美国麻省理工大学：《Communication Systems Engineering（通讯系统工程）》Lecture 10: Link Budget Analysis and Design

Lecture 10: Link Budget Analysis and Design Eytan Modiano AA Dept

Lecture 10: Link Budget Analysis and Design Eytan Modiano AA Dept. Eytan Modiano Slide 1

Signal attenuation TX Channel RX R n The signal suffers an attenuation loss l Received power PR= PT/L Received snr=E,/No, Eb=Pr/Rb Antennas are used to compensate for attenuation loss Capture as much of the signal as possible L=(4d T Rx→PR=P1G1GL T R L= free space loss, d-distance between Tx and rx n= signal wavelength

Signal attenuation Channel PT + Rx n(t) PR L • The signal suffers an attenuation loss L – Received power PR = PT/L – Received SNR = Eb/N0, Eb = PR/Rb • Antennas are used to compensate for attenuation loss – Capture as much of the signal as possible GT GR Tx PT L = (4πd/λ)2 Rx PR = PT GTGR/L L = free space loss, d = distance between Tx and Rx Eytan Modiano Slide 2 λ = signal wavelength Tx

Antenna Gains R ARI/2 r is the effective area of the antenna For Parabolic antenna Ar=Tn D2/4 m=illumination efficiency factor, 0.5<n<0.6 d= dish diameter GR n(D/n)2 PR=PTGTD2n/(4d)

Antenna Gains GR = AR4π/λ2 AR is the effective area of the antenna For Parabolic antenna AR = πηD2/4 η = illumination efficiency factor, 0.5 GR = η(πD/λ)2 => PR = PTGTD2η/(4d)2 Eytan Modiano Slide 3

Antenna beamwidth Beamwidth is a measure of the directivity of the antenna Smaller beamwidth concentrated power along a smaller area Free space loss assumes that power is radiated in all directions An antenna with a smaller beamwidth concentrates the power hence yields a gain For parabolic antenna, 0: -70ND Gain(G)s proportional to(e8)-2 Hence a doubling of the diameter D increases gain by a factor of 4

θ λ θ Antenna Beamwidth θB • Beamwidth is a measure of the directivity of the antenna – Smaller beamwidth concentrated power along a smaller area • Free space loss assumes that power is radiated in all directions • An antenna with a smaller beamwidth concentrates the power hence yields a gain – For parabolic antenna, θB ~ 70λ/D – Gain (GT) s proportional to (θB )-2 – Hence a doubling of the diameter D increases gain by a factor of 4 Eytan Modiano Slide 4

Example(GEO Satellite d=36,000km=36,000000 meters f=4GhZ→>=0.075m P1r=100w,G=18dB Receiver antenna is parabolic with d=3 meters A)What is PR? B)Suppose(E/Norea=10 dB, what is the achievable data rate Rb?

Example (GEO Satellite) d = 36,000 km = 36,000,000 meters fc = 4 Ghz => λ = 0.075m P T = 100w, G T = 18 dB Receiver antenna is parabolic with D = 3 meters A) What is PR? B) Suppose ( E b/N 0)req = 10 dB, what is the achievable data rate R b? Eytan Modiano Slide 5

Repeaters P T2 Tx 6RX PR A repeater simply amplifies the signal to make up for attenuation R1=P/L, Pt?= PRA, Pe R1=PNP2=PN1AML+PN… Let a=L=> PRK=P/L, PnK=KPN PRK/PNK=PTLKPN=1/K(PR1/PN1 Received snr is reduced by a factor of K (E/Nok=l/K(Eb/N

Repeaters Tx PT2 + A PT3 + A + Rx PN PN PN • A repeater simply amplifies the signal to make up for attenuation PR1 = PT/L, PT2 = PR1A, PR2 = PT2/L, … PN1 = PN, PN2 = PN1A/L + PN , ….. Let A = L => PRK = PT/L, PNK = KPN PRK/PNK = PT/LKPN = 1/K (PR1/PN1) Received SNR is reduced by a factor of K Eytan Modiano (Eb/N0)k = 1/K (Eb/N0) Slide 6

Regenerators TX A regenerator demodulates detects and retransmits the signal Each segment has the same PR/PN and the same received Eb/No b= probability of error on a segment(independent between segments Pbloverall)=1-P(no error)=1-(1-Pb)-KPb Now compare repeater to regenerator(e.g. PAM) P,=O2E,/No For repeater: P(overall)=Q(2E,/KNO P(oera)=K(√2EB/N) KO√2E/M)<Q√2EB/KN0)

Regenerators Tx PT ... PN + PN + Rx Tx PT Rx Tx PT • A regenerator demodulates, detects and retransmits the signal – Each segment has the same PR/PN and the same received Eb/N0 – Pb = probability of error on a segment (independent between segments) – Pb (overall) = 1 - P(no error) = 1 - (1-Pb)K ~ KPb • Now compare repeater to regenerator (e.g. PAM) Pb = Q( 2Eb N0 / ) For repeater : Pb (overall) = Q( 2Eb / KN0 ) For regenerator : Pb (overall) = KQ( 2Eb / N0 ) Eytan Modiano KQ( 2Eb N0 / ) < Q( 2Eb / KN0 ) Slide 7

Satellite example Uplink received (Eb/no)u= downlink received (Eb/no)d=10dB PAM modulation P=O(2EB/NO) Repeater: Received(E No)uld=1/2(Eb/No)u= 10 dB -3dB= 7dB => Pb= 5x10-4 from table 7, 55 or 7, 58 Regenerator: Pb(up)=Pb(down)=3X10 (from table with(Eb/No )d=10dB) Hence Pb(up/down)-2 Pb(up)-6X3x10-5 Two orders of magnitude difference between repeaters and regeneration Greater difference with more segments

Satellite example • Uplink received (Eb/N0 )u = downlink received (Eb/N0 )d = 10dB • PAM modulation Pb = Q( 2Eb N0 / ) • Repeater: Received (Eb/N0)u/d = 1/2 (Eb/N0)u = 10 dB - 3dB = 7dB – => Pb = 5x10-4 from table 7.55 or 7.58 • Regenerator: Pb(up) = Pb(down) = 3x10-6 – (from table with (Eb/N0 )d = 10dB) – Hence Pb (up/down) ~ 2 Pb(up) ~ 6x3x10-6 • Two orders of magnitude difference between repeaters and regeneration – Greater difference with more segments Eytan Modiano Slide 8