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Coding and Equalization for High Rate Extensions

Coding and Equalization for High Rate Extensions. Steve Halford, Ph.D. Mark Webster Paul Chiuchiolo Intersil Corporation Palm Bay, FL. Performance & Complexity. W-LAN performance is dominated by multipath Power consumption dominated by receiver complexity

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Coding and Equalization for High Rate Extensions

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  1. Coding and Equalization for High Rate Extensions Steve Halford, Ph.D. Mark Webster Paul Chiuchiolo Intersil Corporation Palm Bay, FL S. Halford, M. Webster, P. Chiuchiolo, Intersil Corp.

  2. Performance & Complexity • W-LAN performance is dominated by multipath • Power consumption dominated by receiver complexity • W-LAN systems spend 90% of time in receive mode • OFDM is designed for both AWGN and multipath • Error correcting code for AWGN • Use guard interval to absorb ISI • Use FFT/IFFT and block structure to simplify receive equalizer • PBCC is optimized for AWGN • Error correcting code for AWGN • Multipath performance depends entirely on receiver OFDM is less complex for W-LAN S. Halford, M. Webster, P. Chiuchiolo, Intersil Corp.

  3. PER fo11 Mbps Multipath with No Equalizer • CCK outperforms PBCC-11 • PBCC requires equalizer • Scramble code does not help multipath ? CMF Receiver w/o Equalization Exponential Fading channel with 1 sample/chip S. Halford, M. Webster, P. Chiuchiolo, Intersil Corp.

  4. Equalizers Types • Linear Equalizer: • Linear filter that inverts the multipath channel • Length of filter depends on number of significant multipath rays • Decision Feedback Equalizer (DFE) • Subtracts interference from past data symbols • Uses hard decisions on received symbols prior to error correction • Uses linear equalizer subsection for pre-cursor taps • Can have reasonable complexity and performance for high SNR cases • Viterbi Equalizer (Maximum likelihood sequence estimate or MLSE) • Optimum equalizer (minimizes the bit error rate) • Finds the most likely sequence of transmitted symbol based on channel • Similar complexity & implementation to decoding a convolutional code S. Halford, M. Webster, P. Chiuchiolo, Intersil Corp.

  5. Linear Equalizer: Complexity for W- LANs • Linear Equalizer complexity is driven by length • Simulations indicate a 15 -20 tap equalizer is req’d • Equalizer taps are typically found by matrix inverse proportional to length of filter • Very high complexity -- once per packet • Adaptive estimation can reduce complexity in theory • Convergence is too slow for Wireless LAN systems • Each symbol also requires L complex multiplies & L-1 complex adds Linear Equalizers are too complex for adequate performance S. Halford, M. Webster, P. Chiuchiolo, Intersil Corp.

  6. Linear Equalizer vs. OFDM: Receiver Complexity IFFT/FFT for OFDM Equalization • 64 point FFT using radix-4 requires 96 complex multiplies • For each symbol, must perform an FFT at receiver • After receiver FFT, equalizer then requires 52 complex multiplies (1 per tone) • Perform once every symbol -- 80*(1/20 x 106) = 4 x 10 -6 seconds • Equivalent to (4 x (96 + 52))/(4 x 10 -6 ) = 148 x 106 real multiplies per second Single Carrier Linear Equalizer Complexity OFDM use of FFT make it less complex than Linear Eq. • Linear Equalizer of length L requires L complex multiplies per symbol • Number of real multiplies = (4*L*11 x 106 ) = L * (44 x 106 ) • Length L must be less than (148/44) = 3.4 to match complexity of IFFT/ FFT combinations • Using pulse shaping makes this worse due to presence of matched filter! • Not required for OFDM • Doesn’t include the complexity of estimating the equalizer taps • Matrix inverse proportional to L ** Based on R. Van Nee & R. Prasad, OFDM for Wireless Multimedia Communications, Artech House Publishers, Boston, MA, 2000. S. Halford, M. Webster, P. Chiuchiolo, Intersil Corp.

  7. Decision Feedback Equalizers Equalized Symbols • Uses WMF and symbol decision feedback to remove ISI • Post cursor filter is only as long as channel • Unlike linear equalizer which is 4-10 times longer than channel • Does not require a matrix inverse to compute! • Whitened Matched Filter length depends on pre-cursor and pulse shaping • Requires a matrix inverse to compute Whitened Matched Filter Symbol Slicer (Hard decisions) Received Data + DFE Channel Post-cursor Filter Removes ISI from channel precursor S. Halford, M. Webster, P. Chiuchiolo, Intersil Corp.

