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OFDM – Orthogonal Frequency Division Multiplexing Dr. Jean Armstrong Department of Electronic Engineering La Trobe University 1 Overview ! Introduction ! applications ! multicarrier systems ! Why use OFDM? ! multipath transmission ! How OFDM works ! Applications of OFDM ! Problems with OFDM ! Research in OFDM 2 Applications of OFDM ! Digital Television ! European and Australian standard ! Wireless Local Area Networks (LANs) ! Hiperlan 2 ! ADSL (asymmetric digital subscriber loop) ! High speed data transmitted along existing telephone lines ! Future mobile telephony? 3 Multicarrier systems ! Single carrier system ! signal representing each bit uses all of the available spectrum frequency W ! Multicarrier system ! available spectrum divided into many narrow bands ! data is divided into parallel data streams each ! transmitted on a separate frequency band W N 4 What is OFDM? ! OFDM is a multicarrier system ! ! uses discrete Fourier Transform/Fast Fourier frequency W N Transform (DFT/FFT) ! sin(x)/x spectra for subcarriers ! Available bandwidth is divided into very many narrow bands Frequency ! ~2000-8000 for digital TV W/N ! ~48 for Hiperlan 2 ! Data is transmitted in parallel on these bands 5 Why is OFDM so popular for new broadband systems? ! Most broadband systems are subject to multipath transmission ! Conventional solution to multipath is an equalizer in the receiver ! high data rates - equalizers too complicated ! With OFDM there is a simple way of dealing with multipath ! relatively simple DSP algorithms 6 What is Multipath? ! More than one transmission path between transmitter and receiver ! Received signal is the sum of many versions of the transmitted signal with varying delay and attenuation 7 Effect of Multipath on Received Baseband Signal 1 2 3 4 5 Signal on Path 1 Received Signal on Path 2 Signal Signal on Path 3 Received signal depends on bits 2 - 4 ! Received signal at any time depends on a number of transmitted bits ! Intersymbol Interference (ISI) ! Need equalizer to recover data 8 ISI gets worse as data rate increases 1 2 3 4 5 Signal on Path 1 Received Signal on Path 2 Signal Signal on Path 3 Received signal depends on bits 1 - 4 ! ISI covers more symbol periods ! Equalizer becomes too complicated 9 How does OFDM solve the multipath problem? ! Data is transmitted in parallel ! longer symbol period ! e.g. for N parallel streams, symbol period is N times as long ! Cyclic prefix ! trick to avoid residual ISI 10 How are signals transmitted in parallel without interference? First three subcarriers ! Each subcarrier has a different frequency ! Frequencies chosen so that an integral number of cycles in a symbol Symbol period period ! Signals are 2π kt −2π lt mathematically T ∫ sin T sin T dt = 0, k ≠ l 0 orthogonal 11 How is data carried on the subcarriers? ! Data is carried by varying the phase or amplitude of each subcarrier ! QPSK, 4-QAM, 16-QAM, 64-QAM Two possible subcarrier values 12 Baseband OFDM system Discrete frequency domain Discrete Time Domain Each input controls Samples of modulated signal at one frequency and multiplexed signals High speed Low- Serial D/A data IFFT Parallel Pass to Conver (complex) to Serial Filter- Parallel -ter ing Transmitter Low- Parallel Serial Received A/D Pass to FFT to high speed Conver Filter- Serial Parallel data -ter ing Receiver 13 How are OFDM signals generated? Typical IFFT Output Samples ! Parallel data streams are used as inputs to an IFFT ! IFFT output is sum of signal samples ! IFFT does modulation and Signal values at the output multiplexing in one step of the IFFT are the sum ! Filtering and D/A of of many samples of many sinusoids - looks random samples results in baseband signal 14 Modulation ! Varying the complex numbers at the IFFT input results in modulation of the subcarriers 8-PSK 16-QAM 15 Signals at Input and Output of Transmitter IFFT High speed Low- Serial D/A data IFFT Parallel Pass to Conver (complex) to Serial Filter- Parallel -ter ing Transmitter Complex value IFFT output representing data gives samples is input to IFFT of modulated multiplexed signal 16 OFDM in a multipath environment - effect on one subcarrier ! Received signal in First symbol Second symbol one symbol period is not a sinusoid Signal on Path 1 ! Causes intercarrier interference (ICI) Signal on Path 2 delay ICI 17 Cyclic Prefix Cyclic Prefix Symbol without prefix Signal transmitted on one subcarrier for one symbol ! Each symbol is cyclically extended ! Some loss in efficiency as cyclic prefix carries no new information 18 Effect of multipath on symbol with cyclic prefix Signal on Path 1 Signal on Path 2 Path delay Cyclic Prefix ! If multipath delay is less than the cyclic prefix ! no intersymbol or intercarrier interference ! amplitude may increase or decrease 19 Frequency selective fading 1 Transmitted Signal Amplitude 0 Main signal + Delayed signal -1 0 0.5 1 1.5 2 Symbol Duration 2 Amplitude Transmitted 0 Signal Main signal + -2 Delayed signal 0 0.5 1 1.5 2 Symbol Duration 20 Spectrum of Received Signal ! Multipath fading causes some frequencies to be attenuated ! Fading is approximately W constant over narrow band ! This is corrected in the receiver 21 Amplitude and phase change ! Multipath delay causes 1 Transmitted Signal change in amplitude and phase of each subcarrier Amplitude 0 Main signal + Delayed signal Change depends on -1 0 0.5 1 1.5 2 2 Symbol Duration ! subcarrier frequency Amplitude Transmitted 0 Signal -2 0 0.5 1 1.5 2 Main signal + Delayed signal ! Corrected in receiver by one complex multiplication Symbol Duration per subcarrier 22 Multipath fading corrected by ‘single tap equalizer’ Parallel One Serial Low- Received Tap A/D to FFT to Pass high speed Equali- Conver data Serial Parallel Filter- zer -ter ing ! Change in phase and amplitude corrected by complex multiplication ! Receiver structure suited to DSP implementation 23 Digital Video Broadcasting (DVB) OFDM is used in the Australian ! digital television system ! 