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materi mengenai radio propagasi, pada mata kuliah wireless and mobile technology
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Propagasi Selular
Pendekatan Analitik dan Empirik
• Mobile Radio Channel Characterisation
• Theoretical approach
– Free space loss
– Plane earth path loss
– Diffraction loss
• Empirical/prediction approach
– Okumura-Hatta - Blomquist-Ladel
– Lee - Alsebrook
– Egli - Ibrahim Parson
• Measurement of large scale and application in coverage prediction
• Some examples
MODEL PROPAGASI SISTEM SELULAR
Model untuk memperkirakan redaman :
• Model teoretis
• Model empiris
• Model Lee
• Persamaan Umum Redaman Propagasi
• Perkiraan Titik demi Titik
• Model Okumura-Hatta
• Faktor Koreksi Undulasi
• Faktor Koreksi Kemiringan
Model Teoretis Sederhana
h1
h2
d = d1 - d0
Karakterisasi Propagasi
Mobile Radio Propagasi
Large-scale propagation Small-scale propagation
Mean signal Signal Variation
Time spreading of signal
Time variation of channel
•Theoretical approach
•Empirical/prediction approach
•Statistical modelling (lognormal for large scale path loss)
Model Teoretis Sederhana
Daya yang diterima melalui gelombang langsung :
Pt = Daya pancar
Gt = Gain antena pemacar (BS)
Gt = Gain antena penerima (MS)
d = Jarak pemancar - penerima
= Panjang gelombang yang dipakai
Daya yang diterima melalui gelombang langsung dan gelombang pantul:
2
rttor/d4
1GGPP
2
2
rttr sinjcos1/d4
1GGPP
Model Teoretis Sederhana
Dengan menurunkan persamaan dalam tanda mutlak, maka diperoleh
persamaan sederhana sebagai berikut :
Persamaan tersebut menghasilkan dua kondisi yang sesuai dg percobaan, yaitu :
• Path loss sebesar 40 dB / dekade (sebanding dengan d-4) atau 12 dB /
oktaf.
Penambahan path loss dari jarak d1 ke d2 = 40 log d2/d1
• Pertambahan gain sebesar 12 dB/dekade atau 6 dB/oktaf untuk setiap
penambahan ketinggian antena BS.
Penambahan gain antena dari h1 ke h2 = 20 log h2/h1
Sedangkan hasil yang tidak sesuai dg percobaan dan perlu faktor koreksi , yaitu:
• Tidak terdapat faktor interferensi (pjg gel.)
Rumus empiris : Pr = f-n dengan 2 < n < 3
• Teoretis : penambahan tinggi antena pada MS : 6 dB/oktaf
empiris : pengurangan tinggi antena 1/2 - nya : gain berkurang 3 dB.
2
221
rttrd
hhGGPP
Theoretical approach
Free space formula
• Received power density at distance d when Tx antena gain Gt is
• Received power when Rx antenna gain Gt is
• Ratio of Rx/Tx power is
• Free space path loss is Lp(FS) [dB] = 32.45 + 20 log f + 20 log d
2
tt
rd4
GWP
4
G
d4
GWW r
2
2
tt
r
2
rt
2
rt
t
r
df4
cGG
d4 GG
W
W
Plane earth propagation
Ratio of Rx/Tx power is
• Path loss model plane earth is Lp(PE) = 120 + 40 log d –20 log ht – 20 log hr
TxRx
ht hr
d
2
2
rt
rt
t
r2j
2
rt
t
r
d
hhGG
W
We-1
d4GG
W
W
Diffraction Loss
• The difference of path length between direct and diffracted ray is
TxRxd1 d2
h (positif)
Tx Rx
d1 d2
h (negatif)
21
21
2
dd
dd
2
h d
Fresnel zone (path clearance)
• The phase difference when h << d1 and h << d2 is
with v is diffraction parameter which can be expressed as
• The n-th Fresnel zone is area between Tx and Rx inside the
ellipsoide with radius of its cross section of rn where
2
21
21
2
v2dd
dd
2
h2d2
21
21
dd
dd2hv
21
21
ndd
ddnhr
Diffraction Loss
Diffraction loss can be computed from
When v=0 (h=0) diffraction
loss is 6 dB above free space loss
When v=-0.8 diffraction
loss is negligible (56 % of
The 1st Fresnel zone is clear)
v
0
4
8
12
16
20
24-3 -2 -1 10 2 3
Empirical Prediction Approach
• Based on signal measurement
– Okumura - Blomquist-Ladel
– Lee - Alsebrook
– Egli - Ibrahim-Peterson
• Mathematical Formulation based on signal measurement
– Hatta (Japan)
– COST-231 (Europe)
Okumura Model
• Okumura develop propagation model based on extensive signal
measurements in Kanto (near Tokyo) areas.
