Satellite Communications

Transcription

1 Signal processing elements Department of Electrical and Computer Science University of Liège Academic year Signal processing elements Example of an analog communication system Main components: 1 signal 2 transmitting channel (cable, radio) 3 electronics (amplifiers, filters, modems, etc) and a lot of engineering!

2 Signal processing elements Outline 1 Signal processing elements Signal information! Source coding (dealing with the information content) Modulation Multiplexing 2 Introduction to radio communications Radiowave propagation Examples of antennas 3 Noise Link budget Outline Signal processing elements Signal information! Source coding (dealing with the information content) Modulation Multiplexing 1 Signal processing elements Signal information! Source coding (dealing with the information content) Modulation Multiplexing 2 Introduction to radio communications Radiowave propagation Examples of antennas 3 Noise Link budget

3 Signal processing elements Signal information! Source coding (dealing with the information content) Modulation Multiplexing Main types of satellite different types of information Astronomical satellites: used for the observation of distant planets, galaxies, and other outer space objects. Navigational satellites [GPS, Galileo]: they use radio time signals transmitted to enable mobile receivers on the ground to determine their exact location (positioning). Earth observation satellites: used for environmental monitoring, meteorology, map making. Miniaturized satellites: satellites of unusually low masses and small sizes. For example, for educational purposes (OUFTI-1). Communications satellites: stationed in space for the purpose of telecommunications. Modern communications satellites typically use geosynchronous orbits, or Low Earth orbits (LEO). Example: constellation of GPS satellites 6 planes with a 55 angle with the equator, spaced by 60 and with 4 satellites per plane (24 satellites in total) Located on high orbits (but sub-geostationary)/revolution in 12 hours Transmitting power of 20 to 50[W]

4 Galileo I Positioning system promoted by the European commission and the ESA. Galileo GPS Orbital period 20 hours 15 hours 10 hours Geostationary Earth Orbit COMPASS MEO satellites GLONASS 5 hours Radius of orbit Iridium 40 Mm 30 Mm 20 Mm 10 Mm Hubble Height above sea level 10 Mm 20 Mm 30 Mm miles miles mph ISS km/h km/h miles miles mph km/h Orbital speed Galileo II Orbital altitude: 23,222 [km] (MEO - Medium Earth Orbit) 3 orbital planes, 56 inclination, separated by 120 longitude Constellation of 30 satellites (with working 24 [3x8] satellites and 6 [3x2] spares)

5 Deployment of Galileo First launches: 2 satellites in October 2011, 2 satellites in October These were test satellites. First Full Operational Capability satellite launched in November August 2014, two more satellites (but... injected on a wrong orbit). November 2017: 15 satellites fully operational, 3 for testing or not available. Types of data streams Types of data Control data Payload Measurements Remote sensing data Localization data Broadcasting Digital data Characteristics Must be very reliable Unicast communication for mobile ground station Accurate signals with constant monitoring High volume of downstream data Accurate time reference (synchronization) Digital television channels Voice + data (Internet) for remote areas Because the purposes of data sent are different, the mechanisms to transmit the data are designed according to the constraints. Simplified typography of data streams: control data payload (+ some unavoidable overhead)

6 Signal processing elements Main issues related to signals Signal information! Source coding (dealing with the information content) Modulation Multiplexing 1 Signal source handling (preparation of the signal, at the source, in the transmitter): filtering (remove what is useless for communications) analog digital (digitization) remove the redundancy in the signal: compression 2 Signal over the channel: signal shaping to make it suitable for transmission (coding, modulation, multiplexing, etc) signal power versus the noise signal (protect the signal against noise effects) Digitization I Signal processing elements Signal information! Source coding (dealing with the information content) Modulation Multiplexing

7 Digitization II Signal processing elements Signal information! Source coding (dealing with the information content) Modulation Multiplexing Digitization = from analog to digital analog digital g(t) samples g[it ], with i = 0, 1, 2,... and T = a time period signal over time sampling rate series of samples each sample is coded with n bits (quantization) in the end, we have a bitsream: Digitization III Signal processing elements Signal information! Source coding (dealing with the information content) Modulation Multiplexing Digitization in numbers: 1 f s : sampling frequency Let W be the highest frequency of the signal to be converted theoretical lower bound: f s > 2W practical rule (Nyquist criterion): f s > 2.2W 2 n: number of bits par sample (quantization) 3 bit rate = f s n signal band W f s n bit rate units Hz Hz sample/s b/sa. b/s audio [300 Hz, 3400 Hz 8000 sa./s 8 64 kb/s (telephone) 3400 Hz] audio (CD) [0 Hz, 20 khz] 20 khz 44.1 ksa./s kb/s

