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OFDM as a Multicarrier Modulation: A Convenient Framework for Time-Frequency Processing in Wireless Communications Jacek Ilow, Ph.D. Associate Professor Department of Electrical and Computer Engineering Dalhousie University Halifax,Canada J.ilow@dal.ca http://www.dal.ca/~jilow http://radio-1.ee.dal.ca/~ilow OFDM History • High-data-rate communications systems are limited not by noise, but often more significantly by the intersymbol interference (ISI) due to the memory of the dispersive communications channel. – If the symbol rate exceeds the duration of channel impulse response (CIR), mechanisms must be implemented in order to combat the effects of ISI. • Channel equalization techniques can be used to suppress the echoes caused by the channel. • Significant research efforts have been invested into the development of such channel equalizers – Another approach is to utilize an FDM system which employs a set of subcarriers in order to transmit information in parallel subchannels over the same channel. • The data throughput of each channel is only a fraction of the data rate of the single-carrier system having the same throughput. Frequency Selective Channel Why OFDM? Single Carrier Multicarrier • Uses the entire bandwidth • Splits bandwidth into subchannels • Short symbol times • Sends information in parallel • This causes ISI • OFDM: orthogonal subcarriers 1 0.8 frequency response frequency response 0.6 OFDM is a considerable option when the channel introduces ISI 0.4 0.2 Applications: ADSL, DAB, DVB, Hiperlan/2, ... 0 -0.2 frequency OFDM – Orthogonal Frequency Division Multiplexing -0.4 frequency 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 2001-05-31 FDM (Frequency Division Multiplexing) Vs. OFDM Frequency Power FDMA Bc cos(2pf0t) Bm Frequency channel X BPF Serial X BPF Time To S Parallel cos(2pf1t) (S/P) X BPF cos(2pfN-1t) OFDM History • In 1971, Weinstein suggested using a digital implementation based on the DFT. – The DFT is by its nature cyclically redundant in the frequency domain. – The associated harmonically related frequencies can be used as a set of subchannels carriers required by the OFDM system. Multipath can be described in two domains: time and frequency Time domain: Impulse response time time time Impulse response Frequency domain: Frequency response time time time f time Sinusoidal signal as input Frequency response Sinusoidal signal as output Modulation techniques: monocarrier vs. multicarrier Channel Channelization N carriers Similar to Guard bands FDM technique B B Pulse length ~1/B Pulse length ~ N/B – Data are transmited over only one carrier – Data are shared among several carriers and simultaneously transmitted Drawbacks Advantages Furthermore – Selective Fading – Flat Fading per carrier – It is easy to exploit – Very short pulses – N long pulses Frequency diversity – ISI is compartively long – ISI is comparatively short – It allows to deploy 2D coding techniques – EQs are then very long – N short EQs needed – Dynamic signalling – Poor spectral efficiency – Poor spectral efficiency because of band guards because of band guards To improve the spectral efficiency: Eliminate band guards between carriers To use orthogonal carriers (allowing overlapping) Orthogonal Frequency Division Modulation N carriers Symbol: 2 periods of f0 Transmit f + Symbol: 4 periods of f0 f B Symbol: 8 periods of f0 Channel frequency Data coded in frequency domain Transformation to time domain: response each frequency is a sine wave in time, all added up. Decode each frequency bin separately Receive time f B Time-domain signal Frequency-domain signal Each subcarrier is modulated at a low enough rate that dispersion (ISI) is not a problem. Subcarriers must be spaced so that they do not interfere. S(f) f0 f1 fN-1 Bandwidth, B cos(2pf0t) x LPF Detector x LPF Detector r(t) P/S cos(2pf1t) x LPF Detector cos(2pfN-1t) Demodulator Orthogonal Frequency Division Multiplexing (OFDM) OFDM is a special case of multicarrier transmission that permits subchannels to overlap in frequency without mutual interference increased spectral efficiency. OFDM exploits signal processing technology to obtain cost-effective means of implementation. Mulitple users can be supported by allocating each user a group of subcarriers. Bandwidth, ~ B/2 Spectrum of OFDM Signal When N is large, the power spectral density (PSD) of the transmitted signal is PSD of OFDM Signal OFDM transmission system (time continuous) Transmitter Channel ld(M) d0 (i) Mod. g (t) 0 d1 (i) b(i b ) Mod. g (t) sa (t) S 1 Source S/P dN-1(i) Mod. gN-1(t) channel ca(t) Receiver T ld(M) ^ d0 (i) Demod. h0 (t ) (t) ^0(t ) s ^ ^ b(i b ) d1 (i) Demod. h1 (t ) ^a (t) s ^ s1 (t ) Dest. P/S ^ dN-1 (i) Demod. hN-1 (t) ^N-1(t) s