Multi-Carrier Trasmissio over Mobile Radio Chaels Jea-Paul M.G. Liartz Philips Research ad TU/e
Outlie Itroductio to OFDM Discussio of receivers for OFDM ad MC-CDMA Itercarrier Iterferece, FFT Leakage New receiver desigs Simulatio of Performace Coclusios
OFDM OFDM: a form of MultiCarrier Modulatio. Differet symbols are trasmitted over differet subcarriers Spectra overlap, but sigals are orthogoal. Example: Rectagular waveform -> Sic spectrum
Applicatios Fixed / Wirelie: ADSL Asymmetric Digital Subscriber Lie Mobile / Radio: Digital Audio Broadcastig (DAB) Digital Video Broadcastig - Terrestrial (DVB-T) Hiperla II Wireless 394 4G (?)
I-FFT: OFDM Trasmissio Trasmissio of QAM symbols o parallel subcarriers Overlappig, yet orthogoal subcarriers User symbols cos(ω c t) cos(ω c t+ ω s t) cos(ω c t+ iω s t) = Serial-toparallel Serial-to- Parallel I-FFT Parallel-to- Serial cos(ω c t+ (N-)ω s t)
I-FFT: OFDM Trasmissio Trasmissio of QAM symbols o parallel subcarriers Overlappig, yet orthogoal subcarriers e ψ k ( t) = Ts j ω k t t [, T ] s otherwise with ω ω + kω ; k =,,..., N k = s c Although the subchaels overlap, they do ot iterfere with each other at f = f k ;(k =,,...,N c -). Ideed, they are orthogoal: T s ψ ( t) ψ ( t) dt = δ ( k k * l l)
OFDM Subcarrier Spectra Symbol duratio : iverse of subcarrier spacig plus cyclic prefix Frequecy Samplig rate : iverse of trasmit badwidth Pulse shape i time domai: rectagle Π(t / NT s ) s( t) N t N F = aπ S(f) = a ( N Ncp ) T = + s = sic ( f ( N + N ) Ts) cp = ( f ( N + N ) Ts) si cp f ( N + N )Ts cp
OFDM Subcarrier Spectra OFDM sigal stregth versus frequecy. Rectagle <- FFT -> Sic before chael after chael Frequecy
Cyclic Prefic / Cyclix postfix CP OFDM SYMBOL T cp T s T The legth of the cyclic prefix should be made loger tha the experieced impulse respose to avoid ISI ad ICI. However, the trasmitted eergy icreases with the legth of the cyclic prefix. The SNR loss due to the isertio of the CP is give by SNR T = log T loss where T cp deotes the legth of the cyclic prefix ad T=T cp +T s is the legth of the trasmitted symbol. cp
Coded OFDM Received sigal at a subcarrier is ot affected by trasmitted symbols i ay other subcarrier Symbol data ca be recovered usig simple sigle tap data estimatio Viterbi decoder helps recover bits from subcarriers i deep fade + = N N N N a a H H y y M M O M = ˆ ˆ N y N y H H a a N M O M Static Eviromet Ave BER curves: slope ~ degree of diversity o fadig chael = l mf j l m l s e h H π )τ ( 2
Sigle Frequecy Networks OFDM is robust agaist delay spread We ca mis use this by trasmittig a sychroous sigal from two trasmit sites
The Wireless Multipath Chael
OFDM ad MC-CDMA i a rapidly time-varyig chael Doppler spread is the Fourier-dual of a delay spread
Mobile Multipath Chael Collectio of reflected waves, each with radom agle of arrival radom delay Agle of arrival is uiform Doppler shift is cos(agle) Doppler Spectrum U-shaped power desity spectrum
