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Ofdmpres2 Tutorial on OFDM and MIMO OFDM

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  • 1. An Introduction To OFDM John Wiss 1
  • 2. OFDM Origins • • • • OFDM is a modulation type whereby the information coming from a single source is intentionally split up into many carriers (subcarriers) to combat multipath effects and to add a dimension of “diversity” to the transmit signal Initial work in 1960s for military applications OFDM stands for “Orthogonal Frequency Division Multiplexing” – “Orthogonal” in the sense that each information-bearing subcarrier may be demodulated without interference from adjacent subcarriers – “Frequency Division” in the sense that the subcarriers are generated as frequency-disjoint coupled carriers with fixed spacing and modulation type – “Multiplexed” in the sense they are synthesized into a single channel Error-correction coding essential because some subcarriers may be in deep fades so encoding of all information bits with interleaving necessary 2
  • 3. OFDM-BASED SYSTEMS • • • IEEE 802.11a was the first wireless networking standard with widespread usage in unlicensed 5 GHz band providing up to 54 Mbps  16.67 MHz wide channel containing 52 subcarriers with BPSK, QPSK, 16-QAM, 64-QAM modulation on each subcarrier  OFDM “symbol rate” of 250 ksym/sec and up to 288 bits/symbol of encoded information IEEE 802.11g is a dual mode system fusing 802.11b WiFi and 802.11a except at a lower frequency band (unlicensed 2.4 GHz) UWB- Multiband OFDM is the leading contender for ultra-wideband communications (>100 Mbps)  Hopped OFDM over three bands to spread energy for short range high-speed communications • Spatially diverse Vector OFDM (VOFDM) • • •  Multiple Input/Multiple Output (MIMO) diversity to combat flat fading Wideband Networking Waveform for military communications 4-G Cellular IEEE 802.16 Metropolitan Area Networking--OFDMA 3
  • 4. • One QAM symbol per subcarrier 4
  • 5. Why Use OFDM? • There are a few ways to cope with multipath channels:  Use spread spectrum techniques to allow separation of paths  Direct Sequence Spreading (CDMA/DSSS)—Low bps/Hz  Use Frequency Hopping (Bluetooth, GSM)—MAC inefficiencies/complex  Use high bandwidth single-carrier signal —Large delay spread vs Tsym  Use lower data rates to allow channel to be flat over signal bandwidth • The problem is that the signal bandwidth needs to be as narrow as possible to mitigate multipath (the symbol period needs to be as long as possible), Unless…  The signal is made bandwidth-inefficient in order to perform combining of dispersed rays (e.g., RAKE combining)  The optimal signal would be one which has high bandwidth efficiency and immunity to channel variations due to multipath • Lower complexity equalization for given delay spread than single-carrier modulation  OFDM allows tightly packed carriers to convey information orthogonally and with high bandwidth efficiency 5
  • 6. Equalization Complexity • Let’s compare equalization complexity of a single carrier (SC) system with the same total bandwidth as an OFDM system subject to similar channel conditions  Frequency domain equalization (via FFT) for OFDM Rx  Decision feedback equalization for SC Rx • OFDM complexity grows slightly greater than linear with BW*Delay Spread product • Single carrier complexity grows quadratically with BW*Delay Spread product •Single Carrier Case  GMSK or OQPSK 24 Mbps  Delay Spread = 250 nsec  Requires 20 FF, 20 FB taps •OFDM Case  QAM 52-OFDM 24 Mbps (QAM 16)  Delay Spread = 250 nsec  64 Point FFT  52 Subcarriers  Guard Interval = 800 nsec  Rsym = 250 kHz FEEDFORWARD FILTER (FFF) Cmplex Data In D Tap 0 D Tap 1 D Tap 2 D FEEDBACK FILTER (FBF) Tap 3 D [ . ]* X X Tap FB2 + X From other Taps FFF D + X + From FBF Taps µLMS + Tap FB3 1 SPS Error Eq. Output Slicer Decisions + + D(k) {Training, Demod Decisions} Tap FB1 Tap FB0 [ . ]* µ4 6 Single Carrier DFE is 10 times as complex!!! D X D + Adj Proc. • GMSK Eq (LMS) = 2*20*24*10 (960E6) rmult/sec • OFDM (radix 4)= 96*106 = (96E6) cmult/4µsec = 96E6 rmult/sec D Tap 4 Peamble Sequence 6 Error X
