Kidapawan-north Cotabato

4

INTRODUCTION Microwaves are electromagnetic waves with wavelengths longer than those of terahertz (THz) frequencies, but relatively short for radio waves. Microwaves have wavelengths approximately in the range of 30 cm (frequency = 1 GHz) to 1 mm (300 GHz). This range of wavelengths has led many to question the naming convention used for microwaves as the name suggests a micrometer wavelength. However, the boundaries between far infrared light, terahertz radiation, microwaves, and ultra-highfrequency radio waves are fairly arbitrary and are used variously between different fields of study. The term microwave generally refers to "alternating current signals with frequencies between 300 MHz (3×108 Hz) and 300 GHz (3×1011 Hz). The existence of electromagnetic waves, of which microwaves are part of the frequency spectrum, was predicted by James Clerk Maxwell in 1864 from his Maxwell's equations. In 1888, Heinrich Hertz was the first to demonstrate the existence of electromagnetic waves by building an apparatus that produced and detected microwaves in the UHF region. The design necessarily used horse-and-buggy materials, including a horse trough, a wrought iron point spark, Leyden jars, and a length of zinc gutter whose parabolic cross-section worked as a reflection antenna. Point-to-point microwave radio links have many uses. They can be used as studio-to-transmitter (STL) links for radio and television broadcasting stations, and they can also link the head-ends (antenna sites) of many cable television installations to their distribution systems. Another very common application of microwave links is a part of a communications network involving telephone, data, or television signals.

5

Some microwave systems use only one link or hop, while others are multi-hop systems that use repeaters to extend the system beyond the line-of-sight range of a single link.

1.1

Background of the Study Microwaves are generally described as electromagnetic waves with frequencies that range from approximately 500 MHz to 300 GHz or more. Microwave systems use line-of-sight propagation and require repeaters approximately every 40km, depending on the terrain. It propagates signals through Earth’s atmosphere between transmitters and receivers often located on top of towers spaced about 24km to 48km apart.

6

7

TRANSMISSION CALCULATION: LINK 1 (KIDAPAWAN NORTH COTABATO TO MT. TALOMO) SITE INFORMATION Geographical Location Site A: Kidapawan, North Cotabato Longitude: 125° 4’ 0” E Latitude: 7° 1’0” N Site B: Mt. Talomo Longitude: 125° 17’ 50” E Latitude: 7° 7’ 25” N Bearing Site A: 54 ° Southeast Site B: 22 ° Southeast Site Ground Elevation (Mean Sea Level) Site A: 200m Site B:1800m Site Terrain Type Site A: Urban Site B: Woodland Antenna Height Site A: 20m Site B: 20m DESIGN PARAMETERS Reliability Requirement: 99.9999% Configuration: Non-protected (1+0) Traffic Capacity: 4 x E1 main plus 4 x E1 spare (8 x E1) Path Length: 28Km

8

CHANNEL PLANS Frequency Band: 13 GHz Frequency Range: 12.75 GHz- 13.25 GHz Low Band Range: 12.75 GHz to 12.986GHz High Band Range: 13.014 GHz to 13.25 GHz Duplex Spacing: 500 MHz Traffic Capacity: 4 x E1 main plus 4 x E1 spare (8 x E1) Channel bandwidth for 8 x E1: 14 MHz FREQUENCY PLAN No. of Duplex Channel * Divide the smaller bandwidth between the high band and low band with the channel bandwidth. No. of Duplex Channel = 13.014 GHz – 12.75 GHz 14 MHz = 19 Channels Transmit Frequency * Select 7 channel spacing above the high band and low band edge. 14 MHz x 7 = 98 MHz Low Band Frequency 12.75 GHz + 98 MHz = 12.848 GHz High Band Frequency 13.014 GHz + 98 MHz = 13.112 GHz EQUIPMENT INFORMATION Transmitter Output Power Site A: 25 dBm Site B: 25 dBm Receiver Input Threshold Site A: -86.5 dBm Site B: -86.5 dBm 9

Waveguide Length Site A: Rigid Waveguide Length = 17m + 8.5m + 1.2m =26.7 m Flexible Waveguide Length = 0.5m + 1.3m + 0.5m = 2.3 m Site B: Rigid Waveguide Length = 17m + 8.5m + 1.2m = 26.7 m Flexible Waveguide Length = 0.5m + 1.3m + 0.5m = 2.3 m Waveguide Unit Attenuation Note: Use WR 75 Site A: Rigid: 0.049 dB/ft = 0.1607 dB/m Flexible: 0.15dB/ft = 0.492 dB/m Site B: Rigid: 0.049 dB/ft = 0.1607 dB/m Flexible: 0.15 dB/ft = 0.492 dB/m Rigid Waveguide Loss (RWL) RWL = (Rigid waveguide length) x (Waveguide unit attenuation)RIGID Site A:

RWL = (26.7m)(0.1607dB/m) = 4.29069 dB

Site B:

RWL = (26.7m)(0.1607dB/m) = 4.29069 dB

Flexible Waveguide Loss (FWL) FWL = (Flexible waveguide length) x (Waveguide unit attenuation) FLEXIBLE Site A: RWL = (2.3m)(0.492dB/m) = 1.1316 dB

10

Site B: RWL = (2.3m)(0.492dB/m) = 1.1316 dB Total Waveguide Loss (TWL) TWL = RWL + FWL Site A: TWL = 4.29069 dB + 1.1316 dB = 5.42229 dB Site B: TWL = 4.29069 dB + 1.1316 dB = 5.42229 dB Connector Losses (CL) CL = (Loss of connector) x (No. of connectors) Site A:

CL = (0.15dB/connector) x (5connectors) = 0.75 dB

Site B:

