Special Topics ECE 4823
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Date Created: 11/02/15
Nyquist Pulses Instructor MA Ingram ECE4823 g Receiver Filter Baseband output is a superposition of filtered pulses plus filtered noise aAZ xnpt7nTSnt aAan ainTQert 130 1207 040 g Sampling in the Receiver The baseband representation of the receiver in additive Gaussian white noise AWGN aAan oi nTS vt aAwa mTSinTgm I 9 TS mm sample zeromean Gaussian RVs g Ideal Situation Ideally the m h sample depends on only the m h symbol and the noise aAwa stinTgm anmvm I Ts I Necessary Condition To have this ideal situation we must have ng quotTg or alternatively 130 fxtinrg 50 an 72 VT 0 T T 3 1 mn 0 min g Received Signal Example Suppose the ml mm and m1st symbols were 1 1 1 respectively The signal is constrained only at me sarrple points 2 m3T Mars Mfrs mm NonIdeal Situation Suppose the received pulse did not satisfy the condition but did this instead in f 507 nrs 5r 03507 TS 035m TS 94mg 3T Jr VT 0 T 2T 3T Intersymbol Interference ISI The ml mm and m1st received samples become 13vm711vm 707erquotH1 The Negative Effect of ISI The worst case dominates the probability if bit error 13v mil 1vm Nyquist Pulses Pulses that satisfy the condition for no 151 are called Nyquist Pulses 130 fawn 50 Sinc Pulse The sinc pulse is a Nyquist pulse smogTS w mTS 3T ZM o 739 2T 3T Fourier Transform of Sinc Pulse The FT of the sinc pulse is the brick wall characteristic Hm f Popular Alternative Raised Pros and Cons of Sinc g Cosine The FT has the narrowest possible Single parameter or bandwidth of all Nyquist pulses Noncausal Rolloff too gradual g Raised Cosine Formulas g Excess Bandwidth Pahlavan 95 The bandwidth of any pulse will be gtlt o T MT 1 Oillillr lZT greater than that of the sinc Nyquist pulse HR Tlli nTlm EJl I mffle39fEWHX This percentage is the excess bandwidth chU slumT coscmtT t Fquot H PM l MD mT FwyT SI Pros of Raised Cosine g Summary Smoeth FIT gEtFersymbol interference 151 can dominate Easy to build filters that approximate it Falls off as 1t3 Slnc Isthe Ny uIst Pulse With the least Can apprOXImate a delayed pulse With a bandWIdth bu It IS Impractlcal causal filter response Raised Cosine is a popular Nyquist Pulse Excess Bandwidth indicates how much broader is the bandwidth than that of the sinc Nyquist Pulse Nsyquist Pulses are pulses that do not cause I I in an AWGN channel Level Crossings and Fade Durations Instructor MA Ingram ECE4823 Normalized Fading Process Begin with the channel fading process normalized to the local rms signal level Local average m dB subtracted mm veal data g Normalized Threshold Level p Pick a level or threshold P R Hem where R is the unnormalized threshold and 7 2 7 N47 SW Rm lE ht E mt veal data Level Crossing Rate LCR The LCR at threshold p is the expected rate at which the normalized envelope passes the value p with a positive slope slgnal Erlv lrl dB 0 A Hh mm pm llllllllIl llllllllllllll l mm veal data Trends We expect the highest rate around p 0 dB tapering off gently for lower thresholds and abruptly for higher thresholds The maximum Do ler frequency just scales the horizontal axis and therefore the rate nutleal data g LCR For Rayleigh Fading For Rayleigh fading and isotropic scattering Clarke s Model the LCR is given by V Z fdpeiD2 where is the maximum Doppler frequency LCR for Isotropic Scattering g LCR For a Ricean Channel and a NonRandom Component Stuber 2001 Stuber 2001 If we assume isotropic scattering plus a nonrandom component then the LCR can be approximated as Lines are theoretical resulB assuming a 4 K K 2 constant AOA power 2quot 1 1fdpe p 10 distribution plus a E nonrandom component 8 where 1 is the modified Bessel Function of the first symbols represent E kind zero order simulation results using 3 1 2 a multipath fading 9 simulator 3 10x je d6 5 27 0 Speed Estimation Average