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Optimal Receivers in Multipath: Single-Carrier and OFDM
Month 2000 doc.: IEEE /xxx March 2001 Optimal Receivers in Multipath: Single-Carrier and OFDM Mark Webster Steve Halford Webster & Halford, Intersil John Doe, His Company
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Optimal Receivers in Multipath
March 2001 Optimal Receivers in Multipath What is an optimal single-carrier receiver? What is an optimal multi-carrier (OFDM) receiver? How do single-carrier receivers fall short of optimality? How do multi-carrier receivers fall short of optimality? This presentations hopes to provide these answers Webster & Halford, Intersil
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March 2001 What Does Optimal Mean? Given a transmit signal and channel type, the optimal receiver minimizes the probability of error Channels Addressed Flat bandlimited channel Non-flat bandlimited channel (frequency-selective due to multipath) Transmit signal design is not discussed Water pouring spectrum FEC Coding Shaping Webster & Halford, Intersil
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Flat Band-Limited Channel: Single Carrier
March 2001 Flat Band-Limited Channel: Single Carrier Tx Spectrum Rx Spectrum Symbol Rate = R Hz Noise freq freq -R/2 R/2 -R/2 R/2 Nyquist Transmit Filter Symbol Constellation Map (e.g., QPSK) Matched Filter Bit Decode Tx Bits + R Hz Symbol Impulses White Gaussian Noise Webster & Halford, Intersil
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Flat Band-Limited Channel: Multi-Carrier
March 2001 Flat Band-Limited Channel: Multi-Carrier Rx Spectrum Bank of Tx Pulses Bank of Matched Filters Noise freq -R/2 R/2 Symbol Constellation Points + + Simple Idea: Slice Spectrum into Narrow Segments Identical to previous Slide White Gaussian Noise IFFT FFT Webster & Halford, Intersil
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Frequency-Selective Multipath Channel: Single Carrier
March 2001 Frequency-Selective Multipath Channel: Single Carrier R/2 -R/2 Rx Spectrum freq Noise Maximized SNR of desired symbol But, can suffer serious intersymbol interference Multipath Combiner MLSE Decoder Nyquist Transmit Filter Channel Matched Filter Equalize Pre-cursor ISI Multipath Channel Viterbi Equalizer Viterbi FEC Decode + R Hz Symbol Impulses Whitened Matched Filter White Gaussian Noise G. David Forney, Jr., “Maximum Likelihood Sequence Estimation of Digital Sequences in the Presence of Intersymbol Interference,” IEEE Trans. Info. Theory, May 1972 Webster & Halford, Intersil
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Frequency-Selective Multipath Channel: Multi-Carrier
March 2001 Frequency-Selective Multipath Channel: Multi-Carrier Rx Spectrum Bank of Tx Pulses Bank of Matched Filters Noise freq SNR- Weight Soft Decisions -R/2 R/2 Symbol Constellation Points + + White Gaussian Noise Simple Idea: Slice Spectrum into Narrow Segments IFFT FFT Webster & Halford, Intersil
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Multipath Channel: Multi-Carrier Equations
March 2001 Multipath Channel: Multi-Carrier Equations Rcvd Bin Sample Tx Bin Constellation Point Maximum Likelihood Decoding Joint Gaussian Probability Function Log-Likelihood Function Bin SNR’s Webster & Halford, Intersil
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802.11a OFDM Receiver Rx Spectrum Bank of Tx Pulses Bank of
March 2001 802.11a OFDM Receiver Rx Spectrum Bank of Tx Pulses Bank of Matched Filters freq -R/2 R/2 MLSE Decoder SNR- Weight Soft Decisions Viterbi FEC Decode Symbol Constellation Points + + White Gaussian Noise IFFT FFT Webster & Halford, Intersil
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Single-Carrier Implementation Short Comings
March 2001 Single-Carrier Implementation Short Comings Rx Spectrum May require many taps Must be computed Compute matrix Invert matrix (8 x 8 ?) Matrix elements estimated Noise Must be estimated From Limited Preamble freq -R/2 R/2 MLSE Decoder Nyquist Transmit Filter Channel Matched Filter Equalize Pre-cursor ISI Viterbi Equalizer Viterbi FEC Decode + R Hz Symbol Impulses Whitened Matched Filter White Gaussian Noise Many states (trellis) required Branch metrics change packet-to-packet RSSE loses performance Webster & Halford, Intersil
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OFDM Implementation Short Comings
March 2001 OFDM Implementation Short Comings SNR’s must Be Estimated From Freq Response Rx Spectrum Bank of Tx Pulses Bank of Matched Filters Noise freq SNR- Weight Soft Decisions -R/2 R/2 Symbol Constellation Points + + Guard Interval Loss GI too long (low multipath) GI too short (very high multipath) White Gaussian Noise IFFT FFT Webster & Halford, Intersil
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March 2001 Conclusions Both single-carrier and multi-carrier receiver architectures exist which provide optimal performance in theory In practice, the trade between OFDM versus single carrier depends upon many factors and is complex Webster & Halford, Intersil
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