CL = (0.15dB/connector) x (5connectors) = 0.75 dB

Antenna Misalignment Loss Site A: 0.25dB Site B: 0.25dB Antenna Polarization Vertical Polarization

PATH LOSSES Free Space Loss (AFSL) AFSL = 92.44 + 20 log f + 20 log D Where

f = frequency used in GHz D = total path length or distance in kilometers (km) AFSL = 92.44 + 20 log 13 + 20 log 28 AFSL = 143.6620277 dB

11

Oxygen Absorption Loss (Ao) For frequencies below 57GHz:   6.09 4.81 A o =  7.9x10-3 + 2 +  ( 1x10-3 ) f 2 D 2 f + 0.227  ( f - 57 ) +1.5  Where

f = frequency used in GHz D = total path length or distance in kilometers (km)

  6.09 4.81 A o = 7.9x10-3 + 2 +  ( 1x10-3 ) ( 132 ) ( 28 ) 2 13 + 0.227 ( 13 - 57 ) +1.5   A o = 0.219421637 dB

(

Water Vapor Loss A H2O

)

For frequencies below 350GHz   -4 2 3 9 4.3 A H2 O = 0.067 + + +  10 fαD 2 2 2 ( f - 22.3) + 7.3 ( f -183.3) + 6 ( f - 323.3) +10   Where f = frequency used in GHz α = water vapor density in gm/m3 = 12gm/m3 D = total distance or path length in kilometers (km)  3 A H2 O = 0 .0 6 7 + 2 ( 1 3 - 2 2) .3 

+ 7( .3

9 + 2 1 )3 - 1 8 3( .3

+ 6)

4 .3 + -4 2 1 3 - 3 2 3 .3

2

+ 10

(1 0 )(1 3 ) (1 2 ) ( 2 8 )

A H2 O = 0.564099437dB

12

  

13

SYSTEM GAIN CALCULATIONS Fade Margin (Fm) Fm = 30logD +10log ( 6Abf ) -10log ( 1- R ) - 70 Where

f = frequency, GHz R = reliability expressed as decimal (0.999999) A = roughness factor = 4 over water or a very smooth terrain = 1 over an average terrain = 0.25 over a rough, mountainous terrain b = factor to convert a worst case month probability = 1 to convert an annual availability to a worst month basis = 0.5 for hot humid area = 0.125 for very dry or mountainous area = 0.25 for average land area

Fm = 30logD +10log ( 6Abf ) -10log ( 1- R ) - 70

Fm = 30log28 +10log ( 6 ) ( 0.25 ) ( 0.125 ) ( 13) -10log ( 1- 0.999999 ) - 70 Fm = 37.28418718dB Path Attenuation (Lp) L p = 92.3 + 20logf + 20logD L p = 92.3 + 20log13 + 20log28 L p = 143.5220277dB Transmitted Power Output: 25dBm Threshold Level: -86.5 dBm Median Received Power Median Received Power = Threshold Level + Fm Median Received Power = -86.5 + 37.28418718 Median Received Power = -49.21581282dB

14

Total Fixed Losses Total Fixed Losses = ( waveguide loss + connector loss ) SiteA + ( waveguide loss + connector loss )SiteB

Total Fixed Losses = ( 5.42229 + 0.75 ) + ( 5.42229 + 0.75 ) Total Fixed Losses = 12.34458dB

Total Losses (TL) Total losses = total fixed loss + path attenuation Total losses = 12.34458 +143.5220277 Total losses = 155.8666077dB Net Path Loss Net path loss = transmitter power - median received power Net path loss = 25dBm - ( -49.21581282 ) Net path loss = 74.21581282dB Computed Antenna Diameter, d Fade Margin = RSL - RTH RSL = Fade Margin + RTH = 37.28418718 + (-86.5) = -49.21581282 dB RSL = transmitter power output – connector losses(TX and RX) – waveguide losses(TX and RX) + AGT – misalignment loss(TX and RX) – AFSL – A0 – AH2O + AGR -49.21581282 dB = 25dBm – (0.75 dB + 0.75 dB) – (5.42229 dB + 5.42229 dB) + AGT – (0.25dB + 0.25dB) - 143.6620277 dB 0.219421637 dB - 0.564099437dB + AGR AGT + AGR = -25dBm + (0.75 dB + 0.75 dB)+ (5.42229 dB + 5.42229 dB) + (0.25dB+0.25dB)+143.6620277dB+ 0.219421637 dB + 0.564099437dB - 49.21581282 dB = 83.07431595 dB Let AGT = AGR = 41.53715798 dB

15

log -1

8

d=

3x10 πf

At 10

η 8

3x10 π(13GHz) d = 1.18m

log -1

d=

41.53715798 10 0.55

Computations using the Computed Value of the Antenna Diameter Tower Height HT = HA + 1/ 2 (d) Where

HT = Tower Height, meters HA = Antenna Height, meters D = Antenna Diameter, meters

Site A:

HT = 20m + 1/ 2 (1.18m) = 20.59m

Site B:

HT = 20 + 1/ 2 (1.18m) = 20.59m

System Gain (GS)  πfd  A t = 10logη    c 

2

Site A:  πfd  A t = 10logη    c 

2

 π ( 13x109 ) ( 1.18 )   A t = 10log0.55  3x108   A t = 41.52070645dB

2

16

Site B:

 π ( 13x109 ) ( 1.18 )   A r = 10log0.64  3x108   A r = 42.17887929 dB

2

G s = Fm + TL - At - Ar G s = 37.28418718 +155.8666077 - 41.52070645 - 42.17887929 G s = 109.4512091 dB Antenna Diameter Site A: Computed Value: 1.18m (3.87’) Site B: Computed Value: 1.18m (3.87’) Antenna Gain (AG)  πfd  A G = 10logη    c  Where