Fade Duration The LCR can be used to estimate the The average fade duration is the speed of a mobile average period of time the normalized envelope is below a level 0 Signal Env in dB 0 pin dB The average of these Average Fade Duration Impacts Interleaver Depth Deinterleaving The interleaver breaks up the fade so that At the receiver the reverse operation is forward error correction FEC codes can performed correct errors from fading Read data into columns At the At the Transmitter Receiver just before Read data in Just after modulation as r WS demodulation a fade effects only one column if interleaver is deep enough Read data out as columns Other Linear Techniques Instructor MA Ingram ECE4823 g Recall Linear Modulation I st is the output of the modulator I g is the complex envelope Ipt is the basic pulse I x is the nth symbol sl Regle f t 0A2xmoi v Overview of Techniques I Differential PSK DPSK Inexpensive Quadrature Phase Shift Keying QPSK Twice as spectrally ef cient than BPSK Offset QPSK OQPSK reduce envelope variation 7r4 QPSK reduces envelope variations to a laser extent than OQPSK can be noncoherently detected g Recall the BPSK Receiver I The local oscillator must match the phase of the incoming carrier 399 AatJTZcosZift a mo m Durrp 1 EilherOorrrdunng cos 3 eachsymbol period mm W gt Local Oscillator depen symbol I DPSK I Differential PSK does not require the Local Oscillator phase to match the incoming carrier phase I The information is carried in the d erence between the phases of the present and previous symbol waveforms DPSK Receiver I Received signal in last symbol period is used as the Local Oscillator for the present symbol period Aat Tl c0424 a mo no Differential Encoding 1 no change in phase 0 change in phase Mi 0 1 0 1 g DPSK Performance Because the Local Oscillator has some additive noise the BER is not as low as for coherent BPSK 1 839 P b1te1ror ex 7 5 MA 2 p NU SNR Penalty DPSK has an SNR penalty relative to BPSK of less than 2 dB for BERlt1E2 In other words 817 ND must be as much as 2 dB larger for DPSK to achieve the same BER as BPSK F39hil error QPSK QPSK is like BPSK except the phase can take four values instead ofjust two sl RegleW g0 AZ xnw nTS 4 34 7 4 734 xnee 9 9 e SI QPSK Signal Space Diagram The bases functions are cosine and sine The cosine component is called the In Phasequot component The sine component is called the Quadrature component Q g Square Pulse Case A QPSK waveform sway cow Ticos2 zi sm a Tism m s where we7r4371477z473714 and magnum 85 is the symbol energy 5 85 is the bit energy QPSK2 BPSKs sgmo Jams a Ticosan zy Jasin a sin27f 5 One BPSK Signal Another BPSK Signal The two BPSK signals are separated in the receiver using two LOs one a cosine the other a sine QPSK Performance BER same as BPSK for the same 8 For the same data rate QPSK has a bandwidth half of that of BPSK SAflsinczlf lrssinczf lrsl 85 sir02f if 12TH sinczf if 12 Pulseshaping Effects Because of realistic pulse shaping the envelope of BPSK or QPSK is not constant Undesirable because linear ampli ers which are not as power ef cient and more expensive are required Bandlimmng causes amplitude at 180 phase changes to go to zero BPSK Example sinc2 bf Offset QPSK Since the QPSK waveform is just a superposition of two independent BPSK waveforms why not shift one relative to the other by half a symbol period to make the envelope more constant l Channel Q Channel Offset QPSK Performance By switching the phase twice as often as QPSK the max phase change becomes 90 degrees instead of 180 degrees so amplitude not forced to zero by bandlimiting Same spectrum as QPSK Same BER as QPSK 7r4 QPSK A differential encoding technique that allows a maximum of a 1350 phase shift at symbol transitions Used in mobilepersonal radio standards 15 54 and 15136 and in the European TETRA standard for private business radio Burr 2001 