Practical Radio Propagation Models

Radio Propagation Models

Radio propagation model equations Log-distance path model Average received power Average path loss Log-normal shadowing model

Outdoor Propagation Models Okumura’s Model Most widely used models for signal prediction in urban areas Applicable in frequency range of 150 MHz-1920 MHz and distances of 1 km – 100 km Base station heights of 30 m – 1000 m

Okumura Model equations - Median value of propagation path loss - Free space propagation loss - Median attenuation relative to free-space - Base station antenna height gain factor - Mobile antenna height gain factor - Gain due to type of environment

Free space propagation loss LF LF = -10 log [ l2/ (4pd)2] Wavelength l,m = 3 x 108/f Frequency f, Hz d = Transmitter-receiver distance, m

Gain factor calculations

Median attenuation relative to free space (Amu(f,d)), over a quasi-smooth terrain [ from Oku68 © IEEE] 100 70 Urban Area ht = 200m hr = 3m 80 70 60 60 50 50 40 d (km) 30 Median Attenuation, A(f,d) (dB) 40 20 10 5 30 2 1 20 10 70 100 200 300 500 1000 2000 700 3000 Frequency f (MHz)

Correction factor, GAREA, for different types of terrain [ from Oku68 ©IEEE] 35 30 Open Area 25 20 Quasi Open Area 15 Correction Factor , GAREA (dB) Suburban Area 10 5 100 200 300 500 1000 2000 700 3000 Frequency f (MHz)

Hata Model for different terrains |

Hata Model parameters - Frequency in MHz from 150 MHz - 1500 MHz - Effective transmitter ( base station) antenna height (in meters) ( 30 m – 200 m) - Effective receiver ( mobile) antenna height (in meters) ( 1 m – 10 m) - T-R separation distance in km - Correction factor for effective for effective mobile height

Correction factor Small City Large City

PCS Extension to Hata Model Extension of Hata Model to GHz Developed by EURO-COST ( European Cooperative for Scientific & Tech. Research)

PCS Extension to Hata Model limits Model valid for following range of parameters

Indoor Propagation Models PCS (Personal Communication System) requires good models for propagation inside buildings Indoor radio channel differs from outdoor models Distances covered are much smaller Variability of channel is much greater for a much smaller T-R separation distance Indoor channels may be classified as either Line-of-sight (LOS) or Obstructed (OBS)

Log-distance indoor model Log-normal power law where n, s depend on surrounding & building type

Log-distance indoor model- Example Given the following measurements: Pr (1 m) = 0 dBm Pr (2 m) = -20 dBm Pr (5 m) = -30 dBm Pr (10 m) = -40 dBm Determine the value of n and s using log-distance model

Log-distance indoor model- Solution Step 1: Predicted vlaues Using Pr’(d) = Pr(d0) – 10nlog(d/d0) Pr’(1) = 0 dBm – 10nlog(1/1) = 0 Pr’ (2 m) = 0 dBm – 10nlog(2/1)=-3n Pr (5 m) = 0 dBm – 10nlog(5/1)=-7n Pr (10 m)=0 dBm–10nlog(10/1)=-10n

Log-distance indoor model- Solution Step 2: Mean squared error E between measured and predicted values E= (0-0)2 + (-20+3n)2+(-30+7n)2+(-40+10n)2 Step 3: Minimization of error E dE/dn = 0 => 2 x 3 x (-20+3n) +2 x 7 x (-30+7n) +2 x 10 x (-40 +10n) = 0  => 158n = 670 => n = 4.24

Log-distance indoor model- Solution Step 4: Calculation of standard deviation s s2 = E/Number of measurements =[(0-0)2 + (-20+3n)2+(-30+7n)2+(-40+10n)2]/4 Putting n = 4.24 s2 = 14.72 => s = 3.83

Path Loss Exponent and Standard Deviation Measured in Commericial/Office Buildings [Anderson et al., 94] Building Frequency (MHz) n (db) Retail Stores 914 2.2 8.7 Grocery Store 1.8 5.2 Office, hard partition 1500 3.0 7.0 Office, soft partition 900 2.4 9.6 1900 2.6 14.1 s †

Path Loss Exponent and Standard Deviation Measured in Factory (LOS) Buildings [Anderson et al., 94] Frequency (MHz) n (db) Factory LOS Textile/Chemical 1300 2.0 3.0 4000 2.1 7.0 Paper/Cereals 1.8 6.0 Metalworking 1.6 5.8 s †

Path Loss Exponent and Standard Deviation Measured in Home/Factory (OBS)Buildings [Anderson et al. 94] Building Frequency (MHz) n (db) Suburban Home Indoor to Street 900 3.0 7.0 Factory OBS Textile/Chemical 4000 2.1 9.7 Metalworking 1300 3.3 6.8 s †

Seidel Model – Same floor measurements In-building site-specific propagation model Reduces the standard deviation (s) between measured and predicted path loss to around 4dB, as compared to 13dB when only a log-distance model was used nSF = ‘same floor’ measurement exponent FAF = Floor attenuation factor for a specified number of building floors PAF = Partition attenuation factor

Seidel Model – Multi floor measurements When measurments are made across different floors, then model is modified: nMF = ‘multifloor’ measurement exponent PAF = Partition attenuation factor

Path Loss Exponent and Standard Deviation Measured for All Buildings [Seidel et al., 1992] s (db) Number of locations All Buildings All locations 3.14 16.3 634 Same Floor 2.76 12.9 501 Through One Floor 4.19 5.1 73 Through Two Floors 5.04 6.5 30 Through Three Floors 5.22 6.7 Grocery Store 1.81 5.2 89 Retail Store 2.18 8.7 137

Path Loss Exponent and Standard Deviation Measured for Office Building 1 [Seidel et al., 1992] s (db) Number of locations Office Building 1: Entire Building 3.54 12.8 320 Same Floor 3.27 11.2 2.38 West Wing 5th Floor 2.68 8.1 104 Central Wing 5th Floor 4.01 4.3 118 West Wing 4th Floor 3.18 4.4 120

Path Loss Exponent and Standard Deviation Measured for Office Building 2 [Seidel et al., 1992] s (db) Number of locations Office Building 2: Entire Building 4.33 13.3 100 Same Floor 3.25 5.2 37

Free-space plus linear Path Attenuation Model [Devasirvathan et al, 90] - Attenuation constant for channel (dB/n) FAF- Floor attentuation factor PAF- Partition attentuation factor

Free Space Plus Linear Path Attenuation Model parameters [Devasirvathan et al, 90] Location Frequency a —Attenuation (dB/m) Building 1:4 story 850 MHz 0.62 1.7 GHz 0.57 4.0 GHz 0.47 Building 2:2 story 0.48 0.35 0.23 †