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# INTEG HI SPEED COMM CRTS ECSE 6961

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This 109 page Class Notes was uploaded by Immanuel Brakus PhD on Monday October 19, 2015. The Class Notes belongs to ECSE 6961 at Rensselaer Polytechnic Institute taught by Staff in Fall. Since its upload, it has received 21 views. For similar materials see /class/224776/ecse-6961-rensselaer-polytechnic-institute in ELECTRICAL AND COMPUTER ENGINEERING at Rensselaer Polytechnic Institute.

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Date Created: 10/19/15

Physical constants aB 05292 A Bohr radius aB 05292 X 10 10 m 80 88542 X 10 12 AsVm absolute dielectric constant e 16022 X 10719 C elementary charge c 29979 X 108 ms velocity of light in vacuum ERyd 13606 eV Rydberg energy g 98067 m s2 acceleration on earth at sea level due to gravity G 66873 X 10 11 m3 kg s2 gravitational constant F GM mr2 h 66261 X 10 34 Js Planck constant h 41356 X 10 15 eVs h 10546 X 10 34 Js h h2n h 65821 X 10 16 eVs k 13807 X 10 23 JK Boltzmann constant k 86175 X 10 5 eVK no 12566 X 10 6 VsAm absolute magnetic constant me 91094 X 10 31 kg free electron mass N Am 60221 X 1023 mol 1 Avogadro number R kNAVO 83145 J K71 mol 1 ideal gas constant Note The dielectric permittivity of a material is given by s Sr 80 where Sr and so are the relative and absolute dielectric permittivity respectively The magnetic permeability of a material is given by p pr 110 where ur and 110 are the relative and absolute magnetic permeability respectively Useful conversions 1 eV 16022 X 10 cv 16022 X 10 J E hv hclt 12398 eVltnm kT 2586 meV at T300 K kT 2525 meV at T 20 C 29315 K ECSE 6961 The Wireless Channel Shiv Kalyanaraman shivku1naecserpiedu Google Shiv RPI Slides based upon books by TseViswanath Goldsmith Rappaport J Andrews etal Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 1 Google shiv rpiquot Rensselaer Polytechnic Institute 1V mar a yanaraman Wireless Channel is Very Different Wireless channel feels very different from a wired channel El Not a pointtopoint link El Variable capacity errors delays El Capacity is shared with interferers Characteristics of the channel a ear to chan e randoml with time which makes it difficult to design reliable systems with guaranteed performance Cellular model vs reality f 4 7v it Part 21 an Wersiln vliiivd V39le Part h a more realistic case whore base in WlllI 1 each cell is exagnnul 5iatlullS are 113913913gularly placed and roll plumes house the 39 t ha station 2 Google shiv rpiquot Basic Ideas Path Loss Shadowing Fading El Variable decay of signal due to environment multipaths mobility Path Loss Alone Shadowing and Path Loss Mullipath Shadowing and Path Loss iv 0 log d Rensselaer Polytechnic Institute Source A Goldsmith book Figure 210 Contours of Constant Received Power Shivkumar Kalyanaraman Google shiv rpiquot Attenuation Dispersion Effects ISI Intersymbol interference 1S1 m m W Distance 6 Rensselaer Polytechnic Institute ShleU mar Kalyanaraman Source Prof Raj Jain WUSTL 4 Google shiv rpi Wireless Multipath Channel Channel Quality Time Channel varies at two spatial scales Large scale fading path loss shadowing Small scale fading Multipath fading frequency selectivity coherence bw 500kHz Doppler timeselectivity coherence time 25ms Rensselaer Polytechnic Institute Shleumar Kalyanaraman 5 Google shiv rpiquot MultiPath Interference Constructive amp Destructive t y y t t l 0 01 02 03 04 05 06 07 08 09 1 time nanoseconds 2 17 e of 1 n 2 t t t a 01 02 03 07 03 09 1 04 05 06 time nanoseconds Fhe difference between constmctive interference top and destructive nitetference bottom at C 95 GHz is less than 01 nanoseconds in phase which coll esponds to about 3 cm araman 6 Google shiv rpi Rensselaer Polyte Mobile Wireless Channel w Multipath Direction of travel gt deep fades F ast Fading Multipath Slow Fading Shadowing Path LOSS CW 1 T J h I D 2km D 5km tlme Rensselaer Polytechnic Institute Kalyanaraman l 7 Google shiv rpi Game plan El We wish to understand how physical parameters such as El carrier frequency El mobile speed El bandwidth El delay spread El angular spread impact how a wireless channel behaves from the cell planning and communication system point of View El We start with deterministic physical model and progress towards statistical models which are more useful for design and performance evaluation Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 8 Google shiv rpiquot Rensselaer Polytechnic Institute Largescale Fading Path Loss Shadowing Shivkumar Kalyanaraman Google shiv rpi Largescale fading CellSite Planning El In free space received power attenuates like lr2 El With re ections and obstructions can attenuate even more rapidly with distance Detailed modelling complicated El Time constants associated with variations are very long as the mobile moves many seconds or minutes El More important for cell site planning less for communication system design Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 10 Google shiv rpiquot Path Loss Modeling El Maxwell s equations El Complex and impractical El Free space path loss model El T00 simple El Ray tracing models EIRequires sitespecific information El Empirical Models El Don t always generalize to other environments El Simpli ed power falloff models El Main characteristics good for highlevel analysis Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 11 Google shiv rpiquot FreeSpace Propagatlon El If oscillating eld at transmitter it produces three components CI The electrostatic and inductive elds that decay as ld2 or ld3 CI The EM radiation eld that decays as ld power decays as ld2 CI Rensselaer Polytechnic Institute Kalyanaraman 12 Google shiv rpiquot Electric Far Field amp Transfer Function El sz a sinusoid cos 2nft El Electric Field source antenna EU t 6 U SW f quot5 2W f gain as I I t 1 r09 Iiquot 27Tff El Product of antenna gains 0L r El Consider the function H 139 1 r transfer function kumar Kalyanaraman 13 Googlc shiv rpi Freespace and received elds Path Loss I m m P101 EIRP 4nd2 47ml 3 Pd 5 3 201r power ux density Pd Note Electric Field E decays as Ir but Power Pd decays as 1r2 Path Loss in dB Wm2 n 5 A PL dB 2 10105110 E dB Pf 47H m is therpi39odnct of the transmit and receive antenna eld radiation patterns in the LOS direction Rensselaer Polytechnic Institute Shivkumar Kalyanaraman l 4 Googlc shiv rpiquot Decibels dB dBm dBi El dB Decibel 10 log 10 PrPt Logratio of two signal levels Named after Alexander Graham Bell For example a cable has 6 dB loss or an ampli er has 15 dB of gain System gains and losses can be addedsubtracted especially when changes are in several orders of magnitude El dBm dB milliWatt Relative to 1mW ie 0 dBm is 1 mW milliWatt Small signals are ve eg 83dBm Typical 8021 lb WLAN cards have 15 dBm 32mW of output power They also spec a 83 dBm RX sensitivity minimum RX signal