LDPC Overview and Implementation

LDPC Overview and Implementation

Signal Processing for OFDM Communication Systems Eric Jacobsen Minister of Algorithms, Intel Labs Communication Technology Laboratory/ Radio Communications Laboratory July 29, 2004 With a lot of material from Rich Nicholls, CTL/RCL and Kurt Sundstrom, of unknown whereabouts www.intel.com/labs Communication and Interconnect Technology Lab Outline OFDM What and Why Subcarrier Orthogonality and Spectral Effects Time Domain Comparison Equalization Signal Flow PAPR management Cool Tricks www.intel.com/labs 2 Communication and Interconnect Technology Lab Digital Modulation Schemes Single Carrier PSK, QAM, PAM, MSK, etc. Demodulate with matched filter, PLLs

Common Standards: DVB-S, Intelsat, GSM, Ethernet, DOCSIS Multi-Carrier OFDM, DMT Demodulate with FFT, DSP Common Standards: DVB-T, 802.11a, DAB, DSL-DMT www.intel.com/labs 3 Communication and Interconnect Technology Lab What is OFDM? Orthogonal Frequency Division Multiplexing Split a high symbol rate data stream into N lower rate streams Transmit the N low rate data streams using N subcarriers Frequency Division Multiplexing (FDM) & Multi-Carrier Modulation (MCM) N subcarriers must be mutually orthogonal N exp j 2 f t 2 Subcarrier spacing = f Partition available bandwidth into N orthogonal subchannels Complex Baseband OFDM Signal

s(t) exp j 2 f t Stream 1 ... ... Hold (Thold = 1/f sec) ... High Rate Complex Symbol Stream Serial to Parallel Stream -N/2 f -N(f)/2 0 (N-1)(f)/2 N exp j 2 1 f t 2

Stream N/2-1 OFDM Conceptual Block Diagram www.intel.com/labs 4 Communication and Interconnect Technology Lab Why OFDM? Reduces symbol rate by more than N, the number of subcarriers Fading per subcarrier is flat, so single coefficient equalization Reduces equalizer complexity O(N) instead of O(N 2) Fully Captures Multipath Energy For Large Channel Coherence Time, OFDM/DMT can Approach Water Pouring Channel Capacity Narrowband interference will corrupt small number of subcarriers Effect mitigated by coding/interleaving across subcarriers Increases Diversity Opportunity Frequency Diversity Increases Adaptation Opportunities, Flexibility Adaptive Bit Loading OFDMA PAPR largely independent of modulation order Helpful for systems with adaptive modulation

www.intel.com/labs 5 Communication and Interconnect Technology Lab Downsides of OFDM Complexity FFT for modulation, demodulation Must be compared to complexity of equalizer Synchronization Overhead Cyclic Extension Increases the length of the symbol for no increase in capacity Pilot Tones Simplify equalization and tracking for no increase in capacity PAPR Depending on the configuration, the PAPR can be ~3dB-6dB worse than a singlecarrier system Phase noise sensitivity The subcarriers are N-times narrower than a comparable single-carrier system Doppler Spread sensitivity Synchronization and EQ tracking can be problematic in high doppler environments www.intel.com/labs 6 Communication and Interconnect Technology Lab

Subcarrier Orthogonality Orthogonality simplifies recovery of the N data streams Orthogonal subcarriers = No inter-carrier-interference (ICI) Time Domain Orthogonality: Every subcarrier has an integer number of cycles within T OFDM Satisfies precise mathematical definition of orthogonality for complex exponential (and sinusoidal) functions over the interval [0, TOFDM ] Frequency Domain Orthogonality: ICI = 0 at f = nf0 f Some FDM systems achieve orthogonality through zero spectral overlap BW inefficient! f OFDM systems have overlapped spectra with each subcarrier spectrum having a Nyquist zero ISI pulse shape (really zero ICI in this case). BW efficient! www.intel.com/labs 7 Communication and Interconnect Technology Lab OFDM Signal (Time & Frequency)

TIME DOMAIN: 2 OFDM subcarriers (BPSK) 1.5 1 0.5 0 -0.5 -1 -1.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Time (Normalized by Tofdm) 1.6 1.8 2 FREQUENCY DOMAIN: OFDM Subcarriers 2 through 10 1 0.8 0.6 0.4 0.2 0

-0.2 -0.4 0 2 4 6 8 Frequency (Normalized by 1/Tofdm) 10 12 www.intel.com/labs 8 Communication and Interconnect Technology Lab Practical Signal Spectra Single carrier signals require filtering for spectral containment. This signal has narrow rolloff regions which requires long filters. Magnitude 0 10

20 30 0 500 1000 Frequency 1500 2000 OFDM spectra have naturally steep sides, especially with large N. The PAPR is often higher, which may result in more spectral regrowth. The blue trace is an unfiltered OFDM signal with 216 subcarriers. The red trace includes the effects of a non-linear Power Amplifier. www.intel.com/labs 9 Communication and Interconnect Technology Lab Time-Domain Comparisons ... ... ...