  8. Decision Feedback Equalizers: Performance • DFE performs well when: • High SNR since symbol decision must be correct • Incorrect decision lead to burst of equalizer generated noise • This will limit range of W-LAN more than AWGN performance • Post-cursor filter is sufficiently long • Possible to use decisions after error correction • Would allow operation at lower SNR • Long processing delay and very high complexity DFE won’t work due to high SNR & complexity of WMF S. Halford, M. Webster, P. Chiuchiolo, Intersil Corp.

  9. MLSE/Viterbi Equalizer Whitened Matched Filter Viterbi Equalizer Received Data Equalized Symbols • Equalizer estimates the most likely sequence based on knowledge of the channel and the received data • Optimum bit error rate performance • No matrix inverse required • Only need to estimate channel • Equalization is similar to decoding a convolutional code • Searches a trellis of possible paths to find the most likely • For adequate performance, MLSE is the most likely equalizer for PBCC-11,PBCC-22, and higher • Need to track 4 or more paths for adequate performance MLSE S. Halford, M. Webster, P. Chiuchiolo, Intersil Corp.

  10. MLSE: Complexity Considerations • Complexity is similar to convolutional decoder • Number of states depends on constellation size and number of multipath rays being tracked Number of States in MLSE ** Example Eight times as complex as the 64 state PBCC-11/OFDM decoder& only 4 rays are being tracked! • Track 4 rays for 8-level PSK (PBCC-22) • Number of states = 83 =512 states ** See pg. 590, J. G. Proakis, Digital Communication, 3rd Ed., McGraw-Hill, 1995. S. Halford, M. Webster, P. Chiuchiolo, Intersil Corp.

  11. OFDM is nearly MLSE • OFDM uses a guard interval to absorb multipath interference • Outside the guard interval, signal is multipath free • Multipath causes individual tones to fade • After FFT, each tone is multipath free • Relative fade is known from channel estimation • Viterbi Decoder of error correction code gives MLSE in multipath • Reliability of each soft-decision is weighted by known fade • Optimum receiver is realized with only a FFT • True provided multipath is entirely inside guard interval • Path delay less than 800 nSecs S. Halford, M. Webster, P. Chiuchiolo, Intersil Corp.

  12. OFDM Multipath Tolerance • OFDM proposal includes 800 nSecs Guard Interval • Equivalent to 800e-9 x 11e6 = 8.8 paths at PBCC symbol rate • Multipath tolerance equivalent to tracking 8 paths • FFT complexity is approximately half the complexity of a 64 state decoder Equivalent SC MLSE Complexity This is 8192 times the complexity of the 256 state decoder! S. Halford, M. Webster, P. Chiuchiolo, Intersil Corp.

  13. Convolutional Coding & Complexity • Encoding process is relatively low complexity • Consists of shift registers and combiners • Decoding complexity depends on code properties • Decoders are based on Viterbi algorithm • Viterbi algorithm finds best path into each possible state • Complexity depends on the number of states in decoder • Number of states determines size of the trellis searched by VA • PBCC-11 & OFDM use a 64-state decoder • PBCC-22 uses a 256-state decoder • Trellis size (& complexity) is 4x the equivalent OFDM decoder OFDM has a less complex error correction code S. Halford, M. Webster, P. Chiuchiolo, Intersil Corp.

  14. 256 state code vs. 64 state code 0.8 dB Advantage for PBCC-22 at 1% PER 1.0 dB Advantage for PBCC-22 at 10% PER 0.8-1.0 dB Coding Gain with 4x Decoder Complexity Is 1 dB worth the increased complexity? S. Halford, M. Webster, P. Chiuchiolo, Intersil Corp.

  15. Scramble Code • PBCC-11 & PBCC-22 include a scramble code • Changes the constellation mapping on a per symbol basis • Purpose has never been demonstrated Doesn’t change AWGN performance Doesn’t change multipath performance S. Halford, M. Webster, P. Chiuchiolo, Intersil Corp.

  16. Scramble Code with Equalizer • Does the scramble code help when used with an equalizer? S. Halford, M. Webster, P. Chiuchiolo, Intersil Corp.