level required for lleps reception For example 125 mW is 21 dBm and 250 mW is 24 dBm commonly used numbers El dBi dB isotropic for EIRP Effective Isotropic Radiated Power The gain a given antenna has over a theoretical isotropic point source antenna The gain of microwave antennas above 1 GHZ is generally given in dBi El dBd dB dipole The gain an antenna has over a dipole antenna at the same frequency A dipole antenna is the smallest least gain practical antenna that can be made A dipole antenna has 214 dB gain over a 0 dBi isotropic antenna Thus a simple dipole antenna has a gain of 2 14 dBi or 0 dBd and is used as a standard for calibration The term dBd or sometimes just called dB generally is used to describe antenna gain for antennas that operate under lGHz 1000Mhz Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 15 Google shiv rpiquot dB calculations Effective Isotropic Radiated Power EIRP El EIRP Effect Isotropic Radiated Power effective power found in the main lobe of transmitter antenna a EIRP 13th El In dB EIRP is equal to sum of the antenna gain Gt in dBi plus the power Pt in dBm into that antenna El For example a 12 dBi gain antenna fed directly with 15 dBm of power has an Effective Isotropic Radiated Power EIRP of 12 dBi 15dBm 27 dBm 500 mW Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 16 Google shiv rpiquot Path Loss Example 1 Carrier Frequency Example 21 Consider an indoor wireless LAN with ft UUU MHzr o ells of radius 86 31 m and nondirectional antennas Under the free space path loss model what transn 39t39pmm39is39iequired at the access point such that all ter minals within the cell receive a minimum power of 10 n W How does this change if the system frequency is 5 GHZ397 Solution We must nd the transmit power such that the teinlinals at the cell botuidaiy receive the minimum required power We obtain a fonnula for the required transmit power by inverting 27 to obtain 4m 2 P P Substituting in G l nondirectional antennas 0ny 33 m z 10 m and P 1JIW yields Pt lL5W 161 dBV Recall that P Watts equals ltl rg1 l7 de dB relative to one fan and 1llrzg1 3P ttll dBm dB relative to one milliwatt At 5 GHZ only A 06 changes so Pt filly 1642 dBWi CI Note effect of frequency f 900 Mhz vs 5 Ghz El Either the receiver must have greater sensitivity or the sender must pour 44W of power even for 10m cell radius Rensselaer Polytechnic Institute ShleU mar Kalyanaraman Source A Goldsmith book 17 GOOSIC I shiv rpiquot Path Loss Example 2 Interference amp Cell Sizing Example 31 Consider a user in tlte downin of a cellular srstent wltere tlte desired base station is at a distance of 500 meters and there are numerous nearby interfering base stations transmitting at the some power level Iftltere are 3 inteifering base stations at a distance of lnn 3 It a distance of 7 lnn and 10 at a distance of 4 Ian use tlte entpiricalpatll lossfortnnla to nd the sigital tointeiference ratio SIR i e the noise is neglected when n 3 and tlten when a 5 El Desired signal power Put PtPoflgto573 El I rf me erence power PM 111mg gu 32 3 mind u SIR 5mm 3 El SIR is much better with higher path loss exponent on 5 El Higher path loss smaller cells gt lower interference higher SIR Rensselaer Polytechnic Institute Kalyanaraman Source J Andrews et 211 book 18 GOOSIC I shiv rpiquot Path Loss Range vs Bandwidth Tradeoff El Frequencies lt l GHZ are often referred to as beachfront spectrum Why El L High frequency RF electronics have traditionally been harder to design and manufacture and hence more expensive less so nowadays El A Pathloss increases 002 El A signal at 35 GHZ one of WiMAX s candidate frequencies will be received with about 20 times less power than at 800 MHZ a popular cellular frequency El Effective path loss exponent also increases at higher frequencies due to increased absorption and attenuation of high frequency signals El Tradeoff El Bandwidth at higher carrier frequencies is more plentiful and less expensive El Does not support large transmission ranges El also increases problems for mobilityDoppler effects etc El WIMAX Choice El Pick any two out of three high data rate high range low cost Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 19 Google shiv rpiquot Ray Tracing El Models all signal components El Re ections El Scattering El Diffraction El Diffraction signal bends around an object in its path to the receiver El Diffraction Path loss exceeding 100 dB El Error of the ray tracing approximation is smallest when the receiver is many wavelengths from the nearest scatterer and all the scatterers are large relative to a wavelength and fairly smooth El Good match w empirical data in mral areas along city streets TXRX close to ground LAN with adjusted diffraction coefficients Shivkumar Kalyanaraman Rensselaer Polytechnic Institute 20 Google shiv rpiquot Re ection Diffraction Scattering E 7 A7 quotquot Re ectionRefraction large objects gtgtl Scattering small Objects IOugh surfaces lt foilage lamposts street signs El 900Mhz 9 30 cm El 24Ghz 9 139 cm El 58Ghz 9 575 cm DiffractionShadowin bendin around shar ed es Rensselaer Polytechnic Institute g p g ShleU mar Kalyanaraman 21 Google shiv rpiquot Classical 2ray Ground Bounce model T transmitter Em r Ems 1 R receiver II II 39 e J l i I 7 P N MC 2 4mm 2P Kain1 2 P r 4rd Ad t 3913 t39 Pr dBm Pt dBm llng10G1 2010g10luh 7 4llopmd39 Rensselaer Polytechnic Institute OllthUllldl Kalyanaraman Source A Goldsmith book derivation in book22 GOOSIE I shiv rpi 2ray model observations CI The electric field ips in sign canceling the LOS eld and hence the path loss is Ofd394 rather than Ofd39Z CI The frequency effect disappears El Similar phenomenon with antenna arrays El Near eld farfield detail explored in next slide El Used for celldesign Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 23 Google shiv rpiquot 2ray model distance effect critical distance El d lt h constructive if El ht lt d lt do constructive and destructive if multipath fading upto critical distance El dc lt d only destructive interference Eic lizthri k El Piecewise linear approximation w slopes O 20 dBdecade 4O dBdecade Rensselaer Polytechnic Institute Source A Goldsmith book UUUMHL Rll 111 50111 17 2111 G L G l TqurAy model received Slgn l prEr cg Renewed powev Pr de 4 1591501 Received Power versus Distance for TwoRay Model Shivkumar Kalyanaraman 24 Google shiv rpiquot 2ray model example cell design Example 22 Determine the critical distance for the tworay model in an urban microcell 11 10m 12 3 n1 and an indoor microcell In 3 m 1r 2 in for fr 2 GHZ Solution 10 JilzgllrA 339 600 meters for the 1n39ban microcell arid 160 metersZEfor the indoor system A cell radius of 800 in in an urban iilieroealls y stenl is a bit large urban nii39c romllsd39oday are on the order of 100 in to maintain large capacity However if we used a cell size of 800 n1 under these system parameters signal power would fall o as 12 inside