Lecture 5-2010

Lecture 5-2010 - Wireless Communications Lecture 5 Moeness...

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Unformatted text preview: Wireless Communications Lecture 5 Moeness Amin ECE Dept. Villanova University Path Loss • The path strength variations reflect the power variations of the electric field received by the antenna and depends heavily on the propagation environment. The average loss in power at the receiver as it moves away from the transmitting antenna Mean Trend Small fluctuations of the signal due to shadowing effects of building or natural features Large Scale Fading Rapid fluctuations of the signal due to channel multipath Small Scale Fading Signal Propagation in Free Space • The relationship between transmitted power P t and received power P r is • G r is the transmitter antenna gain and G t is the receiver antenna gain. Define the normalized received power at 1 m Loss in power is 20dB/decade=6 dB/octave. Transmission delay is 3 ns/meter P r / P t = G r G t ( λ 4 π d ) 2 P o = P t G r G t ( λ 4 π ) 2 P r = P o / d 2 Effect of Multipath P r = P t h 1 2 h 2 2 d 4 transmitter receiver d h h d e P P j r r 2 1 2 2 2 2 , 1 λ π λ π φ ρ φ = Δ = Δ + ≈ Δ d 1 = ( h 1 + h 2 ) 2 + d 2 ≈ d + ( h 1 + h 2 ) 2 2 d , d 2 = ( h 1 − h 2 ) 2 + d 2 ≈ d + ( h 1 − h 2 ) 2 2 d 1 − e j Δ φ ≈ Δφ , h 1 h 2 d Forth Power Law, 40 dB/decade Path Loss Model 98 . 21 log 20 log 20 log 10 log 10 + + − − − = d G G L r t λ Path loss in dB Using isotropic antennas with the frequency in megahertz and the distance in kilometers, dB d f L 44 . 32 log 20 log 20 + + = Path Loss Model • Average received signal power decreases logarithmically with distance where n is the path loss exponent, d is the T-R separation distance, and d o is the close in reference distance (far field position, 1 km for large coverage and 1m for microcellular systems). PL ( dB ) = PL ( d o ) + 10 n log( d / d o ) Free space 2 Urban area cellular radio 2.7-3.5 Shadowed urban cellular radio 3-5 In building line of sight 1.6-1.8 Obstructed in Building 4-6 Obstructed in factories 2-3 Lognormal Distribution • When reaching the mobile station, the radio wave will have been shadowed, i.e., traveled through different obstructions such as: Buildings, Tunnels, Hills, Trees, and others • Each obstruction presents its own attenuation constant as well as thickness. • If the i-th obstruction has an attenuation constant and thickness where are, respectively, the amplitudes of the wave after and before the i-th obstruction α i Δ r i E i = E i − 1 exp( −α i Δ r i ) E i , E i − 1 Continue • The signal leaving the nth obstruction is given by • It is reasonable to admit that the attenuation factor and thickness vary randomly from obstruction to obstruction • Define Y, • The probability density function of Y is E n = E o exp( − α i Δ r i i = 1 n ∑ ) E n = E o exp( x ), x = − α i Δ r i i = 1 n ∑ , p ( x ) = 1 2 πσ x exp( − ( x − m x ) 2 2 σ x 2 ) Y = log y = log E n E o = x log e ) 2 ) ( exp( 2 1 ) ( 2 2 Y Y y M Y Y p σ σ π − − = Continue • Excess path loss, which is the difference between the received...
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Lecture 5-2010 - Wireless Communications Lecture 5 Moeness...

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