Introduction to Diversity Instructor MA Ingram EOE4823 Motivation 8 If a fading radio signal is received through only one channel then in a deep fade the signal could be lost and there is nothing that can be done SEDiversity is a way to protect against deep fades Diversity Choice in Fading 8 The key create multiple channels or branchesthat have uncorrelated fading t The fading of two highly in is with correlated channels uncorrelated fading Diversity 1 8 Common assumption signals that scatter off of different objects fade independently 3 Diversity is created when these signals are separated in the receiver 38Examples RAKE receiver separates paths by delay PATH DIVERSITY iZiMultibeam antenna separates paths by angle ANGLE DIVERSITY Diversity 2 3 Another way to create diversity change the relative phases of the multipath signals 88Examples ElIdentical antennas slightly different locations SPACE DIVERSITY EiSame signal received on different RF carriers FREQUENCY DIVERSITY Required carrier separation depends inverser on delay spread Diversity 3 3 Still other ways to generate diversity Edual polarized antennas POLARIZATION DIVERSITY successive retransmission in a channel with Doppler spread TIME DIVERSITY Time separation depends inversely on Doppler spread Antenna Separation for Spatial Diveristy 3 The required separation distance between antennas for spatial diversity depends on the angular spread of multipath l W YY Y Y Wdesprad Narrow spread Spacing can be as srnall as Spacing may need to be as Wide 0 25 Wavelerig as 30 Wavelerig s Typlcal for indoor enannels Typlcal for tall base stations Fading as a Function of Rx Posi 39on Wide Angle Spread Large angle spread implis large variation over short distance deg Maciniiude dB 2 4n inn 2n 7 llllllk l llllll I llle 2U 4U EU EU lEIEI Distance in halfnwavelenglhs Phase Relative amplitude and anglenofrarrival of paths Fading as a Function of Rx Position Narrow Angle Spread Small angle spread implies slow variation over distance iyiiilli i illlliiiiiiiiiii iillllll39lllll39l llllllllllllllllllllllllllllllllllllllllllllllllll Phase clecl Maanitude dB El ZEI AU El El lEIEI Relative amplimde and Dismnce in halfnwavelenglhs anglenofrarrival of paths along direciion ee wread Directional Antennas Limit Angular Spread 3 Highly directional antennas or phased arrays make multipath seem to have a narrow angular spread as Ifyou want to use such antennas or arrays for diversity channels they must be spaced widely apart I 7 A pnased array Diversity Combining 380nce you have created two or more diversity channels what do you do with them Types of Diversity Combining 3 Selection diversity Pick the branch with highest signal power 3 Magtltimal Ratio Combining MRC Branches weighted prior to summing MRCMatched ltermaximizes SNR ofdsired h 39 ise signal in additive w ite Gaussian no ecessary to estimate branch gains 3 Minimum Mean Squared Error MMSE Same as MRC in absence of colored interference Twobranch Spatial Diversity Sn w 2 Rx Antenna Rx Antenna 1 2 Nurse n m rnsnh nu rsnhz n Maximal Ratio Combining The recewed swgna s rnsnhnn rsnhz n The maxwrrum hkehhood decwswon stausuc x drhnn r mm WZ NEWS mm hzm SNR After Diversity Combining Received EhINn with Diversity Hamperth WEVZMWM EhmeAM M39me Huade Eiii39l nwwrlnr wrnrw W wrwrmr Summingan in rmlira E 1 5M1 En r any NnZ v Pv 8 Let the received EbNEl without diversity on the ith br anch be denoted 7 Mn a atfading channel 7 is a random variable 3 If L diversity branches have iid 739s then the EbNEl after MRC diversity combining is L new 1va 7ch Z 739 branch 11 The CDFs of SNR Improvement The CDFs of SNR lmproveme t Factor for MRC on the L39 ear Scale Factor for MRC on the Log Scale 10000 Vials 0f 3 Choppiness at H C Gaussian bottom endIs channel because I dId SEObserve shift to only 10000 the right as well ias as a more cal orientation