Introduction 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 http://www.ie.u-ryukyu.ac.jp/~wada/ 11/2/29 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? 11/2/29 2
Outline Background, history, application Review of digital modulation FDMA vs. Multi-carrier modulation Theory of OFDM Multi-path Summary 11/2/29 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 11/2/29 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 11/2/29 5
Brief history of OFDM First proposal in 195 s Theory completed in 196 s DFT implementation 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) 11/2/29 6
Digital modulation basics Digital modulation modulates three parameters of sinusoidal signal. A, θ k fc, st () = 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 11/2/29 7
Symbol Waveform Digital Information 1 1 carrier ASK PSK FSK Symbol length 11/2/29 8
Multi bit modulation carrier BPSK 1 1 1bit per symbol 1 11 1 1 QPSK 2bit per symbol Symbol length 11/2/29 9
Mathematical expression of digital modulation Transmission signal can be expressed as follows s( t) = cos( 2π f a = k cos θ = s( t) = k cos θ, cos( 2π k Re[( a k + b s(t) can be expressed by complex base-band signal ( a + jb ) k e j2πfct k k c jb t + θ ) k f c ) e k = sin θ t) sin θ sin( 2π k j 2πfc t Indicates carrier sinusoidal Digital modulation 11/2/29 1 ] k f c t) ( a + jb ) e Digital modulation can be expressed by the complex number k k j2πfct
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 1 2 2 1 1 2 2 1 1 2 2 QPSK Q I 1 7π /4 1 2 1 2 11/2/29 11
Quadrature Amplitude Modulation (QAM) 16QAM Q 64QAM Q I I 11/2/29 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-band signal ( a + jb ) k k Q Plot of the coefficients gives the constellation map I 11/2/29 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 f c2 f c3 f cn Carrier frequency Guard band Radio frequency 11/2/29 14
Japan VHF channel assignment Channel number Frequency (MHz) 1 9-96 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 11/2/29 15
Multi-carrier modulation Use multiple channel (carrier frequency) for one data transmission data DEMULTIPLEX cos( 2πf 1 t) cos( 2πf 2 t) cos( 2πf 1 t) cos( 2πf 2 t) LPF LPF MULTIPLEX data cos( 2πfN t) cos( 2πfN t) LPF 11/2/29 16
Spectrum comparison for same data rate transmission Multi carrier frequency Single carrier frequency OFDM frequency 11/2/29 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 11/2/29 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 ) 11/2/29 19
Sinusoidal Orthogonality m,n: integer, T=1/f T T T T cos( 2πmf t) cos( 2πnf t) dt = 2 T sin( 2πmf t) sin( 2πnf t) dt = 2 cos( 2πmf t) sin( 2πnf t) dt = ( m= n) ( m n) ( m= n) ( m n) Orthogonal Orthogonal Orthogonal 11/2/29 2
A sub-carrier of f=nf a cos( 2πnft) b sin( 2πnft) n n 2 2 n n n n = a + b cos( 2πnf t + φ ), φ = tan 1 b a n n Amplitude and Phase will be digitally modulated n cycles Time t= t=t 11/2/29 21
Base-band OFDM signal N 1 { π π } sb() t = ancos( 2 nft ) bnsin( 2 nft ) n= T n= n=1 n=2 n=3 n=4 n=5 n=6 s B (t) 11/2/29 22
How a n,b n are caluculated from s B (t) - Demodulation Procedure - T s ()cos( t 2πkf t) dt B N 1 n= { } a cos( 2πnft) cos( 2πkftdt ) b sin( 2πnft) cos( 2πkftdt ) n T = n T = a k 2 T T sb() t { sin( 2πkft) } dt = b k 2 According to the sinusoidal orthogonality, a n,b n can be extracted. In actual implementation, DFT(FFT) is used N is roughly 64 for WLAN, thoudand for Terrestrial Video Broadcasting T 11/2/29 23
Pass-band OFDM signal S B (t) is upcoverted to pass-band signal S(t) f c frequency shift N 1 { π } { π } [ ] n c n c st () = a cos 2 ( f + nf) t bsin 2 ( f + nf) t n= 11/2/29 24
Actual OFDM spectrum f c +(k-1)f f c +kf f c +(k+1)f 11/2/29 25
OFDM power spectrum Total Power spectrum is almost square shape 11/2/29 26
OFDM signal generation N 1 Direct method needs { π } { π } [ ] n c n c st () = a cos 2 ( f + nf) t bsin 2 ( f + nf) t n= N digital modulators N carrier frequency generator Not practical In 1971, method using DFT is proposed to OFDM siganal generation 11/2/29 27
OFDM signal generation in digital domain Define complex base-band signal u(t) as follows [ ] s () t = Re u() t B N 1 j2πnft u() t = d e, d = a + jb n = Perform N times sampling in period T u k Nf n n n n 1 k 2 π nk j N N j2 nf N 1 π Nf = d n e = d n e n = nk N 1 2 j N = d n π e k 12 N 1 ( =,,, L, ) n = 11/2/29 28 n = u(k) = IFFT (d n ) = IFFT(a n + jb n )
OFDM modulator cos( 2πfCt) Bit stream M A P S / P I-DFT P / S Real Imag sin( ) 2πf t C generated AIR ~d N-1 BPF 11/2/29 29
OFDM demodulation s( t ) = LPF N 1 n = [ a cos { 2π ( f + nf ) t} b sin { 2π ( f + nf ) t} ] n [ s( t ) cos( 2πf C 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 n { sin( 2πf t) }] = { a sin( 2πnf t) + b cos( 2πnf t) } s ( ) 11/2/29 3 C n n = Q t N 1 I Q n n = ut () = s() t + js () t = d e d n = FFT(u(k)) c n j2πnf t 1 2 1 2 I
OFDM demodulator (Too simple) Channel T u n e r cos( 2πfCt) π/2 LPF LPF A / D S / P DFT P / S Bit Stream 11/2/29 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 Time Symbol period T=1/f 11/2/29 32
Multi-path Delayed wave causes interference Path 2 Direct Path Building Base Station Path 3 Mobile Reception 11/2/29 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 11/2/29 34
Guard Interval T g T g OFDM symbol(1/f ) T g Copy signal By adding the Gurard Interval Period, ISI can be avoided T g OFDM symbol (1/f ) Direct Delayed Sampling Period 11/2/29 35
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 11/2/29 36
Multiple Frequency Network f3 f1 Area 3 f1 Area 1 Area 2 f2 Area 4 Frequency utilization is low 11/2/29 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 11/2/29 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 11/2/29 39