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 << d1 and h << d2 is 2 h 2 d1 d 2 v2 2 d1d 2 2 with v is diffraction parameter which can be expressed as 2
v
d
h
2 d1 d 2 d1d 2
• The n-th Fresnel zone is area between Tx and Rx inside the ellipsoide with radius of its cross section of rn where rn
h
n d 1d 2 d1 d 2
Diffraction Loss
Diffraction loss can be computed from 0 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)
4 8 12 16
20 24
-3 -2 -1 0 1 2
3
v
Empirical Prediction Approach • Based on signal measurement – Okumura – Lee – Egli
- Blomquist-Ladel - Alsebrook - 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.
Hatta and COST-231 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.
Okumura –Hatta Model 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
Lp(open) = Lp(urban) –4.78(logf)2 + 18.33 log f – 40.94
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
RUMUS REDAMAN PERAMBATAN
PELAYANAN 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 Urban Area
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. Pr
Pro Pro
r ro
f fo log
r ro
n o
(linier )
n log
f fo
o
(dB)
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).
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
L B [dB] 20 log
h0 hm 548 Wfx10
3
16
– 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
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 2 wavelength
•
•
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.
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