Equivalent EQ Length Multipath Delay Profile Previous Symbol Cyclic Prefix Single Carrier Symbol Period FFT Window tg tg Last tg portion of symbol OFDM Symbol Period Residual energy from previous symbol due to multipath is inconsequential up to this point in time By greatly increasing the symbol period the fading per subcarrier becomes flat, so that it can be equalized with a single coefficient per subcarrier. The addition of the cyclic prefix eliminates InterSymbol Interference (ISI) due to multipath. www.intel.com/labs 10 Communication and Interconnect Technology Lab Frequency Domain Equalization

Design System Such That TDelay Spread < TGuard and BCoherence > BSubcarrier Subcarriers are perfectly orthogonal (no ISI or ICI) Each Subcarrier experiences an AWGN channel Equalizer Complexity : Serial Data Rate = 1/T, OFDM Symbol Rate = 1/(NT) FEQ performs N complex multiplies in time NT (or 1 complex mult per time T) Time domain EQ must perform MT complex multiplies in time T where M is the number of equalizer coefficients Channel Frequency Response (at time t) Subcarrier n Frequency www.intel.com/labs 11 Communication and Interconnect Technology Lab 802.11a PHY Block Diagram I Guard Interval Insertion Window DAC

HPA I&Q Q FEC Encoder Interleaver QAM Mapping Pilot Insertion S/P Data Descrambler FEC Decoder Deinterleaver QAM Demap Channel Estimation & Correction P/S

RSSI I Duplexer DAC Data Scrambler To MAC Sublayer BPF /2 ADC IFFT (TX) FFT(RX) P/S S/P Guard Interval Removal LPF LNA Digital

LPF Symbol Timing Frequency Correction Frequency Offset Estimation Signal Detect AGC Q /2 ADC BPF LPF www.intel.com/labs 12 Communication and Interconnect Technology Lab 802.11a Processing

802.11a is a TDD contention-based, bursty protocol Full acquisition, synchronization, and EQ training can be performed for each burst or frame The short training symbols provide timing, AGC, diversity selection, and initial carrier offset The long training symbols provide fine synchronization and channel estimation Two FFT periods allow 3dB increase in channel estimation SNR by combining (averaging) the estimates Tracking is facilitated by the four pilot tones www.intel.com/labs 13 Communication and Interconnect Technology Lab 802.11a 802.11a Time/Frequency Time/Frequency Signal Signal Structure Structure DATA FRAME 53 Subcarriers (48 data, 4 pilot, 0 @ DC) FREQUENCY 8.125 MHz Short Training Symbols

Long Training Symbols Data Symbols 0 -8.125 MHz Indicates Pilot Tone Location 800 ns 4 s TIME www.intel.com/labs 14 Communication and Interconnect Technology Lab DVB-T DVB-T Time/Frequency Time/Frequency Signal Signal Structure Structure Since DVB-T is a continuous transmit signal, channel estimation is facilitated easily by rotating pilots across the subcarrier indices. Interpolation provides channel estimation for every subcarrier.

This figure is from reference [4] www.intel.com/labs 15 Communication and Interconnect Technology Lab Peak to Average Power Ratio Single Carrier Systems PAPR affected by modulation scheme, order, and filtering Constant-envelope schemes have inherently low PAPR For example: MSK, OQPSK PAPR increases with modulation order e.g., 64-QAM PAPR is higher than QPSK As Raised Cosine excess bandwidth decreases, PAPR increases Squeezing the occupied spectrum increases PAPR Multi-Carrier Systems PAPR affected by subcarrier quantity and filtering PAPR is only very weakly connected to modulation order PAPR increases with the number of subcarriers Rate of increase slows after ~64 subcarriers The Central Limit Theorem is still your friend Whitening is very effective at reducing PAPR Symbol shaping decreases PAPR www.intel.com/labs 16 Communication and Interconnect Technology Lab

PAPR with 240 subcarriers PAPR Cumulative Distribution Function 1 N = 240 requires no more than 1dB additional backoff compared to 802.11a, and about 3.5dB more than a single-carrier system. 64-QAM 20% RRC 0.9 P(PAPR < Abscissa) 0.8 64-QAM OFDM-48 802.11a 0.7 0.6 64-QAM OFDM-240 0.5

The results shown use only data whitening for PAPR reduction. Additional improvements may be possible with other techniques. 0.4 0.3 0.2 0.1 0 3 4 5 6 7 8 9 10 11

12 PAPR (dB) www.intel.com/labs 17 Communication and Interconnect Technology Lab PAPR Mitigation in OFDM Scrambling (whitening) decreases the probability of subcarrier alignment Subcarriers with common phase increase PAPR Symbol weighting reduces the effects of phase discontinuities at the symbol boundaries Raised Cosine Pulse weighting Works well, requires buffering Signal filtering Easier to implement www.intel.com/labs 18 Communication and Interconnect Technology Lab Time-Domain Weighting The phase discontinuities between symbols

increase the size of the spectral sidelobes. Tapered Regions Weighting the symbol transitions smooths them out and reduces the sidelobe amplitudes. Typically RaisedCosine weighting Is applied. This figure is informative content from the IEEE 802.11a specification. The two-fft period case applies only to preambles for synchronization and channel estimation. www.intel.com/labs 19 Communication and Interconnect Technology Lab Effect of Symbol Weighting With no RC weighting With 1% RC weighting Applying a tiny bit of symbol weighting in the time domain has a significant effect on PAPR. In this case only 1% of the symbol time is used for tapering. The blue trace is prior to the PA, the red trace after.