Performance Metrics 1 SNR per brt after cornbrrrrrrg rh EbNu 3 SNR per brt berore combrnrng per drversrty branch rd andom varrables that depend on me radrng e e Wrm MRC and K Hd branches 7 72le Where 7 EM rs me average SNR per brt per branch and K rs me rrurnber of branches Performance Metrics 3 S The probabrlrty densrty function pdf of yb fryb x Probabrlrty of error for grverr yh P n zz erfcel n m Probabrlrtyofoutage Rm Ifrmwn n Average BER Jemwmdn n Performance Met 5 4 SEWhen the average SM per branch 721 is greater than 10 dB P can be approximated as 1 K 2K71 471 K for coherent BPSK Therefore error rate decreass inversely with no ofdiversity branches Divers y Gain Dryersrty gerrr rs the detrease rn the requrred SNR per branch m achreye a dared ge BER m Raylergh famer on each dryersrty branch R251 lts shown rer coherent apex xrrprwemenr rn Req d SNR he drmrms rrum m2 Jada t rrumzma dB X Antenna Gain 8 The antenna gain is the ratio ofthe average SNR on the output of the array combiner to the average SNR per branch of the array Transmit Diversity 3 The use of multiple antenna element at the transmitter to create diversity in the receiver Mumre Retewer Example Symbul w Flalladin w 3 no 5 caused by mullipath 151 atr trally treated rer cup or the equarrze Wrth MLEE Ember m 2 n m3 gwe 27 lo dryerslty Base Statrun rransmmer Samar ma mm mm Spacetime Block Coding 8 Less receiver complexity than Rakeequalizer 8 Decoding gives MRC performance 8 Requires no channel knowledge at Transmitter Alamouti s space time block codes can have two polarlzauons tanner tnan two antennas Alamouti s Scheme Input at ume to so 51 Alamoun IEEE JSAC Oct 19 input at tnne t1 5 1 55 TX Antenna TX Antenna 1 2 hl 2 RX Antenna quot0 Nolse n1 OutputatmnetO r ns0h1 s1h2nO Outputatmnet1 r1 s o hZslh1n1 Combl ing Scheme A amoun lEEE JSAC Oct 1996 r Let r then r HS01 nmwhere 71 S 7 so n 7 quot0 H7 h1 h2 017 31 01 quot1 7h 7h Observe thatHi39s aquotscale d unitaffmatn39x m 3959quot HHHQh2Ih 2IZEJ fl Combl ing Concluded 3 Observe that two timeslots are required for two symbols code rate1 8 If total transmit power is conserved decrease diversity gain by 10logloN EThis decrease is the power splitting loss ElThis loss is also suffered by the time transmit diversity discussed prior to STBC Combining cont d Simple linear combining matched ltering So E01 HHr HHHS01 nm lh12h22sm HHnm H4 Y Gaussian noise Diversity from two branches Average BER Results Alamou lEEE JSAC Oct 1996 15 20 25 30 35 40 45 50 5 faded EbNo per receive antenna CDMA Instructor Mary Ann Ingram ECE 4823 g Motivation BER depends on bit energy not on the bandw39dth Large bandwidth signals are less sensitive to multipath fading less vulnerable to jamming can be concealed can share a common bandwidth without interfering with each other g CodeDivision Multiple Access Allows multiple users to share same bandwidth at the same time Each user s waveform is like an independent noise random process Interference appears as white noise Matched filter pulls out desired user s waveform suppresses interference Direct Sequence Spread g Spectrum DSSS DSSS is one popular way to make the noiselike waveforms for CD Maximallength shift registers make binary sequences that have noiselike properties mstage shift register produces a sequence with a period of length 2m1 g DSSS Baseband Waveform Binary noise sequence is mapped to a chip spreading sequence of 1 s Each user gets a different spreading secluence Baseband Waveform E TS 2TS 3TS ll T5 5 s 1 Information waveform T Short code 5 example Chips The spreading sequence comprises chips very short pulses with width Tc There are an integer number of chips for each data symbol JL data SWbo chip mm Codes for Different Users Their crosscorrelation is nearly zero MSequences Maximallength or msequences are a wellknown class of spreading sequences Generated with a linear