• Propagation environments are classified into:
• Urban areas (highly dense populated areas)
• Suburban areas (moderate population)
• Open/rural areas (few population, rare building/structure)
• Okumura develop propagation loss (mean and variance) in the form of
curves of propagation loss vs distance for different parameters, such as
frequencies, antenna heights, ground curvature/undulation, etc).
• Okumura curves often used by others to construct mathematical models.
• Masaharu Hatta makes use of Okumura model and transform Okumura curves into Hatta mathematical formulas, therefore the name of Okumura-Hatta model.
• Project COST - 231 in Europe further develop mathematical formula of Hatta model for use in DCS/PCS frequencies (1800 MHz).
• Hatta model is valid for urban area, and corrections factors are provided for suburban and open areas.
• Hatta dan COST-231 models are the most common models used in cellular system due to their simple use with reasonable accuracy.
Hatta and COST-231 Models
Okumura –Hatta Model
Lp(open) = Lp(urban) –4.78(logf)2 + 18.33 log f – 40.94
For urban area:
Lpu [dB] = 69.55 + 26.16 log f – 13.82 log hb – a(hm) + (44.9 – 6.55 log hb) log d
Model Okumura - Hatta• Okumura melakukan percobaan di daerah Tokyo dg menggunakan :
• Tinggi antena BS : 200 m
• Tinggi antena Ms : 3 m
• Hatta menyatakan hasil percobaan Okumura dalam bentuk persamaan :
KLASIFIKASI
DAERAH
PELAYANAN
RUMUS REDAMAN PERAMBATAN
Urban Area
Lu = 69,55 +26,16 log fc – 13,82 log hb – a (hm) + (44,9
– 6,55 log hb) log R……………..(dB)
Faktor koreksi untuk tinggi antena stasiun mobil
yang bergantung kepada tipe daerah urban yang
dibagi sebagai berikut :
Medium – small city :
a (hm) = (1,1 log fc – 0,7) hm – (1,56 log fc – 0,8) ….(dB)
Large City
a (hm) = 8,29 (log fc 1,54 hm)2 – 1,1 , fc < 200 MHz
a (hm) = 3,2 (log fc 11,75 hm)2 – 4,97 , fc > 400 MHz
Sub Urban Area Lsu = Lu (urban area) – 2 [log (fc/28)]2 – 5,4 ….(dB)
Open Area Lo = Lu (urban area) – 4,78 (log fc)2 + 18,33 log fc –
40,94 ….(dB)
Keterangan :
fc = frekuensi kerja yang berharga : 150 MHz – 1500 MHz
hb = tinggi antena stasiun tetap (RBS) : 30 m – 200 m
hm = tinggi antena stasiun mobil (MS) : 1 m – 3 m
R = jarak pemancar penerima : 1 km – 20 km
Model Lee...
Dua pendekatan umum untuk menentukan 2 parameter tsb. :
• Jika tipe daerah atau struktur bangunan tidak sama dengan hasil
pengukuran yang telah ditabelkan di atas, maka harus dilakukan
pengukuran.
r = jarak dari BS ke MS dlm km
ro = jarak dari BS ke MS 1,6 km.
= konstanta propagasi dalam dB/dekade
o = faktor koreksi parameter terhadap keadaan sebenarnya, antara lain
parameter : tinggi antena BS ( 1), tinggi antena MS ( 2), daya pancar BS
( 3), gain antena BS ( 4), gain antena MS ( 5).
)dB(f
flogn
r
rlogP
)linier(f
f
r
rPP
o
oo
ro
o
n
oo
ror
Model Lee...
Kondisi standar yang digunakan Lee, dalam mencari konstanta propagasi :
• Frekuensi fo : 900 MHz
• Tinggi BS : 30,48 m (100 ft)
• Daya pada antena BS : 10 Watt (40 dBm)
• Gain antena BS : 6 dB terhadap dipole
• Tinggi antena MS : 3 m (6 ft)
• Gain antena MS : 0 dB terhapadap dipole
Dengan menggunakan data tersebut, Lee melakukan percobaan di berbagai
daerah dengan hasil seperti digambarkan pada gambar di halaman berikut.
Model Lee(Persamaan Umum)
Perkiraan area ke area menurut Model Lee membutuhkan 2 parameter :
• Daya pada jarak tertentu biasanya 1,6 km / mil (Pro)
• Kemiringan redaman atau path loss slope ( ).
