The RadioChannel - Princeton University

The Radio ChannelCOS 463: Wireless NetworksLecture 14Kyle Jamieson[Parts adapted from I. Darwazeh, A. Goldsmith, T. Rappaport, P. Steenkiste]

Motivation The radio channel is what limits most radio systems – the mainchallenge!– Understanding its properties is therefore key tounderstanding radio systems’ design There is no single radio channel, but instead variation inmany different properties– Carrier frequency, environment (e.g. indoors, outdoors,satellite, space) Many different models covering many different scenarios2

Channel and Propagation Models A channel model describes what happens– Gives channel output power for a particular input power– “Black Box” – no explanation of mechanism– Requires appropriate statistical parameters (e.g. loss, fading) A propagation model describes how it happens– How signal gets from transmitter to receiver– How energy is redistributed in time and frequency– Can inform channel model parameters3

Modeling (from a high-level perspective)log(distance)4

Today1. Large scale channel models– Free space model– Two-ray ground model2. Small-scale channel models3. Equalization: Coping with the channel5

The dBm unit If we take one milliwatt as areference then we have a unit ofabsolute power called dBm:PdBm æ P1 ö 10 log10 ç -3 è 10 øWhere P1 is the power we want toexpress in dBm, in WattsPower (linear)10 W1W100 mW10 mW1 mW10 µW1 µW1 nW1 pWPower (dBm)40 dBm30 dBm20 dBm10 dBm0 dBm-20 dBm-30 dBm-60 dBm-90 dBm6

Goal: Power BudgetTxRadioRx RadioPRX (dBm) PTX (dBm) Gains (dB) – Losses (dB) Receiver needs a certain SINR to be able to decode the signal Factors reducing power budget:– Noise, attenuation (multiple sources), longer range, fading Factors improving power budget:– Antenna gain, transmit power7

Goal: Predict average received signal strengthgiven a transmitter-receiver separation distanceLARGE-SCALE CHANNELMODELS8

Transmitting in Free Space!" unit areaTotal spherical surface area: 4- . Deliver !" Watts to an omnidirectional transmitting antenna So then power density (Watts per unit area) at range d is # – Independent of wavelength (frequency)%&'()*W/m29

Idealized Receive Antenna Effective aperture !": fraction of incident power density pcaptured and received()* – %& Larger antennas at greater λ capture more power So power received ,- is the product of the power density andeffective aperture:,. /0,- (43)05010

Antenna Gain Antennas don’t radiate power equallyin all directions– Specific to the antenna design Model these gains in the directions ofinterest between transmitter, receiver:– Transmit antenna gain Gt– Receive antenna gain Gr11

Friis Free Space Channel Model Power received !" is the product of the power received byidealized antennas, times transmit and receive antenna gains:! % %" &'!" (4*)','12

Ground Reflection (Two-Ray)Propagation ModelTransmitterReceiver'(')* Commonly occurs in mobile cellular environments Near transmitter: multipath oscillation due to constructive and destructiveinterference Far from transmitter (! ℎ , ℎ& ), reflection always approximately out of phasewith line of sight path: rapid attenuation13

Today1. Large scale channel models2. Small-scale channel models3. Equalization: Coping with the channel14

Small-scale versus large-scale modeling Small-scale models: Characterize the channel over at most a fewwavelengths or a few seconds15

Radio Propagation Mechanismsreflectionscatteringdiffraction Reflection– Propagation wave impinges on object large compared to λ e.g. the surface of the Earth, buildings, walls, etc. Diffraction– Path from transmitter to receiver obstructed by surface with sharp irregular edges– Waves bend around obstacle, even when LOS (line of sight) does not exist Scattering– Objects smaller than radio wavelength (i.e. foliage, street signs etc.)

