TelecommunicationsCommunication System Designers’ GoalUseful RelationshipsExamplesDerived Decibel UnitsVoltages (examples)Gains and LossesCommunications ExampleSpecial ValuesOther ExamplesRadio Frequency RadiationHalf PowerIsotropic RadiationIsotropic Radiation (cont’d)Typical Antenna PatternsParabolic Reflector AntennaLobesCassegrain Reflector AntennaModulationModulation (cont’d)Link BudgetLink RequirementsTermsMore DetailsSlide 25Slide 26Slide 27ExampleData RatesData Rates (cont’d)Slide 31Sample RateSampling Oscillatory PhenomenaData CompressionTelemetryError Detection and CorrectionParity CheckSlide 38Error Correction without RetransmissionHamming (cont’d)Slide 41Hamming ExampleHamming Example (cont’d)Probability of Errors – Simple ParityProbability of Errors – Hamming CodeTelecommunicationsAERSP 401BCommunication System Designers’ Goal•Maximize information transfer•Minimize errors/interference•Minimize required power•Minimize required system bandwidth•Maximize system utilization•Minimize costUseful Relationships•Decibels–A logarithmic unit originally devised to express power ratios but used today to express a variety of other ratios as well where P1 and P2 are the two power levels being compared210110logPPower ratio in dBP=Examples•Loss1,000 watts (P1) 10 watts (P2)•Gain10 watts (P1) 1,000 watts (P2) Telephone cable line10 101010log 10log 201,000dB dB= = =-10 101,00010log 10log 2010dB dB= = =20 dB means 100 times moreP2P11 milePower inPower outThe unit decibel was named after Alexander Graham Bell. The unit originated as a measure of power loss in one mile of telephone cable. Also, hearing is based on decibel levels.Derived Decibel Units•The dBm:•Example: 20W is what in dBm?•The dBW:•Example conversions10( )( ) 10log1Power mWPower dBmmW=310 1020 20 10( ) 10log 10log 431 1W x mWPower dBm dBmmW mW= = =+10( )( ) 10log1Power WPower dBWW=dBm dBW Watts Milliwatts (mW)+50 +20 100 100,000+30 0 1 1,000+10 -20 -0.01 10Voltages (examples)22210 1010log 20log1 010 20100 40: 'ref refout out out outref ref ref refPower VP VP V P VP V P VExamplesV dBV dBV dBNote dB s are NOT absolute but RELATIVE measures��� � � � � �� � =� � � � � �� � � � � �� � � � � �===Gains and Losses•Power is gained via amplification and lost via absorption or resistance•Gains and losses are expressed in dB (usually the W or m are dropped)Communications Example10101010log:1 110log10logoutinreceivedtransmituplinkoutinuplinkPA a dB APuplinkPx dBP X XPB b dB BP= � =� �� �= � - =� �� �� �� �� �= � =� �� �1010:1 110log10logtransmitreceiveddownlinkoutindownlinkdownlinkPy dBP Y YPC c dB CP� �� �= � - =� �� �� �� �� �= � =� �� �PinAttenuation: x dBAttenuation: y dBGain: a dBGain: c dBGain: b dB( )ABCTotal ratio Total gain a x b y c dBXY= = - + - +Special Values13 ( 3 )22 3 ( 3 )110 ( 10 )10outinoutinoutinPIf dB gain or dB lossPPor if dB gain or dB lossPPIf dB gain or dB lossP= � -= � + -= � -Other Examples•Sound levels:–If Pref is the sound power resulting in a barely audible sound,6090outrefdB normal conversationPin dBdB jet aircraft on runwayP���Radio Frequency Radiation•RF signals travel at the speed of light in air (atmosphere) and space (vacuum)•c = speed of light in vacuum = 2.998x108 m/sec (186,200 miles/sec)•Wavelength,  =c/f –f – frequency•Beam width:  (rad)  /D –D = aperture width or diameter–Defines how “spread out” the beam isHalf Power•A 3 dB drop in power represents the half-power pointIsotropic Radiation•Aperture – area of a receiving or transmitting antenna through which all signal is assumed to pass.•If transmitting antenna radiates equally in all directions, it is called isotropic•The fraction of power received from an isotropic radiator at a distance, d, is:–where Ar is the aperture area of the receiving antenna24receivedrtransmittedPAPdp=Isotropic Radiation (cont’d)•Receiver is not 100% efficient, so including efficiency factor, z,–Z  0.55•Transmitting antenna designed to focus radiation (i.e. not isotropic) –Can also be expressed in dB24receivedrtransmittedPzAPdp=power received from the antennaGain of transmitting antennapower received if antenna were isotropic=Typical Antenna Patterns•DipoleG<10 dBi•HornG=10-20 dBi•SlotG< 10 dBiParabolic Reflector Antennaparallel beamsfocal point21010logiDG z dBpl� �� �=� �� �� �� �� �D – diameter - wavelengthz - efficiencyLobes•Backlobes•SidelobesCassegrain Reflector AntennaModulation•Definition–Altering a signal to make it convey information (either analog or digital)•AM (Amplitude Modulation)–Changes amplitude (frequency constant)•FM (Frequency Modulation)–Changes frequency (amplitude constant)Frequency modulationModulation (cont’d)•Changing the phase of the signal•For digital data, these methods are also called–ASK – amplitude shift keying–FSK – frequency shift keying–PSK – phase shift keyingLink Budget•Allocation of various losses and gains in the communication link between Earth and the spacecraft•Similar to signal-to-noise ratio, but Eb/No pertains to digital datab l t s a r io sestimatedE PL G L L G Lreceived energy per bitN kT R noise density� �= =� �� �Link Requirements•For data•(Eb/No)estimated – (Eb/No)required  3 dB•For commands•(Eb/No)estimated – (Eb/No)required  20 dB•This difference is known as the link marginTerms•P – transmitter power•Ll – line loss (between transmitter and antenna)•Gt – transmitter antenna gain•Ls – space loss (inverse square in distance)•k – Boltzmann’s constant•La – transmission path loss (atmosphere and rain absorption) •Gr – receive antenna gain•Ts – system noise temperature•R – data rate•Li – implementation loss (-2 dB),228.60brl t s a io sdB estdBEGP L G L L R LN T� �� � � �= + + + + + + - +� �� � � �� �� � � �� �More Details( )( )10( ) 10log10log10(100) 201 ( )in dBW transmitter power in WattsExample: transmitter generates 100 Watts output power, then line loss typical value= peak transmitter antenna gain+ translt ptPP dBWL dBG G Lq== ==-= +23310 10 101221159.59 20log 20log 10logloss due to pointing errror pointing error (deg)transmitter frequency (GHz),