Crosstalk β caused by Doppler Y = [y, y,.., y N ] T, with y m = Σ a β m, T s β m, is the trasfer for a sigal trasmitted at subcarrier ad received at subcarrier m, β m, Iw = i= D 2 exp{ j(ω i c sic m + + ω i + ω jπ ( m)} For uiform agles of arrivals of waves, ICI power spilled from trasmit subcarrier ito received subcarrier m = + equals 2 f sic + x dx * PT fs P = E ch β+, β +, = 8π 2 ( x ) where f is the maximum Doppler shift, ad P T the local mea received power, per subcarrier s ) T i ω ω i s 2 jω T i s + Power or variace of ICI Power, Variace of ICI - -2-3 P P P2 P3 3rd tier subcarrier 2d tier subcarrier Neighborig subcarrier -4.5.5 2 2.5 3 3.5 4 4.5 5 Normalized Doppler [fm/fsub] Doppler spread / Subcarrier Spacig
ICI caused by Doppler Power or variace of ICI Power, Variace of ICI - -2-3 P P P2 P3 3rd tier subcarrier 2d tier subcarrier Neighborig subcarrier -4.5.5 2 2.5 3 3.5 4 4.5 5 Normalized Doppler [fm/fsub] Doppler spread / Subcarrier Spacig
Maximum attaiable speed
BER i a mobile chael Local-Mea BER for BPSK - -2-3 -4-5 OFDM, db MC-CDMA, db OFDM, 2 db OFDM, 3 db MC-CDMA, 2 db 3 db Local-mea BER for BPSK, versus atea speed. Local mea SNR of, 2 ad 3 db. Compariso betwee MC- CDMA ad ucoded OFDM for f c = 4 GHz Frame duratiot s = 896µs FFT size: N = 892. Sub. spacig f s =.7 khz Data rate 9.4 Msymbol/s. -6-7 5 5 2 25 3 35 4 Atea Speed (m/s) Atea Speed [m/s]
Mobile OFDM weakess: IterCarrier Iterferece A effective descriptio of ICI y = [H + Ξ H ] a + desired self-iterferece where: H is a diagoal matrix with the complex trasfer fuctio per subcarrier H is the temporal derivative of H: H = dh/dt Ξ is the ICI spreadig matrix: a system value, fixed! a is a vector of trasmitted data is vector of white Gaussia oise
Radom Complex-Gaussia Amplitude It ca be show that for p + q is eve E H ( p) H *( q) m = ( 2πf ) D p+ q ( p + q )!! ( p + q)!! + ( ) q j p+ q j( m) T rms ω s ad for p + q is odd. This defies the covariace matrix of subcarrier amplitudes ad derivatives, allows system modelig ad simulatio betwee the iput of the trasmit I-FFT ad output of the receive FFT.
Chael estimatio DVB-T H estimatio based o pilots i frequecy domai data carriers pilots empty carriers time OFDM symbol frequecy
Estimatio of H DVB-T pilots data carriers pilots empty carriers time OFDM symbol frequecy I every OFDM symbol, iitial estimates of H at every pilot subcarriers ca be obtaied. I every OFDM symbol, estimate of H at each subcarrier is obtaied: Spectral Wieer Filterig Iput: Iitial estimates of H at several (scattered) pilot positios.
Wieer Filterig for OFDM
Achievable car speeds with BB sigal processig 2 Sigle atea CoSyS result 5 O the market
Receiver : MMSE Matrix Iversio Receiver sees Y = QA+ N, with Q=DIAG(H)+ Ξ DIAG(H () ) Calculate matrix Q = DIAG(H)+ Ξ DIAG(H () ) Compute MMSE filter W = Q H [Q Q H + σ 2 I N ] -. Performace evaluatio: Sigal power per subcarrier Residual ICI ad Noise ehacemet from W
ICI Hadlig: Brute force Matrix Iversio SNR of decisio variable. Simulatio for N = 64, MMSE Wieer filterig to cacel ICI 3 Covetioal OFDM MMSE equalizatio 25 2 MMSE ICI caceller Output SINR 5 Covetioal OFDM 5 Doppler Diversity 2 3 4 5 6 7 Subcarrier umber
