacity relief program. Thepropagation model helps to determine where the cell sites should be placed toachieve an optimal location in the network. If the propagation model used is noteffective in placing cell sites correctly, the probability of incorrectly deploying acell site in the network is high. The performance of the network is affected by the propagation model chosenbecause it is used for interference predictions. As an example, if the propagationmodel is inaccurate by 6 dB (provided S/I ϭ 17 dB is the design requirement), thenthe signal-to-interference ratio, S/I, could be 23 dB or 11 dB. Based on traffic con-ditions, designing for a high S/I could negatively affect financial feasibility. On theother hand, designing for a low S/I would degrade the quality of service. The propagation model is also used in other system performance aspectsincluding handoff optimization, power level adjustments, and antenna placements.Although no propagation model can account for all variations experienced in reallife, it is essential that one should use several models for determining the pathlosses in the network. Each of the propagation models being used in the industryhas pros and cons. It is through a better understanding of the limitations of eachof 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 231models. The Okumura/Hata model has been used extensively both in Europe and
  2. 2. 3.9 Propagation Path-Loss Models 67North America for cellular systems. The COST 231 model has been recommendedby the European Telecommunication Standard Institute (ETSI) for use in PersonalCommunication Network/Personal Communication System (PCN/PCS). In addi-tion, we also present the empirical models proposed by International MobileTelecommunication-2000 (IMT-2000) for the indoor office environment, outdoorto indoor pedestrian environment, and vehicular environment.3.9.1 Okumura/Hata ModelOkumura analyzed path-loss characteristics based on a large amount of experimentaldata collected around Tokyo, Japan [6,11]. He selected propagation path conditionsand obtained the average path-loss curves under flat urban areas. Then he appliedseveral 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 fitOkumura curves. Hata’s equations are classified into three models: 1. Typical Urban L50(urban) ϭ 69.55 ϩ 26.16 log fc ϩ (44.9 Ϫ 6.55 log hb)log d Ϫ 13.82 log hb Ϫ a(hm)(dB) (3.25)where: a(hm) ϭ correction factor (dB) for mobile antenna height as given by: • For large cities a(hm) ϭ 8.29[log (1.54hm)]2 Ϫ 11 fc Յ 200 MHz (3.26) a(hm) ϭ 3.2[log (11.75hm)]2 Ϫ 4.97 fc Ն 400 MHz (3.27) • For small and medium-sized cities a(hm) ϭ [1.1 log (fc) Ϫ 0.7]hm Ϫ [1.56 log (fc) Ϫ 0.8] (3.28)