OFDM Basics Mathematical Description of an OFDM System 1/2 N 1 • time continuous s(t ) dn (i) g t iTS e j 2p f nt representation of an n0 OFDM transmitter: g (t ) rect t /TS , f n nf n /TS N 1 j 2p nt /TS dn (i) e , iTS t i 1TS n0 • time discrete N 1 j 2p nkTA /TS representation of sk (i) s(t) t iT kT dn(i) e , k [0,1,2,..., N 1] S A n0 an OFDM transmitter: N TS /TA N 1 dn (i) e j 2p nk / N = IDFT d0(i), d1(i),..., d N 1(i) n0 OFDM Basics Mathematical Description of an OFDM System 2/2 N 1 • time discrete dn (i) rk (i) e j 2p kn/ N ˆ representation of k 0 an OFDM receiver: = DFT r0(i), r1(i),..., rN 1(i) • Complete System: ˆ d DFTN IDFTN (r)c OFDM Basics Symbol Rate Model of an OFDM System Transmitter Discrete ld(M) d0 (i) s0 (i) Channel Mod. 0 0 d1 (i) s1 (i) Mod. 1 1 s(i,k) Source S/P IDFT P/S ga (t) dN-1 (i) sN-1(i) Mod. N-1 N-1 sa (t) channel ca (t) Receiver ld(M) d0 (i) r0 (i) Demod. 0 0 (t) ra (t) d1 (i) r1 (i) ha (t) Demod. 1 1 r(i,k) Dest. P/S DFT S/P TA dN-1(i) rN-1(i) Demod. N-1 N-1 OFDM Basics Including a “cyclic prefix” To combat the time dispersion: including ‘special’ time guards in the symbol transitions co p y Furthemore it converts Linear conv. = Cyclic conv. CP T (Method: overlap-save) Tc Without the Cyclic Prefix Including the Cyclic Prefix Symbol: 8 periods of fi CP Symbol: 8 periods of fi Passing the channel h(n) Passing the channel h(n) Yi(t) Yi(t) Channel: h( n) =( 1 ) –n/ n n=0 ,…,2 3 Yi(t) Initial transient The inclusion of a CP Final transient remains within maintains the orthogonality remains within Initial transient Loss of orthogonality Decaying transient the CP the CP Yj(t) Yj (t) Symbol: 4 periods of fi Symbol: 4 periods of fi CP functions: – It acomodates the decaying transient of the previous symbol – It avoids the initial transient reachs the current symbol OFDM Modulator cos(2pfct) Real x Bit Stream S/P IDFT P/S S BPF s(t) Img x sin(2pfct) OFDM Demodulator x LPF r(t) cos(2pfct) Received A/D S/P DFT P/S Bit p/2 Stream x LPF IEEE 802.11 Wireless LAN • IEEE 802.11 standard: – unlicensed frequency spectrum: 900Mhz, 2.4Ghz, 5.1Ghz, 5.7Ghz and 802.11b 802.11a Frequency Band The 802.11 Protocol Stack www.ieee802.org/11/ 802.11a System Specification t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 GI2 T1 T2 GI OFDM Symbol GI OFDM Symbol Short training sequence: Long training sequence: AGC and frequency offset Channel estimation • Sampling (chip) rate: 20MHz • Chip duration: 50ns • Number of FFT points: 64 • FFT symbol period: 3.2ms • Cyclic prefix period: 16 chips or 0.8ms – Typical maximum indoor delay spread < 400ns – OFDM frame length: 80 chips or 4ms – FFT symbol length / OFDM frame length = 4/5 • Modulation scheme – QPSK: 2bits/sample – 16QAM: 4bits/sample – 64QAM: 6bits/sample • Coding: rate ½ convolutional code with constraint length 7 OFDM Transmitter (HIPERLAN/2 / IEEE802.11a) d0(i) Map. Mod. d1(i) Map. N source CC S/P d2(i) IDFT PS/GI DAC Map. . . . dN-1(i) Map. • channel coding (convolutional codes with Viterbi decoding) • IDFT: discrete realized filter bank (very efficient FFT) • cyclic prefix / guard interval (GI) prevents intersymbol interference (ISI) OFDM Basics OFDM Receiver (HIPERLAN/2 / IEEE802.11a) e 0 d0(i) Mod. Demap. e1 d1(i) Demap. SYNC N -1 ADC PE -1 DFT e2 P/S CC dest. GI d2(i) Demap. . eN-1 . Viterbi . dN-1(i) decoder • Synchronization – FFT window position (time domain) – sample and modulation frequency correction • Pre equalizer (PE) for impulse compression • OFDM: Orthogonal Frequency Division Multiplexing – separate multiplicative channel correction on each subcarrier – equalizer coefficient design: en = 1 / Cn circular convolution OFDM Basics Channel Estimation (CE): Training Symbols • burst structure of HIPERLAN/2 and IEEE802.11a – short symbols for AGC and raw synchronization – training sequence (TS): 2 identical symbols per subcarrier (52) – data OFDM symbols with 48 user data and 4 pilot symbols each – pilot symbols for fine synchronization (insufficient for channel estimation) f 16.5 MHz AGC … 0 SYNC TS 0 8 16 24 t in ms Channel Estimation Spectrum Mask Power Spectral Density -20 dB -28 dB -40 dB -30 -20 -11 -9 9 11 20 30 f carrier Frequency (MHz) • Requires extremely linear power amplifier design. Carrier orthogonality by Discrete Multi-Tone (DMT) modulation enables their partial overlap OFDM spectra of individual subcarriers • DMT used in Digital Subscribe Line (xDSL) • Usable frequency band is separated into 256 small frequency bands (or subchannels) of 4.3125 kHz each (ADSL) • Within each subchannel, modulation uses quadrature amplitude modulation (QAM) • By varying the number of bits per symbol within a subchannel, the modem can be rate-adaptive • DMT uses the fast Fourier transform (FFT) algorithm for modulation and demodulation