8 Signal processing elements Signal information! Source coding (dealing with the information content) Modulation Multiplexing Analog and digital signals: don t confuse information and its representation! Analog information signal Digital information signal Analog representation Analog representation Characterization of signals over the channel Analog signal bandwidth [Hz] Signal to Noise Ratio (S/N or SNR) Reasons for going digital: Digital signal bit rate [bit/s] Bit Error Rate (BER) bandwidth of the underlying channel [Hz] possibility to regenerate a digital signal better bandwidth usage Example (better bandwidth usage: from analog to digital television) analog PAL television channel: bandwidth of 8[MHz] digital television, PAL quality 5[Mb/s] With a 64-QAM modulation, whose spectral efficiency is 6 b/s per Hz. A bandwidth of 8[MHz] allows for 48[Mb/s]. Conclusion: thanks to digitization, there is room for 10 digital television channels instead of 1 analog television channel.

9 Software organization of a transmitter/receiver: the OSI reference model Consequence: encapsulation overhead OSI reference model vs Internet model (+ some corresponding Internet protocols)

10 Elements of a communication system I Figure: Block diagram of a communication channel for a single signal. Elements of a communication system II

11 Outline Signal processing elements Signal information! Source coding (dealing with the information content) Modulation Multiplexing 1 Signal processing elements Signal information! Source coding (dealing with the information content) Modulation Multiplexing 2 Introduction to radio communications Radiowave propagation Examples of antennas 3 Noise Link budget Signal processing elements Signal information! Source coding (dealing with the information content) Modulation Multiplexing Information theory and channel capacity: there is maximum bit rate (the sky is not the limit...)! I Theorem (Shannon-Hartley) The channel capacity C (conditions for the Bit Error Rate BER 0) is given by ( C [b/s] = W log S ) N (1) where W is the channel bandwidth in Hz S N the Signal to Noise ratio (in watts/watts, not in db).

12 Consequences of the capacity theorem Let R b be the bit rate [b/s] and E b the energy per bit [Joule/b], we have S = E b R b [Watt], and N = N 0 W (where N 0 is the noise spectral power density; N 0 = k B T as shown later). Therefore: ( C = W log E ) b R b (2) N 0 W The ratio R b W is defined as the spectral efficiency given in [b/s] per [Hz]. Consequences: the capacity is bounded (there is a maximal limit), related to 1 the E b N 0 ratio. We only have control over E b. 2 the spectral efficiency. for a fixed E b N 0 ratio and spectral efficiency, C can only be increased by increasing the bandwidth. But the bandwidth is a scarce resource. Impact of errors on the transmission: bit/packet error rate Assume a packet of size N and let P e be the probability error on one bit ( Bit Error Rate, BER). The probability for the packet to be correct is Therefore the packet error rate is For large packets and small P e, this becomes Example (1 P e ) N. (3) P P = 1 (1 P e ) N. (4) P P 1 (1 NP e ) = N P e. (5) With N = 10 5 bits and a bit error rate of P e = 10 7, P P We thus need to lower P e error detection/correction mechanisms

13 Forward Error Coding A simplistic example of Forward Error Coding (FEC) consists to transmit each data bit 3 times, known as a (3,1) repetition code. Received bits Interpreted as (error free) (error free) Other forward error codes Hamming code Reed Solomon code Turbo code,...

14 Outline Signal processing elements Signal information! Source coding (dealing with the information content) Modulation Multiplexing 1 Signal processing elements Signal information! Source coding (dealing with the information content) Modulation Multiplexing 2 Introduction to radio communications Radiowave propagation Examples of antennas 3 Noise Link budget Signal processing elements Modulation: principles Signal information! Source coding (dealing with the information content) Modulation Multiplexing Principle Modulation is all about using of a carrier cosine at frequency f c for transmitting information. The carrier is A c cos(2πf c t) Frequency modulation [FM] s(t) = A(t)cos(2πf (t)t + φ(t)) Amplitude Phase Amplitude modulation [AM] Phase modulation [PM]

15 Consequences of modulation frequency band is shifted towards the carrier frequency ( f c ) bandwidth modification, compared to that of the modulating signal m(t) Effects of Amplitude Modulation on the spectrum ( s(t) = A c m(t)cos(2πf c t) ) M(f ) W 0 +W (a) S(f ) f USB f c W f c LSB f c + W 0 (b) LSB f c W f c USB f f c + W Demodulation of an AM modulated signal: principles Received signal: s(t) = m(t)cos(2πf c t). Task: recover m(t). Principles of a synchronous demodulation. At the receiver: 1 acquire a local, synchronous, copy of the carrier f c build a local copy of cos(2πf c t) 2 multiply s(t) by cos(2πf c t): [cosa cosb = 1 2 cos(a b) cos(a + b)] s(t)cos(2πf c t) = m(t)cos 2 (2πf c t) (6) 3 filter out the 2f c components 1 2 m(t) = m(t)[ cos(2π(2f c)t)] (7) = 1 2 m(t) m(t)cos(2π(2f c)t)] (8)

16 Demodulation of an AM modulated signal: interpretation in the spectral domain AM spectrum Spectrum of the carrier A c /2 A c /2 1/2 1/2 Mixer f c f f c f f f c c Spectrum of the mixed signal A c /2 A c /4 A c /4 2f c f W c W f c 2f c f Signal spectrum A c /2 W W f Basic digital modulation (coding) techniques I

17 Basic digital modulation (coding) techniques II Quadrature modulation It is possible to use both a cosine and a sine: s(t) = m 1 (t)cos(2πf c t) m 2 (t)sin(2πf c t) (9) m 1 (t)cos(2πf c t) cos(2πf c )t m 1 (t) m 2 (t) π 2 + s(t) sin(2πf c )t m 2 (t)sin(2πf c t)

18 Quadrature demodulation: principles s(t) = m 1 (t)cos(2πf c t) + m 2 (t)sin(2πf c t) is the modulated signal. We want to recover m 1 (t) and m 2 (t) Step 1: multiply by cos(2πf c t) [remember that cosa cosb = 1 2 cos(a b) cos(a + b) and that cosa sina = 1 2 sin(2a)] s(t) cos(2πf c t) = m 1 (t)cos 2 (2πf c t) + m 2 (t)sin(2πf c t)cos(2πf c t) = 1 2 m 1(t) m 1(t)cos(2π(2f c )t) m 2(t)sin(2π(2f c )t) Step 2: filter to keep the baseband signal 1 2 m 1(t) Steps 3 and 4: multiply by sin(2πf c t) and low-pass filter to get m 2 (t) Purposes of the quadrature modulation There are 2 possible uses/advantages for a quadrature modulation: 1 [Bandwidth savings by a factor of 2] Send two signals in the same bandwidth s(t) = m 1 (t)cos(2πf c t) + m 2 (t)sin(2πf c t) (10) Both m 1 (t)cos(2πf c t) and m 2 (t)sin(2πf c t) have exactly the same bandwidth, that is [f c W, f c + W ] where W denotes the original bandwidth of m 1 (t) and m 2 (t). 2 [Easier demodulation] A coherent demodulation of m(t)cos(2πf c t + φ c ) requires the perfect knowledge of f c and φ c at the receiver. However, it is sometimes difficult to synchronize the receiver. Therefore, s(t) = m(t)cos(2πf c t + φ c ) + m(t)sin(2πf c t + φ c ) (11) is sometimes used. At the receiver, m(t), the signal of interest can be obtained by m 2 (t)cos 2 (.) + m 2 (t)sin 2 (.) = m(t).

19 Outline Signal processing elements Signal information! Source coding (dealing with the information content) Modulation Multiplexing 1 Signal processing elements Signal information! Source coding (dealing with the information content) Modulation Multiplexing 2 Introduction to radio communications Radiowave propagation Examples of antennas 3 Noise Link budget Signal processing elements Multiplexing: combining several sources Mechanisms to share resources between users: Frequency Division Multiplexing (FDM) Time Division Multiplexing (TDM) Code Division Multiplexing (CDM) Space Division Multiplexing + combinations! Signal information! Source coding (dealing with the information content) Modulation Multiplexing

20 Frequency Division Multiplexing (FDM) X 1 (f ) f X 2 (f ) f 1 f 1 f 1 f f X 3 (f ) f 2 f 2 f 2 f f f 3 f 3 f 3 f Multiplexed signal Demultiplexing f 3 f 2 f 1 f 1 f 2 f 3 f Multiplexed signal f 3 f 2 f 1 f 1 f 2 f 3 f f 1 f 2 f 3 f 1 f 2 f 3 X 1 (f ) X 2 (f ) X 3 (f ) f f f

21 Time Division Multiplexing (TDM) Spread spectrum for Code Division Multiplexing Principle of spread spectrum: multiply a digital signal with a faster pseudo-random sequence (spreading step) Binary data waveform T b (one bit) t F B 0 B f Spreading sequence t F NB 0 NB f Spread sequence T c t F (N + 1)B 0 f (N + 1)B At the receiver, the same, synchronized, pseudo-random sequence is generated and used to despread the signal (despreading step)

22 Code Division Multiple Access Each user is given its own code (multiple codes can be used simultaneously) Code Physical channel Frequency Time User 1 User 2 Free channel Summary

23 Outline Signal processing elements Introduction to radio communications Radiowave propagation Examples of antennas 1 Signal processing elements Signal information! Source coding (dealing with the information content) Modulation Multiplexing 2 Introduction to radio communications Radiowave propagation Examples of antennas 3 Noise Link budget Signal processing elements Satellite link definition Introduction to radio communications Radiowave propagation Examples of antennas

24 Frequency bands But it is also common to designate the carrier frequency and bandwidth directly. Regulatory bodies International Telecommunications Union (ITU): Radio-communications Sector (ITU-R) service regions organizes WARC (World Administrative Radio Conference) - worldwide allocation of frequencies Regional body: European Conference of Postal and Telecommunications Administrations (CEPT)

25 Excerpt of the allocation plan/radio spectrum (by the ITU) Frequency allocations [2] Radio-communications service Typical up/down link Terminology Fixed satellite service (FSS) 6/4[GHz] C band 8/7[GHz] X band 14/12.1[GHz] Ku band 30/20[GHz] Ka band 50/40[GHz] V band Mobile satellite service (MSS) 1.6/1.5[GHz] L band 30/20[GHz] Ka band Broadcasting satellite service (BSS) 2/2.2[GHz] S band 12[GHz] Ku band 2.6/2.5[GHz] S band Note that frequencies for down links are usually lower than for up links: this is because the power loss increases with the frequency. The use of higher frequencies allows larger bandwidths, better tracking capability and minimizes ionospheric effects. But it also requires greater pointing accuracy

26 Frequency allocations [2] Radio-communications service Typical up/down link Terminology Fixed satellite service (FSS) 6/4[GHz] C band 8/7[GHz] X band 14/12.1[GHz] Ku band 30/20[GHz] Ka band 50/40[GHz] V band Mobile satellite service (MSS) 1.6/1.5[GHz] L band 30/20[GHz] Ka band Broadcasting satellite service (BSS) 2/2.2[GHz] S band 12[GHz] Ku band 2.6/2.5[GHz] S band Orbits Note that frequencies for down links are usually lower than for up links: this is because the power loss increases with the frequency. The use of higher frequencies allows larger bandwidths, better tracking capability and minimizes ionospheric effects. But it also requires greater pointing accuracy considerations: distance between user and satellite. delay (increases with the distance) attenuation of the signal (increases with the distance) relative position of the user/satellite pair

27 Signal processing elements Introduction to radio communications Radiowave propagation Examples of antennas Outline 1 Signal processing elements Signal information! Source coding (dealing with the information content) Modulation Multiplexing 2 Introduction to radio communications Radiowave propagation Examples of antennas 3 Noise Link budget Signal processing elements Introduction to radio communications Radiowave propagation Examples of antennas Radiowave propagation d P R P T Important issues: channel characteristics attenuation (distance) atmospheric effects wave polarization rain mitigation antenna design power budget (related to the Signal to Noise ratio)

28 Two main types of radiation pattern Reciprocity Theorem (Reciprocity for antennas) The electrical characteristics of an antenna such as gain, radiation pattern, impedance, bandwidth, resonant frequency and polarization, are the same whether the antenna is transmitting (T ) or receiving (R). Theorem (Strong reciprocity) If a voltage is applied to an antenna A and the current is measured at another antenna B, then an equal current (in both amplitude and phase) will appear at A if the same voltage is applied to B.

29 Inverse square law of radiation The power flux density (or power density) S, over the surface of a sphere of radius r a from the point P, is given by (Poynting vector) S a = P t 4πr 2 a [ W m 2 ] Effective Isotropic Radiated Power [EIRP] (12) Definition (EIRP) The Effective Isotropic Radiated Power (EIRP) of a transmitter is the power that the transmitter appears to have if the transmitter were an isotropic radiator (if the antenna radiated equally in all directions). From the receiver s point of view, where: P t = P T G T (13) P t is the power of a imaginary isotropic antenna. P T is the transmitter power and G T is its gain (in that direction). If the cable losses can be neglected, then EIRP = P T G T.

30 Effective area Definition (Effective area) The effective area of an antenna is the ratio of the available power to the power flux density (Poynting vector): A eff,r = P R S eff,r (14) Theorem The effective area of an antenna is related to its gain by the following formula λ 2 A eff,r = G R (15) 4π By reciprocity, all these results are equally valid for a transmitting antenna T. Friis s relationship d P R We have P T P R = S eff,r A eff,r ( PT G T = 4πd 2 ) A eff,r = ( PT G T 4πd 2 ) ( λ 2 ) 4π ( ) λ 2 G R = P T G T G R 4πd Free space path loss L FS = ( λ 4πd ) 2 ɛ = P T P R = Friis s relationship ( 4πd λ ) 2 1 G T G R

31 Decibel as a common power unit x 10log 10 (x)[db] (16) P [dbm] = 10log 10 P [mw] 1[mW] (17) x [W] 10log 10 (x)[dbw] 1[W] 0[dBW] 2[W] 3[dBW] 0,5[W] 3[dBW] 5[W] 7[dBW] 10 n [W] 10 n [dbw] Orders of magnitude in satellite communications: transmitter power: 100[W] 20[dB] received power: 100[pW] = [W] 100[dB] Free space losses

32 Are high frequencies less adequate? In [db], Friis s relationship becomes ɛ = logf [MHz] + 20logd [km] G T [db] G R [db] The attenuation (loss) increases with f. So?! Remember that So, A eff = G λ2 4π (18) ( ) 4πd 2 ( ) 1 4πd 2 λ 2 λ 2 ɛ = = (19) λ G T G R λ 4πA T 4πA R = λ2 d 2 = c2 d 2 A T A R f 2 (20) A T A R It all depends on the antenna gains! Are high frequencies less adequate? In [db], Friis s relationship becomes ɛ = logf [MHz] + 20logd [km] G T [db] G R [db] The attenuation (loss) increases with f. So?! Remember that So, A eff = G λ2 4π (18) ( ) 4πd 2 ( ) 1 4πd 2 λ 2 λ 2 ɛ = = (19) λ G T G R λ 4πA T 4πA R = λ2 d 2 = c2 d 2 A T A R f 2 (20) A T A R It all depends on the antenna gains!

33 Practical case: VSAT in the Ku-band [1] Antenna gains: 48.93[dB] The free space path loss is, in [db], L FS = logf [MHz] + 20logd [km] = 205.1[dB] The received power is, in [db], P R = P T + G T + G R L FS (21) = = 97.24[dB] (22) In [W], the received power is P R = = [W] = 189[pW] (23) Signal processing elements Introduction to radio communications Radiowave propagation Examples of antennas Outline 1 Signal processing elements Signal information! Source coding (dealing with the information content) Modulation Multiplexing 2 Introduction to radio communications Radiowave propagation Examples of antennas 3 Noise Link budget

34 Signal processing elements Terrestrial antennas Introduction to radio communications Radiowave propagation Examples of antennas Beamwidth and aperture

35 Ground station antenna Parabolic (dish) antenna Radiation pattern

36 Deployable antenna Horn antenna and waveguide feed

37 Yagi antenna Patch array antenna

38 Phased array antenna Radiowave propagation mechanisms + Doppler effect

39 Earth atmosphere absorption Expressed in terms of the wavelength:λ[m] = c f = [m/s] f [Hz] Attenuation due to atmospheric gases Zenith attenuation due to atmospheric gases (source: ITU-R P.676-6) [O 2 and H 2 0 are the main contributors]

40 Rain attenuation Total path rain attenuation as a function of frequency and elevation angle. Cloud attenuation Location: Washington, DC, Link Availability: 99% Cloud attenuation as a function of frequency, for elevation angles from 5 to 30

