The Free Space Wireless Link (Text Section 8-5 )

Home , Fresnel zone

EELE445 Lecture 39

Isotropic Radiator

• Power is radiated equally in all directions • F= flux density in Watts/m2

• Also use Field strength, Fs= Volts/m

P Watts F = t 4pR 2 m 2 Pt

1 Flux Density and Field Strength P Watts F = t 4pR 2 m 2

m m = = o = 120p = 377W Z o e e o

P120p 30P Volts = F · Z = t = t F s o R 2 4p R 2 meter

Real Antenna – Not Isotropic Polar Plot of Normalized F

0dB

2 Polar Antenna Beam Pattern

Some common antenna gains

3 Some common antenna gains

4 5 Free Space Path Loss (Friss loss): Combining : PG A P = t t e watts r 4pR2

Pt = transmitt power in watts

Gt = antenna gain in watts/watt

Ae = effective receive antenna area in meters squared R = distance between transmitt and receive antennas in meters

It can be shown that : 4pA G = e where l is the wavelengt h in meters l2 Think of this as the number of wavelengths the area of the antenna intersects

6 Free Space Path Loss (Friss loss): given A e and f, we know the gain G l2 PG G l2 A = r P = t t r e 4p r 4pR 2 4p

PtGtGr Pr= 2 æ 4pR ö ç ÷ è l ø free space (Friss) path loss is : 2 æ 4pR ö Lp º ç ÷ è l ø

Free Space Path Loss (Friss loss):

7 Free Space Path Loss (Friss loss):

Figure 8–25 Galaxy I (134° W longitude) antenna pattern EIRP footprint contours given in dBw units). [Courtesy of Hughes Communications, Inc., a wholly owned subsidiary of Hughes Aircraft Company.]

8 Figure 8–25 Galaxy I (134° W longitude) antenna pattern EIRP footprint contours given in dBw units). [Courtesy of Hughes Communications, Inc., a wholly owned subsidiary of Hughes Aircraft Company.]

9 C band 4 to 8 GHz X band 8 to 12 GHz

Ku band 12 to 18 GHz

Figure 8–8 Communications satellite in geosynchronous orbit.

gtu=55 dBi

Lu gru=20 dBi 5 0 0 0 gamp k

m 36,000 km

gtd=16 dBi

grd=51 dBi

10 Figure 8–9 Simplified block diagram of a communications satellite transponder.

Figure 8–10 64-GHz satellite transponder frequency plan for the downlink channels. (For the uplink frequency plan, add 2225 MHz to the numbers given above.)

11 Link Budget and Wireless Link Example

EELE445 Lecture 40

Satellite Relay The “Bent Pipe”

12 Figure 8–8 Communications satellite in geosynchronous orbit.

Figure 8–8 Communications satellite in geosynchronous orbit.

gtu=55 dBi

Lu gru=20 dBi 5 0 0 0 gamp k

m 36,000 km

gtd=16 dBi

grd=51 dBi

13 Earth Bulge Earth Bulge When planning for paths longer than seven miles, the curvature of the earth might become a factor in path planning and require that the antenna be located higher off the ground. The additional antenna height needed can be calculated using the following formula:

D 2 where H = H = Height of earth bulge (in feet) 8 D = Distance between antennas (in miles)

= =1,201,250 feet !

14 A full Link Budget will also include a noise analysis

15 Additional Link Path Loss Factors: Fading and Atmospheric Absorption

Additional Link Path Loss Factors: Fading and Atmospheric Absorption

16 Additional Link Path Loss Factors: Antenna Pointing Error

Additional Link Path Loss Factors: Rainfall

17 Additional Link Path Loss Factor: Elevation Angle

Plane Earth Loss-

•Free space path loss only applies when the wave does not interact with the ground. •Examples: mountain top links and satellite links •The loss is higher with ground interaction or when the wave passes through a material.

EELE445-13

18 Plane Earth Loss- LOS

• When the wave interacts with the ground or some other obstruction we no longer have free space propagation

Plane Earth Loss with line of site-LOS

19 Fresnel Diffraction ( non LOS)

• Non-LOS communication involves an additional loss due to Diffraction

Earth Bulge with Fresnel Diffraction http://www.cisco.com/univercd/cc/td/doc/product/wireless/bbfw/ptop/p2pspg02/spg02ch2.htm#xtocid19

Minimum Antenna Height The minimum antenna height at each end of the link for paths longer than seven miles (for smooth terrain without obstructions) is the height of the First Fresnel Zone plus the additional height required to clear the earth bulge. The formula would be: D D 2 H = 43.3 + 4F 8 where H = Height of the antenna (in feet) D = Distance between antennas (in miles) F = Frequency in GHz

20 Tower Height Line of Sight Height of Tower to Tower Height Required Over Tallest Distance Between Avoid Flat Earth Obstacle In Line-of-Sight to Provide 60% Antenna Towers Curvature Fresnel Zone Clearance 2.4GHz 802.11b/g 5.8 GHz 802.11a (Fresnel Zone Radius = (Fresnel Zone Radius = 39 Feet) 25 Feet) 8 Miles 10 feet 33 25 10 Miles 15 feet 38 30 12 Miles 20 feet 43 35 14 Miles 25 feet 48 40 16 Miles 30 feet 53 45 18 Miles 40 feet 63 55 20 Miles 50 feet 73 65 22 Miles 60 feet 83 75 24 Miles 70 feet 93 85 26 Miles 80 feet 103 95 28 Miles 100 feet 123 115 32 Miles 125 feet 148 140

Path Loss: Free Space vs Ground effects

21 Plane Earth Loss

multiple signals arrive at the receive antenna

Plane Earth Loss

22 Plane Earth Loss

Plane Earth Loss

23 Plane Earth Loss - PEL Plane earth loss includes ground reflections

2 2 Pr æ l 2hmhb ö hmhb 2p = Lpel » ç k ÷ » 4 k = Pt è 4pr r ø r l

Plainearthloss,dB : LpeldB = 40log r - 20log hm - 20log hb

Plane Earth Loss: Example

24 Empirical Path Loss

d g(d ) = d -n1 (1 + )-n2 d b

See text eq 8-47

Mobile Signal The received power of a mobile wireless signal is not constant

25 Lecture 39 BER- Bit Error Rate

EELE445

Figure 7–2 Error probability for binary signaling.

26 Figure 7–4 Receiver for baseband binary signaling.

Figure 7–4 Receiver for baseband binary signaling.

27 Figure 6–17 Integrate-and-dump realization of a matched filter.

Figure 6–17 Integrate-and-dump realization of a matched filter.

28 The best we can do: Bit Error Rate for Polar baseband, BPSK, QPSK :

Pe = Q( 2(Eb / N 0 )) The Best we can do!

for unipolar baseband, OOK, coherent FSK :

Pe = Q( Eb / N 0 )

2 Eb = ATb = v(t) dt the energy per bit òT b

N 0 is the noise density watts / Hz

Figure 7–5 Pe for matched-filter reception of several binary signaling schemes.

29 Figure B–7 The function Q(z) and an overbound,

for practicalBER numbers :

1 2 Q(z) » e-z / 2 2p z

Q, ERF, and ERFC functions

30 Q, ERF, and ERFC functions

Q, ERF, and ERFC functions

31 Q, ERF, and ERFC functions

Q, ERF, and ERFC functions

32 Figure 7–13 Matched-filter detection of QPSK.