  • 7. Indoor Channels ETSI/BRAN Low Mobility Indoor 7
  • 8. Indoor Channels (Cont) Small Room Fading (amb. Motion) Tunnel Fading (amb. Motion) k = 0 → Gaussian, k = ∞ → Rayleigh k is the ratio of power of the direct path to the scattered paths 8
  • 9. Outdoor Channels Tx Height=15 m, 3.5 GHz/Outdoor Vs Antenna Height—12 &15dBi antennas 3km Separation 9
  • 10. 10
  • 11. -- Channel can be inverted (Equalized) by spectrum division 11
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  • 16. OFDM Channel Estimation • Each subcarrier corrected by a single tap (complex) equalizer • Typically have training symbols with to train frequency domain equalizer • Sometimes have embedded pilot subcarriers that are used to estimate channel  Uniformly spaced throughout symbol to allow interpolation between pilots to correct data-bearing subcarriers • Data subcarriers corrected post-FFT in frequency domain • Additional performance by weighting soft decisions based on channel estimates 16
  • 17. 17
  • 18. Insert Short Train Standard (52-Carrier) Mode Spectrum For Various Output Backoffs 10 0 -10 -20 -30 10 dB OBO -40 12 dB OBO -50 -60 Linear PA -70 -80 -2.0E+7 -1.5E+7 -1.0E+7 -5.0E+6 0.0E+0 5.0E+6 Frequency (MHz) 1.0E+7 1.5E+7 -8 -6 -4 -2 0 2 4 6 8 -8 -6 -4 -2 0 2 4 6 8 -8 -6 -4 -2 0 2 4 6 8 I 1 I Conv. Encode PN Data 0 Interleave Subcarrier Mapper QAM Map Q Add Cyclic Prefix IFFT Spectral Window Digital To Analog Polyphase Interpolate Oscillator Phase Noise Effects PA Nonlinearity Effects To Channel 10 0 -10 Normalized Pout Vs Pin GaAsTEK ITT6401FM -20 DAC Compensate Insert Long Train 1.2 -30 -40 Phase PSD Sxx(f) -50 A0cos(2π f1t+Φ 1 (t)) -60 -70 -80 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 A1cos(2π f2t+Φ 2(t)) A3cos(2π f3t+Φ 3(t)) 0.8 Y=1 for (X>2.0) 0.6 0.4 Y = 0.0781X^3-0.5285X^2+1.245X for (0<X<2) 0.2 -f3 -f2 -f1 f1 f2 f3 0 Freq. 0 0.5 1 1.5 2 2.5 Pin (Normalized : 1dB compression Pt=1.0) --Real Units α 1 exp( jφ1 ) S( t − τ1 ) α 0 exp( jφ 0 ) S( t − τ 0 ) α 2 exp( jφ 2 ) S( t − τ 2 ) QAM 64 Uncoded BER Performance {Enhanced 105-Carrier Mode} 1.0E-2 1.0E-3 10 0 Channel Sample Output Of H0-H15 Under Severe Multipath 1200 1000 -10 1.0E-4 Peak Multipath Peaks 800 1.0E-5 Right Adjacent Left Adjacent 600 -20 400 1.0E-6 Multipath peak > 0 (1) Theory (2) Simulation 200 -30 0 1.0E-7 -200 -40 -400 -50 -60 -512 Additive Noise + AGC -600 7400 -312 -112 88 288 I DQM Decimate Q Filter Analog To Digital Fs = 40,80M Short Train Correl Noise Average Decimate By 2 Filter Frequenc y Respons e 10 RADIX 2 STAGE 128-Points Multipath Resistant Detection RADIX 8 FFT A STAGE 1 {64-Points} Orthogonalizer RADIX 8 FFT B STAGE 1 {64-Points} Mag 0 By 2 -10 -20 -40 7550 7600 7650 7700 7750 7800 20 21 22 23 24 Ecarr/No (dB) RADIX 8 FFT A STAGE 2 {64-Points} RADIX 8 FFT B STAGE 2 {64-Points} Channel Inverter Unscramble 64-pt Transform -50 -60 UNSCRAMBLE 128-pt Transform Phase Noise Reduction Algorithm Slicer Adaptive Filters -70 -80 -90 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Frequency (1.0 = Ny quist) 0.8 0.9 1 Decimate By 4 Filter Frequenc y Respons e 20 By 4 0 -20 250 -40 200 -60 150 -80 -100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Frequency (1.0 = Ny quist) 0.8 0.9 1 100 50 0 -50 -100 0 500 1000 1500 25 26 27 28 Equalization Tap Update AGC -30 7500 Programmable FFT Mag Gen Test Statistic 1.0E-8 7450 488 Burst Detector/Orthogonalizer/Synchronizer Amplitude Spectrum (dB) Q 8 6 4 2 0 -2 -4 -6 -8 Pilot Carriers Amplitude Spec trum (dB) Su bca rrie r# 8 6 4 2 0 -2 -4 -6 -8 8 6 4 2 0 -2 -4 -6 -8 10 0 -10 -20 -30 -40 -50 -60 -70 -80 Real System Up to 64 QAM Per Carrier 2000 2500 Time (Samples) 3000 3500 4000 18 De-Interleave And Decode PN Data Out 3 2.0E+7