the cell and interference from neighbormg cells would fall off as 14 and thus would be greatly reduced Similarly 160 111 is quite large for the cell radius of an indoor system as there would typically be many walls the signal would have to go through for an indoor cell radius of that size So an indoor system would typically have a smaller cell radius on the order of 1020 in El Design the cell size to be lt critical distance to get 0d 22 Qower decay in cell and 0M outside El Cell radii are typically much smaller than critical distance Rensselaer Polytechnic Institute ShleU mar Kalyanaraman Source A Goldsmith book 25 GOOSIC I shiv rpiquot El Ground and 13 wall re ections El Falloff with distance squared d z El El El Empirical studies d V where 2 lies anywhere between two and SIX Rensselaer Polytechnic Institute 10Ray Model Urban Microcells Dominance of the multipath rays which decay as d over the combination of the LOS and groundre ected rays the tworay model which decays as d 4 Shivkumar Kalyanaraman 26 Google shiv rpiquot El Used when path loss dominated by re ections El Most important parameter is the path loss eXponent y determined empirically El Cell design impact If the radius of a cell is reduced by half when the propagation path loss eXponent is 4 the transmit power level ofa base station is reduced by 12dB 10 log 16 dB El Costs More base stations frequent handoffs Rensselaer Polytechnic Institute Simpli ed Path Loss Model d y BthKjo zgygS Shivkumar Kalyanaraman 27 Google shiv rpiquot Path Loss Exponents for Diffe Environment Free xpucc Urlun urcu cellular radio Sliihlu 6d urban ucllultlr mdm in hmlding lineUIuglil Obstructed in building Obxlructcd in Ltctnricx Rensselaer Polytechnic Institute Typical largescale path loss rent Environments Path Loss Exponent n 7 27 in 35 3 in 5 6 to 18 4106 7 x Lu 3 svaumar halyanaraman Source Rappaport and A Goldsmith books 28 Google shiv Empirical Models El Okumura model El Empirically based sitefreq speci c El Awkward uses graphs El Hata model El Analytical approximation to Okumura model El Cost 136 Model El Extends Hata model to higher frequency El WalflshBertoni El Cost 136 extension to include diffraction Commonly used in cellular system simulations Rensselaer Polytechnic Institute 2 GHZ from rooftops Shivkumar Kalyanaraman 29 Google shiv rpiquot Empirical Model Lee s Model on a LogLog scale dBm Eg Lee Model g s i 3 52 39 5 g 2 I g a a I I i I I km 1 gt 1 10 d a Standard Deviation 7 to 10 dB 2 Gml mhwml m Rensselaer Polytechnic Institute Kalyanaraman 30 Google shiv rpi Empirical Path Loss Okamura Hata COST231 El Empirical models include effects of path loss shadowing and multipath El Multipath effects are averaged over several wavelengths local mean attenuation LMA El Empirical path loss for a given environment is the average of LMA at a distance d over all measurements El Okamura based upon Tokyo measurements 1100 lm 1501500MHz base station heights 30100m median attenuation over freespaceloss 10 l4dB standard deviation PLUM dB d flmu l 1RErl El Hata closed form version of Okamura PLurbanUj dB 595526161Dg10 7 13521ng 10UI1 7 HUM 44A 7 U551U3 wlltluglMtl 231 CI COST 231 Extensions to 2 GHz PL WMHMMB lj3353 lluglquotE7l352l gm lf7u1r39ll97655 Ingrid11 l gmrlC39Al 234 I Rensselaer Polytechnic Institute our Vixuiucu aniy anal aiucui I Source A Goldsmith book 31 Google I shiv rpiquot Indoor Models El 900 MHz lO20dB attenuation for 1 oor 6lOdB oor for next few oors and frequency dependent El Partition loss each time depending upton material see table El Outdoortoindoor building penetration loss 820 dB decreases by 14dB oor for higher oors reduced clutter El Windows 6dB less loss than walls if not lead lined Rensselaer Polytechnic Institute I Kalyanaraman 32 Googlc shiv rpiquot Path Loss Models Summary I Path loss models simplify Maxwell s equations I Models vary in complexity and accuracy El Power falloff with distance is proportional to d2 in free space d4 in two path model El General ray tracing computationally complex El Empirical models used in 2G3GWimaX simulations El Main characteristics of path loss captured in simple model PrPtKd0dV Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 33 Google shiv rpiquot Shadowing B 11PM I 0 E m4 Figure 33 Shadowing can cause large deviations from path loss predictions El Lognormal model for shadowing rV x Rensselaer Polytechnic Institute Shivkumar Kalyanaraman 34 Google shiv rpiquot Shadowmg Measured largescale path loss All Measurement Locations n4 1 40 v 130 3 1 20 5 V 1 10 n n O 1 5 100 Cl 0 90 80 70 01 T R Separation km Figure 417 Scatter plot of measured data and corresponding MMSE path loss model for many Rensselaer Polywities in Germany For this data I 27 and a tm dB from Sei91 IEEE anaraman 35 Google shiv rpiquot LogNormal Shadowing El Assumption shadowing is dominated by the attenuation from blocking objects El Attenuation of for depth d Sd eiad 0c attenuation constant El Many objects 5dt em di 2 eiadt dt 2 dz is the sum of the random object depths El Cental Limit Theorem CLT adt log sd Nu a El log sd is therefore lognormal Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 36 Google shiv rpiquot Area versus Distance Coverage model with Shadowing model i Pr Pym gt7 09 eons na SIGNAL ABOVETHRESHOLD U 1 min 118 Family 0 curves reianng iractiun of IoIaI area wilh sugnai above threshuid um as m of probability of signal above threshold on the cell boundary Figure 2 10 Contours of Cousmul Received Power Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 37 Google shiv rpiquot Outage Probability w Shadowing Ijmz39n 10 logl If 10 1 g10d0v U L dB P1121111 1 Q Example 25 Find the outage probability at 150 m for a Channel based on the combined path loss and shadowing mod els of Examples 23 and 24 assuming a transmit power of Pt 10 dBm and minimum power requirement PM 71105 dBmt SolHim We have P 11 111W 10 dBm Pond llthBm L507 141141501 lt ll5dBm l 7 Q Pruitt 7 10139101 7 1071033110dl0 quotwas 7 I57llo21l50 m F7 397 1Qlt 110 it 5i Jl l Au outage probabilities of 1 is a typical target in wireless system designs El Need to improve receiver sensitivity ie reduce Pmin for better coverage Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 38 Googlc shiv rpiquot Shadowing Modulation Design Consider a Willi 39base station BS mmnmnimting to a subscribei with the ChamIelparaineteits39 1 5 Po 741MB do int as UdB We assume a tranxmit power of B 1 Watt 30 dBnI a bandwidth of B 10 A111 and due to rate 12 convolutional codes a received SNR of 1 4t 7 dB is required for l GQA I whilejnst 3 dB is required for BPSK K Finallr we consider only ambient noise with a apical power spectral density afND 7173lBlllHZ with an additional receiver noise gure of Nf osti The question is this At a distance of 500 meters from the base station what is the likelihood that the BS can i eliablv send BPSK or I 6 4411 El Simple path lossshadowing mOdeI