Performace of (Blocked Bad) Matrix Iversio 3 Output SINR 25 2 5 MMSE k = 4 Cov OFDM 5 Covetioal OFDM MMSE equalizatio simplified MMSE 5 5 2 25 3 Iput SNR N = 64, v = 2 km/h, f c = 7 GHz, T RMS = µs, samplig at T = µs. f Doppler = 3.5 khz, Subc. spacig f sr = 3.25 khz: Compare to DVB-T: v = 4 km/h, f c = 8MHz: f doppler = Hz while f sr =.7 khz
ICI cacellatio ICI Cacellatio If H ad a are kow for all, ICI ca be removed almost completely from ay subcarrier. N m = ym = y ' Ξ a = H a + m, H ' Implemet Ξ as FFT - Ramp - FFT m m k Ξ Cacel Doppler Y + + - ICI FFT weigh FFT H A
ICI cacellatio ICI Cacellatio However, H ad a are ot kow to the receiver: They have to be estimated Full cacellatio y' Partial cacellatio: â is used oly to cacel iterferece it caused to p closest subcarriers y' m m = = y y m m N = Ξ m+ p / 2 Ξ = m p / 2 ˆ m, H' aˆ ˆ m, H' aˆ O average: Cacelig ICI origiatig from 4 closest subcarriers reduced the ICI power by 6 db Cacelig ICI origiatig from closest subcarriers reduced the ICI power by db
Receiver : Matrix Iversio Amplitudes Magitude i db - -2-3 -4 Determied by speed of atea, ad carrier frequecy First derivatives -5-6 -7 Amplitudes Derivatives -8 2 3 4 5 6 7 Subcarrier umber Simulatio of chael for N = 64, v = 2 km/h f c = 7 GHz, T RMS = µs, samplig at T = µs. f Doppler = 3.4 khz, Subcarrier spacig f sr = 3.25 khz, sigal-to-ici = 8 db
Receiver : Matrix Iversio SNR of decisio variable. Simulatio for N = 64, MMSE Wieer filterig to cacel ICI 3 Covetioal OFDM MMSE equalizatio 25 2 MMSE ICI caceller Output SINR 5 Covetioal OFDM 5 2 3 4 5 6 7 Subcarrier umber
Simplified Matrix Iversio Ratioale ICI dimiishes with icreasig subcarrier differece Approximate Ξ by bad matrix with 2k+ o-zero diagoals Matrix Q is approximately Q = [I + ] Λ small, ~ Ξ diag(v ()./ V) Λ diagoal of amplitudes V Approximate Q - = [I - ] Λ Complexity ~2kN
Performace of (Simplified) Matrix Iversio 3 Output SINR 25 2 5 MMSE k = 4 Cov OFDM 5 Covetioal OFDM MMSE equalizatio simplified MMSE 5 5 2 25 3 Iput SNR N = 64, v = 2 km/h, f c = 7 GHz, T RMS = µs, samplig at T = µs. f Doppler = 3.5 khz, Subc. spacig f sr = 3.25 khz: Compare to DVB-T: v = 4 km/h, f c = 8MHz: f doppler = Hz while f sr =.7 khz
Multi-Carrier CDMA
Multi-Carrier CDMA Various differet proposals. () DS-CDMA followed by OFDM (2) OFDM followed by DS-CDMA (3) DS-CDMA o multiple parallel carriers First research papers o system () i 993: Fettweis, Liartz, Yee (U.C. Berkeley) Fazel (Germay) Chouly (Philips LEP) System (2): Vadedorpe (LLN) System (3): Milstei (UCSD); Sourour ad Nakagawa
Multi-Carrier CDM Trasmitter S/P N B Code Matrix C N A I-FFT N P/S What is MC-CDMA (System )? a form of Direct Sequece CDMA, but after spreadig a Fourier Trasform (FFT) is performed. a form of Orthogoal Frequecy Divisio Multiplexig (OFDM), but with a orthogoal matrix operatio o the bits. a form of Direct Sequece CDMA, but the code sequece is the Fourier Trasform of the code. a form of frequecy diversity. Each bit is trasmitted simultaeously (i parallel) o may differet subcarriers.