  • 19. OFDM Waveform/Receiver • 802.11a/g uses training symbols that can be used to estimate/correct gain frequency offsets and to equalize the channel and Pilot carriers to correct phase offsets during the data symbols • VOFDM uses dense training structure in the data symbols to allow for interpolation between pilots to equalize data-bearing carriers 19
  • 20. The Peak to Average Power (PAPR) Problem • 802.11a/g consists of 52 subcarriers which are modulated using Digital rather than analog techniques forcing output PA backoffs of ~5-9 dB from P1 • The peak signal envelope is the vector sum of the instantaneous amplitude and phases of the 52 subcarriers rotating at n∆F where n ranges from –26 to +26 (in the case of 802.11a) • The PAPR is more dependent on the number of subcarriers than the modulation on each subcarrier when the #subcarriers grow QAM 64 52-Carrier OFDM W/Shaping Crest Factor PDF 4E-2 4E-2 3E-2 3E-2 2E-2 2E-2 1E-2 99.9 % =9.5 dB 5E-3 0E+0 -25 -20 -15 -10 -5 0 5 Amplitude Relative To Mean Amplitude (dB) (mean=0 dB) 10 15 20
  • 21. The Phase Noise and AFC Problem • Since the subcarriers are packed closely (at the 1st Null of Sinx/x) frequency errors in the Rx will cause signal leakage and Inter-carrier interference • Phase Jitter will cause the carriers to leak as well • However, for 802.11a/g 64 QAM-OFDM the single carrier phase noise spec. is adequate to supress LOT (loss of orthogonality) • Low OFDM symbol rate (250 Ksym/sec) implies low loop bandwidth which may allow a lot of Flicker Noise through QAM 64 -OFDM Loss Vs Jitter 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 RMS Phase Jitter (Degrees) 1.6 1.8 2 21
  • 22. OFDM Waveform Design • The parameters to design are function of channel characteristics  Number of subcarriers  Efficiency, delay spread of channel  Subcarrier bandwidth  Mobility/Time variation of channel, coherence BW of channel  Guard period  Delay spread of channel, modulation order • Fundamental Design criterion of OFDM is that the channel must appear flat across one subcarrier bandwidth • Coherence BW determines subcarrier bandwidth to ensure flatness • Cyclic prefix period must be > delay spread of channel  For BPSK/QPSK-OFDM cyclic prefix should be > 1 x Delay Spread  For QAM 16 cyclic prefix should be > 2 x Delay Spread  For QAM 64 cyclic prefix should be > 3.5 x Delay Spread • For efficiency want guard period to be less than 50% or so of total symbol period—determines # subcarriers/symbol 22
  • 23. Non-Idealities / Mitigation /Modem Design • Peak-Average Power Problem  The signal band consists of many closely-spaced subcarriers (in fact, overlapped by 50%)  With large modulation orders, the signal behaves like bandlimited Gaussian noise The signal envelope exhibits a Rayleigh density—different than SC modulations Mitigate by either clipping signal or by modifying data or adding sacrificial subcarriers to reduce PAPR  Low order modulations can be improved by phase whitening the BPSK or QPSK subcarriers  Data symbols may be multiplied by one of N stored sequences —Sequence with lowest PAPR is transmitted along with best sequence index Peak Cancellation  Coding Techniques—Golay complementary codes etc.  Sacrifice subcarriers to cancel biggest peaks (need about 50% for canceling to limit PAPR < 3 dB) 23