feedback shift register A register of length m generates a code N long where N2m1 g Generating MSequences The p s are the coefficients of a primitive polynomial Autocorrelation of the M g Sequence Very much like an impulse LAZAIZU 7W SI Processing Gain The number of chips per symbol is the processing gain PG This is also PG B where Em and B are the bandwidths of the chips and the data symbols respectively Usually BSS gtgt B g Signal Model for kth User ska 1sz mkrpkrcos27zfcr 6 ES symbol energy mk information waveform for k th user pk spreading sequence for k th user B bandwidth of mk BSS bandwidth Ofpk Received Signal Model No Multipath rtZKSkth knt Assume K users and that the kth user s signal is delayed by 1 g Correlator Receiver Assume user 1 s delay 71 is known To receive the signal of user 1 correlate the received signal with user 1 s spreading sequence delayed by 71 25 mm x 7 n coswco 7 a 54 M H 75 TjJQH in sAFrkgtnltrgtlmi ncos2mtin5ldt g Multiuser Interference The receiver correlates to the code of the desired user Every undesired usel s code has a small amount of residue because of imperfect orthogonality The multiuser interference from each user is approximated as a Gaussian RV based on a Central Limit Theorem argument Contribution of lots ofchips g Simplified Correlator Output 21 1 5 1 Y 77 Y is the multiple access interference part Yis N0U based on Central Limit Theorem 7 is the thermal noise part SI Random Sequence Model The analysis of the BER for DSSS assumes that the K 1 interfering spreading sequences are random and Nchips long The BER is obtained by averaging over all possible spreading sequences including the desired sequence Therefore a gt 0 02 is proportional to K d a IS Inverser proportional toN g BER for BPSK Assuming AWGN 1 K71 Na 77 3N 2E m 3 assumpuonof n Chip and phase asynchronv up is dropped ifsvnchronous Reduces to standard BPSK BER expression when K1 g Graceful Degradation Narrowband Interference Unlike TDMA 10 Interference signal is spread and then ltered 10quot 10 Co plex envelope of desired signal Film Increases 10 351119 E 10 Ts 2T5 3T5 T8 2T5 3T5 Else gradually as 2 V W E 10 1 E 10 T8 are added g 10 I i Co plex envelope of desired signal lter 10 l 5 matched E TS 2TS 3TS 1 l E TS 2TS 3TS 0 Sling 10 m 20 3o 40 so 50 70 so 90 1 Interference bandwidth NmWOfuwva 391 spreads out to B but TS gt 5 bandwidth of filter is only B Baseband TappedDelay Line Model g of Received Complex Envelope 5 Statistical Models Of Tap Gains Under the widesense stationary uncorrelated scattering WSSUS assumption the tap gains are uncorrelated complex RVs A reasonable model for the tap gain magnitudes a is Rayleigh with exponentially 510 Complex tap gains Complex decreasing mean square values noise ZU 5 ma sma v EOt12 Ce l delay gpread g 0616 70 L W h rm Re7ltte c St gce 1 Correlator RAKE Receiver 5 The Decision Variable The RAKE receiver output is Spreadingsequence L L71 L717 2 N 1 2820 48 ZYiJk pk quotk Conjugate 11 k1 i1 path gains not needede where the selfinterference is modulation IS e ual ener Sq gy YmlRegmgl Decision Variable uk and generally nonGaussian and correlated Frequency Shift Keying FSK Instructor MA Ingram ECE4823 Why Study FSK Constant envelope More efficient less costly power ampli ers Gaussian minimum shift keying GMSK a special type of FSK is used in the European digital cellular communications system GSM Angle Modulation General form Mt A cos27y2t W0 Phase modulation PM Wt lg ma wnete k constant mmodulaung Sig al Exampls BPSK QPSK BPSK etc Frequency modulation FM Wt 27 nlkIm dr Wnetexg constant mr modulaung Sigria Examples FSK Continuous Phase BFSK Illustration Phase continuity is important to reduce bandwidth NR2 BMW data Il BFSK waveform W Mary Continuous Phase FSK Recall FM phase zzzjkmrdr The modulating waveform is pulse amplitude modulated PAM m0 Zlng rr where I e i1i3iMe1 and