Multipath Radio Propagation Receiver gets multiple copies of signal– Each copy follows different path, with different path length– Copies can either strengthen or weaken each other Depends on whether they are in or out of phase Enables communication even when transmitter and receiver are not in “line of sight”– Allows radio waves effectively to propagate around obstacles, therebyincreasing the radio coverage area Transmitter, receiver, or environment object movement on the order of λsignificantly affects the outcome– e.g. 2.4 GHz à λ 12 cm, 900 MHz à 1 ft17

Sinusoidal carrier, line of sight only Baseband transmitted signal: ! " 1 0'– Transmitted signal: cos(2-./ ")Transmittera, d, τReceiver Represent path attenuation a, length d with a complex number:– Complex channel ℎ 234567/922-( mod ?) Received signal: : " ℎ ; ! " (no noise)18

Adding a reflecting pathh2 (a2,d2,τ2)Transmitter Receiverh1 (a1 1,d1,τ1)Channel is now ℎ ℎ# ℎ% &# '(%)* /- &%'(%)*./h120(2% mod 6)20(2# mod 6)h2 Conclusion: At different λ, fading is different in frequency19

Reflections cause frequency selectivity Interference between reflected and line-of-sight radio wavesresults in frequency dependent fadingReceived Power (dBm)3530252015-400-2000200Frequency (kHz)400 Coherence bandwidth Bc: Frequency range over which thechannel is roughly the same (“flat”)

How does frequency selectivity arise?(Another look)Path 2TransmitterPath 1Receiver21

How does frequency selectivity other look)d1Receive antennad2 d1Path 1(shorter):d121100-1-1ß Distance from receive antenna0510d215202530-2221100-1-1-2Sum:d12-2Path ncy quency 222

Stationary transmitter, moving receiverReceiverantenna Suppose reflecting wall, fixed transmit antenna, no other objects– Receive antenna moving rightwards at velocity v Two arriving signals at receiver antenna with path lengthdifference 2(d r(t))23

How does fading in time arise?Receiverantenna Path length difference 2(% ' ( ) If mod - à receive 0/– Destructive interference If mod - 0 à receive 2– Constructive interference.λ/2λsum24

Channel Coherence Time Radio carrier frequency ! #/%– Speed of light: c; Wavelength of the signal: λ Change in path length difference of λ/2 moves from constructiveto destructive interference– Receiver movement of λ/4: coherence distance– Time transmitter, receiver, or objects in environment take tomove a coherence distance: channel coherence time Tc Walking speed (2 mph) @ 2.4 GHz: 15 milliseconds Driving speed (20 mph) @ 1.9 GHz: 2.5 milliseconds Train/freeway speed (75 mph) @ 1.9 GHz: 1 millisecond25

Another perspective: Doppler Effect Movement by the transmitter, receiver, or objects in theenvironment creates a Doppler Shift " "%và26

Stationary transmitter, moving receiver:From a Doppler PerspectiveReceiverantenna % & '()* ),- Doppler Shift of a path " – vradial is the radial component of the receiver’s velocity vector alongthe path Positive 4 with decreasing path length, negative 4 withincreasing path length Suppose v 60 km/h, fc 900 MHz– Direct path " 50 89, reflection path " 50 8927

Stationary transmitter, moving receiver:From a Doppler Perspective Channel Doppler Spread Ds: maximum path Doppler shift, minus minimum pathDoppler shift Suppose v 60 km/h, fc 900 MHz– Direct path " 50 '(, reflection path " 50 '(– Doppler Spread: 100 Hz Results in sinusoidal “envelope” at frequency Ds / 2:Received signal5 msReceiverantenna28

Channel Coherence Time:From a Doppler Perspective Sinusoidal “envelope” at frequencyReceived signal Transition from 0 to peak in #!"!":#)*2 – So qualitatively significant change in time %& (!" Alternate definition of channel coherence time29

What does the channel look like in time?a2,d2,τ2Transmittera1Channel impulseresponse h(t)a1,d1,τ1a1Receivera2Delay spread Tdτ1τ2t30

Power delay profile (PDP) Power received via the path with excess time delay !" isthe value (height) of the discrete PDP component at !"P(τ) corresponds to h(τ) 2P(τ)t0 # #%#&#' #(

