Communication Systems Engineering Episode 1 Part 8 pdf

Channel

PT

Rx +

n(t)

PR

L

– Received power P R = P T /L

– Received SNR = E b /N 0 , E b = P R /R b

– Capture as much of the signal as possible

Tx

Rx PR = PT GTGR/L

GR = AR4 π / λ2

AR is the effective area of the antenna For Parabolic antenna AR = πη D2/4

η = illumination efficiency factor , 0.5 < η < 0.6

D = dish diameter

=> GR = η ( π D/ λ )2

=> PR = PTGTD2η /(4d)2

Eytan Modiano

θθθ λλλ

θθθ

θB

– Smaller beamwidth concentrated power along a smaller area

hence yields a gain – For parabolic antenna, θB ~ 70λ/D

– Gain (G T ) s proportional to (θB ) -2

– Hence a doubling of the diameter D increases gain by a factor of 4

d = 36,000 km = 36,000,000 meters

fc = 4 Ghz => λ = 0.075m

PT = 100w, GT = 18 dB Receiver antenna is parabolic with D = 3 meters

A) What is PR?

Eytan Modiano

Repeaters

PT3

P R1 = P T /L, P T2 = P R1 A, P R2 = P T2 /L, …

P N1 = P N , P N2 = P N1 A/L + P N , …

Let A = L => P RK = P T /L, P NK = KP N

P RK /P NK = P T /LKP N = 1/K (P R1 /P N1 )

Regenerators

PN

+

PN

– Each segment has the same P R /P N and the same received E b /N 0

– P b = probability of error on a segment (independent between segments)

– P b (overall) = 1 - P(no error) = 1 - (1-P b ) K ~ KP b

P b = Q( 2E b / N0 )

For repeater : P b (overall) = Q( 2E b / KN0 )

For regenerator : P b (overall) = KQ( 2E b / N0 )

Eytan Modiano KQ( 2E / N ) < Q( 2E / KN )

Satellite example

– => Pb = 5x10 -4 from table 7.55 or 7.58

– (from table with (E b /N 0 ) d = 10dB)

– Hence P b (up/down) ~ 2 P b (up) ~ 6x3x10 -6

regeneration