2

AG f d η

= antenna gain in dB = frequency in GHz = diameter of the antenna in meters = antenna efficiency η = 0.55 for transmitter antenna η = 0.64 for receiver antenna c = speed of light = 3 x 108 m/s

Low Band Frequency Site A:  πfd  A G = 10logη    c 

2

 π ( 12.848x109 ) ( 1.18 )   A G = 10log0.55  3x108   A G = 41.41854996dB

2

Site B:

17

 πfd  A G = 10logη    c 

2

 π ( 12.848x109 ) ( 1.18 )   A G = 10log0.64  3x108   A G = 42.0767228dB High Band Frequency

2

Site A:  πfd  A G = 10logη    c 

2

 π ( 13.112x109 ) ( 1.18 )   A G = 10log0.55  3x108   A G = 41.59521821dB

2

Site B:  πfd  A G = 10logη    c 

2

 π ( 13.112x109 ) ( 1.18 )   A G = 10log0.64  3x108   A G = 42.25339106dB

2

PATH LOSSES Free Space Loss AFSL = 92.44 + 20 log f + 20 log D Where

f = frequency used in GHz D = total path length or distance in kilometers (km)

Low Band Frequency AFSL = 92.44 + 20 log 12.848 + 20 log 28 AFSL = 143.5598712 dB High Band Frequency AFSL = 92.44 + 20 log 13.112 + 20 log 28

18

AFSL = 143.7365394 dB

Oxygen Absorption Loss (Ao) For frequencies below 57GHz:   6.09 4.81 A o =  7.9x10-3 + 2 +  ( 1x10-3 ) f 2 D 2 f + 0.227  ( f - 57 ) +1.5  Where

f = frequency used in GHz D = total path length or distance in kilometers (km)

Low Band Frequency   6.09 4.81 A o = 7.9x10-3 + +  ( 1x10-3 ) ( 12.8482 ) ( 28 ) 2 2 12.848 + 0.227 ( 12.848 - 57 ) +1.5   A o = 0.218195213 dB

High Band Frequency   6.09 4.81 A o = 7.9x10-3 + +  ( 1x10-3 ) ( 13.1122 ) ( 28 ) 2 2 13.112 + 0.227 ( 13.112 - 57 ) +1.5   A o = 0.22033675 dB

(

Water Vapor Loss A H2O

)

For frequencies below 350GHz   -4 2 3 9 4.3 A H2 O = 0.067 + + +  10 fαD 2 2 2 ( f - 22.3) + 7.3 ( f -183.3) + 6 ( f - 323.3) +10   Where

f = frequency used in GHz α = water vapor density in gm/m3 = 12gm/m3 D = total distance or path length in kilometers (km)

Low Band Frequency 19

 3 A H2 O = 0 .0 6 7 + 2 ( 1 2 .8 4 8 - 2) 2 .3 

+( 7 .3

9 + 2 1 2 .8) 4 8 - 1( 8 3 .3

+ 63)

4 .3 + -4 2 +1120.8 4 8 - 3 2 3 .

2

(1 0 )(1 2 .

A H2 O = 0.545749513dB High Band Frequency  3 A H2 O = 0.067 + 2 ( 13.112 - 22.3) + 7.3( 

9 + 2 13.112 -183.3 )

(+ 6

4.3 + 2 13.112 3) - 323. + 10

-4

 (102 )(13.112) (12)(28)  

A H2 O = 0.578035188 dB Total System Loss (TSLoss) TSLoss = RWL (Tx and Rx) + FWL (Tx and Rx) + Total Connector Loss (Tx and Rx) + AFSL + A H2 O + AO + AMLoss (TX and RX) Low Band Frequency TSLoss = (4.29069 dB+4.29069dB) + (1.1316 dB+1.1316 dB) + (0.75dB+0.75 dB) + 143.5598712 dB+ 0.545749513dB + 0.218195213 dB + (0.25dB+0.25dB) TSLoss = 157.1683928dB High Band Frequency TSLoss = (4.29069 dB+4.29069 dB) + (1.1316 dB+1.1316 dB) + (0.75dB+0.75 dB) + 143.7365394 dB +0.578035188 dB +0.22033675 dB + (0.25dB+0.25dB) TSLoss =157.3794913 dB

Total System Gain (TGS) TGS = Tx Output Power (TxOP) + Antenna Gain (Tx and Rx) Low Band Frequency TGS = 25dB + ( 41.41854996 dB+ 42.0767228 dB) TGS = 108.4952728 dB 20

High Band Frequency TGS = 25dB + ( 41.74120299 dB+ 42.25339106 dB) TGS = 108.9945941 dB Power Input to Receive (RSL) RSL = Total System Gain (TGS) – Total System Loss (TSLoss) Low Band Frequency RSL = 108.4952728 dB - 157.1683928dB RSL = - 48.67312 dB High Band Frequency RSL = 108.9945941 dB - 157.3794913 dB RSL = - 48. 53088207dB Power Input to Receiver (RSL) Low Band Frequency Parameter Site A: Transmitter Transmitter Power Output Connector Losses Waveguide Losses Antenna Gain Antenna Misalignment Loss Environmental Losses Free Space Loss Oxygen Absorption Water Vapor Absorption Site B: Receiver Antenna Misalignment Loss Antenna Gain Waveguide Losses Connector Losses Power Input to Receiver (RSL) High Band Frequency Parameter Site A: Transmitter Transmitter Power Output Connector Losses Waveguide Losses