2048 point IFFT ! 1705 subcarriers used ! Flexible standard TV ! variable error coding ! variable cyclic prefix ! variable constellation ! 4QAM, 16QAM, 64QAM ! Broadcast system ! mode determined by broadcaster 24 DVB - single frequency network DVB designed to allow the ! same frequency to be used for the same channel throughout a region ! Single Frequency Network ! More than one received signal ! like extreme multipath ! Reason for large number of TV subcarriers Antenna Antenna ! 8000 subcarrier option allows greater distance between transmitters 25 OFDM in ADSL ! OFDM used in ADSL is usually called ‘Discrete Multitone’ (DMT) ! Two way transmission ! transmission can be tailored to the particular channel ! Baseband system ! only real (not complex signal can be transmitted) 26 Frequencies used for ADSL Power Spectral Density Upstream ADSL with Echo Cancelling (EC) POTS Frequency 0-4 kHz Downstream 25-1104 kHz Power Spectral Density ADSL with Frequency Division Upstream POTS Downstream 138-1104 kHz Frequency Duplexing (FDD) 27 OFDM/DMT in ADSL Power Spectral Density Upstream POTS Downstream 138-1104 kHz Frequency ! 256 subcarriers ! Test signals transmitted ! received signal and noise level of each tone measured ! Large constellations used on good tones 28 Hiperlan-2 - Wireless LAN ! 64 point FFT, 52 subcarriers used ! Different modes ! signal constellation, error coding, cyclic prefix ! Two way channel ! feedback be used to determine transmission mode 29 OFDM Problems ! High peak-to-average power ratio ! peak signals power much greater than average signal power ! need very linear amplifiers with large dynamic range ! Very sensitive to frequency errors ! tight specifications for local oscillators ! Doppler limitation 30 High peak-to-average power ! OFDM signal is sum of many separate sinusoids ! In worst case may all add constructively ! High peaks occur rarely 31 Solutions to peak-to-average power High speed Low- Serial D/A data Parallel Pass to IFFT Conver (complex) to Serial Filter- Parallel -ter ing Transmitter ! Coding to avoid the peaks - Monash ! Clip the peaks - La Trobe ! Predistort the signal to compensate for the amplifier nonlinearity - Victoria University 32 Frequency Sensitivity Frequency W/N ! Individual subcarriers have sin(x)/x spectrum ! Large sidelobes result in sensitivity to frequency offset ! Subcarriers no longer orthogonal ! Tight specifications on local oscillators 33 Research at La Trobe University ! Peak-to-average power reduction ! clipping ! effect on signal constellation ! clipping noise added at transmitter ! Alternative modulation schemes based on OFDM ! polynomial cancellation coded OFDM (PCC-OFDM) 34 PCC-OFDM - solution to frequency sensitivity 1 1 1 0.5 0.5 0.5 0 0 0 -0.5 -0.5 -0.5 -1 -1 -1 -5 0 5 10 -5 0 5 10 -5 0 5 10 Frequncy Frequncy Frequncy ! By coding the subcarriers in pairs frequency sensitivity can be reduced ! Would have been a better basis for DVB 35 ISI/ICI of OFDM and PCC-OFDM OFDM PCC-OFDM ! Concentration of subchannels in time and frequency domain reduce ICI and ISI 36 PCC with overlapping symbol periods 0 T/2 T 3T/2 2T ! Symbols are overlapped ! ISI is deliberately introduced ! equalizer required in receiver to recover data 37 PCC-OFDM receiver structure exp (− j 2π ( f c + ∆ f )t ) y0,i z0,i v0,i v0,i−1 v0,i−2 " T/2 " " " Weight T/2 " LPF Delay BPF X and line yN−1,i DFT and zN−1,i sum vN−1,i Delay vN−1,i−1Delay vN ADC 2 2 2 − ,i−2 1 One DFT operation Data clocked in at rate T/N every T/2 Vi−1 " Two- Vi Dimensional ˆ Di Vi+1 Equalizer " ! Requires two dimensional equalizer ! Properties of PCC-OFDM mean that only a few terms along the diagonal are significant 38 Performance in a multipath channel 0 10 -1 ! PCC-OFDM outperforms OFDM 10 Advantages increase -2 10 ! as delay spread Bit Error Ra te -3 10 increases -4 tolerance to delay 10 ! 10 -5 four line a r s ta ge s - 10dB four line a r s ta ge s - 15dB spread depends on equalizer length, not OFDM - 10dB OFDM - 15dB -6 length of cyclic prefix 10 0 5 10 15 20 25 30 de la y s pre a d (T/64) N=64, OFDM cyclic prefix length =6T/64 39 Conclusions ! OFDM is used in many applications ! solution to multipath ! good digital signal processing algorithms ! Any questions? 40 Baseband OFDM system High speed Low- Serial D/A data Parallel Pass to IFFT Conver (complex) to Serial Filter- Parallel -ter ing Transmitter Low- Parallel Serial Received A/D Pass to FFT to high speed Conver Filter- Serial Parallel data -ter ing Receiver 41

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