Pendekatan Analitik dan Empirik
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
d = d1 - d0
h1
h2
Karakterisasi Propagasi
Mobile Radio Propagasi
Large-scale propagation
Mean signal
Small-scale propagation
Signal Variation
•Theoretical approach
•Empirical/prediction approach
•Statistical modelling
(lognormal for large scale path
loss)
Time
spreading of
signal
Time
variation of
channel
Model Teoretis Sederhana
Daya yang diterima melalui gelombang langsung :
Por
Pt
Gt
Gt
d
=
=
=
=
=
Pt G t G r
1
4 d/
2
Daya pancar
Gain antena pemacar (BS)
Gain antena penerima (MS)
Jarak pemancar - penerima
Panjang gelombang yang dipakai
Daya yang diterima melalui gelombang langsung dan gelombang pantul:
Pr
Pt G t G r
1
4 d/
2
1 cos
jsin
2
Model Teoretis Sederhana
Dengan menurunkan persamaan dalam tanda mutlak, maka diperoleh
persamaan sederhana sebagai berikut :
Pr
Pt G t G r
h1 h 2
d2
2
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.
Theoretical approach
Free space formula
• Received power density at distance d when Tx antena gain Gt is
Wt G t
Pr
4 d2
Wt G t 2 G r
Wr
• Received power when Rx antenna gain Gt is
4 d2 4
• Ratio of Rx/Tx power is
Wr
Wt
2
G tG r
4 d
c
G tG r
4 df
• Free space path loss is Lp(FS) [dB] = 32.45 + 20 log f + 20 log d
2
Plane earth propagation
Rx
Tx
d
ht
hr
Ratio of Rx/Tx power is
Wr
Wt
2
G tG r
4 d
1- e
j
• Path loss model plane earth is
20 log ht – 20 log hr
2
Wr
Wt
hthr
G tG r
d2
2
Lp(PE) = 120 + 40 log d –
Diffraction Loss
h (positif)
Tx
d1
d2
d1
Tx
d2
h (negatif)
Rx
Rx
• The difference of path length between direct and diffracted ray is
d
h 2 d1 d 2
2 d1d 2
Fresnel zone (path clearance)
• The phase difference when h 36 for 90 % confidence
interval.
Regression from Measurement Data
Select several locations at d1
And perform measurement
For the mean path loss
Repeat for d2 and d3, etc
d1
d2
d3
Plot the mean value of
Path loss as a function of
Distance
See next page
Cell site (Tx)
Obtain the Mean and Std Deviation
Measurement for urban, suburban,
and open areas
At a constant radius,
path loss can be difference
79
From regression we can
75
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 dB
Path loss [dB]
85
x
x
x
o
x
x
o
x
o
x
o
o
o
o
#
o
#
#
4
o o
suburban
open #
#
3
o
o
o
x x
o
o
x x
x
o
o
x
urban
x
x
x
6
Distance d [km]
#
#
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
d1
Cell site
(Tx)
d2
d3
JARAK JANGKAU BTS
• Contoh data :
Frekuensi kerja BS
Sistem modulasi FM dengan F
Daya pancar BS
faktor derau
Tinggi antena BS
Tinggi antena MS
Gain antena BS
Gain antena MS
Redaman feeder di BS
:
:
:
:
:
:
:
:
:
800 MHz
12 KHz
10 Watt
7 dB
40 m
1,5 m
8,5 dB
2 dB
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. :
P( rd ro )
1 erf ( x )
x
0 .9
rd
1
md
erf ( x )
1,30
x
1,30
103,2 m d
daerah urban 6,8 dB ;
Maka m d
94,36 dBm
md = nilai rata-rata sinyal penerimaan pada jarak d dari BS (logaritmik, dBm)
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 =
L =
69,55 + 26,16 log (800) - 13,82 log 40 - 0 +
(44,9 - 6,55 log (40)) log R
123, 35 + 34,4 log R
d. Jarak jangkau sebuah BS
Atx
Power (P)
Loss (T)
Arx
Redaman perambatan (L)
Perhitungan Jarak Jangkau RBS
d. Jarak jangkau sebuah BS
Jarak jangkau dihitung sbb. :
Pr
-94,36
L
= Pt - T + Atx - L + Arx - a
= 40 - 2,5 8,5 - L + 2 - 3,2
= 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. :
hp
35 m
60 m
25 m
3m
5m
4km
6km
Frekuensi kerja sistem tersebut = 900 MHz.
Hitung redaman total sistem dengan penghalang tersebut.
Jawaban : Soal Model Lee
(Perhitungan Titik Demi Titik)
• Kondisi Dengan Penghalang
Jawab :
hp
dihitung 20,8 m
Panjang gelombang
V
20,8
2
1
1 / 3 4000
Dari grafik diperoleh V
ao
28,1
20 log10
Maka redaman rambat
300
900
1
6000
1/ 3 m
1,04
1,04 diperoleh a z
14 dB
20 log 900 107,18 dB
107,18 dB 14 dB
121,18 dB
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.