gr is a pulse with area 12 Integrated Pulse Let q be the integrated pulse 40 jgmdr g0 41 1 N Modulation Index The FSK phase can be written mt Zak 2 1m 7 um I kf is the modulation index k 2fde with units of cyclessymbol period I is the peak frequency deviation l The sum increments in multiples of 12 Example Suppose gm is the rectangular pulse kf 10 and In1 then Orthogonal Waveforms BFSK has the following waveforms 50 icos2 ffdt 0lttltTS 522 c052 f 7fdt 0lttltTS Iffdn4TS for n a positive integer these waveforms will be orthogonal BFSK Coherent Detection mom 7 mt g BFSK Noncoherent Detection 2ND PWFSK error expi 81 Comparison In terms of BER CBFSK is to NBFSK as BPSK is to DPSK The SNR for FSK is half as large as it is for PSK 2 PEPKerrurgtQ If Pmenmgtg 5 l 2ND 1 5 1 PM 27797 Eexp PM 27707 Eexp Cellular Systems Instructor M A Ingram ECE 4823 g A Finite Resource Spectrum is like real estate they just don t make it anymore Webb 99 Cellular systems enable a service provider to serve more customers within a limited spectrum allocation Before Cells A single antenna would serve all the customers in the service area Service provider was limited to a certain One Call per Channel A different channel for every active call Even with trunking demand quickly exceeded resources i System Bandwidth Only 15 users can be served with 15 channels I Frequency Reuse Partition the service area into smaller cells One antenna base station serves each cell transmitting lower power using only a subset of the available channe s Adjacent cell uses a mutually exclusive subset of channels Original channel subset used in a cell that is far away from the rst cell Cells Total number of channels C are used in one i A is Four cells A l l to a cluster System Bandwidth gt g Reuse in Each Cluster The same C channels are used simultaneously in another cluster Max no of users C times no of clusters Another cluster g Cochannel Interference In the 4cell cluster case the nearest interfering signal comes from 2 cells over g Transmit Power Constraint The power transmitted by each base station needs to be large enough to cover its own cell but small enough to not cause too much interference in the cochannel cells As cells get smaller transmit power is reduced Smaller Cells Serve More Users The cells can be made small enough in support any user density Macrocells g Cluster Size N l Nonly takes values Nz 2zjj2 where i andj are nonnegative integers Examples i2j 0 N4 i2j1N7 A 7rcell cluster Location Rule To find the nearest cochannel cell move icells along a chain of hexagons turn 60 degrees counterclockwise and movej cells i2j1N7 Measures of Quality of the Received Signal Signaltonoise ratio SNR Signaltointerference ratio SIR SNR Ratio of received desired signal power over the average noise power in the receiver SNR Pd PW SNR can be improved b Increasing the transmitted power Decreasing the ran e Using a better low noise ampli er LNA SIR Ratio of received desired signal power over the received interference power P SIR mi n is the number of Z P interfering base stations 11 If all base stations increase their transmitted power by the same amount the SIR doesn t change g Computing Received Power Let aim be the d39smnce m the desired transmitter do be a reference dismnce depends on anmnna height PO be the power received at the reference dismnce n be the path loss exponent aetoezl for mobile cellular P P 0125 3 I Worst Case Interference The SIR is worst for a mobile on the edge ofa cell Ifall base stations transmit equal power SIR can be expressed den 7 125 SIR e en 2 do 11 In this example there are six interferers g Cochannel Reuse Ratio R majorquot radius of hexagonal cell Ddistance between centers of nearest cochannel cells QDRCochannel reuse ratio Increasing Q decrases interference Q JSN where Ncluster size
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