Application of the 1% RC window meets the green transmit mask. www.intel.com/labs 20 Communication and Interconnect Technology Lab Cool and Interesting Tricks OFDMA Different users on different subcarriers Adaptive Bit Loading Seeking water filling capacity Adaptation to Channel Fading Adaptation to Interference www.intel.com/labs 21 Communication and Interconnect Technology Lab OFDMA Subcarrier Division Pilot Tones Data Subcarriers ... Control User #1 User #2

User #3 User #N-1 User #N Redundant Control The 802.16 standard describes multiple means to implement OFDMA. In one mode each users signal occupies contiguous subcarriers which can be independently modulated. Another mode permutes each users subcarriers across the band in a spreading scheme so that all users subcarriers are interlaced with other users subcarriers. The first method allows for adaptive modulation and the second method increases frequency diversity. www.intel.com/labs 22 Communication and Interconnect Technology Lab Subcarrier Division with TDM Each color is for a distinct terminal. Subcarriers Control Subcarriers Redundant Control Subcarriers OFDM Symbols www.intel.com/labs

23 Communication and Interconnect Technology Lab Channel Frequency Response Multipath Frequency Selective Fading Frequency (MHz) -5 -4 -3 -2 -1 0 1 2 3 4 5 5 Response (dB) 0 -5

-10 -15 -20 -25 -30 Shannons Law applies in each flat subinterval v = 100 km/hr f = 2 GHz t = 0.5 m sec www.intel.com/labs 24 Communication and Interconnect Technology Lab Adaptive Bit Loading -5 -4 -3 Frequency (MHz) -2 -1 0 1 2

3 4 5 Response (dB) 5 0 High SNR At Receiver 6 bps/Hz -5 4 bps/Hz -10 -15 -20 2 bps/Hz Deep Fade (Bad) 0 bps/Hz -25 -30 Low SNR At Receiver Channel Bandwidth 64 QAM

16 QAM QPSK Sub Carriers OFDM Symbol www.intel.com/labs 25 Communication and Interconnect Technology Lab Signal level Per-Subcarrier Per-Subcarrier Adaptive Adaptive Modulation Modulation Frequency www.intel.com/labs 26 Communication and Interconnect Technology Lab References [1] IEEE Std 802.11a-1999 [2] Robert Heath, UT at A, http://www.ece.utexas.edu/~bevans/courses/realtime/lectures/20_OFDM/346,22,OFDM and MIMO Systems [3] Hutter, et al, http://www.lis.ei.tum.de/research/lm/papers/vtc99b.pdf [4] Zabalegui, et al, http://www.scit.wlv.ac.uk/~in8189/CSNDSP2002/Papers/G1/G1.2.PDF

www.intel.com/labs 27 Communication and Interconnect Technology Lab Backup No! Go forward! www.intel.com/labs 28 Communication and Interconnect Technology Lab Cyclic Prefix (Guard Interval) Delay Spread Causes Inter-Symbol-Interference (ISI) and Inter-Carrier-Interference (ICI) Non-linear phase implies different subcarriers experience different delay (virtually all real channels are non-linear phase) Adding a guard interval between OFDM symbols mitigates this problem Zero valued guard interval will eliminate ISI but causes ICI Better to use cyclic extension of the symbol Symbol #1 TOFDM Symbol #2 TOFDM TG TFFT

ICI Subcarrier #2 Subcarrier #1 (delayed relative to #2 ) Guard interval eliminates ISI from symbol #1 to symbol #2 Cyclic extension removes ISI and ICI ! 3.5 cycles of subcarrier #1 inside the FFT integration period ICI ! www.intel.com/labs 29 Communication and Interconnect Technology Lab DVB-T DVB-T Time/Frequency Time/Frequency Signal Signal Structure Structure Since DVB-T is a continuous transmit signal, channel estimation is facilitated easily by rotating pilots across the subcarrier indices. Interpolation provides channel estimation for every subcarrier. This figure is from reference [3]

www.intel.com/labs 30 Communication and Interconnect Technology Lab Advantages SCM OFDM Single Frequency Networks Sensitivity (margin) Simple EQ Complexity Flexibility Memory Statistical Mux Phase noise sensitivity Frequency registration Reduced PA Backoff Less Overhead (no cyclic prefix) OFDMA BW, TDMA LOW SNR, avoid DFE PAPR not affected by

modulation order. Automatically integrates multipath. IEEE Politics www.intel.com/labs 31

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