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Reminder: Friis free space equation Reminder: Short range 2-ray propagation model Estimation of the Ricean K-factor Measurement 1 - fixed antennas Measurement 2 - one antenna moving
Friis free space equation
Source:
[] Rappaport - Wireless Communications
L
GGd
PdP rttr1
4
2
• The formula is a valid predictor for Pr for d which are in the far-field of the transmitting antenna - Fraunhofer region i.e. when inductive and electrostatic fields become negligible and only radiation field remains
df=2D2/ , df>>D and df>>• For fc = 5.3 GHz and the antenna size D = 7 cm
df=17.31 cm , df >> 7 cm and df>>5.66 cm
ddBLdBGdBGdBPdBP rttr log*20][][][4
log*10][][2
ddBmdBmdBmdBmPr log*2039.4611][ (1)
Short range 2-ray propagation model
Source:
[] Rappaport - Wireless Communications
td
dERt
d
dEtdE ccTOT coscos, 0000
2
ddR
dK
irir
irirR
2
2
||cossin
cossin
)()( tvVtg
Characterize the complex signal path gain of the narrowband wireless channel as
Estimation of the Ricean K factor
Relate the equation to the two moments that can be estimated from the measurements of received power versus time
tVvEtvEVGtrue*22 Re*2)(
The second moment is the rms fluctuation of G about Gtrue.
2*4422 Re*2)( tVvEtvEGGEG truev
Source:
[] Greenstein et. al - Moment method estimation of the Ricean K factor
Estimation of the Ricean K factor
)1(22 VGtrue
Under the assumption that the v(t) is complex Gaussian, zero mean, this can be written as:
)2(2 2242 VGv
Source:
[] Greenstein et. al - Moment method estimation of the Ricean K factor
If we can estimate the left-hand side of 1 and 2 from the data, then we have two equations with two quantities that we need.
222vtrue GGV
2
2
V
K
222vtruetrue GGG
And finally, the Ricean K-factor is: