Satellite Communications

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Satellite Communications Tutorial J P Silver E-mail: [email protected]

1 ABSTRACT This tutorials discusses the key areas of satellite communications, discussing the various elements of a satellite communications system eg antennas, path loss etc. The communication system elements can then be connected together and analysed to determine a link budget.

2 FREQUENCIES FOR MICROWAVE SATELLITE COMMUNICATIONS The frequencies used for microwave satellite communications are determined by (i) the absorption of the atmosphere as a function of frequency (ii) the antenna size needed to produce a beam with the required angular spread (iii) international agreements/regulations

2.1 ATMOSPHERIC ABSORPTION Figure 1 & Figure 2 indicates the average atmospheric absorption as a function of frequency at different altitudes above sea-level and the effects of rain and fog. Note that the figures cover different frequency ranges. Note 1. The first graph shows resonant absorption peaks due to different molecules in the atmosphere at particular frequencies. Usually these frequencies are avoided for communications applications, though in special cases they may be deliberately used so that the signal will not propagate beyond a certain range - eg covert military signals, or mobile communications where the limited frequency range available means that the same frequency must be re-used many times in different communication cells.

Figure 1 Average atmospheric absorption of millimeter waves. A: Sea level ; T = 20˚C; P = 760mm; PH2O = 7.5g/m3. B : 4 km; T = 0˚C; PH2O = 1g/m3 .

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- see below for the allocation from 4990 to 7075MHz.

Figure 2 Atmospheric absorption of millimeter waves due to fog and rain.

Note 2 The second graph covers a much broader frequency range, from microwave to optical and beyond. It shows that although rain and fog increase the attenuation of microwave signals the attenuation is still considerably less at the lower microwave frequencies (up to 15GHz, for example) than at optical frequencies, so that microwave frequencies will maintain communication links and remote sensing observations under conditions where optical links will fail. 2.1.1 Antenna size The basic (approximate) relationship between wavelength and antenna size is θ (radians) ≈ λ D where θ is the angular breadth of the main beam between the 3dB points and D is the maximum dimension across the antenna aperture. An aperture of 10 wavelengths will give a beamwidth of about 6°. At low frequencies the wavelength is large, implying a large antenna. As the frequency increases the antenna size reduces for a given beamwidth but the attenuation of the atmosphere increases. A compromise must be made. Note that atmospheric attenuation is not a problem for satellite-tosatellite links, so these may involve mm-wave frequencies and very small antennas. 2.2 INTERNATIONAL REGULATIONS The use of different frequency bands for different applications has been agreed through various international agencies

Allocation to Services Region 1 Region 2 4990 – 5000 FIXED MOBILE except aeronautical mobile RADIO ASTRONOMY Space Research (passive) 795 5350 – 5255 RADIOLOCATION Space Research 713 798 5650 – 5725 RADIOLOCATION Amateur Space Research (deep space) 664 801 803 804 805 5725 – 5850 FIXED SATELLITE (Earth-to-space) RADIOLOCATION Amateur 801 803 805 806 807 808 5850 – 5925 5850 – 5925 FIXED FIXED FIXED-SATELLITE FIXED(Earth-to-space) SATELLITE MOBILE (Earth-to-space) MOBILE 806 Amateur Radiolocation 806 5850 – 5925 FIXED FIXED-SATELLITE (Earth-to-space) MOBILE 791 809

Region 3

5850 – 5925 FIXED FIXEDSATELLITE (Earth-to-space) MOBILE Radiolocation 806

Note: • Region 1: Europe, Africa, N Asia; Region 2: N & S America; Region 3: rest of Asia • Upper case entries eg FIXED indicate a definite allocation for the service in the frequency band. Lower case entries show services that may be allowed. • Numbers - such as 795 - refer to regulations which apply to the frequency band. 2.3 ORBITING AND GEOSTATIONARY SATELLITES 2.3.1 Orbiting satellites • lower orbits - cheaper to launch. Eg remote sensing satellites at about 800km altitude (about 1/8 earth radius). • not available all the time for communication links • ideal for collecting data - eg remote sensing - transmitting data back periodically to fixed earth stations. Earth coverage obtained by rotation of earth beneath satellite.