  3. 3. 68 3 Radio Propagation and Propagation Path-Loss Models 2. Typical Suburban ΄ ΂ ΂ 28 ΃ ΃ Ϫ 5.4 ΅ dB f 2 c L50 ϭ L50(urban) Ϫ 2 log ᎏ (3.29) 3. Rural L50 ϭ L50(urban) Ϫ 4.78(log fc)2 ϩ 18.33 log fc Ϫ 40.94 dB (3.30)where: fc ϭ carrier frequency (MHz) d ϭ distance between base station and mobile (km) hb ϭ base station antenna height (m) hm ϭ mobile antenna height (m) The range of parameters for which the Hata model is valid is: 150 Յ fc Յ 2200 MHz 30 Յ hb Յ 200 m 1 Յ hm Յ 10 m 1 Յ d Յ 20 km3.9.2 Cost 231 ModelThis model [19] is a combination of empirical and deterministic models forestimating the path loss in an urban area over the frequency range of 800 MHz to2000 MHz. The model is used primarily in Europe for the GSM 1800 system. L50 ϭ Lf ϩ Lrts ϩ Lms dB (3.31) or L50 ϭ Lf when Lrts ϩ Lms Յ 0 (3.32)where: Lf ϭ free space loss (dB) Lrts ϭ roof top to street diffraction and scatter loss (dB) Lms ϭ multiscreen loss (dB) Free space loss is given as: Lf ϭ 32.4 ϩ 20 log d ϩ 20 log fc dB (3.33) The roof top to street diffraction and scatter loss is given as: Lrts ϭ Ϫ16.9 Ϫ10 log W ϩ 10 log fc ϩ 20 log ⌬hm ϩ L0 dB (3.34)
  4. 4. 3.9 Propagation Path-Loss Models 69where: W ϭ street width (m) ⌬hm ϭ hr Ϫ hm m L0 ϭ Ϫ10 ϩ 0.354␾ 0 Յ ␾ Յ 35° L0 ϭ 2.5 ϩ 0.075(␾ Ϫ 35) dB 35° Յ ␾ Յ 55° L0 ϭ 4 Ϫ 0.114(␾ Ϫ 55) dB 55° Յ ␾ Յ 90°where: ␾ ϭ incident angle relative to the street The multiscreen (multiscatter) loss is given as: Lms ϭ Lbsh ϩ ka ϩ kdlog d ϩ kf log fc Ϫ 9 log b (3.35)where: b ϭ distance between building along radio path (m) d ϭ separation between transmitter and receiver (km) Lbsh ϭ Ϫ18 log (11 ϩ ⌬hb) hb Ն hr Lbsh ϭ 0 hb Ͻ hrwhere: ⌬hb ϭ hb Ϫ hr, hr ϭ average building height (m) ka ϭ 54 hb Ͼ hr ka ϭ 54 Ϫ 0.8hb d Ն 500m; h b Յ hr ka ϭ 54 Ϫ 0.8⌬hb(d/500) d Ͻ 500m; h b Յ hrNote: Both Lbsh and ka increase path loss with lower base station antenna heights. kd ϭ 18 hb Ͻ hr 15⌬h b kd ϭ 18 Ϫ ᎏ h b Ն hr ⌬hm kf ϭ 4 ϩ 0.7(fc / 925 Ϫ 1) for mid-size city and suburban area with moderatetree density ΂ 925 ΃ fc kf ϭ 4 ϩ 1.5 ᎏ Ϫ 1 for metropolitan area The range of parameters for which the COST 231 model is valid is: 800 Յ fc Յ 2000 MHz 4 Յ hb Յ 50 m
  5. 5. 70 3 Radio Propagation and Propagation Path-Loss Models 1 Յ hm Յ 3 m 0.02 Յ d Յ 5 km The following default values may be used in the model: b ϭ 20–50 m W ϭ b/2 ␾ ϭ 90° Roof ϭ 3 m for pitched roof and 0 m for flat roof, and hr ϭ 3 (number of floors) ϩ roofExample 3.7Using the Okumura and COST 231 models, calculate the L50 path loss for a PCSsystem in an urban area at 1, 2, 3, 4 and 5 km distance (see Table 3.1). Assumehb ϭ 30 m, hm ϭ 2 m, and carrier frequency fc ϭ 900 MHz. Use the following datafor the COST 231 model: W ϭ 15 m, b ϭ 30 m, ␾ ϭ 90°, hr ϭ 30 m COST 231 Model L50 ϭ Lf ϩ Lrts ϩ Lms Lf ϭ 32.4 ϩ 20 log d ϩ 20 log fc ϭ 32.4 ϩ 20 log d ϩ 20 log 900 dB Lf ϭ 91.48 ϩ 20 log d dB Lrts ϭ Ϫ16.9 Ϫ 10 log W ϩ 10 log fc ϩ 20 log ⌬hm ϩ L0 ⌬hm ϭ hr Ϫ hm ϭ 30 Ϫ 2 ϭ 28 mTable 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 22.30 157.59Note: The table applies to this example only.
