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1 Fundamentals of Propagation and Basic Equations. Outdoor Propagation Indoor Propagation Models to compute PL and Preceived in Outdoor and Indoor Communications. Examples of real situations. Gustavo Fano 1

2 Propagation Mechanisms Reflection Propagating wave impinges on an object which is large compared to wavelength. E.g., the surface of the Earth, buildings, walls, etc. Diffraction Radio path between transmitter and receiver obstructed by surface with sharp irregular edges. Waves bend around the obstacle, even when LOS does not exist. Scattering Objects smaller than the wavelength of the propagating wave E.g., foliage, street signs, lamp posts. Basics Equations of Propagation Friis Free Space Equation (unobstructed line-of-sight path between T-R) Pr(d)=Pt.Gt.Gr.λ 2 /(4πd) 2 Received Power in Free space [W] If Gt=Gr=1 P LS =10log(Pt/Pr) 4π d PL FS = 20log [db] Path loss free space Valid only in Far Field. λ df=2d 2 /λ Far Field Region d>df Pr(d)=10log(Pr(d 0 )) dbm +20log(d 0 /d) Received Power Free Space[dBm] Pr = Pt.Gt.Gr.ht 2.hr 2 /d 4 Received Power. Perfect Ground Reflection Γ=-1 2

3 Received Power vs. Distance. Pt=1W, 2W, 5W, 10W, 20W, 50W. Gr=Gt=1, ht=50m, hr=1m, freq=900mhz. Perfect Ground reflection. 1.E-07 1.E-08 Prec.[W] 1.E-09 1.E-10 1.E-11 1.E-12 1.E Distance[m] 3

4 Path loss models based on distance Perhaps the simplest propagation model is called the d n model, where RSSI is determined by the distance between T and R for a given path loss exponent: PL = PL(d 0 ) + 10nlog(d/d 0 ) [db] (1) PL(d 0 )=20log(4πd/λ) [db] d 0 : Reference distance in Far Field. Typically d 0 = 1m (indoor) d 0 = 100 or 1000m (outdoor). d: Distance between T-R. n: Path loss exponent, depends on environment. PL(d 0 ): Power losses at distance d 0, measured or calculated at Far Field. PL: Power losses at distance d. PL gives an average value. 150 Path Loss vs Distance PL(d) [db] distance[m] PL(d), n=1.7 In builduing LOS PL(d), n=2 Free Loss Space PL(d), n=3 urban area PL(d), n=4 shadow urban cellular radio 4

5 Outdoor Propagation Important Factors Irregular Terrain Electrical Properties (ε and σ) of terrain: Sand Dry Soil Humid Soil Concrete Sea Water Fresh Water Obstacles: Distance between T-R Frequency between T-R Environmental Conditions: Buildings Trees Foliage Rain Snow Refractive index of atmosphere Environment Path Loss Exponent n Free Space 2 Urban Area Cellular Radio 2.7 to 3.5 Shadowed Urban Radio 3 to 5 Cellular In Building Line of Sight 1.6 to 1.8 Obstructed in Building 4 to 6 Obstructed in Factories 2 to 3 5

6 Link Budget Calculations. Example Consider a wireless system with: Pt=0.1W to 3W, Gt=Gr=1, freq.=900mhz, BWreceiver=30KHz, Freceiver=10dB, SNRreceiver>25dB. Plot the maximum separation distance vs. Power transmitted for this system in the case of Shadowed Urban (n 4) Thermal Noise: N=K.T 0.B.F or N(dBm) = -174dBm+10.logB+F(dB) T 0 = 290 K room temperature in K. K = J/ K, Boltzman Constant. F = Noise Figure of the receiver (usually 5 to 10dB) B = Bandwidth of the receiver [Hz] N=-174dBm+10log(30000)+10dB=-119dBm Signal to Noise Ratio: SNR(dB) < Pr - N Pr > 25dB-119dBm=-94dBm Pr=Pt.Gt.Gr/PL Pr(dB)=Pt+Gr+Gt-PL=Pt+0dB+0dB-PL=Pt-PL PL(1Km)=20log(4π.1000m/(1/3m))=91.5dB PL = 91.5dB log(d/1Km) Pr=Pt-PL=Pt-[91.5dB log(d/1000m)] -94dBm dmax=1000m.10 (-94dBm+91.5dBm-Pt)/40 Maximum Distance between T-R vs. Power Transmitted. BW=30KHz, f=900mhz, SNR(receiver min)=25db, F=10dB,Gt=Gr=1 Maximum Distance [Km Power Transmitted [mw] 6

