Wireless ChannelsAda Poon, Bob BrodersenBerkeley Wireless Research CenterUniversity of California, BerkeleyEarth-Ionospheric Waveguide3 – 30 kHz,very low frequency (VLF)Large wavelength (>10 km)Wave can’t penetrate to the lowest layer of ionosphere.Long distance telegraphy broadcastingNavigation systemsSubmarine communicationsIonosphereEarthSurface Wave Diffraction30 – 300 kHz,low frequency (LF)Wave follows the curvature of earth.Long distance communicationsNavigation systemsEarthIonospheric Reflection & Refraction3 – 30 MHz,high frequency (HF)Wave is refracted by the layers of ionosphere and eventually, totally reflected and returns to the earth.Radio broadcastingIonosphereEarthTropospheric Scattering30 – 300 MHz,very high frequency (VHF)Wave is scattered by the particles in the troposphere.Military applicationsMulti-channel telephonyTroposphereEarthFour Basic Propagation MechanismsWaveguideDiffractionReflection & RefractionScatteringCellular SystemsOutdoor environment0.3 – 3 GHz, ultra high frequency (UHF)Propagation mechanisms:» Waveguiding along streets» Diffraction around hills» Reflection from buildings» Scattering by plantsWireless LANIndoor environment3 – 30 GHz, super high frequency (SHF)Propagation mechanisms:» Waveguiding along corridors» Diffraction around door openings» Reflection from walls» Scattering by furnitureWe are studying electrical engineering, but most of us don’t like to get too involved into classic electrodynamics.Characterization ParametersPath lossDelay spreadDoppler shiftAngular spreadCoherence timeCoherence bandwidthFriis Transmission FormulaPR= PT·?In free space, path loss isd transmitter-receiver separationGRreceiver antenna gainGTtransmitter antenna gainλwavelengthHow about in a scattering environment?()222241−∝⋅= dGGdPPTRTRπλPath Loss Exponent, nIn a scattering environment, the path loss isTypical values inUrban 2.7 – 3.5Sub-urban 3 – 5Indoor LOS 1.6 – 1.8 (< 2, why?)Indoor NLOS 2 – 6nTRdPP−∝UWB, LOS802.11a, LOS802.11b, LOSUWB, NLOS802.11a, NLOS802.11b, NLOSMultipath Modeliυiτiκˆ∑=−−−=LiiNiiifjtjieeft122)ˆˆ()ˆˆ()ˆ,ˆ,,( kkκκΓkκHδδτππυikˆiΓDoppler shiftdelaydirection of departuredirection of arrivalpolarizationikˆiκˆvMaximum Doppler Shiftλυvfim== maxFrequency spread, fmFor example, if a cell phone is moving at 60 km/hr using a 900 MHz carrier, the maximum Doppler shift is 50 Hz.vDelay SpreadDelay spread1τ2τ3τ4τtiiiidTττminmax −=Sample MeasurementsDelay Spread vs. FrequencyInsensitive to the choice of coordinatesLarger delay spread in the office environmentDelay spread increases with frequencyDelay Power Profiles and Arrival PDFsAngular SpreadCoordinates: Transmit elevation spreadTransmit azimuth spreadReceiveTiiTiiTθθminmax −=Θ()TiTiiφθ,ˆ=k()RiRiiφθ,ˆ=κTiiTiiTφφminmax −=ΦRiiRiiRθθminmax −=ΘRiiRiiRφφminmax −=ΦSample MeasurementsAngle Power Profiles and Arrival PDFs∑=−−−=LiiNiiifjtjieeft122)ˆˆ()ˆˆ()ˆ,ˆ,,( kkκκΓkκHδδτππυCoherence Bandwidth, Coherence Time[]0~)ˆ,ˆ,,()ˆ,ˆ,,(*kκHkκH ftfTtc+ΕCoherence time, TcCoherence bandwidth, Wcikˆiκˆv[]0~)ˆ,ˆ,,()ˆ,ˆ,,(*kκHkκH ftWftc+ΕChange of Domains)ˆ,ˆ,,( kκH ft)ˆ,ˆ,,( kκHτt),,,(TRft rrHarray topologyarray topology),,,(TRt rrHτChannel Characterization(υi, τi, θi)’sextractiongeometry & dielectric properties of environmenteffective scattererdistributiondistribution(t, f, rR, rT) correlationMeasurement Ray tracing Abstract modelingarray topologyfrequency spreaddelay spread,angular spreadcoherence timecoherence bandwidth),,,( θ∆θτ∆τpath