41 Total attenuation The ITU recommends that all tropospheric contributions to signal attenuation are combined as follows: A T (p) = A G + (A R (p) + A c (p)) 2 + A s (p) (24) where: A T (p) is the total attenuation for a given probability A G (p) is the attenuation due to water vapor and oxygen A R (p) is the attenuation due to rain A c (p) is the attenuation due to clouds A s (p) is the attenuation due to scintillation (rapid fluctuations attributed to irregularities in the tropospheric refractive index) Service Level Agreement (SLA) Customers ask for a guaranteed level of quality: this leads to a Service Level Agreement (SLA) with the satellite operator. In engineering terms: introduction of power margins!

42 Signal processing elements Noise Link budget Outline 1 Signal processing elements Signal information! Source coding (dealing with the information content) Modulation Multiplexing 2 Introduction to radio communications Radiowave propagation Examples of antennas 3 Noise Link budget Signal processing elements Noise Link budget Noise Theorem (Nyquist s formula for a one-port noise generator) The available power from a thermal source in a bandwidth of W is where P N = k B T W (25) k B = 1, [J/K] is the constant of Boltzmann ( 198[dBm/K/Hz] = 228.6[dBW/K/Hz]), T is the equivalent noise temperature of the noise source W is the bandwidth of the system Thermal noise is one the main sources of noise in a satellite put electronics in the cold zone of a satellite

43 Noise in two-port circuits Definitions Noise Factor (F ): [provided by the manufacturer] F = ( SN ) in ( SN ) out > 1 (26) Noise Figure (NF): NF=10 log 10 F (27) Effective noise temperature T e (T 0 = 290[K]): Noise factor of a two-port cascade T e = T 0 (F 1) (28) (F 01 1)γ an1 (f ) F 01 (F 02 1)γ an1 (f ) F 02 γ an1 (f ) G 1 G 1 F 01 γ an1 (f ) G 2 Figure: Cascading two-port elements. For a two-port network with n stages, F 0 = F 01 + F 02 1 G 1 + F 03 1 G 1 G 2 + = F 01 + n i=2 F 0i 1 i 1 j=1 G j (29) Likewise, T e = T e1 + T e2 G 1 + T e3 G 1 G 2 + = T e1 + n i=2 T ei i 1 j=1 G j (30)

44 Receiver front end I Figure: Block diagram of a typical receiver. Receiver front end II Rule of thumb: highest gain (G 1 ) and best noise figure (F 01 ) first. Then F 0 = F 01 + F 02 1 G 1 + F 03 1 G 1 G 2 + F 01 + F 02 1 G 1 (31) T e = T e1 + T e2 G 1 + T e3 G 1 G 2 + T e1 + T e2 G 1 (32)

45 Example of the calculation of a noise budget [1] Low Noise Amplifier: T LA = 290 ( ) = 438[K] Line. For a passive two-port circuit, the noise factor is equal to the attenuation: F 0 = A. T Line = 290 ( ) = 289[K], G Line = 1 2 The effective noise temperature, including the antenna noise, is T e = t A + T e1 + T e2 G 1 + T e3 G 1 G 2 + (33) = }{{} = 509.3[K] (34) Typical values for the increase in antenna temperature due to rain [1]

46 Signal processing elements Noise Link budget Outline 1 Signal processing elements Signal information! Source coding (dealing with the information content) Modulation Multiplexing 2 Introduction to radio communications Radiowave propagation Examples of antennas 3 Noise Link budget Signal processing elements Noise Link budget Example of parameter values for a communication satellite [1] Parameter uplink downlink Frequency 14.1[GHz] 12.1[GHz] Bandwidth 30[MHz] 30[MHz] Transmitter power [W] [W] Transmitter antenna gain 54[dBi] 36.9[dBi] Receiver antenna gain 37.9[dBi] 52.6[dBi] Receiver noise figure 8[dB] 3[dB] Receiver antenna temperature 290[K] 50[K] Free space path loss (30 elevation) 207.2[dB] 205.8[dB]

47 Clear sky down link performance [2] Signal processing elements For further reading Noise Link budget L. Ippolito. Systems : Atmospheric Effects, Satellite Link Design and System Performance. Wiley, G. Maral, M. Bousquet. Systems: Systems, Techniques and Technology. Wiley, J. Gibsons. The Communications Handbook. CRC Press, Wikipedia.