Pr HP D Pr PdB39 lOluglO Pr 1010g10P0 lfilog10 039 1010ng 30dan 401B 81lB z lB 91le dB El Find Noise power It0tr lB NO Nf 10 log1U B 173 SdB 70 9ample an 39 Google shiv rpi Rensselaer Polytechnic Institute Shadowing Modulation Design Contd D SINR 2 91dBm dB 98mm 148 dB El Without shadowing X 0 BPSK works 100 16QAM fails all the time El With shadowing Gs 6dB BPSK 16QAM n Pquot4 3 B m r in P21imB P 3 p 4 J T 7 U 1 3 2 our 37075 El 75 of users can use BPSK modulation and hence get a PHY data rate of 10 MHZ l bitsymbol 3912 5 Mbps El Less than 1 of users can reliably use 16QAM 4 bitssymbol for a more desirable data rate of 20 Mbps El Interestingly for BPSK wo shadowing we had 100 and 16QAM 0 Rensselaer Polytechnic Institute Kalyanaraman 40 Google shiv rpiquot SmallScale Fading RayleighRicean Models Multipath amp Doppler Rensselaer Polytechnic Institute Shivkumar Kalyanaraman 41 Google shiv rpi Smallscale Multipath fading System Design El Wireless communication typically happens at very high carrier frequency eg fc 900 MHz or 19 GHz for cellular El Multipath fading due to constructive and destructive interference of the transmitted waves El Channel varies when mobile moves a distance of the order of the carrier wavelength This is about 03 m for 900 Mhz cellular El For vehicular speeds this translates to channel variation of the order of 100 Hz El Primary driver behind wireless communication system design Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 42 Google shiv rpiquot Fading Small Scale vs Large Scale 30 3s 340 3 g 45 9 50 E 55 a 60 65 14 15 l6 17 18 19 20 21 22 23 24 25 2639 27 28 T R Sepmtion meters Rensselaer 1 01er cnmc msutute mum A a Mum mua 43 Google shiv rpiquot Source 1 SingleTap Channel Rayleigh Dist n El Path loss shadowing gt average signal power loss El Fading around this average El Subtract out average gt fading modeled as a zeromean random process El Narrowband Fading channel Each symbol is long in time CI The channel ht is assumed to be uncorrelated across symbols gt single tap in time domain El Fading w many scatterers Central Limit Theorem El In phase cosine and quadrature sine components of the snapshot r0 denoted as r1 0 and rQ0 are independent Gaussian random variables El Envelope Amplitude 739 1392 is Rayleigh El Received POWCI Z r I is exponentially distributed Rensselaer Polytechnic Institute Kalyanaraman 44 Google shiv rpiquot Source 2 Multipaths PowerDelay Pro le multipath propagation 6525 Jim an nu mm W a DEIDDI n Base Station BS Channel Impulse Response Channel amplitude h correlated at delays 1 Each tap value kTs Rayleigh distributed actually the sum ofseveral sub paths Rensselaer Polytechnic Institute A a p th1 O n path2 ljpaihB l 9 Path Delay Mobile Station MS hz hi ho hpii h gtT n 2Ta VT Shivkumar Kalyanaraman 45 Google shiv Eg Power Delay Pro le WLANindoor 0 4 l39 RMS Delay Spread 4540 ns I lquot 0 50 0 50 100 150 200 250 300 350 400 450 O l h A Mexlmum Excess Delay lt 10 dB 84 ns l J Threshold LOVEI 20 dB l I J h A UAV39A39 V IN 39wuwvwma W Mean Excess Delay 4505 n5 Normalized Received Power 18 Scale L c l I I l I I l I Excess Delay ns Figure 510 Example of an indoor power delay profile rms delay spread mean excess delay maximum excess delay 10 dB and threshold level are shown aman 46 Google shiv rpiquot Rens Multipath TimeDispersion gt Frequency Selectivity The impulse response of the channel is correlated in the timedomain sum of echoes El Manifests as a powerdelay pro le dispersion in channel autocorrelation lnction AAt Equivalent to selectivity or deep fades in the frequency domain Delay Spread 5 N 50m indoor 7 1w outdoorcellular Coherence Bandwidth Bc 5 OOkHz outdoorcellular 7 ZOMHZ indoor Implications High data rate symbol smears onto the adjacent ones ISI D DUDE Multipath Mm HU s 1 4 TRAIS effeCtS 4 N O 1 s u AT if TRJ39LIS the channel in time top Similarly the shape of the multipth intensity pro le AAAT detelmines the correlation pattein of the channel frequency response bottom KSIISSSld l I UlyLSUIlJLlC lIlSLlLLlLS 39 M nun J A Mu 47 Google shiv rpiquot Source 3 Doppler NonStationary Impulse Response l7 t W A Set of multipaths changes 05 ms 112 hl ho Ill 1 NE T huilhl 7 Rensselae I TS 215 I 39 39 VTs h l V V VT yanaraman 4g Goomrpi Dopple Dispersion Frequency gt TimeSelectivity CI The doppler power spectrum shows dispersion atness N doppler spread 100200 Hz for vehicular spee 5 El Equivalent to selectivity or deep fades in the time domain correlation envelope El Each envelope point in timedomain is drawn from Rayleigh distribution But because of Doppler it is not HD but correlated for a time period N Tc correlation time Doppler Spread Ds N 100 Hz vehicular speeds lGHz El Coherence TiIne Tc 255ms El Implications A deep fade on a tone can persist for 255 ms Closedloop estimation is valid only for 255 ms U PtAf ht A fr fD f1 fr l fD f Figure 318 The shape of the Doppler power spectrum p Af determines the con39elation envelope of the channel in time top 49 Google shivrpiquot Fading Summary TimeVarying Channel Impulse Response I t T I7Tt At ho ho 1b trueth I The 2 1 lTs VTS Figure 313 The delay T corresponds to how long the channel impulse response lasts The channel is time varying so the channel impulse response is also a function of time ie 11039 ft and can be quite di erent at time t At than it was at time 1 El At each tap channel gain h is a Rayleigh distributed r v The random process is not IID El Response spreads out in the timedomain 5 leading to intersymbol interference and deep fades in the frequency domain frequencyselectivity caused by multipath fading El 3 Response completely vanish deep fade for certain values oft Timeselectivity caused Wdoppler effects frequencydomain dispersion spreading Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 50 Google shiv DispersionSelectivity Duality h T t Selective In I H f t frequency Disperslve in time H gt T g f A hT 2 Selective in IHf t time Dlsperslve 1n requency I 39 t 39 39 139 Figure 319 The dispei siouiselectivity duality Dispersion in time causes frequency selectivity while dis persion in frequency causes time selectivity Rensselaer Polytechnic Institute Shivkumar Kalyanaraman Google shiv rpi DispersionSelectivity Duality Contd l PtAf ht Rayleigh T 1 D39 My t39 c ISQ HJI 4 fr Af f39 f D fr f4 f D A ATAT lHf Ba m 5 THAIS e AT f TBAIS Figure 318 The shape of the Doppler power spectulm pAAf deteuuines the con elatiou envelope of E the channel in time top Similarly the shape of the multipth intensity pro le ATLAT detennines the correlation pattern of the channel frequency response bottom Fading Jargon El Flat fading no multipath ISI effects El Eg narrowband indoors El Frequencyselective fading multipath ISI effects El Eg broadband outdoor El Slow fading no doppler effects El Eg indoor Wifi home networking El Fast Fading doppler effects timeselective channel El Eg cellular vehicular El Broadband cellular