Dua pendekatan umum untuk menentukan 2 parameter tsb. :
• Membandingkan tipe daerah / struktur bangunan
Lee Model
Lee formulated the path loss of being
Lp[dB] = L0 + log d ; with L0 is path loss at d = 1 km and is the
path loss slope.
Area L0 [dB] (dB/decade]
Free space 91.2 20
Open/rural area 90.4 43.5
Suburban area 104.3 38.4
New Ark 105.5 43.1
Philadelphia 112.8 36.8
New York City 117.5 48
Tokyo 128.1 30.5
Egli Model
Based on Plane Earth Theoretical model with correction factors
Lp [dB] = 120 + 40 log d – 20 log ht – 20 log hr +
• Where ht and hr is Tx and Rx antenna height respectively, d is path length
and = 20 log (f/40) in dB for correction of carrier frequency.
• Egli model is derived from propagation measurement using the carrier
frequencies of between 90 and 1000 MHz.
• Egli model is therefore has a limited application for such an area which can
be considered as a plane earth situation.
Blomquist-Laded Model
• This model considers the combination of free space, plane earth,
and diffraction loss models together.
• The model is expressed as
Lp [dB] = Lfree space +{(Liplane earth – Lfree space)2 + (Ldiffraction)2}1/2
• For more than one diffraction mechanisms, diffraction loss is
computed using multiple diffraction loss from Bullington, Epstein
Peterson, and Deygout models.
• For situation with no diffraction, this model become the plane earth
model
Alsebrook Model
• Based on measurement in British cities areas (Birmingham and Bath at frequencies
of between 75 and 450 MHz.
• For flat areas Lp [dB] = Lplane earth +LB + , where LB is correction for building and is
correction for UHF frequencies.
• For hilly areas Lp [dB] = Lfree space +{(Liplane earth – Lfree space)2 + (Ldiffraction)2}1/2 + LB
+
• Correction for building is
– Where ho is average height of building, hm is mobile antenna height, effective
width of street, and f is carrier frequency
• Correction of carrier frequency is increasing linearly from 0 to 15 dB as frequency
increases from 200 to 500 MZ
1610Wfx548
hhlog20]dB[L
3
m0
B
Ibrahim-Peterson Model
• Based on measurement in London areas at freq 168 – 900 MHz with Base
antenna height 46 m.
• Semi empirical formula based on regression analysis from signal
measurement, which is then correlated with plane earth model for
corrections.
• Path loss model is Lp [dB] = 40 log d – 20 log(hbhm) +
= 20 + f/40 +0.18 L – 0.34 H +K
Where
L = land use factor (percentage of area covered by building)
H = terrain factor (different of average ground height between Tx and Rx)
K = urbanisation factor (K = 0.094 U – 5.9 [dB]), U is the percentage of building
having 4 or more floors)
Path Loss Measurement
The received signal looks like this
• The proper measurement distance is L = 2 because if measurement
distance is too short may not give the mean value (signal still
varying) and if too long may average out large scale (large scale
variation is smoothed out).
• The number of measurement samples n >36 for 90 % confidence
interval.
2 wavelength
Regression from Measurement Data
Select several locations at d1
And perform measurement
For the mean path loss
Repeat for d2 and d3, etc
Plot the mean value of
Path loss as a function of
Distance
See next page
Cell site (Tx)
d1 d2
d3
Obtain the Mean and Std Deviation
Measurement for urban, suburban,
and open areas
At a constant radius,
path loss can be difference
From regression we can
obtain the best fit for the mean
as well as the std deviation
around the mean
Example for urban : path loss
Slope = 33.2 dB/decade and
Std dev. = 7 dBDistance d [km]
Path
loss [d
B]
urban
suburban
open
x x
x
x x
x x x
x x
x x
x x
x x
o o o
o o o
o o
o o
o o
o o
o
o o
# #
# #
# #
#
3 4 6
79
85
75
Application in Coverage prediction
• Example at distance d2 = 4 km (see previous page for urban area)
• Path loss at 4 km is 79 dB.