  6. 6. 3.9 Propagation Path-Loss Models 71 L0 ϭ 4 Ϫ 0.114(␾ Ϫ 55) ϭ 4 Ϫ 0.114(90 Ϫ 55) ϭ 0 Lrts ϭ Ϫ16.9 Ϫ 10 log 15 ϩ 10 log 900 ϩ 20 log 28 ϩ 0 ϭ 29.82 dB Lms ϭ Lbsh ϩ ka ϩ kd log d ϩ kf log fc Ϫ 9 log b ka ϭ 54 Ϫ 0.8hb ϭ 54 Ϫ 0.8 ϫ 30 ϭ 30 ⌬hb ϭ hb Ϫ hr ϭ 30 Ϫ 30 ϭ 0 m Lbsh ϭ Ϫ18 log 11 ϩ 0 ϭ Ϫ18.75 dB b 15⌬h 15 ϫ 0 kd ϭ 18 Ϫ ᎏ ϭ 18 Ϫ ᎏ ϭ 18 ⌬hm 28 ΂ 925 fc ΃ 900 ΂ 925 ΃ kf ϭ 4 ϩ 0.7 ᎏ Ϫ 1 ϭ 4 ϩ 0.7 ᎏ Ϫ 1 ϭ 3.98 (for mid-sized city) Lms ϭ Ϫ18.75 ϩ 30 ϩ 18 log d ϩ 3.98 log 900 Ϫ 9 log 30 ϭ 9.72 ϩ 18 log d dBOkumura/Hata Model L50 ϭ 69.55 ϩ 26.16 log fc ϩ (44.9 Ϫ 6.55hb)log d Ϫ 13.82 log hb Ϫ a(hm) dB a(hm) ϭ (1.1 log fc Ϫ 0.7)hm Ϫ (1.56 log fc Ϫ 0.8) ϭ (1.1 log 1800 Ϫ 0.7)(2) Ϫ (1.56 log 900 Ϫ 0.8) ϭ 1.29 dB L50 ϭ 69.55 ϩ 26.16 log 900 ϩ (44.9 Ϫ 6.55 log 30)log d Ϫ 13.82 log 30 Ϫ 1.29 dB ϭ 125.13 ϩ 35.23 log d dB (refer to Table 3.2) The results from the two models are given in Figure 3.9. Note that thecalculated path loss with the COST 231 model is higher than the value obtainedby 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
  7. 7. 72 3 Radio Propagation and Propagation Path-Loss Models 160 155 COST 231 model Hata model 150Path loss in [dB] 145 140 135 130 125 1 1.5 2 2.5 3 3.5 4 4.5 5 Distance from transmitter in [km]Figure 3.9 Comparison of COST 231 and Hata-Okumura models.3.9.3 IMT-2000 ModelsThe operating environments are identified by appropriate subsets consisting ofindoor office environments, outdoor to indoor and pedestrian environments, andvehicular (moving vehicle) environments. For narrowband technologies (such asFDMA 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 ofthe many signal components become important. In addition, for some technologies(e.g., those using power control) the path-loss models must include the couplingbetween all co-channel propagation links to provide accurate predictions. Also,in some cases, the shadow effect temporal variations of the environment must bemodeled. The key parameters of the IMT-2000 propagation models are: • Delay spread, its structure, and its statistical variation • Geometrical path loss rule (e.g., dϪ␥, 2 Յ ␥ Յ 5) • Shadow fading margin • Multipath fading characteristics (e.g., Doppler spectrum, Rician vs. Rayleigh for envelope of channels) • Operating radio frequency
  8. 8. 3.9 Propagation Path-Loss Models 73Indoor Office EnvironmentThis environment is characterized by small cells and low transmit powers. Bothbase stations and pedestrian users are located indoors. RMS delay spread rangesfrom around 35 nsec to 460 nsec. The path loss rule varies due to scatter andattenuation by walls, floors, and metallic structures such as partition and filingcabinets. These objects also produce shadowing effects. A lognormal shadowingwith a standard deviation of 12 dB can be expected. Fading characteristic rangesfrom Rician to Rayleigh with Doppler frequency offsets are determined by walk-ing speeds. Path-loss model for this environment is: L50 ϭ 37 ϩ 30 log d ϩ 18.3 · n΄ ΂ n ϩ 2 ΃/΂ n ϩ 1 ΃ Ϫ 0.46 ΅ dB (3.36)where: d ϭ separation between transmitter and receiver (m) n ϭ number of floors in the pathOutdoor to Indoor and Pedestrian EnvironmentThis environment is characterized by small cells and low transmit power. Basestations with low antenna heights are located outdoors. Pedestrian users arelocated on streets and inside buildings. Coverage into buildings in high power sys-tems is