vehicular gt Fast frequencyselective Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 53 Google shiv rpiquot SingleTap Narrowband Flat Fading Rensselaer Polytechnic Institute Fading Details Shivkumar Kalyanaraman Google shiv rpi Normal Vector RV Rayleigh ChiSquared fxX 1 Exponential Rayleigh 0606 Unlform 039 l 1 v b a I t O 039 a b x The rayleigh exponential and uniform pdf 5 X Xv Xn is Normal random vector K is Rayleigh eg magnitude of a complex gaussian channel X1 jX2 K 2 is ChiSguared W ndegrees of freedom When n 2 chisquared becomes exponential egz gower in complex gaussian channel sum of squares Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 55 Google shiv rpiquot Rayleigh Ricean Nakagamim fading Typical slmululed Rayleigh fading at the corner Receiver speed 7120 km hr Raylelgh 7 7Rlcesn wlth K 1 7 7 7 Nakagamlwllh m 2 Signal Level 43 naout rms D 50 1 DD 1 50 200 250 Elapsed ms hglue 1 w I Inb Figure 515 A Iypical Rayleigh ladmg envelope 3190 MHz 1mm Fun93 lEEE l hm m cmgc recon Ricean used when there is a dominant LOS path K parameter strength of LOS to nonLOS K 0 gt Rayleigh Nakagamim distribution can in many cases be used in tractable analysis of fading channel performance More general than Rayleigh and Ricean Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 56 Google shiv rpiquot Rayleigh Fading Example Example 32 Consider a channel with Rayleigh fading and average received power Pr 20 dBm Find the prob ability that the received power is below 10 dBm Solution we have P 20 dBm 100 mVxK We want to nd the probability that Z 2 lt 10 dBm 10 vai Thus tzkmy fmi 1 0 100 ff100d 095 El Nontrivial 1 probability of m deep fades Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 57 Google shiv rpiquot Rayleigh Fading Fade Duration Example average fade duration is LZT 1 N mm lt Z LZ Level Crossing Rate Z f 2 ti L 39 Z i1 Z 72 1 f2 7 I fDVQF I Example 33 Consider a voice system with acceptable BER when the received signal power is at or above half its averaglt values If the BER is below its acceptable level for more than 120 ms users will tum off their phone Find the mug of Doppler values in a Rayleigh fading channel such that the average time duration when users have unacceptabh voice quality is less than t 60 ms Solution The target received signal value is half the average so P0 511 and thus p Vii We require 5 2 lt r 000 39 fl fn and thus ff 2 r 7 lUUHE 01 Hz Faster motion amp do ler better et out of fades DES Uuugm blllV up Effect of Rayleigh Fading 5 20 25 30 SN R symbol energynoise in dB Figm e 322 Flat fading causes a loss of at least 2030 dB at reasonable BER values Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 59 Google shiv rp39 Broadband FrequencySelective Fading Rensselaer Polytechnic Institute Fading Details Multipath Shivkumar Kalyanaraman 60 Google shiv rpi Broadband Fading Multipath Frequency Selectivity i T E i Local C scattering 2 main multlpalhg 2 V El A few major multipaths and lots of local scatterers gt each channel sample tap can be modeled as Rayleigh El A tap period generally shorter than a symbol time El Correlation between tapped values Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 61 Google shiv rpiquot Recall Electric Far Field amp Transfer Function El sz a sinusoid cos 2nft El Electric Field source antenna Eff 6 U 861quot f 2 fquot339 4 gain as I r09 uquot os m39 f El Product of antenna gains 0L ErUf f 39 j3927frC El Consider the function Hf M DC transfer function kumar Kalyanaraman 62 Google shiv rpi Re ecting wall Ray Tracing Superposition 39l l zmsmit A 1tonn o 39 Vull rowiw antenna El Superposition of phasesinged attenuatedwgaves I 1 ms 217 7 i 1 E 01527le 1 Eff E o W o 7 e quot121Lv39 El Phase difference 34 r r depends uponfamp r El Constructive or destructive interference El Peaktovalley coherence distance El Delay sgread T r 4 11 3 El Coherence bandwidth 111 Ellf pattern changes 1 requency changes on the order of coherence bandwidth Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 63 Googlc shiv rpiquot Symbol Time El a path2 I I path3 n Halli Delay Delay spread 1 Es Rensselaer Polytechnic Institute Power Delay Pro le gt InterSymbol interference Symbol Time l r H El Higher bandwidth gt higher symbol rate and smaller time persymbol El Lower symbol rate more time energy persymbol If the delay spread is longer than the symbolduration symbols will smear onto adjacent symbols and cause symbol errors H l Symbol Error If symbol rate Mbps 5 5 39 W No Symbol Error 1kbpsg energy is collected over the full symbol period for detection Shivkumar Kalyanaraman 64 Google shiv rpiquot Effect of Bandwidth taps 0n MultiPath Fading 1 h I I I I I H I I I I 39 U I I I I E 7m I 5A 20 22 3 40 39 g 40 I I E I u I g 1 39 f zuo Ml 7 f 700 a a 1 Fquot I I I I 70 50 100 50 100 250 300 350 400 450 500 L45 L5 055 L6 550 Ims 17 075 KLK 045 09 095 I Time Ian l Icqucnq IGHz cJ L 0001 I I I I 0 I I I I I Imam A I 00qu g A I 4 00002 I5 I I 0 g 40 l I 4 J 700002 t 4101104 51 quotm 39 39 4 I I ALUUWI 750 llt 40IIHz l ALUIXM 4mm I I I 410 I l I I 50 mo 150 100 2er 100 350 Inn 450 son 550 um um um Imx 0m 07 MI 072 073 074 075 Ina Imc Ins hcqucncy 3sz Effective channel depends on both physical environment and bandwidth Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 65 Google shiv rpI Multipaths amp Bandwidth Contd El Even though many paths with different delays exist corresponding to finerscale bumps in ht El Smaller bandwidth gt fewer channel taps remember Nyquist CI The receiver will simply not sample several multipaths and interpolate what it does sample gt smoother envelope ht CI The power in these multipaths cannot be combined El In CDMA Rake Equalization Receiver the power on multipath taps is received rake ngers gain adjusted and com ine El Similar to bandpass vs matched filtering see next slide Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 66 Google shiv rpiquot Rake Equalization Analogy Bandpass vs Matched Filtering Simple Bandpass low bandwidth Filter excludes noise but misses some signal power in other mpath taps A band puss ller emcludu Hui b A t a Matched Filter includes more signal power weighted according to size gt maximal noise rejection amp signal power aggregation l l i ii A maidled ller indud ignd numponems reigned awarding io lheir Size M new A J39W L R l l A l Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 67 Google shiv rpiquot Power Delay Pro le MeanRMS Delay Spreads The power delay pro le ALL also called the multipath intensity pro le is de ned as the autocorrelation 352 A with At I 1437 th47 0 The power delay pro le represents the average power associated with a given multipath delay and is easily measured empirically The average and nus delay spread are typically de ned in terms of the power delay pro le ACT as fom TACTIT I 354 IT foxAA dT I Table 32 Some typical RMS delay spread and approximate coherence bandwidths for different