3-1©2008 Raj JainCSE574sWashington University in St. LouisA Review of Key Wireless A Review of Key Wireless Physical Layer ConceptsPhysical Layer ConceptsRaj JainProfessor of CSE Washington University in Saint LouisSaint Louis, MO [email protected] slides are available on-line at:http://www.cse.wustl.edu/~jain/cse574-08/3-2©2008 Raj JainCSE574sWashington University in St. LouisOverviewOverview! Basic Concepts:" Coding, Phase-Shift Keying (PSK), QAM, Decibels" Channel Capacity, Nyquist Theorem, Shannon's Theorem, Hamming Distance, Error Correction" Antenna, Reflection, Diffraction and Scattering, Multipath Propagation! Recent Development:" Spread Spectrum, Code Division Multiple Access" OFDM " Turbo Codes3-3©2008 Raj JainCSE574sWashington University in St. LouisElectromagnetic SpectrumElectromagnetic Spectrum! Wireless communication uses 100 kHz to 60 GHzWireless3-4©2008 Raj JainCSE574sWashington University in St. LouisFrequency, Period, and PhaseFrequency, Period, and Phase! A Sin(2πft + θ), A = Amplitude, f=Frequency, θ = PhasePeriod T = 1/f, Frequency is measured in Cycles/sec or Hertz3-5©2008 Raj JainCSE574sWashington University in St. LouisWavelengthWavelength! Distance occupied by one cycle! Distance between two points of corresponding phase in two consecutive cycles! Wavelength = λ! Assuming signal velocity v"λ= vT"λf = v" c = 3*108 m/s (speed of light in free space) = 300 m/μsDistanceAmplitude3-6©2008 Raj JainCSE574sWashington University in St. LouisTime and Frequency DomainsTime and Frequency DomainsFrequencyAmplitudeFrequencyAmplitudeFrequencyAmplitudef3fAAf3fA/3A/33-7©2008 Raj JainCSE574sWashington University in St. LouisDecibelsDecibels! Attenuation = Log10 PinPout! Example 1: Pin = 10 mW, Pout=5 mWAttenuation = 10 log 10(10/5) = 10 log 102 = 3 dB! Example 2: Pin = 100mW, Pout=1 mWAttenuation = 10 log 10(100/1) = 10 log 10100 = 20 dBBelPinPoutdecibel! Attenuation = 10 Log10 VinVoutdecibel! Attenuation = 20 Log103-8©2008 Raj JainCSE574sWashington University in St. LouisCoding TerminologyCoding Terminology! Signal element: Pulse (of constant amplitude, frequency, phase)! Modulation Rate: 1/Duration of the smallest element =Baud rate! Data Rate: Bits per second! Data Rate = Fn(Bandwidth, signal/noise ratio, encoding)PulseBit+5V0-5V+5V0-5V3-9©2008 Raj JainCSE574sWashington University in St. LouisPhasePhase--Shift Keying (PSK)Shift Keying (PSK)! Differential PSK: 0 = Same phase, 1=Opposite phaseA cos(2πft), A cos(2πft+π) ! Quadrature PSK (QPSK): Two bits11=A cos(2πft+45°), 10=A cos(2πft+135°), 00=A cos(2πft+225°), 01=A cos(2πft+315°)Sum of two signals 90° apart in phase (In-phase I , Quadrature Q), Up to 180° phase difference between successive intervals111000 01013-10©2008 Raj JainCSE574sWashington University in St. LouisQAMQAM! Quadrature Amplitude and Phase Modulation! QAM-4, QAM-16, QAM-64, QAM-256! Used in DSL and wireless networksBinary QAM-401100001 11QAM-16IQIQIQ3-11©2008 Raj JainCSE574sWashington University in St. LouisAntennaAntenna! Transmitter converts electrical energy to electromagnetic waves! Receiver converts electromagnetic waves to electrical energy! Same antenna is used for transmission and reception! Omni-Directional: Power radiated in all directions! Directional: Most power in the desired direction! Isotropic antenna: Radiates in all directions equally! Antenna Gain = Power at particular point/Power with IsotropicExpressed in dBiPr= PtGtGr(λ/4πd)2Omni-Directional Directional Isotropic3-12©2008 Raj JainCSE574sWashington University in St. LouisReflection, Diffraction, ScatteringReflection, Diffraction, ScatteringEflection ⇒ Phase shiftiffractioncattering3-13©2008 Raj JainCSE574sWashington University in St. LouisReflection, DiffractionReflection, Diffractionand Scatteringand Scattering! Reflection: Surface large relative to wavelength of signal" May have phase shift from original" May cancel out original or increase it! Diffraction: Edge of impenetrable body that is large relative to λ" May receive signal even if no line of sight (LOS) to transmitter! Scattering" Obstacle size on order of wavelength. Lamp posts etc.! If LOS, diffracted and scattered signals not significant" Reflected signals may be! If no LOS, diffraction and scattering are primary means of reception3-14©2008 Raj JainCSE574sWashington University in St. LouisMultipath PropagationMultipath PropagationInter-symbol Interference! Delay Spread = Time between first and last versions of signal! Fading: Fluctuation in amplitude, phase or delay spread! Multipath may add constructively or destructively ⇒ Fast fading3-15©2008 Raj JainCSE574sWashington University in St. LouisDoppler ShiftDoppler Shift! If the transmitter or receiver or both are mobile the frequency of received signal changes! Moving towards each other => Frequency increases! Moving away from each other => Frequency decreasesFrequency difference = velocity/WavelengthExample: 2.4 GHz => l= 3x108/2.4x109= .125m120km/hr = 120x1000/3600 = 33.3 m/s Freq diff = 33.3/.125 = 267 Hz3-16©2008 Raj JainCSE574sWashington University in St. LouisChannel CapacityChannel Capacity! Capacity = Maximum data rate for a channel! Nyquist Theorem: Bandwidth = BData rate < 2 B! Bi-level Encoding: Data rate = 2 × Bandwidth05V! Multilevel: Data rate = 2 × Bandwidth × log 2MExample: M=4, Capacity = 4 × Bandwidth3-17©2008 Raj JainCSE574sWashington University in St. LouisShannon's TheoremShannon's Theorem! Bandwidth = B HzSignal-to-noise ratio = S/N ! Maximum number of bits/sec = B log2(1+S/N)! Example: Phone wire bandwidth = 3100 HzS/N = 30 dB 10 Log 10S/N = 30Log 10S/N = 3S/N = 103= 1000Capacity = 3100 log 2(1+1000)= 30,894 bps3-18©2008 Raj JainCSE574sWashington University in St. LouisHamming DistanceHamming Distance! Hamming Distance between two sequences = Number of bits in which they disagree! Example: 011011110001---------Difference 101010 ⇒ Distance =33-19©2008 Raj JainCSE574sWashington University in St. LouisError Correction ExampleError Correction Example! 2-bit words transmitted as 5-bit/wordData Codeword00 0000001 0011110 1100111 11110Received = 00100 ⇒ Not one of the code words ⇒ ErrorDistance (00100,00000) = 1 Distance (00100,00111) = 2Distance (00100,11001) = 4 Distance (00100,11110) = 3⇒ Most likely 00000 was sent. Corrected data = 00b. Received = 01010 Distance(…,00000) = 2 = Distance(…,11110)Error detected but cannot be correctedc. Three bit errors will not be detected.
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