included in the vehicular environment. RMS delay spread varies from 100to 1800 nsec. A geometric path-loss rule of dϪ4 is applicable. If the path is a line-of-sight on a canyon-like street, the path loss follows a rule of dϪ2, where there isFresnel zone clearance. For the region with longer Fresnel zone clearance, a pathloss rule of dϪ4 is appropriate, but a range of up to dϪ6 may be encountered dueto trees and other obstructions along the path. Lognormal shadow fading witha 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 dBis appropriate. Rayleigh and/or Rician fading rates are generally set by walkingspeeds, but faster fading due to reflections from moving vehicles may occur some-times. The following path-loss model has been suggested for this environment: L50 ϭ 40 log d ϩ 30 log fc ϩ 49 dB (3.37) This model is valid for non-line-of-sight (NLOS) cases only and describesthe worst-case propagation. Lognormal shadow fading with a standard deviationequal to 10 dB is assumed. The average building penetration loss is 18 dB with astandard deviation of 10 dB.Vehicular EnvironmentThis environment consists of larger cells and higher transmit power. RMS delayspread from 4 microseconds to about 12 microseconds on elevated roads in hilly ormountainous terrain may occur. A geometric path-loss rule of dϪ4 and lognormal
  9. 9. 74 3 Radio Propagation and Propagation Path-Loss Modelsshadow fading with a standard deviation of 10 dB are used in the urban andsuburban areas. Building penetration loss averages 18 dB with a 10 dB standarddeviation. In rural areas with flat terrain the path loss is lower than that of urbanand suburban areas. In mountainous terrain, if path blockages are avoided byselecting base station locations, the path-loss rule is closer to dϪ2. Rayleigh fad-ing rates are determined by vehicle speeds. Lower fading rates are appropriate forapplications using stationary terminals. The following path-loss model is used inthis environment: L50 ϭ 40(1 Ϫ 4 ϫ 10Ϫ2⌬hb)log d Ϫ 18 log (⌬hb) ϩ 21 log fc ϩ 80 dB (3.38)where: ⌬hb ϭ 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 delayspreads. Measurements in outdoor environments show that rms delay spread canvary over an order of magnitude within the same environment. Delay spreadscan have a major impact on the system performance. To accurately evaluate therelative performance of radio transmission technologies, it is important to modelthe variability of delay spread as well as the “worst case” locations where delayspread is relatively large. For each environment IMT-2000 defines three multipathchannels: 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 therms values of delay spread for each channel and for each environment.Table 3.3 Rms delay spread (IMT-2000). Channel “A” Channel “B” Channel “C” Environment ␶rms (ns) % Occurrence ␶rms (ns) % Occurrence ␶rms (ns) % Occurrence Indoor office 35 50 100 45 460 5 Outdoor to 100 40 750 55 1800 5 indoor and pedestrian Vehicular 400 40 4000 55 12,000 5 (high antenna)