7 Indoor Propagation Important Factors: Floors Ceilings Walls Partitions Distance Frequency With the decreasing carrier wavelengths in PCS, factors such as: Position of desks Doors are open or closed Movement of people Propagation models can be used to estimate the received signal strength indication (RSSI). Table 1. Losses for various partitions Partition Loss [db] Freq.[MHz] Metal Wall Aluminium siding Concrete wall Foil Insulation Sheet rock 2dB 9600 Dry Plywood 1dB 9600 Table 2. Floor to Floor losses Number of Floors Total losses [db] Freq.[MHz] Trough 1 floor Trough 2 floor Trough 3 floor Trough 4 floor Table 3. Exponents n for different environments Type of partition n Free Space 2 Movable walls 2.4 Fixed Walls 3 7

8 -70dbm -60dBm -50dBm Frequency = 870MHz, Pt = -10dbm, n = 3 (fixed walls). Antenna = Isotropic, G=1, Transmitter and Receiver in the same floor 4π d 4π 1m PL( d 0 = 1m) = PLFS = 20log = 20log 31.25dB λ 0.344m PL( d = 9m) = 31.25dB log(9m /1m) = 31.25dB dB 60dB Pr = 10dBm 60dB = 70dBm (Outermost Circule) 8

9 -80dBm -70dBm -60dBm Frequency = 870MHz, Pt = -10dbm, n = 4.2 (fixed walls). Antenna = Isotropic, G=1, Transmitter 1 st Floor. Receiver 2 nd Floor. ( ) PL( d = 7m) = 31.25dB log(7m /1m) = 31.25dB dB 67dB Pr 10dBm 67dB = 77dBm (outermost Circule) 9

10 -70dBm -60dBm -50dBm Frequency = 870MHz, Pt = -10dbm, n = 2. Antenna = Isotropic, G=1. Transmitter and Receiver in the same floor PL=PL(d 0 )+10nlog(d/d 0 )+ Σ[(Pi)(AFi)] +FAF [db] (2) n= 2 FAF: Floor Attenuation Factor (Table2) AFi: Partition attenuation of element i Point A (d = 4m) PL = 31.25dB + 10.(2).log(4m /1m) + 3dB + 0dB = 46. 3dB Pr = 10dBm 46.3dB = 56.3dBm 57dBm Loss of wall 3dB FAF=0dB 10

11 -80dBm -70dBm -60dBm Frequency = 870MHz, Pt = -10dbm, n = 2. Antenna = Isotropic, G=1. Transmitter first floor. Receiver second floor. 11

12 REFERENCES. BOOKS and JOURNAL 1) Robert K. Morrow. Site-Specific Engineering for Indoor Wireless Communications. Applied Microwave and Wireless. March 1999, p ) T.Rappaport. Wireless Communications. Principles and Practice. Prentice Hall.Chap ) D.Pozar Microwave Engineering. Chap.12, p.685, Atmospheric effects, Second J.Wiley&Sons, WEBSITES 1) Complete Tutorial by T.S. Rappaport about Propagation and Radio System Design Issues in Mobil Radio Systems. 2) Technical Note on Indoor Wireless Radio propagation at 900 MHz and 2.4 GHz -- A great Introduction to Indoor Propagation Effects. Multipath fading, Radio Propagation & Diffraction Calculator v1.01 (WIN3.11 or 95 ~70K) "Narrowband Multipath Fading: A Simple Model" -- A math Introduction to Multipath Fading (~73K) Radio Propagation" -- A great Introduction to Propagation Effects (~402K) Wireless RF Performance Evaluation Tool RCalc 3.13 (WIN3.11 or 95 ~182K) 3) Introduction to Indoor Radio Propagation 4) Several topics of RF, Wireless and S.Spectrum. 5) Indoor and Microcell Design Tool Suite 12

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