Pendekatan Analitik dan Empirik

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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

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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

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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

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Model Teoretis Sederhana

Daya yang diterima melalui gelombang langsung :

P_t = Daya pancar

G_t = Gain antena pemacar (BS)

G_t= Gain antena penerima (MS)

d = Jarak pemancar - penerima

= Panjang gelombang yang dipakai

Daya yang diterima melalui gelombang langsung dan gelombang pantul:

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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 : P_r = 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.

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Theoretical approach

Free space formula

• Received power density at distance

d

when Tx antena gain

G

_t

is

• Received power when Rx antenna gain

G

_t

is

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Plane earth propagation

Ratio of Rx/Tx power is

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Diffraction Loss

• The difference of path length between direct and diffracted ray is

T

_x

_d

R

x

1

d

₂

h (positif)

T

_x

d

1

d

2

R

_x

h (negatif)

2 1

2

d

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Fresnel zone (path clearance)

• The phase difference when

h

<<

d

₁

and

h

<<

d

₂

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

r

_n

where

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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 1

st

_{Fresnel zone is clear)}

v

0

4

8

12

16

20

24

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Empirical Prediction Approach

• Based on signal measurement

– Okumura - Blomquist-Ladel

– Lee - Alsebrook

– Egli - Ibrahim-Peterson

• Mathematical Formulation based on signal measurement

– Hatta (Japan)

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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).

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• 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.

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Okumura

–

Hatta Model

L_p(open) = L_p(urban) –4.78(logf)2 _{+ 18.33 log}_f – _40.94

For urban area:

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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

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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

r_o = jarak dari BS ke MS 1,6 km.

= konstanta propagasi dalam dB/dekade

o = faktor koreksi parameter terhadap keadaan sebenarnya, antara lain

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Model Lee...

Kondisi standar yang digunakan Lee, dalam mencari konstanta propagasi :

• Frekuensi f_o : 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

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Model Lee

(Persamaan Umum)

Perkiraan area ke area menurut Model Lee membutuhkan 2 parameter :

• Daya pada jarak tertentu biasanya 1,6 km / mil (P_ro)

• Kemiringan redaman atau path loss slope ( ).

Dua pendekatan umum untuk menentukan 2 parameter tsb. :

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Lee Model

Lee formulated the path loss of being

L

_p

[dB] =

L

₀

+ log

d

;

with

L

₀

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

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Egli Model

Based on Plane Earth Theoretical model with correction factors

L_p [dB] = 120 + 40 log d – 20 log h_t – 20 log h_r +

• Where h_t and h_r 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.

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Blomquist-Laded Model

• This model considers the combination of free space, plane earth,

and diffraction loss models together.

• The model is expressed as

L_p [dB] = L_{free space} +{(L_{iplane earth} – L_{free space})2 _{+ (}_L

diffraction)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

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Alsebrook Model

• Based on measurement in British cities areas (Birmingham and Bath at frequencies of between 75 and 450 MHz.

• For flat areas L_p [dB] = L_{plane earth} +L_B + , where L_B is correction for building and is correction for UHF frequencies.

• For hilly areas L_p [dB] = L_{free space} +{(L_{iplane earth} – L_{free space})2 _{+ (}_L

diffraction)2}1/2 + LB

+

• Correction for building is

– Where h_o is average height of building, h_m 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

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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 L_p [dB] = 40 log d – 20 log(h_bh_m) +

= 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)

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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.

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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 _d

2

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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 dB

Distance d [km]

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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

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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

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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. :

m_d = nilai rata-rata sinyal penerimaan pada jarak d dari BS (logaritmik, dBm)

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Perhitungan Jarak Jangkau RBS

c. Redaman di daerah Urban (contoh di daerah urban) :

Nilai f_c = 800 MHz,

Tinggi antena BS h_b = 40 m

Tinggi antena MS h_m = 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

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Perhitungan Jarak Jangkau RBS

d. Jarak jangkau sebuah BS Jarak jangkau dihitung sbb. :

P_r = P_t - T + A_tx - L + A_rx - 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.

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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

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Jawaban : Soal Model Lee

(Perhitungan Titik Demi Titik)

• Kondisi Dengan Penghalang

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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 – L_f + G_t – L_u +G_r – L_B  L_u=40 -7+13 +100+3-3 = 146 dB

Hatta L_pu=69.55+26.16 log(1.8x103_{)-13.82 log(40) + [44.9-6.55 log(40)] log R}