  10. 10. 3.10 Indoor Path-Loss Models 753.10 Indoor Path-Loss ModelsPicocells cover part of a building and span from 30 to 100 meters [13,15]. Theyare used for WLANs and PCSs operating in the indoor environment. The path-lossmodel for a picocell is given as: ᎏ Lp ϭ Lp(d0) ϩ 10␥ log d ϩ Lf(n) ϩ X␴ dB (3.39)where: ᎏ Lp(d0) ϭ reference path loss at the first meter (dB) ␥ ϭ path-loss exponent d ϭ distance between transmitter and receiver (m) X␴ ϭ shadowing effect (dB) Lf (n) ϭ signal attenuation through n floors Indoor-radio measurements at 900 MHz and 1.7 GHz values of Lf per floor are ᎏ10 dB and 16 dB, respectively. Table 3.4 lists the values of Lp(d0), Lf (n), ␥, and X␴.Partition dependent losses for signal attenuation at 2.4 GHz are given in Table 3.5. ᎏTable 3.4 Values of Lp(d0), ␥, Lf (n) and X␴ in Equation 3.39. Environment Residential Office Commercial ᎏ 38 38 38 Lp(d0) (dB) ␥ 2.8 3.0 2.2 Lf (n) (dB) 4n 15 ؉ 4(n ؊ 1) 6 ؉ 3(n ؊ 1) X␴ (dB) 8 10 10 Table 3.5 Partition dependent losses at 2.4 GHz. Signal attenuation through Loss (dB) Window in brick wall 2 Metal frame, glass wall in 6 building Office wall 6 Metal door in office wall 6 Cinder wall 4 Metal door in brick wall 12.4 Brick wall next to metal door 3
  11. 11. 76 3 Radio Propagation and Propagation Path-Loss Models Femtocellular systems span from a few meters to a few tens of meters. Theyexist in individual residences and use low-power devices using Bluetooth chips orHome RF equipment. The data rate is around 1 Mbps. Femtocellular systems usecarrier frequencies in the unlicensed bands at 2.4 and 5 GHz. Table 3.6 lists thevalues of Lp(d0) and ␥ for LOS and NLOS conditions.Example 3.8In a WLAN the minimum SNR required is 12 dB for an office environment.The background noise at the operational frequency is Ϫ115 dBm. If the mobileterminal transmit power is 100 mW, what is the coverage radius of an access pointif there are three floors between the mobile transmitter and the access point?Solution • Transmit power of mobile terminal ϭ 10 log 100 ϭ 20 dBm • Receiver sensitivity ϭ background noise ϩ minimum SNR ϭ Ϫ115 ϩ 12 ϭ Ϫ103 dB • Maximum allowable path loss ϭ transmit power Ϫ receiver sensitivity ϭ 20 Ϫ (Ϫ103) ϭ 123 dB ᎏ • Lp(d0) ϭ 38 dB, Lf (n) ϭ 15 ϩ 4(3 Ϫ 1) ϭ 23 dB, ␥ ϭ 3, and X␴ ϭ 10 dB (from Table 3.4) Maximum allowable path loss ϭ 123 ϭ 38 ϩ 23 ϩ 10 ϩ 30 log d d ϭ 54 m3.11 Fade MarginAs we discussed earlier, the local mean signal strength in a given area at a fixedradius, 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 normalrandom 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 (atd ϭ R) wherein a mobile would experience a received signal above the receiversensitivity. The receiver sensitivity is the value that provides an acceptable signalunder Rayleigh fading conditions. The probability distribution function for a log-normally distributed random variable is: 1 p(S) ϭ ᎏ eϪ[(S Ϫ Sm) /(2␴s )] 2 2 ᎏ (3.40) ␴sΊ 2␲
  12. 12. 3.11 Fade Margin 77Table 3.6 Values of A and ␥ for femtocellular systems. Center ᎏ Environment frequency (GHz) Scenario Lp(d0)(dB) ␥ Indoor office 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 5.2 LOS (same 47 2 to 3 residence floor) NLOS (same 4 to 5 floor) NLOS & room 4 to 6 in higher floor directly above Tx NLOS & room 6 to 7 in higher floor not directly above Tx The probability for signal strength exceeding receiver sensitivity PSmin(R) isgiven as ͵ ϱ ϪS ΂ ΃ 1 1 S PSmin(R) ϭ P[S Ն Smin] ϭ p(S)dS ϭ ᎏ Ϫ ᎏ erf ᎏ min ᎏ m (3.41) Smin 2 2 ␴sΊ2Note: See Appendix D for erf, erfc and Q functions.Example 3.9If the mean signal strength and receiver sensitivity are Ϫ100 dBm and Ϫ110 dBm,respectively and the standard deviation is 10 dB, calculate the probability forexceeding signal strength beyond the receiver sensitivity.Solution Ϫ110 ϩ 100 ΂ ΃ 1 1 PSmin(R) ϭ ᎏ Ϫ ᎏ erf ᎏᎏ ϭ 0.5 ϩ 0.5 erf(0.707) ϭ 0.84 ᎏ 2 2 10Ί2