WilVlAX Environment f GHz RMS delay TRMS ns Coherence bandwidth BC z 573 MHZ Reference Urban 91 1300 15 22 Rural 91 1960 1 22 Indoor 91 270 7 22 Urban 53 44 45 36 Rural 53 66 30 36 Indoor 53 124 161 36 f1 f2 SEC 239 Hf 1zHf2 1 f2 gt BC 239 H f1 and H If3 are uncorrelath Rensselaer Polytechnic Institute Dulth lat Kalyanaraman 68 Google shiv rpi Multipath Fading Example Example 35 Consider a wideband channel with multipath intensity pro le 4 i 00001 0 S 7 S 20 1158 A t739 0 else Find the mean and nns delay spreads of the chaimel and nd the maximimi symbol rate such that a linearly modulated signal transmitted through this channel does not experience 151 Solution The average delay spread is 20 10 J 0 W W 00001d7 J IT V 7 BI ISeC I 2010 00001 I 0 39 The rms delay spread is 2mm it f0 Timph ZOHCVG 0 Tm 2 P WIT We see in this example that the mean delay spread is roughly equal to its inis value To avoid 151 we require linear modulation to have a symbol period that is large relative to nTm Taking this to mean that TS gt anTm yields a symbol period ofTS 925 Isec or a symbol rate ofBS 19114 Kilosymbols per second This is a highly constrained symbol rate for many wireless systems Speci cally for binary modulations where the symbol rate equals the data rate bits per second or bps highquality voice requires on the order of 32 Kbps and highspeed data requires on the order of 10100 Mbps 69 b00816 I shiv rpi Doppler Fast Fading Timeselectivity Rensselaer Polytechnic Institute Fading Details Shivkumar Kalyanaraman 70 Google shiv rpi Doppler Approximate LTI Modeling D r gt r0 vl Elfft 7 0 m9 i931 r HT 9 1 El vlc phase correction 13W f ms 273 Wall rewrite H T0 397 3 5 f 1 quot39391quotquot39 it i39quot 539 Fixed phase amp frequency sh El Do ler fre uenc shift of i c Transmit due to relative motion antenna d El This is no longer LTI unlike Wired HR Channels rt b d El We have to make LTI 1 approximations assuming small timescales only t small vt z 0 El If timevarying attenuation in denominator ignored vt z 0 we can use the transfer function Hf as earlier but with doppler adjustment of 2c Rensselaer Polytechnic Institute ifts Shivkumar Kalyanaraman 71 Google shiv rpiquot Doppler Re ecting Wall Moving Antenna Transmit antenna d gt Wall rm g I 99 U r 7 21 t i n 05 3927f1 7 f i H 2 j 1 F r EPU39 r rU 7 2171 0 7 WT D LELP O ler s read D1 D2 fl3939 CI Note opposite sign for doppler shift for the two waves El Effect is roughly like the product 0ftw0 sinusoids Rensselaer Polytechnic Institute Kalyanaraman 72 Google shiv rpiquot i 5ms M Hii39u39 H Doppler Spread Effect I l i i J i H El Fast oscillations of the order of GHZ El Slow envelope oscillations order of 50 Hz gt peaktozero every 5 ms El Aka Channel coherence time ch c4fi2 Rensselaer Polytechnic Institute J i 391 Mi Mi quot W H J l H i Ii M WI J39HM M Shivkuniar Kalyanaraman 73 Google shiv rpi Twopath mobile Example v 60 kinhr fc 900 MHz Direct path has Doppler shift of roughly 50 Hz fvc Re ected path has shift of 50 Hz Doppler spread 100 Hz Transmit antenna d gt Wall rm 9 gt U Rensselaer Polytechnic Institute Kalyanaraman 74 Google shiv rpiquot Doppler Spread Effect fd1HZ I I I I I I I I EnvelopemB I 2 UI I I 0 0 2 04 06 1 fd 10 HZ I o1lFV f fmV IIIWP v EnvelopewB I 3 on I I I I I O 02 04 06 08 1 12 14 16 15 2 n I I I fd 190 HZ I I g 4 W1quotUWw lw39fal MIerer1NIIIW39ITIWWI WMY nWWIWWWkaIli Imwn frwI M quot 0 012 0394 016 I I I 1 4 116 118 8 1 1 2 timesecond Figure 320 A sample output of the provide Rayleigh fading Matlab function for Doppler frequencies of fD 1 10 and 100 Hz Rensselaer Polytechnic Institute 5UVKU lnar Kalyanaraman I 75 Google shiv rpi Angular Spread Impact on Spatial Diversity El Spacetime channel models El MeanRMS angular spreads similar to multipath delay spread CI The timevarying impulse response model can be extended to incorporate AOA angleof arrival for the array El A6 average received signal power as a function of AoA 6 El Needs appropriate linear transformation to achieve full MIMO gains 39 f tummy I i I m9quoter C W quot i 39J1 quot IT 6 i TrslHMH Rensselaer Pomecmc 1115mm Shivkumar Kalyanaraman 76 Google shiv rpiquot phase Ren El An approximate rule of thumb is 9 P N lon39 Angular Spread and Coherence Distance El gm RMS angular spread of a channel El Refers to the statistical distribution of the angle of the arriving energy El Large GEMS gt channel energy is coming in from many directions El Lot of local scattering and this results in more statistical diversity in the channel based upon AoA El Small GEMS gt received channel energy is more focused El More focused energy arrival results in less statistical diversity CI The dual of angular spread is coherence distance Dc El As the angular spreadT the coherence distance i and vice versa El A coherence distance of 1 means that any physical positions separated by d have an essentially uncorrelated received signal amplitude and Rayleigh fading which assumes a uniform angular spread the well known relation is 77 Tfreq gt better angular diversity alyanaraman Google shiv rpiquot Key Wireless Channel Parameters Table 31 Key wireless channel parameters Symbol Parameter a path loss exponent as Log nonnal shadowing standard deviation fD Doppler spread maximum Doppler frequency g 2 it TC Channel coherence time TC 8 1 51 Tum Chamlel delay spread maximum TRMS Channel delay spread RAIS BC Channel coherence bandwidth Be z T1 HRMS Angular spread RMS Shivkumar Kalyanaraman Rensselaer Polytechnic Institute 78 Google shiv rpiquot Fading Parameter Values Key channel parameters and time scales Symbol Representative values Carrier frequency fC 1 GHZ Communication bandwidth W 1 MHz Distance between transmitter and receiver I 1 km Velocity of mobile v 64 kmh quot13613312 sin ftquot rBF a 52ch quotquotquotquotquotquot 39 395 1737 39 39 39 3956 flz quotquotquot 39 39 Doppler spread of paths corresponding to a tap D3 100 Hz Timescale for change of path amplitude 1 v 1 minute Time scale for Change of path phase 1 4D 5 ms Time scale for a path to move over a tap CUW 20 s Coherence time TC 2 l 4DS 25 ms quot azTy39sEIEa39d quotquotquotquotquotquotquotquotquot 39 Td quotquotquotquot 39 391 It quotquotquot 39 39 Coherence bandwidth WC 2 l 2Td 500 kHz Rensselaer Polytechnic Institute 79 Shivkumar Kalyanaraman Googlc shiv rpiquot SmallScale Fading Summary SmallScale Fading Based on multipath time delay spread Flat Fading Frequency Selective Fading 1 BW of signal lt BW of channel 1 BW ofsignal gt BW ofchannel 2 Delay spread lt Symbol period 2 Delay spread gt Symbol period SmallScale Fading Based on Doppler Spread 1 l Fast Fading 1 High Doppler spread 2 Coherence time lt Symbol period 3 Channel variations faster than base band signal variations Slow Fading 1 Low Doppler spread 2 Coherence time gt Symbol period 3 Channel variations slower than baseband signal variations 11 Figure 511 Types of smallscale fading Rens 80 Google shiv 39 Delay39s