Introduction ti to OFDM Fire Tom Wada Professor, Information Engineering, Univ. of the Ryukyus Chief Scientist at Magna Design Net, Inc wada@ie.u-ryukyu.ac.jp ac http://www.ie.u-ryukyu.ac.jp/~wada/ 1/31/211 1
What is OFDM? OFDM =Orthogonal Frequency Division Multiplexing Many orthogonal sub-carriers are multiplexed in one symbol What is the orthogonal? How multiplexed? What is the merit of OFDM? What kinds of application? 1/31/211 2
Outline Background, history, application Review of digital modulation FDMA vs. Multi-carrier modulation Theory of OFDM Multi-path Summary 1/31/211 3
Why OFDM is getting popular? State-of-the-art high bandwidth digital communication start using OFDM Terrestrial Video Broadcasting in Japan and Europe ADSL High Speed Modem WLAN such as IEEE 82.11a/g/n WiMAX as IEEE 82.16d/e Economical OFDM implementation become possible because of advancement in the LSI technology 1/31/211 4
Japan Terrestrial Video Broadcasting service ISDB-T (Integrated Services Digital Broadcasting for Terrestrial Television Broadcasting) Service starts on 23/December at three major cities (Tokyo, Nagoya, Osaka) Full service area coverage on 26 5.6MHz BW is divided into 13 segments (~43KHz BW) HDTV: 12 segments Mobile TV : 1 segment SDTV: 4 segment Analog Service will end 211 1/31/211 5
Brief history of OFDM First proposal in 195 s Theory completed in 196 s DFT implementation ti proposed in 197 s Europe adopted OFDM for digital radio broadcasting in 1987 OFDM for Terrestrial Video broadcasting in Europe and Japan ADSL, WLAN(82.11a) 1/31/211 6
Digital modulation basics Digital modulation modulates three parameters of sinusoidal signal. A, θ k fc, s ( t ) = A cos( 2π f t + θ ) Three type digital modulation: ASK : Amplitude Shift Keying PSK : Phase Shift Keying FSK : Frequency Shift Keying c k OFDM uses combination of ASK and PSK such as QAM, PSK 1/31/211 7
Symbol Waveform Digital Information 1 1 carrier ASK PSK FSK 1/31/211 Symbol length 8
Multi bit modulation carrier BPSK 1 1 1bit per symbol 1 11 1 1 QPSK 2bit per symbol Symbol length 1/31/211 9
Mathematical expression of digital modulation Transmission signal can be expressed as follows s ( t ) = cos( 2 π f t + θ ) a = k cos θ = s( t) = k cos θ, c cos( 2π k Re[( a k b + k jb k f c ) e k = sin θ t) sin θ sin( 2π k j 2πfc t s(t) can be expressed by complex base-band signal ( a + jb ) e e j2πfct e ( a + jb ) k k Indicates carrier sinusoidal Digital modulation ] k f c k t) Digital modulation can be expressed by the complex number 1/31/211 1 k j2πfc t
Constellation map (a k + jb k ) is plotted on I(real)-Q(imaginary) plane data a k b k π/4 1 3π /4 11 5π /4 1 7π /4 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 QPSK Q 1/31/211 11 I
Quadrature Amplitude Modulation (QAM) 16QAM Q 64QAM Q I I 1/31/211 12
Summary of digital modulation Type of modulation: ASK,PSK,FSK,QAM OFDM uses ASK,PSK,QAM Digital modulation is mathematically characterized by the coefficient of complex base-bandband signal ( a jb ) k + Q k Plot of the coefficients gives the constellation ti map I 1/31/211 13
Frequency Division Multiple Access (FDMA) Old conventional method (Analog TV, Radio etc.) Use separate carrier frequency for individual transmission Occupied BW Channel separation f c1 c1 f c2 f c3 f cn Carrier frequency Guard band Radio frequency 1/31/211 14
Japan VHF channel assignment Channel number Frequency (MHz) 1 9-96 p 2 96-12 3 12-18 4 17-176 5 176-182 6 182-188 7 188-194 8 192-198 9 198-24 1 24-21 11 21-216 12 216-222 Channel Separation = 6MHz 1/31/211 15
Multi-carrier modulation Use multiple channel (carrier frequency) for one data transmission data DEMU LTIPLEX cos( 2πf 1 t) cos( 2πf 1 t) cos( 2πf 2 t) cos( 2πf 2 t) LPF LPF MULT TIPLEX data cos( 2πf N t ) cos( 2πf N t ) LPF 1/31/211 16
Spectrum comparison for same data rate transmission Multi carrier frequency Single carrier frequency OFDM frequency 1/31/211 17
OFDM vs. Multi carrier OFDM is multi carrier modulation OFDM sub-carrier spectrum is overlapping In FDMA, band-pass filter separates each transmission In OFDM, each sub-carrier is separated by DFT because carriers are orthogonal Condition of the orthogonality will be explained later Each sub-carrier is modulated by PSK, QAM Thousands of PSK/QAM symbol can be simultaneously transmitted in one OFDM symbol 1/31/211 18