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• •

•

receive antennas must track satellite lower coverage than geostationary

radius of orbit: altitude: orbital period:

2.3.2 Geostationary satellites • •

Data: 42 000km (about 7 times earth radius) 36 000km 24hours

occupy fixed position with respect to earth above the equator - no tracking required 3 satellites provide coverage for most of earth's surface (not polar regions)

3 LINK BUDGET PT .G T 4π .R 2

2 x 36,000 x 1000 = 0.24 Sec 3 x 10 8

GT

Isotropic power ie If TX transmits as a sphere.

Rx

Tx

Effective area = Aeff

GR

PT PR R

PT .G T 4π .R 2

Received Power

PR =

The link attenuation α in dB is given by

PT GT Aeff 4πR2

Aeff is the receive antenna effective area General antenna relationship: G

⎛ λ ⎞ ⎟⎟ PR = PT G T G R ⎜⎜ ⎝ 4πR ⎠

⎛ 4πR ⎞ ⎛⎜ 1 ⎜ λ ⎟ ⎜⎝ G G ⎝ ⎠ 2

=

4 π Aeff

λ2

2

GR is the Rx antenna gain PT GT is the Effective Isotropic Radiated Power (EIRP). It gives a measure of the power flux. For each satellite contours of constant EIRP can be plotted on the earth's surface. A minimum value of EIRP is required for each type of receiver (eg DBS). Usually the EIRP is given in units of dBW - EIRP[dBW] = 10log10 ( PT GT ) .

⎛

⎞

α = 10 log⎜ PT ⎟ = 10 log ⎝ PR ⎠

T

⎞ ⎟⎟ R⎠

⎛ 4πR ⎞ = 20 log⎜ ⎟ − GT [dB ] − G R [dB ] ⎝ λ ⎠ The first term is called the free space loss - due to the spreading of the radiation, not absorption.

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− 116[dBW] = PT [dBW]+ 30 + 40 − 203− 5 3.1 DBW (DECIBEL WATTS)

∴ PT dBW = 22dBW = 159W

Link budget calculations are often carried out using powers measured in dBW. The power is measured relative to a 1 watt reference power. Power in dBW = 10 log

Power in Watts 1 Watt

⎛ 4πR ⎞ PR [dBW ] = EIRP[dBW ] + G R [dB] − 20 log⎜ ⎟ ⎝ λ ⎠ Corrections must be added to PR for additional losses due to 1. 2. 3. 4.

antenna efficiency - power is lost in the antenna feed structure, also in connections to the receiver atmospheric absorption due to water and oxygen molecules polarisation mismatches of Tx and Rx antennas antenna misalignments - ie boresights of Tx and Rx antennas not aligned

An additional loss factor L is introduced to the link budget equation to take account of these losses. The equations become

P R = PT GT G R

( ) λ 4πR

2

1 L

PR [dBW ] = PT [dBW ] + GT [dB] + G R [dB]− 20 log

( ) 4πR

λ

− L[dB]

and

3.3 ANTENNA BEAMWIDTH AND GAIN The satellite antenna beamwidth must correspond to the area of the earth to be illuminated. This determines the gain of the antenna. The earth station antenna must be able to select a particular geostationary satellite - the satellite spacing in the crowded parts of the geostationary orbit is about 2°, though there may also be frequency discrimination between neighbouring satellites. The following approximate results for a circular aperture antenna may be used to estimate suitable antenna sizes and gains.

( )

πD G =η λ

θ 3dB = 70 λ D the 3dB beamwidth in degrees of the antenna.

3.4 SYSTEM NOISE TEMPERATURE For satisfactory operation a communication link must have:

2. 3.2 LINK BUDGET CALCULATION Calculate the power that must be transmitted from a geostationary satellite to give a power of -116dBW (2.5 × 10-21 W) at a receiver on the earth. Assume f=10GHz, G R = 40dB , GT = 30dB and additional losses of 5dB. R = altitude = 36000km PR [dBW ] = PT [dBW]+ GT [dB]+ G R [dB]− 20 log

( ) 4πR

λ

− L[dB]

2

η is the antenna efficiency, typically 0.6 to 0.7, D is the antenna diameter

1.

Typically L is about 5dB.

EIRP = 22 dBW + 30dB = 52 dBW

a large enough signal for the receiver sensitivity, and a high enough S/N ratio or BER at the receiver output for good quality communication eg for TV reception international regulations require a S/N ratio ≥ 47dB

Information is conveyed by modulating a high frequency carrier with a message signal. The basic quality of a link is expressed in terms of its carrier to noise ratio C/N where C is the power for the unmodulated carrier and N is the noise power, both measured at the receiver input. The signal to noise ratio for an information signal - ie a modulated carrier - depends upon both the C/N ratio for the link and the type of modulation used - ie AM, FM, FSK, PSK etc.

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The noise power associated with the link is specified by the system noise temperature Ts. This is made up from three contributions:

TA 1. antenna noise 2. antenna - receiver connection - a cable or waveguide TC this may include RF, 3. receiver noise TR mixer and IF stage contributions

ture (which must be in degrees K, ie absolute temperature) using the general relationship available noise power = kTB where k is Boltzmann's constant and B is the bandwidth. k = 1.38 × 10-23 J K-1 A useful figure to remember is that at 290K the available noise power density is -174dBm/Hz

In each case the noise power in watts (this is the available noise power) is calculated from the noise tempera3.5 ANTENNA NOISE TEMPERATURE TA satellite Antenna Noise Power NA = kTA.B

Other RF sources eg satellites,galactic sources etc

PR

Ground wave

Radiation into the Back lobes from the surface reflections

Earth surface

Figure 3 Antenna noise temperature as a result of other noise sources including galactic and other satellites.

Referring Figure 3, the antenna noise is due to energy, which is fed to the antenna by unwanted radiation sources, such as stars and galaxies and other communication signals. (The latter are not strictly noise signals in that they will not be random, but their effect on the communication link will be the same as for noise - ie they will worsen the S/N ratio and so they are included here.) Also, the atmosphere itself behaves as a resistive medium, which supplies noise power to the antenna. The output noise power from the antenna N A = kTA B will depend on the positions and temperatures and emissivities of the noise sources and the gain and polar radiation pattern of the antenna.

3.5.1 Antenna pointing to the sky (ground station antenna) In this case the output noise power from the antenna has two components which are represented by the sky temperature, Tsky , and the earth temperature Tearth

Tsky is due to noise originating in the atmosphere. It varies with frequency and the elevation angle E of the antenna. The sky temperature is higher for E=0° (antenna pointing to the horizon) because of the longer path of the radiation through the atmosphere. Elevation angles of less than 10° are usually avoided. The two diagrams Figure 4 and Figure 5 show Tsky for different frequency ranges.

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Radiation into the Back lobes from the surface reflections For a large (≈5m) Cassegraine antenna For a small (≈ 0.5m) antenna Figure 4 Antenna sky noise temperature as a function of frequency and antenna angle.

Tearth ≈ 10K

Tearth ≈ 100K

If an antenna points towards the Sun the noise effective temperature is about 10 000K. This situation should be avoided. 3.5.2 Antenna pointing to the earth Usually the beamwidth is less than or equal to the angle subtended by the earth, so that the earth fills the beam. Then the noise temperatutre of the antenna is about 290K, the physical temperature of the earth.

Figure 5 Sky noise for clear air and 7.5 g/m3 of water vapour concentration (φ is the elevation angle)

3.6 ANTENNA-TO-RECEIVER CONNECTING CABLE Although it is a passive element the cable or waveguide that connects the antenna to the receiver has a noise temperature TC which, contributes to the system noise temperature. A passive component with an insertion loss L has

For E ≥ 10° and f ≤ 15GHz Tsky ≤ 40K.

Tearth arises from radiation which feeds into the antenna

RX IL = L (eg 2dB)

gain = 1/L

via the back lobes of the antenna radiation pattern. Noise figure F = L ∴ effective noise temperature

Te =T0 (L−1) and Gain G = 1/L Tc = To (F-1) = 290(L-1) Where, To = 290K

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3.7 RECEIVER NOISE

TR = Trf +

Receiver noise includes contributions from thermal noise, shot noise and possibly flicker noise. These may arise in the input RF section of the receiver, the mixers used for frequency translation and the IF stages. A schematic diagram of a simple receiver and its equivalent noise circuit is shown below. The total receiver noise figure TR can be calculated from the individual contributions from the usual formula for cascaded circuits.

Figure 6 shows typical equivalent noise temperatures and figures for various devices, which may be used in microwave receivers. 2000

7 1000

Note: This formula follows from the corresponding formula for the noise figure Ftotal for cascaded stages,

Ftotal

F − 1 F − 1 = F1 + 2 + 3 + ... with G1 G1G2

each noise figure replaced by its equivalent effective noise temperature using T e=To (F −1) .

6

700

5 Tunnel diode Amplifier

500 Equivalent noise temperature (K)

Tif Tm + Grf Grf Gm

Mixer

4 FET Amplifier

300 200 150

3 2

Bipolar Transistor amplifier

1.5

100 70

1.0 Uncooled Parametric amplifier

50 30 20

0.25

15 10

Cooled parametric amplifier 0.125

7 0.2

0.4 0.6

1

2

4

6

10

20 40

60 100

Frequency (GHz)

Example LNA

Trf = 50K Mixer

Figure 6 Typical equivalent noise temperature and noise figures of various devices

(low noise amplifier)

Tm = 500K

Grf = 23dB [Grf = 200] Gm = 0dB

[ Gm = 1]

IF stage

TIF = 1000K ∴ TR = 50 +

GIF = 30dB

[ GIF = 1000]

500 1000 + = 50 + 2. 5 + 5 = 57.5 K 200 200 × 1

Usually, the mixer has conversion loss eg suppose Gm = − 10dB ∴ Gm = + 0.1 ∴ TR = 50 +

500 1000 + = 50 + 2. 5 + 50 = 102. 5K 200 200 × 0 .1

Noise figure (dB)

TR = Trf +

8

1500

TR =To (FR −1) FR is the receiver noise figure In the schematic receiver shown in Figure 7.

Tif Tm + Grf Grf Gm

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I.F Amplifier

L.N.A TA

Antenna

I.F Filter

Mixer

Tc

cable Gain = Grf Noise = Trf

Gain = Gm Noise = Tm Gain = Gif Noise = Tif

LO Receiver Noise equivalent circuit

Trf

Tif

Tm Gm

Gain Grf

___ ___ ___

Gain Gif

RX TR

Figure 7 System setup including the antenna, antenna cable feed and receiver. The gains and noise temperatures are defined throughout the system.

3.8 SYSTEM TEMPERATURE If we consider the system temperature for a combination of the antenna and the receiver with a receiver temperature of 102.5K: Antenna + Receiver

(ie at receiver input use noise temperature x gain)

= RX

TA

TS = (TA +TC ) L+ TR

TR

Therefore, TS = TA + TR

TS = TA + TR = 50 + 102.5 = 152. 5K If we now add a cable with IL 2dB [⇒ IL = 1.58] between the antenna and the receiver:

TC = 290 F − 1 = 290 L − 1 Then, the system temperature at the receiver input

TA ⎛ L−1 ⎞ +290⎜ ⎟+TR L ⎝ L ⎠

Using the figures above, TS =

50 ⎛ 1.58−1 ⎞ + 290⎜ ⎟ +102.5= 240.6K 1.58 ⎝ 1.58 ⎠

ie. adding cable with 2dB IL increases TS from 152.5 to 240.6K. This illustrates the very significant effect attenuation at the input has on noise. For this reaon the LNA is often connected directly to the receive antenna.

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3.9 C/N RATIO AT RECEIVER OUTPUT GT

Satellite Transponder Gain = G

Rx

Tx

Cu

GR PT

uplink PR

Ld = Dielectric Loss

R

˜ C = Carrier power

Nv

⎛ λ ⎞ 1 = (PT + G T ).GR .⎜ ⎟ . ⎝ 4π .R ⎠ L 2

Cd at receiver

⎛ λ ⎞ 1 PR =(PT GT )G R ⎜ ⎟ ⎝ 4πR ⎠ L 2

From before:

Power at earth station/Power at satellite down link output

If system temperature is TS (includes antenna noise TA , cable and receiver noise) Noise power (single link) at receiver input is

N = kTS B ∴

⎛ GR ⎞ ⎛ λ ⎞ 1 1 ⎟⎟ ⎜ ⎜⎜ ⎟ ⎝ T s ⎠ ⎝ 4πR ⎠ L kB

EIRP (Tx) ⎛ GR ⎜⎜ ⎝ TS

received down-link carrier power

Free space loss

C (link ) = PR = PT GT N kTs B

Bandwidth

⎞ ⎟⎟ is the receiver figure of merit. ⎠

eg Intelstat ground station ⎞ ⎟⎟=40.7 dBK −1 ⎠

Cd = Cu G Ld

2

Usually the down link is the most critical due to the limited power which is available on board the satellite ( PT ) and the antenna gain GT (limited by its size). Hence, the most critical receiver is the earth station ⎛ GR ⎜⎜ ⎝ TS

Figure 8 Schematic of the RF uplink and downl link signal path

at 4 GHz

The analysis above applies to a single link - ie up-link or down-link, but information transmitted via satellite involves both links. With reference to Figure 8 the total C/N ratio for the two links can be found as follows:

total received down-link power

N = N u G Ld + N d Here N u is the uplink noise at the transponder (satellite). N d is the noise added to the down link. Hence,

N N G Ld + N d N = u = u Cd Cu G Ld Cu

+

Nd Cd

and so

(C

N )total =

(C N ) uplink -1

1 -1 +(C N )downlink

Because of the limited power available on the satellite for the downlink the C/N ratio for this link is usually lower than that for the uplink, and this is the main determining factor for the overall C/N ratio. The total C/N ratio is also reduced by interference on each link, and intermodulation distortion in the transponder, so a more complete expression is

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(C N )total =

(C N )uplink+(C N ) -1

1

+(C I )

-1 downlink

-1 uplink

+(C I )

+(C N )

-1 downlink

−1 intermods

Calculations using the above relationships apply to clear air propagation conditions, but allowance has to be made for additional attenuation and noise which may be introduced on each link due to rainfall or other possible meteorological conditions. The margin that must be allowed depends upon the required reliability (eg link maintained for 99.99% of time, averaged over one year) and the range of climatic conditions which are predicted along the link. The margins also vary with frequency and the angle of elevation. Typical margin values are 2dB (C band) and 8dB (Ku band).

4 MODULATION AND MULTIPLEXING TECHNIQUES

i) Frequency Division Multiplexing (FDM) - each message is placed in a different frequency range by modulating a different carrier frequency. All the messages are combined for transmission. Each satellite link will have a certain bandwidth. The bandwidth may be divided into sub-bands with different sub-bands assigned to each earth station. The figure below shows a set of satellite transponders for (a) a C band and (b) a Ku band system. The C band transponder uses a single down converter (D/C) and signal processing at 4GHz, whereas the Ku be fed together to the HPA (high power amplifier) for amplification.

L.N.A DC

Frequency MUX

6GHz

The multiplexing techniques used are

Frequency DEMUX

Each earth station will, in general, be transmitting and receiving many messages simultaneously to and from a satellite. The messages may be 'phone calls, ratio and band system uses D/C to 1GHz for signal processing followed by up-conversion (U/C) for the down-link. Each sub-band will contain many messages, which will

TV signals and/or computer signals. They are transmitted by modulating a carrier signal in some way - AM, FM, PM (analogue), or ASK, FSK, PSK etc (digital). In a multicarrier system the different messages are combined for transmission by multiplexing. The converse process of demultiplexing is carried out at the receiver

H.P.A

4GHz

C-Band Transponder Figure A Equilizer Multiple Transponders

1GHz

11GHz

L.N.A DC

KU-Band Transponder Figure B

U/C’s

Equilizer

H.P.A

Frequency MUX

14GHz

Frequency DEMUX

1GHz 11GHz

Multiple Transponders

Figure 9 Schematic of two satellite transponders. The top one is a C-Band system and the one on the bottom is a KuBand system. HPA = High power amplifier; DC = Downconverter; U/C = Upconverter.

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In the C band 6/4GHz transponder (Figure 9 A): •

• • • •

• •

•

the uplink is at the higher frequency, so D λ is greater for the (common) receive/transmit antenna – it will have a higher gain the input filter is a fairly wideband bandpass‘roofing’ filter to allow all the uplink frequencies in, but eliminating out-of-band noise LNA – low noise amplifier D/C – down converter to 4GHz (the down-link frequency) for signal processing – error correction, amplification, signal channelling etc. frequency demultiplexing – divides input signal into sub-bands to reduce non-linear distortion during amplification. Each sub-frequency band is processed by a single transponder. equalisers – correct for phase differences between the different frequency components of a signal which are introduced by filters, de-multiplexers etc HPAs – high power amplifiers – to increase power levels before re-transmission on the down-link. Non-linear performance in the HPAs can intoduce harmonics, intermodulation distortion etc band-pass filters at various points remove out-ofband products from the HPAs etc and reduce the background noise, but they cannot remove in-band products – eg 3rd order intermodulation (IM) products

The Ku (14/11GHz) system (Figure 9 – B) has many of the same elements, but the down-link frequency (11GHz) is too high for the elements in each transponder, so the input is mixed down from 14GHz to 1GHz for de-multiplexing and equalisation, then mixed up to 11GHz for power amplification, frequency MUX and re-transmission. 4.1 NON-LINEAR BEHAVIOUR IN HPAS Because each transponder will be processing a very large number of messages simultaneously any nonlinearity in the transponder amplifier will lead to intermodulation which causes interference between the message signals by transferring modulations from one frequency range to another. The diagram Figure 10 shows a non-linear amplifier voltage transfer characteristic and the way in which it leads to signal distortion. The distortion is normally represented in terms of additional harmonics of the input signal, which are introduced by the amplifier. The non-linearity may also be represented in terms of the amplifier power transfer characteristic, which also shows the saturation and saturation power of the amplifier.

Non-linear saturation

Vout

Distorted fo, 2fo, 3fo etc

Vin Pure sinewave fo

Figure 10 The diagram shows the non-linear (in the saturation region) Vout vs vin curve for an amplifier. If a sine-wave is applied to the input the nonlinearity will distort the amplified output sinewave as shown.

Intermodulation can be reduced using back-off, as shown in Figure 11 Figure 11. The input signal signal power is reduced to move below the non-linear segment of the characteristic. The amount of back-off can be expressed in terms of either the input signal back-off or the output signal backoff. A disadvantage of using back-off is that it reduces the efficiency of the amplifier because the RF output from the amplifier is reduced whilst it is still consuming the same DC power. Saturation - IMD PSAT Output power backoff

Pout

Pin

Back off

Figure 11 shows how distortion can be reduced by backing off the input signal from the saturation region to the linear region.

The amount of back-off needed to avoid intermodulation increases with the number of messsages (ie modulated carriers) in the signal which is applied to the trans-

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ponder. One solution is to increase the number of transponders on board the satellite so that each need only handle a restricted bandwidth and number of carriers. This, of course, increases the satellite mass, so a suitable compromise must be reached between the number of transponders and the intermodulation. Back-off modifies the formula for the down-link C/N ratio by making : PT = Pos − BOo Where, Pos is the output power of the HPA at saturation and BOo is the output backoff power . Pos is normally known for a given amplifier, then BOo is adjusted dynamically according to the strength of the input signal. Solid state amplifiers are superior to TWT amplifiers in their linearity. Considerable attention has been devoted to techniques for linearising HPAs to improve their efficiency. This involves extending the linear part of the power amplifier characteristic. ii) Time Division Multiplexing (TDM) - each message is transmitted at a different time. TDM is usually used with digitally coded messages. Whereas with FDM each message is transmitted continuously using a restricted bandwidth, with TDM each message is only transmitted for a small fraction of the available time, but during that time it uses all the available bandwidth. Clearly, a system must be established to regulate the timeslots for each message. This scheduling will itself require the communication of earth stations via the satellite which imposes a network management overhead on the available bandwidth/transmission time. An appropriate balance must be struck between the complexity of the 'housekeeping' of the communication system and the useful communication capacity. An advantage of TDM is that intermodulation distortion can be avoided, because only one message is being amplified at any one time. iii) Code Division Multiplex (CDM) - each message includes a unique code which means that TDMA can be used with different signals being transmitted simultaneously - the code allows the elements of the different messages to be grouped correctly. CDM uses a very wide bandwidth and so this technique is sometimes also known as a spread spectrum technique. 4.2 MULTIPLE ACCESS Multiple access refers to the fact that many earth stations share the same satellite. Signals from several earth sta-

tions may arrive simultaneously at the satellite antenna from which they are fed to the transponder which will process the signals in several ways - eg amplification, error detection and correction, filtering and frequency changing - before feeding the signals back to the satellite antenna for the down link. The uplink and the down link operate at different frequencies to avoid direct coupling of signals from the transmit to the receive channels eg 6/4GHz (C band), 14/11GHz Ku band). The higher frequency is used for the up-link because the satellite antenna has limited size and a higher noise temperature (usually 290K). The gain is higher at the upper frequency for a fixed antenna size. Similarly, the signals transmitted from a satellite will usually be received by all the earth stations. Most of the messages received will not be needed by a specific earth station - they must be filtered out during demultiplexing. In a typical analogue system a transponder may have a bandwidth of 36MHz, but this will be subdivided into 12 sub-bands, each with a bandwidth of 3MHz. When an earth station receives messages from its vicinity via the PSTN network it sorts them out into their destination earth stations. All the messages for a particular earth station are combined to one sub-band for the uplink. They are all processed by the satellite transponder and transmitted to the earth stations, but each earth station will only process its own sub-band. As noted earlier, multiplexing and modulation are separate processes and so various combinations of the different techniques available for each can be used. According to Glover and Grant, the predominant multiplexing/modulation/multiple access technique in current use for PSTN satellite telephony is FDM/FM/FDMA, but this leads to large intermodulation products. Increasingly, digital modulation (PCM) is replacing analogue techniques, leading to TDM/PSK/TDMA. With the systems described so far the communication capacity between different earth stations is essentially 'designed in' when the bandwidths assigned to each station are fixed, and changes cannot easily be made even if demand changes. Capacity can be increased, and made more flexible, by i) using multiple spot beams that can be steered as required to different points on the earth's surface, and ii) by using a switching matrix on board the satellite to co-ordinate the message transmission with the beam direction.