  • 24. Non-Idealities / Mitigation /Modem Design Cont. {PAPR} Shaped Amplitude PDF Vs Quadrature Gaussian Noise Model 8E-1 fm ( m) = 7E-1 6E-1     π  σ 2 =  2 − σ 2 m n 2  (1) Simul. Signal 5E-1  m2 m exp − 2  2σ σ2 n n  (2) Quadrature Noise Model 4E-1 3E-1 µm = 2E-1 1E-1 πσ 2 n 2 σ 2 (equiv) = σ 2 (equiv) ≅ 0.811 • nI nQ 0E+0 -1 0 1 2 Normalized Amplitude 3 4 ES 2 5 • The signal envelope has nearly identical statistics to BL Gaussian Noise (52 Subcarriers) 24
  • 25. Non-Idealities / Mitigation /Modem Design Cont. • Phase Noise & Frequency Errors  The symbol rate of OFDM is slow (equal to the BW of a single subcarrier + 1/Guard Period thus close-in phase noise more critical  Zero IF (Direct Conversion) designs will admit a Flicker noise component  Frequency control very important to keep the subcarriers orthogonal relative to FFT Rx Bin reference. SinX/X leakage will cause InterCarrier Interference  Phase noise will jitter subcarriers (SCs) into each other and a given SC will interfere with all other SCs resulting in a maximum attainable SNR  Phase tracking via pilots or decision-directed techniques allow tracking of so-called “Common Phase Error” Error Power = 2 R ee ( 0 ) = σe = ESig N N −1 ∑ S ( k − m) k =0 φφ Where S( ) = Phase noise PSD, N = # subcarriers 25
  • 26. Non-Idealities / Mitigation /Modem Design Cont. Phase Jitter Max SNR (52 Subcarriers) Maxim um Attainable SNR Vs Phas e Jitter St Dev 45 40 35 30 25 20 15 10 5 0 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Phase Jitter Standard Deviation (Radians) 0.08 0.09 26 0.1
  • 27. Non-Idealities / Mitigation /Modem Design Cont. {Phase, Frequency Recovery} Phase may be recovered by Noting common phase shift of pilot symbols and constructing a loop With this information Frequency information may exploit cyclic prefix since same time waveform is at start & end Of OFDM symbols—Use Lag Product Correlation Symbol Length Less Cyc prefix r ( t − T ) r ( t ) = exp( j2πf d T ) * TCP ∫ h ( τ ) s( t - τ ) 2 2 dτ + n ( t ) n * ( t − T ) I In To Phase Rotator/NCO/FFT Q In 0 ( ARG r * ( t − T ) r ( t ) fd ≅ 2πT FIFO ) ( • )∗ Conjugate X + Freq Est Z -1 ARG ( . ) 0 Switch Select 27
  • 28. Non-Idealities / Mitigation /Modem Design Cont. {Fine Timing Adjust & Tracking} Because each subcarrier is narrowband and typically the OFDM access scheme is TDMA, We can correct spectrally any time offset or residual sampling errors Typically the RF reference is used as the sampling reference so a frequency error may be translated into a ppm error for the sampling frequency error as well –bursts must be short enough so that the total timing slew is << cyclic prefix or guard period ω   Can correct timing drift using FT time scaling property ℑ{ f ( at )} ↔ a F a    1 SCs will rotate at a speed linearly related to their distance from DC subcarrier—rotation in opposite directions for positive vs negative subcarriers—delta phase between subcarrier and its negative frequency complement provides timing frequency error signal—can rotate each subcarrier in direction and rate to stop spinning slow DC fast 28
  • 29. Non-Idealities / Mitigation /Modem Design Cont. {DC Offsets, I/Q Imbalance} • DC Offsets  Zero-IF designs may suffer from large DC offsets  Analog cancellation on I/Q arms  Digital DC offset detection and cancellation feedback to analog  Progressive notch filter near DC  Low-IF improves  Zero (DC) subcarrier not used for data in waveform design • I/Q imbalances  I/Q Imbalance causes positive/negative frequency aliasing  I/Q mismatch will introduce crosstalk between I, Q branches  May be mitigated digitally in Rx to eliminate crosstalk  Isolation of imbalance to one side of link desirable due to multiusers each of which may have different Tx imbalances  Low-IF rather than Zero-IF eliminates problem to a large extent Double complex-mixing mitigates phantom image products 29