p39i v Tohei39ence 39 quotCoherence Fading Design Impacts Eg Wimax Table 33 Summary of Broadband Fading Parameters with Rules of Thumb Quantity IEJILatae Tf39 quotQumllquot WiMAX Design Impact Spherelife B width BE Simple 139 spread Time u hghlmquotquotquot iii39el 9RMS Dis tance If T gtgt T then fre quency selective If T lt T then fre quency at The larger the delay Egread39i39elav tive to the symbol time the n10139e If 5 gtgt T then fre quency selective max FI F the LS Provides a guide to albumen width BS m EEC10 and hence If fd 3 c then slow fading T tli 39n slow n if 3 1 tnen Iast tad ing Tr sinall necessitates frequentquot channel estimation and limits the OFDM symbol din39atigmbut i39 Non LOS channel lots of diversity effectively LOS channel namnclslit i effectively LOS channel not much diversity Non LOS channel lots of diversity 39393939g39matr beamforming vs diversity Deteimines antenna spacing quota uI39 a I o aquot o 01 JUUBIL alllv I39pi quot Rensselaer Polytechnic Institute Mathematical Models Shivkumar Kalyanaraman 82 Google shiv rpi Physical Models El Wireless channels can be modeled as linear timevarying systems yo Z a7tat not Z where ait and Cit are the gain and delay of path i CI The timevarying impulse response is Mm Za t6r n00 El Cons1der rst the spec1al case when the channel 1s lime invariant h7 Z 6126739 77 i Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 83 Google shiv rpiquot TimeInvariance Assumption Typical Channels are Underspread El Coherence time To depends on carrier frequency and vehicular speed of the order of milliseconds or more El Delay spread Td depends on distance to scatterers of the order of nanoseconds indoor to microseconds outdoor El Channel can be considered as timeinvariant over a long time scale underspread El Transfer function amp frequency domain methods can still be applied to this approximately LTI model Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 84 Google shiv rpiquot Baseband Equivalence 55m RH pj97rfct El Easier to analyze complex numbers like ejWT even though all basebandpassband are real signals involving sines and cosines m gtRut fv h uf ltn2 fcf i 3 1t 51112 fcf rf 1527rf3f 11sin2 ft W MIMI W 5u um zf 1f El Passband signal baseband signal ut multiplying a complex carrier eW signal and extracting the real portion El ut complex envelope or complex lowpass equivalent signal Elg Zuadrature concept Cosine and Sine oscillators modulated with xt and yt respectively the Real and Quadrature parts of ut Received Sign a zt gth m c r r W u f d I vt and Ct are baseband equivalents for received and channel Rensselaer Polytechnic Institute Kalyanaraman 85 Google shiv rpiquot Block diagram xm MI I I 391ITUlw lal CH gt 311 I bl Figure 53 impulse response model Rensselaer Polytechnic Institute rm a Bandpass channel impulse response model b baseband equivalent channel rym nu V AHAlily HI l 1I rm 39I e 1141 Shivkumar Kalyanaraman 86 Google shiv rpi PassbandtoBaseband Conversion Block Diagram El Communication takes place at passband f0 W2 fa W2 El Processing takes place at baseband W27 WQ 39Jl rt K QAM sy stem jMm Note transmitted power half of baseband power Rensselaer Polytechnic Institute ShleU mar Kalyanaraman g7 Googlc shiv rpiquot Passband vs Baseband Equivalent Spectrum S f I f j39r fz fc fr S f V H r g r ffgt0 I i 0 f f6 lt 0 1 f El Communication at passband allocated spectrum Processing in baseband modulation coding etc UpconvertDownconvert El sb contains same information as s Fourier transform hermitian around 0 rotation El If only one of the side bands are transmitted the passband has half the ower as the baseband e uivalent Renssgaer Polytechnic Institute q ShleU mar Kalyanaraman 88 Google shiv rpiquot Perpath Complex Baseband Equivalent Channel CI The frequency response of the system is shifted from the passband to the baseband Hbf Hf fc hbm hte j27rfct 2 1967 Ti where a die 927 El Each path 1 is associated with a delay Ti and a complex gain at Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 89 Google shiv rpiquot DiscreteTime Baseband Equivalence With Modulation and Sampling mm WM Q h 2 mm Emmi mU gt T Mt c my 5 Egt 2 ms 277fpt Shh L 2 8mm B SquotM1711 3mm X x 7 W w Rensselaer Polytechnic Institute mar Kalyanaraman 90 Googlc shiv rpi r 31117Tt 7rt 39 Sampling Interpretation 3mm CI Due to the decay of the sinc function the ith path contributes most significantly to the 1th tap if its delay falls in the window lW 12W lW 12W Main contribution I 0 Main contribution I 0 Main Contribution r l 1 Discrete Time Baseband lO relationship Main uuntrihutiun v t 2 ym Z hdm Tm Main Contributan where lurm as the 7 complex channel lter tap at time ml raw function of mainly the gains af U 0f the paths whose delays Ti1 are Close to 39Wv Rensselaer Polytechnic Institute 39 uiuvnbuum Lxuiyanaraman 91 Googlc shiv rpiquot Multipath Resolution LTI Approximation Sampled basebandequiyalent channel model ym Z herdm E E where h is the 1 th complex channel tap he w 2 die j2 fc7 i i and the sum is over all paths that fall in the delay bin 6 1 E 1 J W 2W W 2W System resolves the mnltina rhs 1m to delavs of lVV hf he Sine Efxquot l Shivkumar Kalyanaraman 92 Google shiv rpiquot Rensselaer Polytechnic Institute Baseband Equivalence Summary El Let st denote the input signal with eguivalent lowpass signal um Let ht denote the bandpass channel impulse response with eguivalent lowpass channel impulse response h gtz CI The transmitted signal st and channel impulse response ht are both real so the channel output rt st ht is also real with frequency response R0 H 050 El RU will also be a bandpass signal w complex lowpass representation rt 711 1 f39r3j2 f t E El It can be rewritten after manipulations as m rIRutrgt hzttllvmm Summary Equivalent lowpass models for st ht and rt isolates the carrier terms fc from the analysis Sampled version allows discretetime processing Rensselaer Polytechnic Institute ShlV mar Kalyanaraman 93 Google shiv rpiquot Multipaths in LTI Model FlatFrequencySelective Fading El Fading occurs when there is destructive interference of the multipaths that contribute to a tap he x Z die f i i Delay spread Td I maxm m0 Tjt Coherence bandwidth WC 2 Tid Td ltlt We gtgt w gt single tap flat fading Td gt 7 WC lt W gt multiple taps frequency selective Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 94 Googlc shiv rpiquot Doppler Time Variations in Model Timevarying ym hgmmm 6 delays he m e Z amoe wfirz lii t l fan t 2 Doppler shift of the i th path Doppler spread D3 maxm fCTZlt fCTj t Coherence time TC 2 Di 8 Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 95 Google shiv rpiquot Doppler Spread D5 3 maxij lchit fez0 Doppler spread is proportional to El the carrier frequency f0 El the angular spread of arriving paths 1 TZlt E cos 6i where 6 is the angle the direction of motion makes with the i th path Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 