Energy Conservation by Low Loss Energy Conservation by Low Loss
Path loss models
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EE161 Handout #3 March 31, 2009 EE161 Spring 2009 Wireless Communications Path Loss Models The transmitted signal s(t)= u(t)e j (2πft+φ 0 ) , where u(·) is a complex baseband signal, f is the carrier frequency and φ 0 is a random initial phase (uniformly distributed between 0 and π). Basic propagation mechanisms 1. Reflection 2. Diffraction 3. Scattering Free space loss The received signal r(t)= u(t) λ √ G t G r e j 2πd λ 4πd , where d is the distance, G t and G r are the transmit and receive antenna power gains and λ is the wavelength. The received power P r = P u λ 4πd 2 G t G r . 1
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path loss models
Transcript of Path loss models
EE161 Handout #3March 31, 2009
EE161 Spring 2009
Wireless Communications
Path Loss Models
The transmitted signals(t) = u(t)ej(2πft+φ0),
whereu(·) is a complex baseband signal,f is the carrier frequency andφ0 is arandom initial phase (uniformly distributed between 0 andπ).
Basic propagation mechanisms
1. Reflection
2. Diffraction
3. Scattering
Free space loss
The received signal
r(t) = u(t)λ√GtGre
j 2πd
λ
4πd,
whered is the distance,Gt andGr are the transmit and receive antenna powergains andλ is the wavelength.
The received power
Pr = Pu
(
λ
4πd
)2
GtGr.
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Ground reflection – Two-path model
See figure 2.4 of Goldsmith.
r(t) =λ
4π
√
GtGr
u(t)ej2πd
′
λ
d′+u(t+ τ)Rej
2πd′′
λ
d′′
, (1)
whered′
is the LOS distance,d′′
is the ground reflected distance,τ = d′′
−d′
c is thepath delay and
R =sin θ −
√ǫr − cos2θ
sin θ +√ǫr − cos2θ
,
for horizontal polarization and
R =sin θ −
√ǫr − cos2θ/ǫr
sin θ +√ǫr − cos2θ/ǫr
,
whereθ is the angle of reflection.Ford > dc = 4hthr
λ , we have
Pr ≈GtGr(hthr)
2
d4Pu,
i.e., the signal decays asd−4. For all values ofd a reasonable approximation is
Pr ≈GtGrd
20
d2(1 + (d/dc)2q)1/qPu,
for some values ofq andd0.
General ray tracing
r(t) =λ
4π
√
GtGr
u(t)ej2πl
λ
l+
∑
i∈all paths
u(t+ τi)Riej
2πli
λ
li
.
Simplified path loss model
Pr = PuK
(
d0
d
)γ
,
with γ often between two and six.
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Log-normal shadowing
10 log10
Pr
Pu= 10 log10K − 10γ log10
d
d0+ ψdb,
whereψdb is a zero-mean Gaussian random variable.
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