  13. 13. 78 3 Radio Propagation and Propagation Path-Loss Models Next, we determine the fraction of the coverage within an area in which thereceived signal strength from a radiating base station antenna exceeds Smin. Wedefine the fraction of the useful service area Fu as that area, within an area forwhich the signal strength received by a mobile antenna exceeds Smin. If PSmin is theprobability that the received signal exceeds Smin in an incremental area dA, then 1 Fu ϭ ᎏ ΎPSmindA (3.42) 2␲R Using the power law we express mean signal strength Sm as d Sm ϭ ␣ Ϫ 10␥log ᎏ (3.43) R where ␣ accounts for the transmitter effective radiated power (ERP), receiverantenna gain, feed line losses, etc. Substituting Equation 3.43 into 3.41 we get: Smin Ϫ ␣ ϩ 10␥log(d ⁄ R) 1 1 PSmin ϭ ᎏ Ϫ ᎏ erf ᎏᎏ 2 ᎏ 2 ΄ ␴sΊ2 ΅ (3.44) ᎏ ᎏ Let a ϭ (Smin Ϫ ␣)/(␴sΊ 2 ) and b ϭ (10␥log (d/R))/(␴sΊ 2 ) Substituting Equation 3.44 into 3.42, we get ͵ x{erf[a ϩ b log (x/R)]}dx R 1 1 ІFu ϭ ᎏ Ϫ ᎏ (3.45) 2 2 R 0 Let t ϭ a ϩ b log (x/R), then ͵ a 1 1 ∴Fu ϭ ᎏ Ϫ ᎏe(Ϫ2a)/b e(2t)/berf(t)dt (3.46) 2 b Ϫϱ or 1 ΄ 1 Ϫ ab Fu ϭ ᎏ 1 Ϫ erf(a) ϩ e(1 Ϫ 2ab)/b2 1 Ϫ erf ᎏ 2 ΂ ΄ b ΅΃΅ (3.47) If we choose ␣ such that Sm ϭ Smin at d ϭ R, then a ϭ 0 and 1 Fu ϭ ᎏΆ 1 ϩe1/b [1 Ϫ erf(1/b)] · 2 2 (3.48) Figure 3.10 shows the relation in terms of the parameter ␴s ր␥.
  14. 14. 3.12 Link Margin 79 1.0 PSmin (R ) 0.95 WITH SIGNAL ABOVE THRESHOLD, Fu 0.9 0.85 FRACTION OF TOTAL AREA 0.9 0.8 0.75 0.7 0.8 0.65 0.6 0.7 0.55 σm STANDARD DEVIATION dB; PATH LOSS VARIES AS 0.5 1 r r, PSmin (R) COVERAGE 0.6 PROBABILITY ON AREA BOUNDARY (d R) 0.5 0 1 2 3 4 5 6 7 8 sFigure 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)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 overalllink performance margin [4]. The receiver power Pr is given as: PtGtGr Pr ϭ ᎏ Lp (3.49)where: Pt is the transmitter power Gt and Gr are the gains of transmitter and receiver Lp is the path loss between the transmitter and receiver. In addition, there are also the effects due to receiver thermal noise, whichis generated due to random noise inherent within a receiver’s electronics. This
  15. 15. 80 3 Radio Propagation and Propagation Path-Loss Modelsincreases with temperature. We account for this thermal noise effect with thefollowing: N ϭ kTBw (3.50)where: k ϭ Boltzmann’s constant (1.38 ϫ 10Ϫ23 W/Kelvin-Hz) T ϭ temperature in Kelvin Bw ϭ receiver bandwidth(Hz). Spectral noise density, N0, is the ratio of thermal noise to receiver band-width N0 ϭ N/Bw ϭ kT (3.51) Finally, there is an effect on signal-to-noise (SNR) ratio due to the quality ofthe components used in the receiver’s amplifiers, local oscillators (LOs), mixers,etc. The most basic description of a component’s quality is its noise figure, 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 amplifiers’ noise figures is cumulative,and can be obtained as: Nf,total ϭ Nf1 ϩ (Nf2 Ϫ 1)/G1 ϩ (Nf3 Ϫ 1)/(G1G2) ϩ . . . (3.52)where: Nfk is the noise figure in stage k Gk ϭ gain of the kth stage. By combining all the factors, we can develop a relation that allows us tocalculate the overall link margin PtGtGrAg M ϭ ᎏᎏᎏ (3.53) ΂N ΃ Eb Nf, totalTkLpLfL0Fmargin R ᎏ 0 reqdwhere: Ag ϭ gain of receiver amplifier in dB R ϭ data rate in dB Fmargin ϭ fade margin in dB Tk ϭ noise temperature in Kelvin (Eb / N0)reqd ϭ required value in dB Lp ϭ path losses in dB Lf ϭ antenna feed line loss in dB L0 ϭ other losses in dB