• This path loss is designed for the mean
value at 50 % confidence level
• Since std. Dev for urban in
this example is 7 dB,
therefore to obtain
confidence level of 84 % (1 )
need margin of 7 dB and
for confidence of 97.7 % (2 )
need margin of 14 dB
Cell site (Tx)
d1 d2d3
JARAK JANGKAU BTS
• Contoh data :
Frekuensi kerja BS : 800 MHz
Sistem modulasi FM dengan F : 12 KHz
Daya pancar BS : 10 Watt
faktor derau : 7 dB
Tinggi antena BS : 40 m
Tinggi antena MS : 1,5 m
Gain antena BS : 8,5 dB
Gain antena MS : 2 dB
Redaman feeder di BS : 3,2 dB per 40
a. Menghitung nilai ambang penerimaan dg keandalan thd. Fading cepat
• kTB = 10 log (1,38 x 10-23 . 300 . 2 (12+3,4) )
= - 128,9 dBm
• Faktor derau= 7 dB
• FM threshold = 10 dB
Perhitungan Jarak Jangkau RBS
• Cadangan fading cepat = 8,7 dB
(untuk keandalan 90 %)
TOTAL = - 103,2 dBm
b. Nilai ambang penerimaan dengan keandalan terhadap fading lambat
Nilai ambang sesungguhnya (misal keandalan didasarkan pada 90% fading
cepat dan 90% pada fading lambat) dihitung sbb. :
md = nilai rata-rata sinyal penerimaan pada jarak d dari BS (logaritmik, dBm)
dBm36,94mMaka
;dB8,6urbandaerah
m2,10330,1
mrx
30,1x)x(erf19.0
)x(erf1)rr(P
d
ddd
od
Perhitungan Jarak Jangkau RBS
c. Redaman di daerah Urban (contoh di daerah urban) :
Nilai fc = 800 MHz,
Tinggi antena BS hb = 40 m
Tinggi antena MS hm = 1,5 m
Redaman dapat dinyatakan sebagai fungsi radius sel sbb. :
L = 69,55 + 26,16 log (800) - 13,82 log 40 - 0 +
(44,9 - 6,55 log (40)) log R
L = 123, 35 + 34,4 log R
d. Jarak jangkau sebuah BS
Power (P) Loss (T) Redaman perambatan (L)
Atx Arx
Perhitungan Jarak Jangkau RBS
d. Jarak jangkau sebuah BS
Jarak jangkau dihitung sbb. :
Pr = Pt - T + Atx - L + Arx - a
-94,36 = 40 - 2,5 8,5 - L + 2 - 3,2
L = 139,16
Dari persamaan di halaman sebelumnya (49) diperoleh :
L = 123,35 + 34,4 log R
R = 2,88 km.
Jarak jangkauan BS tersebut dengan contoh data sederhana yang disajikan di
atas menghasilkan radius sel = 2,88 km.
Pada kenyataan tentunya tidak sesederhana seperti contoh perhitungan disini.
Contoh persoalan : Model Lee(Perhitungan Titik Demi Titik)
• Kondisi Dengan Penghalang
Contoh :
Terdapat kontur sbb. :
Frekuensi kerja sistem tersebut = 900 MHz.
Hitung redaman total sistem dengan penghalang tersebut.
5 m
3 m
35 m
25 m
60 m
hp
4 k m 6 k m
Jawaban : Soal Model Lee
(Perhitungan Titik Demi Titik)
• Kondisi Dengan Penghalang
Jawab :
dB18,121dB14dB18,107rambatredamanMaka
dB18,107900log2010log201,28a
dB14adiperoleh04,1VdiperolehgrafikDari
04,16000
1
4000
1
3/1
28,20V
m3/1900
300gelombangPanjang
m8,20dihitunghp
o
z
Example
• A mobile terminal located at the cell’s edge is receiving signal from a BTS in urban area. The minimum signal level (receicer sensitivity) of the MS is – 100 dBm. BTS Tx power is 10 W at 40 m high, feeder loss at BTS is 7 dB, BTS Tx antenna gain is 13 dB, mobile Rx antenna gain is 3 dB, handset body loss is 3 dB. Operating carrier freq is 1.8 GHz.
– Compute cell radius using Okumura-Hatta Model.
– If it were in free space condition, compute the received signal level at the
MS.
• AnswerRx_min = Tx – Lf + Gt – Lu +Gr – LB Lu=40 -7+13 +100+3-3 = 146 dB
Hatta Lpu=69.55+26.16 log(1.8x103)-13.82 log(40) + [44.9-6.55 log(40)] log R
146 = 154.7 – 22.14 + 34.4 log R R = 2.5 km (cell radius).
Lfreespace = 32.45 + 20 log (1.8x103) + 20 log (2.5) = 105.5 dB
Rx = 40 – 7 + 13 – 105.5 + 3 – 3 = - 59.5 dBm (Received signal level if freespace)
Ringkasan
• Propagation path loss (Large scale path loss) is a measure of path loss expressed in terms of the mean value and its variation around the mean.
• Large scale path loss is well known to be lognormally distributed (Normal distribution in dB scale).
• Large scale path loss is useful for prediction of the received signal, coverage prediction, and hand-off control.
• Reliability (confidence level) of the received signal can be computed when path loss slope and the std. dev. of the path loss are known