96 Google shiv rpiquot Degrees of Freedom Complex Dimensions El Discrete symbol Xm is the m h sample of the transmitted signal there are W samples per second El Continuous time signal Xt 1 s E W discrete symbols El Each discrete symbol is a complex number El It represents one complex dimension or degree of freedom El Bandlimited xt has W degrees of freedom per second El Signal space of complex continuous time signals of duration T which have most of their energy within the frequency band W2W2 has dimension approximately WT El Continuous time signal with bandwidth W can be represented by W complex dimensions per second El Degrees of freedom of the channel to be the dimension of the received signal space of ym Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 97 Google shiv rpiquot Statistical Models El Design and performance analysis based on statistical ensemble of channels rather than speci c physical channel hgm x Z die 3277 i El Rayleigh at fading model many small scattered paths I AFIA 1 I unflA 1 ALFA 1 him N JV U7 5 JJV W E N UN U l Complex circular symmetric Gaussian Squared magnitude is exponentially distributed El Rician model 1 lineofsight plus scattered paths MW nA ln 1 Iblllb V Vr u Tva U J Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 98 Google shiv rpiquot 35 715 Statistical Models Correlation over Time Specified by autocorrelation function and power spectral density of fading process Example Clarke s or Jake s model R 39quot39 S m 25 5 05 415 VV r l r Rensselaer Polytechnic Institute I I l I I 200 400 600 800 000 1200 I400 600 1800 2000 712 D2W 0 DJQW 12 Shivkumar Kalyanaraman 99 Google shiv rpiquot Additive White Gaussian Noise AWGN El Complete basebandequivalent channel model wlm N CN0N0 El Special case at fading onetap mrmi r 1mr 1 yLlle IllquotlJlblquotlJ El Will use this throughout the course Shivkumar Kalyanaraman 100 Google shiv rpiquot Rensselaer Polytechnic Institute BER Effect of Fading AWGN vs Fading D 5 1O 15 20 25 30 SN R symbol energynoise in dB Figm e 322 Flat fading causes a loss of at least 2030 dB at reasonable BER values Rensselaer Polytechnic Institute ShleU mar Kalyanaraman 101 Google shiv rpi Types of Channels Types of channel Defining Characteristic Fast fading TC ltlt delay requirement Slow fading TC gtgt delay requirement Flat fading W ltlt WC Frequencyselective fading W gtgt WC Underspread TC1 ltlt T C Rensselaer Polytechnic Institute Shivkumar Kalyanaraman 102 Google shiv rpiquot El We have understood both qualitatively and quantitatively the concepts of path loss shadowing fading multipath doppler and some of their design impacts El We have understood how time and frequency selectivity of wireless channels depend on key Summary physical parameters El We have come up with linear LTI and statistical channel models useful for analysis and design Rensselaer Polytechnic Institute Shivkumar Kalyanaraman 103 Google shiv rpiquot ECSE6961 Internet Protocols Shivkumar Kalyanaraman Rensselaer Polytechnic Institute shivkumaecserpiedu httpwwwecserpiedulHomepagesshivkuma Rensseiaer Poiytechmc institute l Shivku mar Kalyanaraman Overview El ntroductionscourse description amp calendar El Answers to frequently asked questions El Prerequisites El Informal Quiz Rensseiaer Poiytechmc institute 2 Shivku mar Kalyanaraman Course Description Highlights El Syllabus El Core protocols Transport TCP UDP IP Routing AddressingNaming El Advanced topics Multicasting Mobile IP Security Nextgeneration IP Betterthan besteffort Internet Applications El Delivery El Interactive lectures labs informal quizzes email discussion list best2outof3 exams webbased resources Rensselaer Polytechnic institute 3 Shivku mar Kalyanaraman Answers to FAQs El All homeworks due at the beginning of the class indicated on the course calendar El All quizzes are openbook and extremely time limited El Quizzes consist of numerical multiplechoice truefalse and short answer questions See course web page for link to previous offering for previous tests etc El There will be informal quizzes at the beginning of classes once in two weeks to test recently covered material and reading assignments Rensselaer Polytechnic institute 4 Shivku mar Kalyanaraman Prerequisites El Protocol Layers lSOOSI reference model El Physical Layer Coding Manchester El Transmission Media UTP Cat 5 El Data Communication Asynchronous vs synchronous Baud bit and H2 HalfDuplex vs Fullduplex ModulationDemodulation El Packet Transmissions Framing Bit stuffing byte stuffing El Flow Control OnOff Window El Error Detection Parity Checksum Cyclic Redundancy Check Rensselaer Polytechnic lnsltlute 5 Shivku mar Kalyanaraman Prerequisites Cont El Error Recovery Start and Stop Go back n Selective Reject CI LANs Aloha CSMACD Ethernet IEEE 8023 Token RingIEEE 8025 FDDI El Addressing Unicastmulticast LocalGlobal El LAN wiring 10Base5 10Base2 10BaseT 100BaseT4 100BaseTX 100BaseFX El ELANs Hubs Bridges Routers Switches El Routing Distance Vector vs Link State Spanning tree source routing CI Network Layer Connectionless vs connection oriented Rensselaer Polytechnic lnsltlute 6 Shlvku mar Kalyanaraman Informal Quiz Prerequisites T F True or False Datalink refers to the 2nd layer in the lSOOSI reference model Category 5 unshielded twisted pair cable is better than category 3 cable Finding path from one node to another in a large network is a transport layer function It is impossible to send 3000 bitssecond through a wire which has a bandwidth of 1000 Hz Bit stuffing is used so that characters used for framing do not occur in the data part of the frame For long delay paths onoff flow control is better than window flow control Rensselaer Polytechnic tnstttute 7 Shivku mar Kalyanaraman Informal quiz contd Ethernet uses a CS MACD access method 10Base2 runs at 2 Mbps The packets sent in a connectionoriented network are called datagrams Spanning tree algorithm is used to find a loop free path in a network Rensselaer Polytechnic tnstttute 8 Shivku mar Kalyanaraman Informal Quiz 0 Solutions T F Datalink refers to the 2nd layer in the lSOOSI reference model Category 5 unshielded twisted pair cable is better than category 3 cable Finding path from one node to another in a large network is a transport layer function It is impossible to send 3000 bitssecond through a wire which has a bandwidth of 1000 Hz Bit stuffing is used so that characters used for framing do not occur in the data part of the frame For long delay paths onoff flow control is better than window flow control Rensselaer Polytechnic tnstttute 9 Shivku mar Kalyanaraman Informal Quiz 0 Solns contd Ethernet uses a CSMACD access method 10Base2 runs at 2 Mbps The packets sent in a connectionoriented network are called datagrams Spanning tree algorithm is used to find a loop free path in a network Rensselaer Polytechnic tnstttute 10 Shivku mar Kalyanaraman

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