  16. 16. 3.13 Summary 81 Expressing Equation 3.53 in dB, we obtain M ϭ Pt ϩ Gt ϩ Gr ϩ Ag Ϫ Nf, total Ϫ Tk Ϫ Lp Ϫ Lf Ϫ L0 Ϫ Fmargin Ϫ R Ϫ (Eb /N0)reqd dB (3.54)Example 3.10Given a flat 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, arequired Eb /N0 of 10 dB, receiver amplifier gain of 24 dB, noise figure total of6 dB, and a noise temperature of 290 K, find the total transmit power required ofthe transmitter in watts for a link margin of 8 dB. k ϭ 10 log (1.38 ϫ 10Ϫ23) ϭ Ϫ228.6 dBW Lp ϭ 140 dB; Ag ϭ 24 dB; Nf ϭ 6 dB; Fmargin ϭ 8 dB; Gt ϭ 8 dB; Gr ϭ 0 dB; L0 ϭ 20 dB; Lfeed ϭ 12 dB; T ϭ 24.6 dB; R ϭ 39.8 dB; (Eb /N0)reqd ϭ 10 dB;and M ϭ 8 dB From Equation (3.54) Pt ϭ M Ϫ Gt Ϫ Gr Ϫ Ag ϩ Nf, total ϩ T ϩ k ϩ Lp ϩ Lf ϩ L0 ϩ Fmargin ϩ R ϩ (Eb /N0)reqd Pt ϭ 8 Ϫ 8 Ϫ 0 Ϫ 24 ϩ 6 ϩ (24.6 Ϫ 228.6) ϩ 140 ϩ 12 ϩ 20 ϩ 8 ϩ 39.8 ϩ 10 ϭ 7.8 dBW ∴Pt ϭ 100.78 ≈ 6 W3.13 SummaryIn this chapter we discussed propagation and multipath characteristics of a radiochannel. The concepts of delay spread that causes channel dispersion and inter-symbol interference were also presented. Since the mathematical modeling of thepropagation of radio waves in a real world environment is complicated, empiri-cal models were developed by several authors. We presented these empirical andsemi-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
  17. 17. 82 3 Radio Propagation and Propagation Path-Loss Modelsforward error correcting algorithms [3] for improving radio channel performancesare given in Chapter 8.Problems 3.1 Define slow and fast fading. 3.2 What is a frequency selective channel? 3.3 Define 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 flat 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 ϭ 60,000 km; satellite transmit power ϭ 4 W; transmit antenna gain ϭ 18 dBi; receive antenna gain ϭ 50 dBi; and transmit frequency ϭ 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 ϫ 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 Ϫ104 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 Ϫ104 dBm. (a) What is the maximum permitted value of the receiver noise figure, 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
  18. 18. References 83 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 Ϫ96 dBm and the threshold power is Ϫ100 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 figure ϭ 5 dB, Boltzmann’s constant ϭ 1.38 ϫ 10Ϫ23 Joules/K, mobile radiated power ϭ 30 dBm, transmitter cable losses ϭ 3 dB, base station antenna gain ϭ 16 dBi, mobile antenna gain ϭ 0 dBi, fade margin ϭ 10.5 dB, and required Eb /N0 ϭ 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 ϭ 10 W, base station cable loss ϭ 10 dB, base station antenna gain ϭ 8 dBi, base station antenna height ϭ 15 m, mobile station antenna gain ϭ 0 dBi, mobile station antenna height ϭ 1 m, body and matching loss ϭ 6 dB, receiver noise bandwidth ϭ 200 kHz, receiver noise figure ϭ 7 dB, noise density ϭϪ174 dBm/Hz, required SNR ϭ 9 dB, building penetration loss ϭ 12 dB, and fade margin ϭ 10 dB. 3.15 In the Bluetooth device with NLOS, S /N required is 10 dB in an indoor office environment. The background noise at the operating frequency is Ϫ80 dBm. If the transmit power of the device is 20 dBm, what is its coverage?References 1. 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.