MC-CDM (Code Divisio Multiplexig) i Dowlik I the forward or dowlik (base-to-mobile): all sigals origiate at the base statio ad travel over the same path. Oe ca easily exploit orthogoality of user sigals. It is fairly simple to reduce mutual iterferece from users withi the same cell, by assigig orthogoal Walsh-Hadamard codes. BS MS MS 2
Sychroous MC-CDM receiver S/P N N Weigh N I-Code N FFT Matrix Matrix Y W A C - P/S The MC-CDM receiver separates the various subcarrier sigals (FFT) weights these subcarriers i W, ad does a code despreadig i C - : (liear matrix over the complex umbers) Compare to C-OFDM: W := equalizatio or AGC per subcarrier C - := Error correctio decoder (o-liear operatio)
Sychroous MC-CDM receiver S/P N N Weigh N I-Code N FFT Matrix Matrix Y W A C - P/S Receiver strategies (How to pick W?) equalizatio (MUI reductio) w = /β maximum ratio combiig (oise reductio) w = β Wieer Filterig (joit optimizatio) w = β/(β 2 + c) Next step: W ca be reduced to a automatic gai cotrol, per subcarrier, if o ICI occurs
Sychroous MC-CDM receiver S/P N N Weigh N I-Code N FFT Matrix Matrix Y W A C - B P/S Optimum estimate per symbol B is obtaied from B = EB Y = C - EA Y = C - A. Thus: optimum liear receiver ca implemet FFT - W - C - Orthogoality Priciple: E(A-A)Y H = N, where A = WY H Wieer Filterig: W = E AY H (EYY H ) - EAY H diagoal matrix of sigal power EYY H diagoal matrix of sigal plus oise power W ca be reduced to a AGC, per subcarrier w = β β β * * + N T s
MC-CDM BER aalysis Rayleigh fadig chael Expoetial delay spread Doppler spread with uiform agle of arrival Perfect sychroisatio Perfect chael estimatio, o estimatio of ICI Orthogoal codes Pseudo MMSE (o cacellatio of ICI)
Composite received sigal Wated sigal Multi-user Iterferece (MUI) Itercarrier iterferece (ICI) + = = =,,,, ] [ ] [ m N m N s m c c w w N T b x β β = = = ] [ ] [,, c c w b T x k N N k k s MUI β + + + = + =,, ] [ c w a T x N s ICI β
Composite received sigal Wated sigal Multi-User Iterferece (MUI) Itercarrier iterferece (ICI) [ ] = = = = 2, ch 2, ch 2 2 2 E E ) ( ) ( E E N N m k N k k ICI w m c c b N β σ 2,,,, ch 2 2 2 * ch 2 E E E E = = + = A A N k k s MUI MUI MUI w w b N T x x β β σ N s w β N T b x,, = =
BER for MC-CDMA Avg. BER - -2-3 -4-5 (4) OFDM (5) () (2) (3) AWGN 5 5 Local-mea E /N Local-mea E b /N BER for BPSK versus E b /N () 8 subcarriers (2) 64 subcarriers (3) ifiitely may subcarriers (4) 8 subc., short delay spread (5) 8 subc., typical delay spread
Capacity relative to o-fadig chael C OFDM C Coded-OFDM same as N fadig chaels = OFDM N N 2 exp x log2 ( + 2x) dx P 2 Ts P Ts = l 2 N exp 2P T E N 2P T For large P T s /N o a Rayleigh fadig chael, OFDM has.4 bit less capacity per dimesio tha a o-fadig chael. s s MC-CDM Data Processig Theorem: C OFDM = C MC-CDM I practise, we loose a little. I fact, for ifiitely may subcarriers, C MC-CDM = ½ log 2 ( + ςp T s /N ). where ς is MC-CDM figure of merit, typically -4.. -6 db.
Capacity 7 6 No-fadig, LTI 5 Rayleigh Capacity: Bits per Subcarrier 4 3 2 MC-CDM -* : Rayleigh * : MC-CDMA - : LTI -5 5 5 2 25 3 35 4 Local-mea E/N (db) Capacity per dimesio versus local-mea E N /N, o Doppler.
Advatages Simpler user separatio tha with DS-CDMA Higher capacity tha DS-CDMA i dowlik: elegat frame work for doig simultaeous ati-multipath ad iterferece rejectio FFT istead of rake: simpler traiig of receiver
MC-CDMA i uplik I the reverse or uplik (mobile-to-base), it is techically difficult to esure that all sigals arrive with perfect time aligmet at the base statio. Frame mis-aligmets cause severe iterferece Differet Doppler spectra for each sigal Differet chaels for differet sigals Power cotrol eeded BS MS MS 2