  17. Interleavers for W-LAN • Burst Errors will occur in a W-LAN environment • Microwave ovens, photocopiers, & BlueTooth will generate bursts of interference • Duration typically 220 nSecs (photocopier) & 16 ms for microwave***1 • Burst Errors also occur due to MLSE equalizer • Duration depends on # of paths & channel distance • Error burst can overwhelm an FEC code***2 • Interleaver necessary when bursts duration is > 2 symbols • OFDM includes an interleaver to help mitigate PBCC-11 & PBCC-22 need an interleaver! *** 1 K. Blackard, T. Rappaport, & C. Bostian, “Measurements and Models of Radio Frequency Impulsive Noise for Indoor Wireless Communications,” IEEE Journal on Selected Areas in Communications, Vol. 11, No. 7, pg. 991 -1001, September 1993. ***2 See page 366 of G. C. Clark and J. B. Cain, Error-Correction Codeing for Digital Communications, Plenum Press, New York, NY, 1981. S. Halford, M. Webster, P. Chiuchiolo, Intersil Corp.

  18. Approaches to Higher Data Rates • OFDM provides a known, defined path to achieving higher rates • Higher data rates can be achieved by: • Increasing the constellation size and/or decrease code rate • Used by OFDM to give rates of 6 Mbps to 54 Mbps • PBCC-22 uses 8-psk with rate 2/3 code to go from 11 Mbps (QPSK with rate 1/2) to 22 Mbps • Increasing symbol rate • PBCC-33 uses 1.5 times higher clock speed to go from 22 Mbps to 33 Mbps • Increasing the data rate increases the required SNR for AWGN channels • More sensitive to implementation & tracking What is the impact on the equalizer performance and complexity of higher rates? S. Halford, M. Webster, P. Chiuchiolo, Intersil Corp.

  19. Higher Data Rates: Equalizer Complexity • OFDM Equalizer has fixed complexity for all proposed rates • Higher rates does impact performance due to fading of tones • Guard interval however reduces the impact independent of rate • MLSE complexity will grow exponentially when constellation size increases • Higher rates will impact performance • No guard interval to protect from increased ISI sensitivity • Example: Track 4 paths -- Number of states = (constellation size)4-1 • 22 Mbps (8-PSK) requires 83 = 512 states (8x the PBCC-11 decoder) • 33 Mbps (16-QAM) will require 163 = 4096 states (64x the PBCC-11 decoder) • 44 Mbps (64-QAM) will require 643 = 262144 states (4096x the PBCC-11 decoder) Extending PBCC to higher rates by increasing constellation is not practical S. Halford, M. Webster, P. Chiuchiolo, Intersil Corp.

  20. Higher Data Rates: Equalizer Complexity • OFDM uses a fixed symbol rate for all data rates • Guard interval protection is same for all rates • PBCC-33 is PBCC-22 at a higher symbol rate • Pulse shaping used to keep same spectral width • Increasing symbol rate impacts performance • Increasing timing accuracy requirements • Increasing rate increase number of equalizer paths • Example: 8-PSK -- Number of states = 8(number of paths -1) • 22 Mbps (11 Mhz, 4 paths) -- 84-1 = 512 states (8x the PBCC-11 decoder) • 33 Mbps (16.5 Mhz, 6 paths) -- 86-1 = 32,768 states (512x PBCC-11 decoder) • 44 Mbps (22 Mhz, 8 paths) -- 88-1 = 2,097,152 states (32,768x PBCC-11 decoder) Extending PBCC to higher rates by increasing symbol rate is not practical S. Halford, M. Webster, P. Chiuchiolo, Intersil Corp.

  21. Conclusions • Equalization is required for W-LAN systems • Receiver complexity is critical to successful systems • Linear and DFE equalizers are not practical for proposed high rate single carrier systems • MLSE is only viable equalizer for proposed systems • Complexity can grow exponentially • PBCC-22 FEC is 4x as complex as industry standard • Yields less than 1 dB improvement • PBCC-22 inherited the scramble code • Appears to be un-necessary • PBCC-22 lacks an interleaver • Poor performance with burst errors S. Halford, M. Webster, P. Chiuchiolo, Intersil Corp.

  22. Conclusions • OFDM provides near to MLSE performance • Guard interval absorbs multipath • Complexity is small fraction of MLSE for PBCC • Complexity remains fixed for proposed data rates! • OFDM uses industry standard FEC code • OFDM includes an interleaver • OFDM is less complex than PBCC for W-LAN • No hidden complexity details • OFDM gives access to higher than 22 Mbps rates • PBCC complexity grows exponentially S. Halford, M. Webster, P. Chiuchiolo, Intersil Corp.

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