Function

Value

Unit

Given Subtracted Subtracted Added Subtracted

25 0.75 5.42229 41.41854996 0.25

dBm dB dB dB dB

Subtracted Subtracted Subtracted

143.5598712 0.218195213 0.545749513

dB dB dB

Subtracted Added Subtracted Subtracted Computed

0.25 42.0767228 5.42229 0.75 -48.67312317

dB dB dB dB dB

Function

Value

Unit

Given Subtracted Subtracted

25 0.75 5.42229

dBm dB dB

21

Antenna Gain Antenna Misalignment Loss Environmental Losses Free Space Loss Oxygen Absorption Water Vapor Absorption Site B: Receiver Antenna Misalignment Loss Antenna Gain Waveguide Losses Connector Losses Power Input to Receiver (RSL)

Added Subtracted

41.59521821 0.25

dB dB

Subtracted Subtracted Subtracted

143.7365394 0.22033675 0.578035188

dB dB dB

Subtracted Added Subtracted Subtracted Computed

0.25 42.25339106 5.42229 0.75 -48.53088207

dB dB dB dB dB

PATH CACULATIONS/LINK BUDGET Low Band Frequency Transmitter Power Output (TXPO) =25 dBm Transmitter Losses (TL) = waveguide losses + connector losses+ antenna misalignment loss Antenna Gain at the transmitter side (At) Path Losses (PL) = free space loss + oxygen absorption + water vapor absorption Antenna Gain at the receiver side (AR) Receiver Losses (RL) = antenna misalignment + waveguide losses + connector losses RSL=TPO-TL+AT – PL+ AR - RL Actual Transmitter Power Output = TPO-TL = 18.82771 dB Actual Antenna Transmitted Power = TPO-TL+AT = 59.99625996 dB Actual Received Power = TPO-TL+ AT – PT = - 84.32755597 dB Actual Antenna Received Power = TPO-TL+ AT - PT+AR = - 42.50083317 dB Power Input to Receiver (RSL)= TPO-TL+ AT - PT+AR - RL ` = - 48.67312317 dB High Band Frequency Transmitter Power Output (TXPO)= 25 dBm Transmitter Losses (TL) = waveguide losses + connector losses+ antenna misalignment loss Antenna Gain at the transmitter side (At) Path Losses (PL) = free space loss + oxygen absorption + water vapor absorption

22

Antenna Gain at the receiver side (AR) Receiver Losses (RL) = antenna misalignment + waveguide losses + connector losses RSL= TPO-TL+AT – PL+ AR - RL Actual Transmitter Power Output = TPO-TL =18.82771 dB Actual Antenna Transmitted Power = TPO-TL+AT = 60.17292821 dB Actual Received Power = TPO-TL+ AT – PT = - 84.36198313 dB Actual Antenna Received Power = TPO-TL+ AT - PT+AR = - 42.35859207 dB Power Input to Receiver (RSL) = TPO-TL+ AT - PT+AR - RL = -48.53088207dB

23

24

FADE MARGINS Thermal Fade Margin (FMTHERMAL) Low Band Frequency FMTHERMAL = RSL- Receiver Input Threshold = -48.67312317– (-86.5dB)

25

= 37.82687683 dB High Band Frequency FMTHERMAL = RSL- Receiver Input Threshold = -48.53088207– (-86.5dB) = 37.96911793 dB Dispersive Fade Margin (FMDISP) Since the dispersive fade margin is not given in the product specification, it is assumed that the 4xE1 to 8xE1 = 70 to 80 dB dispersive fade margin and has a dispersive factor of 3 for average propagation conditions. FM DISP = 70dB Diffractive Fade Margin (FMDIFF) Since diffraction loss and clutter loss = 0, then FMDIFF = FMTHERMAL Low Band Frequency FMDIFF = 37.82687683 dB High Band Frequency FMDIFF =37.96911793 dB Flat Fade Margin (FMFLAT) -FM DIFF  -FMTHERMAL  FM FLAT = -10log 10 10 +10 10   

Low Band Frequency FM FLAT FM FLAT

-37.82687683  -37.82687683  10 10 = -10log 10 +10    = 34.8165687 dB

26

High Band Frequency  -37.96911793 10 FM FLAT = -10log 10  FM FLAT = 34.95881797dB

+10

-37.96911793 10

  

Effective Fade Margin (FMEFF) FM EFF

-FM DISP  -FM10FLAT  = -10log 10 +10 10   

RD is the fade occurrence factor and considering a dispersive fade margin of 70dB with an average fade factor occurrence of RD = 3. Low Band Frequency -70  -34.8165687  10 FM EFF = -10log 10 +10 10    FM EFF = 34.81525234 dB High Band Frequency -70  -34.95881797  FM EFF = -10log 10 10 +10 10    FM EFF = 34.95745778 dB

RAIN LOSSES CCIR Recommendation 530 Rain Attenuation (ARAIN) Interpolation Formula:

27

Mx = ( log f1 - log fx ) / (log f1 - log f2 ) kx = antilog [ log k1 - Mx ( log k1 - log k2 ) ] α x = α 1 - Mx (α 1 -α 2)

Do = 35e−0.015R0.001% DE = D/[1 + (D/ Do )] Where

Do = effective rain path length (km) D = path length (km) R0.001% = 180 @ N (Philippine Region)

γ = k x ×(R 0.001%) eα x ARain = γDE

Low Band Frequency Interpolation Factors f1 = 12 GHz f2 = 15Ghz fx = 12.848 GHz

k1 = 0.0168 k2 = 0.0335 R1 = 180 @ N

α1 = 1.217 α2 = 1.154

Mx = ( log 12 - log 12.848) / (log 12 - log15 ) Mx = 0.30599812 k x = antilog [ log 0.0168 - 0.3059981(log 0.0168 - log 0.0335)] k x = 0.020750462

