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A DCT-Based Broadband Multicarrier Transceiver

A DCT-Based Broadband Multicarrier Transceiver. Shilpa Satish, Naofal Al-Dhahir, Hlaing. Minn. Dept. of Electrical Engineering University of Texas at Dallas Richardson, TX. Outline. DFT Multicarrier Modulation (MCM) Transceiver Proposed DCT MCM Transceiver

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A DCT-Based Broadband Multicarrier Transceiver

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  1. A DCT-Based Broadband Multicarrier Transceiver Shilpa Satish, Naofal Al-Dhahir, Hlaing. Minn Dept. of Electrical Engineering University of Texas at Dallas Richardson, TX

  2. Outline • DFT Multicarrier Modulation (MCM) Transceiver • Proposed DCT MCM Transceiver • Comparison of DCT-MCM with DFT-MCM • Conclusion

  3. DFT-Multicarrier Modulation (DFT-MCM) • Cyclic prefix in OFDM makes channel matrix circulant, • Guard sequence only restricted to be redundant • If necessary, TEQ shortens channel memory to cyclic prefix length • Currently, DFT is the only orthogonal, channel-independent, and fast size-N transform used to diagonalize ISI channels with no ICI or IBI • Question : Is it the only one with these properties ?

  4. Attractive Features of DCT • Channel-independent • Excellent energy concentration properties • Real Arithmetic • Widely used in imagecodec standards • Fast Computation Algorithm

  5. DCT-Multicarrier Modulation (DCT-MCM) • Question : Can DCT diagonalize ISI channels ? • Martucii in ’94 showed symmetric convolution is related to DCT as circular convolution is related to DFT • Drawbacks: Both channel and input signal is symmetric (50% throughput loss!)

  6. Discrete Cosine Transform (DCT) • Type-II DCTis the most common of all DCT’s

  7. DCT Diagonalization Theorem • Theorem(Sanchez et. al. TSP ’95) : • “Matrices diagonalizable by type-II DCT can be written as the sum of a symmetric Toeplitz matrix T and a Hankel matrix L where” S : upper-shift matrix J : reversal matrix ei : ith unit vector

  8. Design Approach for DCT-MCM • Design of a novel guard sequence • Guard sequence designed to get an equivalent channel of the form T+L where T and L satisfy the previous relations • Split guard sequence into 2 parts and make them symmetric extensions of data sequence • Modify TEQ (prefilter) design • Target response constrained to be symmetric

  9. Guard Sequence Design For a Channel with memory Length-2v Cyclic Prefix Information DFT DCT Length-v Prefix Information Length-v Suffix

  10. Traditional Prefilter (TEQ) Design Noise Information Sequence MMSE + ∑ H ∑ W + + - b Subject to: R is a channel dependent autocorrelation matrix Objective: Shorten channel memory to cyclic prefix length to reduce throughput loss

  11. Modified TEQ Design for DCT-MCM • Incorporation of symmetry condition on shortened CIR Subject to: Objective: Shorten channel impulse response and make it symmetric

  12. Comparison of TEQ Performance MMSE for DCT higher than DFT Optimum TEQ Taps for DCT = 30 and DFT = 20

  13. DCT-MCM System Block Diagram Noise IDCT Information Block Channel Prefilter Add Symmetric Guard P/S DCT Slicer 1-tap equalizer Detected Information Block Remove Symmetric Guard Slicer 1-tap equalizer S/P

  14. Complex DCT-MCM Block Diagram Noise Add Symmetric Guard Make Complex Complex Information Block Real Part IDCT Channel Prefilter Imaginary Part IDCT P/S Complex 1-tap equalizer Real Part Complex Slicer DCT Remove Symmetric Guard Make Complex Complex Detected Information Block Imaginary Part Complex 1-tap equalizer DCT Complex Slicer S/P

  15. Comparison of DCT-MCM with DFT-MCM • Frequency Offset • Channel Estimation Errors • Narrowband Interference on WLAN Environment • Narrowband Interference on DSL Environment

  16. Effect of Frequency Offset y x Horig S W H Equivalent Shortened Channel Model

  17. Frequency Offset DCT-MCM is more robust to frequency offset than DFT-MCM DCT has better spectral compaction and energy concentration property than DFT

  18. Channel Estimation Errors • Training sequence embedded in each block to estimate the channel impulse response for receiver processing • Perfect root-of-unity (PRUS) training sequences achieve lowest channel estimation mean square error Equivalent shortened channel model

  19. Channel Estimation Errors • Channel estimation errors cause more degradation in performance of DCT • DCT still outperforms DFT for high frequency offsets

  20. Effect of Narrow-Band Interference NBI is modeled as a Gaussian stationary random process with auto-correlation sequence :NBI plus thermal noise J is jammer power per affected subchannel

  21. NBI Effect for WLAN Environment DCT-MCM outperforms DFT-MCM for high jammer power Large NBI spread degrades DFT-MCM more than DCT-MCM

  22. NBI Effect for DSL Environment • For DSL, channel information can be fed back to perform transmission bandwidth optimization • Rate Adaptive Water-Filling Loading Algorithm (turn off subchannel affected by NBI) Maximize Rate Fixed energy constraint Subject to:

  23. Effect of NBI (128 Tap TEQ) DCT-MCM more robust to NBI spread NBI Spread 2 subchannels 10 subchannels

  24. Effect of NBI (64 Tap TEQ) DCT-MCM requires longer TEQ than DFT-MCM NBI Spread 2 subchannels 10 subchannels

  25. Conclusion • DCT-MCM is an optimal modulation/demodulation scheme when overall CIR is symmetric and prefix/suffix guard sequences are symmetric extensions of information sequence • DCT-MCM has complexity advantage over DFT-MCM for baseband systems. • DCT-MCM is more robust to Frequency Offset, Narrowband Interference • DCT-MCM has excellent spectral compaction and energy concentration properties • The main disadvantage of the DCT is the necessity of aprefilter to make the CIR symmetric

  26. Publications • N.Al-Dhahir, H. Minn, S. Satish “Optimum DCT-Based Multi-Carrier Transceivers for Frequency-Selective Channels”, IEEE Transactions on Communications, May 2006 • S. Satish, N.Al-Dhahir, H. Minn,”A DCT-Based Broadband Multicarrier Transceiver”, in IEEE SECON Conference, Memphis, April 2006

  27. Thank you

  28. DFT-Multicarrier Modulation (DFT-MCM) Noise Coding & Interleaving IDFT (Size N) Add Cyclic Prefix Information Block Channel Prefilter (only for long channels P/S Decoding & De-Interleaving DFT (size N) Remove Cyclic Prefix Slicer 1-tap equalizer Detected Information Block Slicer 1-tap equalizer S/P

  29. Carrier Service Area Loops

  30. Karhunen-Loeve Transform (KLT) • The KLT completely decorrelates a random signal sequence. • The KLT maximizes the throughputof a ISI Gaussian Channel. • Drawback: Basis Functions need to be predetermined

  31. Multicarrier Modulation • A conventional Multicarrier Modulation (MCM) Scheme • OFDM/DMT based MCM Scheme

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