• Answer
Rx_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
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
d = d1 - d0
h1
h2
Karakterisasi Propagasi
Mobile Radio Propagasi
Large-scale propagation
Mean signal
Small-scale propagation
Signal Variation
•Theoretical approach
•Empirical/prediction approach
•Statistical modelling
(lognormal for large scale path
loss)
Time
spreading of
signal
Time
variation of
channel
Model Teoretis Sederhana
Daya yang diterima melalui gelombang langsung :
Por
Pt
Gt
Gt
d
=
=
=
=
=
Pt G t G r
1
4 d/
2
Daya pancar
Gain antena pemacar (BS)
Gain antena penerima (MS)
Jarak pemancar - penerima
Panjang gelombang yang dipakai
Daya yang diterima melalui gelombang langsung dan gelombang pantul:
Pr
Pt G t G r
1
4 d/
2
1 cos
jsin
2
Model Teoretis Sederhana
Dengan menurunkan persamaan dalam tanda mutlak, maka diperoleh
persamaan sederhana sebagai berikut :
Pr
Pt G t G r
h1 h 2
d2
2
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.
Theoretical approach
Free space formula
• Received power density at distance d when Tx antena gain Gt is
Wt G t
Pr
4 d2
Wt G t 2 G r
Wr
• Received power when Rx antenna gain Gt is
4 d2 4
• Ratio of Rx/Tx power is
Wr
Wt
2
G tG r
4 d
c
G tG r
4 df
• Free space path loss is Lp(FS) [dB] = 32.45 + 20 log f + 20 log d
2
Plane earth propagation
Rx
Tx
d
ht
hr
Ratio of Rx/Tx power is
Wr
Wt
2
G tG r
4 d
1- e
j
• Path loss model plane earth is
20 log ht – 20 log hr
2
Wr
Wt
hthr
G tG r
d2
2
Lp(PE) = 120 + 40 log d –
Diffraction Loss
h (positif)
Tx
d1
d2
d1
Tx
d2
h (negatif)
Rx
Rx
• The difference of path length between direct and diffracted ray is
d
h 2 d1 d 2
2 d1d 2
Fresnel zone (path clearance)
• The phase difference when h 36 for 90 % confidence
interval.
Regression from Measurement Data
Select several locations at d1
And perform measurement
For the mean path loss
Repeat for d2 and d3, etc
d1
d2
d3
Plot the mean value of
Path loss as a function of
Distance
See next page
Cell site (Tx)
Obtain the Mean and Std Deviation
Measurement for urban, suburban,
and open areas
At a constant radius,
path loss can be difference
79
From regression we can
75
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 dB
Path loss [dB]
85
x
x
x
o
x
x
o
x
o
x
o
o
o
o
#
o
#
#
4
o o
suburban
open #
#
3
o
o
o
x x
o
o
x x
x
o
o
x
urban
x
x
x
6
Distance d [km]
#
#
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
d1
Cell site
(Tx)
d2
d3
JARAK JANGKAU BTS
• Contoh data :
Frekuensi kerja BS
Sistem modulasi FM dengan F
Daya pancar BS
faktor derau
Tinggi antena BS
Tinggi antena MS
Gain antena BS
Gain antena MS
Redaman feeder di BS
:
:
:
:
:
:
:
:
:
800 MHz
12 KHz
10 Watt
7 dB
40 m
1,5 m
8,5 dB
2 dB
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. :
P( rd ro )
1 erf ( x )
x
0 .9
rd
1
md
erf ( x )
1,30
x
1,30
103,2 m d
daerah urban 6,8 dB ;
Maka m d
94,36 dBm
md = nilai rata-rata sinyal penerimaan pada jarak d dari BS (logaritmik, dBm)
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 =
L =
69,55 + 26,16 log (800) - 13,82 log 40 - 0 +
(44,9 - 6,55 log (40)) log R
123, 35 + 34,4 log R
d. Jarak jangkau sebuah BS
Atx
Power (P)
Loss (T)
Arx
Redaman perambatan (L)
Perhitungan Jarak Jangkau RBS
d. Jarak jangkau sebuah BS
Jarak jangkau dihitung sbb. :
Pr
-94,36
L
= Pt - T + Atx - L + Arx - a
= 40 - 2,5 8,5 - L + 2 - 3,2
= 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. :
hp
35 m
60 m
25 m
3m
5m
4km
6km
Frekuensi kerja sistem tersebut = 900 MHz.
Hitung redaman total sistem dengan penghalang tersebut.
Jawaban : Soal Model Lee
(Perhitungan Titik Demi Titik)
• Kondisi Dengan Penghalang
Jawab :
hp
dihitung 20,8 m
Panjang gelombang
V
20,8
2
1
1 / 3 4000
Dari grafik diperoleh V
ao
28,1
20 log10
Maka redaman rambat
300
900
1
6000
1/ 3 m
1,04
1,04 diperoleh a z
14 dB
20 log 900 107,18 dB
107,18 dB 14 dB
121,18 dB
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.
• Answer
Rx_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