Characterizing a power delay profile Given a PDP ! "# sampled at time steps "# : Mean excess delay ":̅ Expected value of ! "# : # !("# ) "#"̅ # !("# ) Root mean squared (RMS) delay spread * measures the spread of thepower’s arrival in time– RMS delay spread is the variance of ! "# :* 1 0( ) ",- "̅ -, where ",- / / // 0( /)Maximum excess delay X dB "23 is the greatest delay at which the PDPis greater than X dB below the strongest arrival in the PDP32

Example Indoor PDP EstimationTypical RMS delay spreadsEnvironmentFinite bandwidth ofmeasurementnormally results incontinuous PDPPDP typically hasa decayingexponential formRMS delayspreadIndoor cell10 – 50 nsSatellite mobile40 – 50 nsOpen area(rural) 0.2 !sSuburbanmacrocell 1 !sUrbanmacrocell1 – 3 !sHilly macrocell3 – 10 !s

Indoor power delay profile34

Flat FadingReceived Power (dBm)3530252015-400 Channel-2000200Frequency (kHz)400Slow down à sending data over a narrow bandwidth channel– Channel is constant over its bandwidth– Multipath is still present, so channel strength fluctuates over time How to model this fluctuation?Notshownabove!35

RayleighRayleighfadingFadingmodelModelayleigh fading modelh(τ)x(x(t)a1h(τ)Channelimpulseresponse h(t)a1τ1 a2a3a2 a3τ2 τ3r(t)t'Random gain of kth arriving path: !" !" &!"aini off eachh arrivingi i path:th Gaintheandi Qi channelG Therefore,i off eachh Iarrivingpath:thcomponents ℎ , ℎ' are zero-mean GaussianI and distributedQ componentspare statisticallyy independentpand zero-mean GaussiandistributedThen, amplitude is *Rayleighdistributed*I andpare statisticallyy Soℎ Q ℎcomponents ℎ' is Rayleigh-distributedRayleigh PDFindependentpand zero-distributed Then, amplitude is Rayleigh distributed Phase is uniformly distributed36

Rayleigh fading example37

Putting it all Together: Ray Tracing Approximate solutions to Maxwell’s electromagnetic equations by insteadrepresenting wavefronts as particles, traveling along raysExample propagation model– Apply geometric reflection, diffraction, scattering rulesGeometric optics (Snell’s laws Geometrical Theor Compute angle of reflection, angle of diffractionDiffraction Uniform TD)Diffraction, Finds approximate solution of Maxwell’s equations Mostnearestuseful physicalmodel at frequenciesfromscatterer,and all used forcommunicationsi ti Can predict (i) path loss, (ii) fading Error is smallest when receiver is many λscatterers are large relative to λ Good match to empirical data in rural areas,along city streets (radios close to ground),and indoors Completely site-specific– Changes to site may invalidate modelTxRx38

Today1. Large scale channel models2. Small-scale channel models3. Equalization: Coping with the channel39

Problem: Inter-symbol interference (ISI) Transmitted signal Received signal with ISI40

Problem: Inter-symbol interference (ISI) Transmitted signal Received signal with ISI ISI at one symbol depends on the value of other symbols41

One Solution: Slow down1No ISI Transmitted signal Received signal42

Channel ModelTransmitterdkp(t)Transmit filterWireless ChannelReceiverh(t)yth*(-t)Matched filtery[n]heq(t)!#"Equalizer % ' ) % ) ( %) Composite channel (made up of pulse shape, radiochannel, and matched filter)43

Another Solution I:Zero-forcing EqualizerReceiverNoise: nk yth*(-t)Matched filtery[n]heq(t)!#"Equalizer) %& ' *(')44

PreamblePreamblePacket body Sequence of symbols known to both transmitter &receiver45

Another Solution II: MSE Equalizer Goal: Minimizing mean-squared error (MSE) betweenreceived symbols & transmitted symbols)-& .!"# % & &'( Assumes Receiver has a preamble46

Another Solution III: Decisionfeedback Equalizer Idea: Subtract the interference caused by alreadydetected data (symbols)Noise: nk Decision deviceyty[n]h*(-t)Matched filter w (t)Forward filter !#"-d(t)This part shapes thesignal to work well withthe decision feedback.Feedback filterThis part removes ISI on“future” symbols fromthe currently detectedsymbols.47