OFDM carriers OFDM carrier frequency is n 1/T Symbol period T f = 1 T cos( ( 2π 1 f t + θ 1 ) cos( 2π 2 f t+ θ 2 ) cos( 2π 3 f t+ θ 3 ) cos( 2π 4 f t+ θ 4 ) cos( 2π 5 f t+ θ 5 ) cos( 2π 6 f t + θ 6 ) 1/31/211 19
Sinusoidal Orthogonality m,n: integer, T=1/f T T ( m= n) cos( 2 π mf ) cos( ) t 2πnf t dt = 2 ( m n) T T ( m= n) sin( 2πmf t) sin( 2πnf t) dt = 2 ( m n ) T cos( 2πmf t) sin( 2πnf t) dt = Orthogonal Orthogonal Orthogonal 1/31/211 2
A sub-carrier of f=nf a cos( 2 π nf t ) b sin( 2 π nf t ) n n 2 2 n n n n = a + b cos( 2πnf t + φ ), φ = tan 1 b n a n Amplitude and Phase will be digitally modulated n cycles Time t= t=t 1/31/211 21
Base-band OFDM signal N 1 n= { π π } sb() t = ancos( 2 nft ) bnsin( 2 nft ) T n= n=1 n=2 n=3 n=4 n=5 n=6 s B (t) 1/31/211 22
How a n,b n are caluculated from s B (t) - Demodulation Procedure - T sb ()cos( t 2πkft) dt { } a cos( 2πnft) cos( 2πkftdt ) b sin( 2πnft) cos( 2πkftdt ) N 1 T T = n n n= T = a k 2 T T sb() t { sin( 2πkft) } dt = b k 2 According to the sinusoidal orthogonality, a n n,,b n can be extracted. In actual implementation, DFT(FFT) is used N is roughly 64 for WLAN, thoudand for Terrestrial Video Broadcasting 1/31/211 23
Pass-band OFDM signal S B B( () (t) is upcoverted to pass-band signal S(t) f c frequency shift N 1 1 { π } { π } [ ] n c n c st () = a cos 2 ( f + nf) t bsin 2 ( f + nf) t n= 1/31/211 24
Actual OFDM spectrum f c +(k-1) 1)f f c +kf f c +(k+1) +1)f 1/31/211 25
OFDM power spectrum Total Power spectrum is almost square shape 1/31/211 26
OFDM signal generation N 1 { π } { π } [ ] n c n c st () = a cos 2 ( f + nf) t bsin 2 ( f + nf) t n= Direct method needs N digital modulators N carrier frequency generator Not practical In 1971, method using DFT is proposed to OFDM siganal generation 1/31/211 27
OFDM signal generation in digital domain Define complex base-band signal u(t) as follows = [ ] s t u t B ( ) Re ( ) N 1 j2πnft u() t = d e, d = a + jb n = n n n n Perform N times sampling in period T 1 k 2 π nk j N N k j2 nf N 1 π Nf u = d n e d n e Nf = n = n = nk N 1 2 π j N = n n = d e ( k = 12,,, L, N 1) u(k) = IFFT (d n ) = IFFT(a n + jb n ) 1/31/211 28
OFDM modulator cos( 2πfCt) Bit stream M S P A / I-DFT / P P S Real Imag sin( 2πfCt) generated ~d N-1 AIR BPF 1/31/211 29
OFDM demodulation N 1 [ a cos { 2π ( f + nf ) t } b sin { 2 ( f nf ) } ] s t = ( ) π LPF n = [ s( t ) cos( n c n c + t 2πf C t )] = 1 2 N 1 n = N 1 LPF [ s( t) 2 n = { a cos( 2πnf t ) b sin( 2πnf t )} = s ( t ) 1 n { sin( 2πf t) }] = { a sin( 2πnf t) + b cos( 2πnf t) } s ( ) C n n = Q t N 1 I Q n n = ut ( ) = s ( t ) + js ( t ) = d e d n = FFT(u(k)) (k)) n j2πnf t 1/31/211 3 1 2 1 2 I
OFDM demodulator (Too simple) Channel T u n e r cos( 2πfCt) π/2 LPF LPF A / D S / DFT P P / S Bit Stream 1/31/211 31 D E M A P
Summary of OFDM signal Each symbol carries information Each symbol wave is sum of many sinusoidal Each sinusoidal wave can be PSK, QAM modulated Using IDFT and DFT, OFDM implementation became practical Symbol period T=1/f Time 1/31/211 32
Multi-path Delayed wave causes interference Path 2 Direct Path Building Base Station Pat h 3 Mobile Reception 1/31/211 33
Multi-pass effect No multi-path Symbol k-1 Symbol k Symbol k+1 T=1/f Sampling Period Multi-path Direct Delayed Sampling Period Inter symbol interference (ISI) happens in Multi-path condition 1/31/211 34
Guard Interval T g T g OFDM symbol(1/f ) Copy signal By adding the Gurard Interval Period, ISI can be avoided Direct Delayed T g OFDM symbol (1/f ) Sampling Period 1/31/211 35 T g
Multi-path By adding GI, orthogonality can be maintained However, multi-path causes Amplitude and Phase distortion for each sub-carrier The distortion has to be compensated by Equalizer 1/31/211 36
Multiple Frequency Network f3 f1 Area 3 f1 Area 1 Area 2 f2 Area 4 Frequency utilization is low 1/31/211 37
Single Frequency Network f1 f1 Area 3 f1 Area 1 Area 2 f1 Area 4 If multi-path problem is solved, SFN is possible 1/31/211 38
That s all for introduction Feature of OFDM 1. High Frequency utilization by the square spectrum shape 2. Multi-path problem is solved by GI 3. Multiple services in one OFDM by sharing subcarriers (3 services in ISDB-T) 4. SFN 5. Implementation was complicated but NOW possible because of LSI technology progress 1/31/211 39