  • 30. Soft Symbol/LLR Generation • Typically every bit is encoded in OFDM to provide full time/frequency diversity—for QAM constellations the optimum approach is “Bit/Slice” decisioning—based on bit qualities of symbol. QAM 16 LSB Unweighted Soft Decision Mapping 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -4 -3 -2 -1 0 1 I or Q Input (To Slicer) 2 3 4 QAM 16 MSB Unweighted Soft Decision Mapping 16 14 12 10 8 6 4 Gray-Coded Square QAM 2 0 -8 -6 -4 -2 0 2 I or Q Input (To Slicer) 4 6 8 30
  • 31. MIMO (Multiple-Antenna OFDM) • OFDM is very amenable to space-time diversity  Each subcarrier easy to combine from different antenna  Channel flat over a single subcarrier  Huge BER gains possible with just dual Tx/Rx diversity  Transmitter signal sent to two antennas/Tx chains  Receiver uses two antennas/Rx chains • Strict Line-of-Sight (LOS) not required Channel 31
  • 32. MIMO System (2 Antenna Rx, 2 Antenna Tx—Delay Diversity) Chan Est #1 (Data) Antenna #1 Channel Estimates Via FFT (Training) Antenna #2 Channel Estimates Via FFT (Training) FFT Out #1 FFT Out #2 Chan Est #1 (Data) 32
  • 33. Cross Correlation From Rx Antennas • WT1 & WT2 are the training tone channel estimates HT1, HT2 with delay compensation for antenna 1 and 2 respectively to compute Covariance Matrix R • Channel Estimates are then used with R to form a weighted channel estimate 33
  • 34. Combiner 34
  • 35. Diversity Advantage • Dual Tx/Rx up to 23 dB advantage for 1E-3 Uncoded for flat fading channel over single antenna OFDM 35
  • 36. OFDM for multiple access (OFDMA) • IEEE 802.16.3 uses OFDM as a multiple access scheme for fixed wireless access 36
  • 37. Multicarrier CDMA •Multi-Carrier CDMA is a combination of OFDM & CDMA:  First an OFDM system is used to provide orthogonal carriers, free from ISI.  Second each carrier is modulated by an individual code chip, to provide a spread spectrum system • The main advantage of doing this is that when the multiple-access interference becomes a problem, the resulting linear detectors are much simpler to implement as only a single tap equalizer is required for each channel. • Rake reception can also be employed to exploit the channel diversity by channel matching in the frequency domain allowing optimal reception for a single user. • In the uplink another advantage of MC-CDMA can be exploited. If the signals can be synchronized to arrive within a small fraction of the symbol time ( e.g. indoor, or very small cell environment) then this asynchronism can be overcome by cyclically-extending the signal further allowing synchronous reception of all signals, with no ISI from other users • Makes multiple-access easier with ability to correlate out interfering users 37
  • 38. Spread De-Spread • Transmitter Multiplies symbols by spreading sequence (Walsh etc.) prior to IFFT • Receiver Multiplies symbols by same seq. as was used to transmit after FFT 38
  • 39. Further Reading • • • OFDM for Wireless Multimedia Communications, Van Nee & Prasad, Artech House Publishers, 2000, Boston, MA OFDM Wireless LANs: A Theoretical and Practical Guide, Heiskala & Terry, SAMS Publishers, 2002, Indianapolis, IN “Supplement To Standard For Information TechnologyTelecommunications and Information Exchange Between SystemsLocal And Metropolitan Area Networks-Part 11: Wireless LAN Medium Access Control(MAC) and Physical Layer (PHY) Specifications: High Speed Physical Layer In The 5 GHz Band {IEEE 802.11a}” 39