α x = 1.217- 0.30599812 (1.217- 1.154) α x =1.197722118

Do = 35 e -0.015R0.001% = 35e-0.015(180) = 2.352192946 DE = D/[1 + (D/Do)] DE = 28/[1+ (28/2.352192946) ] DE = 2.169905898

28

γ = k x (R0.001%)α x γ = 0.020750462 (180) 1.19772211 γ =10.43197121 A RAIN = γ DE A RAIN = 10.43197121(2.169905898) A RAIN = 22.63639585 High Band Frequency Interpolation Factors f1 = 12 GHz f2 = 15Ghz fx = 13.112 GHz

k1 = 0.0168 α1 = 1.217 k2 = 0.0335 α2 = 1.154 R1 = 180 @ N

Mx = ( log 12 - log 13.112) / (log 12 - log15 ) Mx = 0.397148791 k x = antilog [ log 0.0168 - 0.397148791 (log 0.0168 - log 0.0335)] k x = 0.022097792

α x = 1.217- 0.397148791 (1.217- 1.154) α x =1.191979626 Do = 35 e

-0.015R0.001% -0.015(180)

= 35 e = 2.352192946

DE = D/[1 + (D/Do)] Where

Do = effective rain path length (km) D = path length (km) R0.001% = 180 @ N (Philippine Region)

DE = 28/[1+ (28/ 2.352192946) ] = 2.169905898

γ =kx(R0.001%)αx γ = 0.022097792 (180) 1.191979626 = 10.77923049

29

ARAIN =

γDE

ARAIN = 10.77923049 (2.169905898)

= 23.38991582 Rain Fade Margin (FMRAIN) FM RAIN = FM THERMAL - ARAIN Low Band Frequency FM RAIN = FM THERMAL - ARAIN FM RAIN = 37.82687683 - 22.63639585 FM RAIN = 15.19048098 dB High Band Frequency FM RAIN = FM THERMAL - ARAIN FM RAIN = 37.96911793 - 23.38991582 FM RAIN = 14.57920211 dB RELIABILTY CALCULATIONS Unfaded Reliability (R) R = ( 1- U ) 100% -FM EFF   K - Q  U =  1.3  10 10  ( f b ) ( d c )  S  

Where

K-Q = regional K-Q value = 1.9 x 10-9 S = standard deviation of the terrain SD = 469.07 f = frequency, GHz d = path length, km b, c = regional climatic factor (b=1.2; c=3.5) FMEFF = effective fade margin

Using: K-Q value of 1.9 x 10-9 b = 1.2 c = 3.5 d = 28 km 30

fH = 12.848 GHz fH = 13.112GHz FM EFF( LOW BAND FREQUENCY ) = 34.81525234 dB FM EFF( HIGH BAND FREQUENCY ) = 34.95745778 dB Low Band Frequency U LBF

  1x10-9   -34.81525234 1.2 3.5 = 10 10  ( 12.848 ) ( 28 ) 1.3    469.07   

U LBF = 2.763895087x10-10 R LBF = 1- ( 2.763895087x10-10 )  100% R LBF = 99.99999997% High Band Frequency   1x10-9   -34.95745778 1.2 3.5 U HBF =  10 10  ( 13.112 ) ( 28 ) 1.3    469.07    U HBF = 2.740949948x10-10 R HBF = 1- ( 2.740949948x10-10 )  100% R HBF = 99.99999997% Rain Reliability (RRAIN) R = 1( U 100% ) -FM RAIN 2   K-Q   10 U =  1.3 10 f    S     FM RAIN 2= FM EFF-A RAIN

Where

K-Q S S f d

(d b ) (

c

)

= regional K-Q value = 1.9 x 10-9 = standard deviation of the terrain = 469.07 = frequency, GHz = path length, km

b, c = regional climatic factor (b=1.2; c=3.5) FMEFF = effective fade margin Using: 31

K-Q value of 1 x 10-9 b = 1.2 c = 3.5 d =28km fH = 12.848 GHz fH = 13.112GHz FM EFF( LOW BAND FREQUENCY ) = 34.81525234 dB FM EFF( HIGH BAND FREQUENCY ) = 34.95745778 dB Low Band Frequency FM RAIN 2 = FM EFF - ARAIN FM RAIN 2 = 34.81525234 - 22.63639585 FM RAIN 2 = 12.17885649dB U LBF

  1x10-9   - 12.17885649 1.2 3.5 = 10 10  ( 12.848 ) ( 28 ) 1.3    469.07   

U LBF = 5.07178855x10-08 R LBF = 1- ( 5.07178855x10-08 )  100% R LBF = 99.99999493% High Band Frequency FM RAIN 2 = FM EFF - ARAIN FM RAIN 2 = 34.95745778 - 23.38991582 FM RAIN 2 = 11.56754196dB   1x10-9   -11.56754196 1.2 3.5 U HBF =  10 10  ( 13.112 ) ( 28 ) 1.3    469.07    U HBF = 5.982637475x10-08 R HBF = 1- ( 5.982637475x10-08 )  100% R HBF = 99.99999402% LINK 1 RELIABILITY

32

R = 99.99999402%

Computations using the Market Value of the Antenna Diameter Use parabolic antenna with a diameter higher than the computed value which is readily available and with a better rain reliability.

33

Use parabolic antenna with a diameter of 1.2 m (4ft) readily available in the market and with a better rain reliability. Tower Height HT = HA + 1/ 2 (d) Where

Site A: Site B:

HT = Tower Height, meters HA = Antenna Height, meters D = Antenna Diameter, meters

HT = 20m + 1/ 2 (1.2m) = 20.545m HT = 20 + 1/ 2 (1.2m) = 20.545m

System Gain  πfd  A t = 10logη    c 

2

Site A:  πfd  A t = 10logη    c 

2

 π ( 13x109 ) ( 1.2 )   A t = 10log0.55  3x108   A t = 41.66669122dB Site B:

2

 π ( 13x109 ) ( 1.2 )   A r = 10log0.64  3x108   A r = 42.32486407 dB

2

G s = Fm + TL - At - Ar G s = 37.28418718 +155.8666077 - 41.66669122 - 42.32486407 G s = 109.1592396 dB Antenna Diameter 34

Site A: Market Value: 1.2m (4’) Site B: Market Value: 1.2m (4’) Antenna Gain (AG)  πfd  A G = 10logη    c  Where

2

AG f d η

= antenna gain in dB = frequency in GHz = diameter of the antenna in meters = antenna efficiency η = 0.55 for transmitter antenna η = 0.64 for receiver antenna c = speed of light = 3 x 108 m/s

Low Band Frequency Site A:  πfd  A G = 10logη    c 

2

 π ( 12.848x109 ) ( 1.2 )   A G = 10log0.55  3x108   A G = 41.56453473dB

2

Site B:  πfd  A G = 10logη    c 

2

 π ( 12.848x109 ) ( 1.2 )   A G = 10log0.64  3x108   A G = 42.22270758dB High Band Frequency

2

Site A:

35

 πfd  A G = 10logη    c 

2

 π ( 13.112x109 ) ( 1.2 )   A G = 10log0.55  3x108   A G = 41.74120299dB

2

Site B:  πfd  A G = 10logη    c 

2

 π ( 13.112x109 ) ( 1.2 )   A G = 10log0.64  3x108   A G = 42.39937583dB

2

Antenna Misalignment Loss Site A: 0.25dB Site B: 0.25dB Antenna Polarization Vertical Polarization

PATH LOSSES Free Space Loss (AFSL) AFSL = 92.44 + 20 log f + 20 log D Where

f = frequency used in GHz D = total path length or distance in kilometers (km)

Low Band Frequency AFSL = 92.44 + 20 log 12.848 + 20 log 28 AFSL = 143.5598712 dB High Band Frequency AFSL = 92.44 + 20 log 13.112 + 20 log 28 AFSL = 143.7365394 dB Oxygen Absorption Loss (Ao) 36

For frequencies below 57GHz:   6.09 4.81 A o =  7.9x10-3 + 2 +  ( 1x10-3 ) f 2 D 2 f + 0.227 ( f - 57 ) +1.5   Where

f = frequency used in GHz D = total path length or distance in kilometers (km)

Low Band Frequency   6.09 4.81 A o = 7.9x10-3 + +  ( 1x10-3 ) ( 12.8482 ) ( 28 ) 2 2 12.848 + 0.227 ( 12.848 - 57 ) +1.5   A o = 0.218195213 dB High Band Frequency   6.09 4.81 A o = 7.9x10-3 + +  ( 1x10-3 ) ( 13.1122 ) ( 28 ) 2 2 13.112 + 0.227 ( 13.112 - 57 ) +1.5   A o = 0.22033675 dB

(

Water Vapor Loss A H2O

)

For frequencies below 350GHz   -4 2 3 9 4.3 A H2 O = 0.067 + + +  10 fαD 2 2 2 ( f - 22.3) + 7.3 ( f -183.3) + 6 ( f - 323.3) +10   Where f = frequency used in GHz α = water vapor density in gm/m3 = 12gm/m3 D = total distance or path length in kilometers (km)

Low Band Frequency  3 A H2 O = 0 .0 6 7 + 2 ( 1 3 .1 1 2 - 2) 2 .3 

+( 7 .3

9 + 2 1 3 .1) 1 2 - 1( 8 3 .3

+ 63)

4 .3 + -4 2 +1130.1 1 2 - 3 2 3 .

2

(1 0 )(1 3

37

AH2O=0.545749352dB High Band Frequency  3 A H2 O = 0.067 + 2 ( 13.112 - 22.3) + 7.3( 

9 + 2 13.112 -183.3 )

(+ 6

4.3 + 2 13.112 3) - 323. + 10

-4

AH2O = 0.578035188 dB

 (102 )(13.112) (12)(28)  

Total System Loss (TSLoss) TSLoss = RWL (Tx and Rx) + FWL (Tx and Rx) + Total Connector Loss (Tx and Rx) + AFSL + AH2o + AO + AMLoss (TX and RX) Low Band Frequency TSLoss = (4.29069 dB+4.29069dB) + (1.1316 dB+1.1316 dB) + (0.75dB+0.75 dB) + 143.5598712 dB+ 0.545749352dB + 0.218195213 dB + (0.25dB+0.25dB) TSLoss = 157.1683958dB High Band Frequency TSLoss = (4.29069 dB+4.29069 dB) + (1.1316 dB+1.1316 dB) + (0.75dB+0.75 dB) + 143.7365394 dB +0.578035188 dB +0.22033675 dB + (0.25dB+0.25dB) TSLoss =157.3794913 dB Total System Gain (TGS) TGS = Tx Output Power (TxOP) + Antenna Gain (Tx and Rx) Low Band Frequency TGS = 25dB + ( 41.56453473 dB+ 42.22270758 dB) TGS = 108.7872423 dB High Band Frequency TGS = 25dB + ( 41.74120299 dB+ 42.39937583 dB) TGS = 109.1405788 dB Power Input to Receive (RSL) 38

RSL = Total System Gain (TSG) – Total System Loss (TSLoss) Low Band Frequency RSL = 108.7872423 - 157.1683958dB RSL = - 48.3811535 dB High Band Frequency RSL = 109.1405788 dB - 157.3794913 dB RSL = - 48.2389125 dB

Power Input to Receiver (RSL) Low Band Frequency Parameter Site A: Transmitter Transmitter Power Output Connector Losses Waveguide Losses Antenna Gain Antenna Misalignment Loss Environmental Losses Free Space Loss Oxygen Absorption Water Vapor Absorption Site B: Receiver Antenna Misalignment Loss Antenna Gain Waveguide Losses Connector Losses Power Input to Receiver (RSL)

Function

Value

Unit

Given 25 Subtracted 0.75 Subtracted 5.42229 41.56453473 Added Subtracted 0.25

dBm dB dB dB dB

Subtracted 143.5598712 Subtracted 0.218195213 Subtracted 0.545749352

dB dB dB

Subtracted 0.25 42.22270758 Added Subtracted 5.42229 Subtracted 0.75 Computed -48.38115346

dB dB dB dB dB

High Band Frequency Parameter Site A: Transmitter Transmitter Power Output

Function Given

Value 25

Unit dBm

39

Connector Losses Waveguide Losses Antenna Gain Antenna Misalignment Loss Environmental Losses Free Space Loss Oxygen Absorption Water Vapor Absorption Site B: Receiver Antenna Misalignment Loss Antenna Gain Waveguide Losses Connector Losses Power Input to Receiver (RSL)

Subtracted 0.75 Subtracted 5.42229 41.74120299 Added Subtracted 0.25

dB dB dB dB

Subtracted 143.7365394 Subtracted 0.22033675 Subtracted 0.578035188

dB dB dB

Subtracted 0.25 42.39937583 Added Subtracted 5.42229 Subtracted 0.75 Computed -48.23891252

dB dB dB dB dB

PATH CACULATIONS/LINK BUDGET Low Band Frequency Transmitter Power Output (TPO)=25 dBm Transmitter Losses (TL) = waveguide losses + connector losses+ antenna misalignment loss Antenna Gain at the transmitter side (At) Path Losses (PL) = free space loss + oxygen absorption + water vapor absorption Antenna Gain at the receiver side (AR) Receiver Losses (RL) = antenna misalignment + waveguide losses + connector losses RSL=TPO-TL+AT – PL+ AR - RL Actual Transmitter Power Output = TPO-TL = 18.82771 dB Actual Antenna Transmitted Power = TPO-TL+AT = 60.14224473 dB Actual Received Power = TPO-TL+ AT – PT = - 84.18157104 dB Actual Antenna Received Power= TPO-TL+ AT - PT+AR = - 42.20886346 dB Power Input to Receiver (RSL)= TPO-TL+ AT - PT+AR - RL ` = - 48.38115346 dB High Band Frequency Transmitter Power Output (TPO)= 25 dBm Transmitter Losses (TL) = waveguide losses + connector losses+ antenna misalignment loss Antenna Gain at the transmitter side (At)

40

Path Losses (PL) = free space loss + oxygen absorption + water vapor absorption Antenna Gain at the receiver side (AR) Receiver Losses (RL) = antenna misalignment + waveguide losses + connector losses RSL=TPO-TL+AT – PL+ AR - RL Actual Transmitter Power Output= TPO-TL =18.82771 dB Actual Antenna Transmitted Power = TPO-TL+AT = 60.31891299 dB Actual Received Power = TPO-TL+ AT – PT = - 84.21599835 dB Actual Antenna Received Power= TPO-TL+ AT - PT+AR = - 42.06662252 dB Power Input to Receiver (RSL)= TPO-TL+ AT - PT+AR - RL = -48.23891252 dB

41

42

FADE MARGINS Thermal Fade Margin (FMTHERMAL) Low Band Frequency FMTHERMAL= RSL- Receiver Input Threshold

43

= -48.38115346 – (-86.5dB) = 38.12884654 dB High Band Frequency FMTHERMAL= RSL- Receiver Input Threshold = -48.2389152– (-86.5dB) =38.2610848 dB Dispersive Fade Margin (FMDISP) Since the dispersive fade margin is not given in the product specification, it is assumed that the 4xE1 to 8xE1 = 70 to 80 dB dispersive fade margin and has a dispersive factor of 3 for average propagation conditions. FM DISP = 70dB Diffractive Fade Margin (FMDIFF) Since diffraction loss and clutter loss = 0, then FMDIFF = FMTHERMAL Low Band Frequency FMDIFF = 38.12884654 dB High Band Frequency FMDIFF =38.2610848 dB Flat Fade Margin (FMFLAT) -FM DIFF  -FMTHERMAL  FM FLAT = -10log 10 10 +10 10   

Low Band Frequency -38.12884654  -38.12884654  10 FM FLAT = -10log 10 +10 10    FM FLAT = 35.11854658 dB

44

High Band Frequency -38.2610848  -38.2610848  FM FLAT = -10log 10 10 +10 10    FM FLAT = 35.25078484dB

Effective Fade Margin (FMEFF) -FM DISP  -FM10FLAT  FM EFF = -10log 10 +10 10    RD is the fade occurrence factor and considering a dispersive fade margin of 70dB with an average fade factor occurrence of RD = 3. Low Band Frequency -70  -35.11854658  FM EFF = -10log 10 10 +10 10    FM EFF = 35.11713545 dB High Band Frequency FM EFF FM EFF

-70  -35.25078484  10 = -10log 10 +10 10    = 35.24933008 dB

RAIN LOSSES CCIR Recommendation 530 Rain Attenuation (ARAIN) Interpolation Formula:

45

M x = ( log f1 - log fx ) / (log f1 - log f2 ) k x = antilog [ log k1 - Mx ( log k1 - log k2 ) ]

α x = α 1 - Mx (α 1 -α 2 )

D = 35e−0.015R0.001% D = D/[1 + (D/ Do)] o

E

γ = kx × (R0.001%)eα x ARain = γDE Where

Do = effective rain path length (km) D = path length (km) R0.001% = 180 @ N (Philippine Region)

Low Band Frequency Interpolation Factors f1 = 12 GHz f2 = 15 GHz fx = 12.848 GHz

k1 = 0.0168 α1 = 1.217 k2 = 0.0335 α2 = 1.154 R1 = 180 @ N

Mx = ( log 12 - log 12.848) / (log 12 - log15 ) Mx = 0.30599812 k x = antilog [ log 0.0168 - 0.3059981(log 0.0168 - log 0.0335)] k x = 0.020750462

α x = 1.217- 0.30599812 (1.217- 1.154) α x =1.197722118 Do = 35 e -0.015R0.001% = 35e-0.015(180) = 2.352192946 DE = D/[1 + (D/Do)] DE = 28/[1+ (28/2.352192946) ] = 2.169905898

γ =kx(R0.001%)α x γ =0.020750462 (180) 1.197722118 γ = 10.43197121 46

A RAIN = γ DE A RAIN = 10.43197121(2.169905898) A RAIN = 22.63639585 High Band Frequency Interpolation Factors f1 = 12 GHz f2 = 15Ghz fx = 13.112 GHz

k1 = 0.0168 α1 = 1.217 k2 = 0.0335 α2 = 1.154 R1 = 180 @ N

Mx = ( log 12 - log 13.112) / (log 12 - log15 ) Mx = 0.397148791 k x = antilog [ log 0.0168 - 0.397148791 (log 0.0168 - log 0.0335)] k x = 0.022097792

α x = 1.217- 0.397148791 (1.217- 1.154) α x =1.191979626 Do = 35 e -0.015R0.001% Do = 35 e-0.015(180) Do = 2.352192946 DE = D/[1 + (D/Do)] Where

Do = effective rain path length (km) D = path length (km) R0.001% = 180 @ N (Philippine Region)

D E = 28/[1+ (28/ 2.352192946)] D E = 2.169905898

γ =k x (R0.001%)α x γ = 0.022097792 (180) 1.191979626 γ = 10.77923049

47

A RAIN = γ DE A RAIN = 10.77923049 (2.169905898) A RAIN = 23.38991582 Rain Fade Margin (FMRAIN) FM RAIN = FM THERMAL - ARAIN Low Band Frequency FM RAIN = FM THERMAL - ARAIN FM RAIN = 38.12884654 - 22.63639585 FM RAIN = 15.49245069 dB High Band Frequency FM RAIN = FM THERMAL - ARAIN FM RAIN = 38.2610848 - 23.38991582 FM RAIN = 14.87116898 dB RELIABILTY CALCULATIONS Unfaded Reliability (R) R = ( 1- U ) 100%  K - Q  U =  1.3  10  S  Where:

-FM EFF 10

 c  ( fb ) ( d ) 

K-Q = regional K-Q value = 1.9 x 10-9 S = standard deviation of the terrain S = 469.07 f = frequency, GHz d = path length, km b, c = regional climatic factor (b=1.2; c=3.5) FMEFF = effective fade margin

Using: K-Q value of 1.9 x 10-9 b = 1.2 c = 3.5 d = 28 km

48

fH = 12.848 GHz fH = 13.112GHz FM EFF( LOW BAND FREQUENCY ) = 35.11713545 dB FM EFF( HIGH BAND FREQUENCY ) = 35.24933008 dB Low Band Frequency   1x10-9   -35.11713545 1.2 3.5 U LBF =  10 10  ( 12.848 ) ( 28 ) 1.3    469.07    U LBF = 2.578298779x10-10 R LBF = 1- ( 2.578298779x10-10 )  100% R LBF = 99.99999997% High Band Frequency   1x10-9   -35.24933008 1.2 3.5 U HBF =  10 10  ( 13.112 ) ( 28 ) 1.3    469.07    U HBF = 2.562795041x10-10 R HBF = 1- ( 2.562795041x10-10 )  100% R HBF = 99.99999997% Rain Reliability (RRAIN) R = 1( U 100% ) -FM RAIN 2   K-Q   10 U =  1.3 10 f     S    FM RAIN 2= FM EFF-A RAIN

Where

K-Q S S f d b, c FMEFF

(d b ) (

c

)

= regional K-Q value = 1.9 x 10-9 = standard deviation of the terrain = 469.07 = frequency, GHz = path length, km = regional climatic factor (b=1.2; c=3.5) = effective fade margin 49

Using: K-Q value of 1 x 10-9 b = 1.2 c = 3.5 d =28km fH = 12.848 GHz fH = 13.112GHz FM EFF( LOW BAND FREQUENCY ) = 35.11713545 dB FM EFF( HIGH BAND FREQUENCY ) = 35.24933008 dB Low Band Frequency FM RAIN 2 = FM EFF - ARAIN FM RAIN 2 = 35.11713545 - 22.63639585 FM RAIN 2 = 12.4807396dB   1x10-9   -12.4807396 1.2 3.5 U LBF =  10 10  ( 12.848 ) ( 28 ) 1.3    469.07    U LBF = 4.731216567x10-08 R LBF = 1- ( 4.731216567x10-08 )  100% R LBF = 99.99999527% High Band Frequency FM RAIN 2 = FM EFF - ARAIN FM RAIN 2 = 35.24933008 - 23.38991582 FM RAIN 2 = 11.85941426dB U HBF

  1x10-9   -11.85941426 1.2 3.5 = 10 10  ( 13.112 ) ( 28 ) 1.3    469.07   

U HBF = 5.593780969x10-08 R HBF = 1- ( 5.593780969x10-08 )  100% R HBF = 99.99999441% LINK 1 RELIABILITY

50

R = 99.99999441%

51