Design and Performance of DCT-Based Multicarrier Transceiver for Broadband Communications

1. Design and Performance of DCT-Based Multicarrier Transceiver for Broadband Communications Shilpa Satish Dept. of Electrical Engineering University of Texas at Dallas Richardson, TX

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

3. DFT-Multicarrier Modulation (DFT-MCM) Fact: Any circulant matrix can be decomposed in the form Guard Sequence is designed as a cyclic prefix to obtain an equivalent channel matrix of the form

4. 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

5. Features of DFT-MCM • DFT is channel independent • Orthogonal Transform • Fast ComputationAlgorithms • Prefilter is required only for long channels

6. 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

7. DFT-Multicarrier Modulation (DFT-MCM) • Currently, DFT is the only orthogonal, channel-independent, and fast size-N transform that is used to diagonalize ISI channels with no Intercarrier Interference (ICI) or Interblock Interference (IBI). • Question : Is it the only one with these properties ?

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

9. 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!)

10. 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

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

12. 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

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

14. Modified TEQ Design for DCT-MCM • Incorporation of symmetry condition on shortened CIR Subject to:

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

16. 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

17. 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

18. Comparison of DCT-MCM with DFT-MCM • Frequency Offset • Channel Estimation Errors • Narrowband Interference on WLAN Environment • Narrowband Interference on DSL Environment • Mobility • Peak to Average Ratio

19. Bit Rate and Gap Approximation Bit Rate Geometric SNR Gap Parameter Pe – Probability of Error Γm-Margin Gain, Γc-Coding Gain, Q(.) is the Q function

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

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

22. 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

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

24. 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

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

26. 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:

27. Carrier Service Area Loops

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

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

30. Effect of Mobility Time-nonselective (slow fading) Time-selective (fast fading)

31. Mobility • Time-Varying Rayleigh-fading Channel generated using Jakes Model where time correlation of each channel tap follows a zero-order Bessel function

32. Receiver Structure TEQ replaced by N-Tap FEQ FEQ coefficients designed using Wiener Equation MMSE Design

33. Number of FEQ Taps Needed N = 128 Full N-tap per subchannel FEQ not required FEQ matrix banded resulting in significant complexity reductions DFT-MCM requires slightly less taps than DCT-MCM

34. Performance of 1% and 10% Doppler • DCT-MCM more robust to Doppler • Increased Doppler provides time diversity, aiding both DCT-MCM and DFT-MCM.

35. Peak to Average Ratio (PAR) • PAR is the ratio of the peak to the average transmit power • Higher PAR requires more HPA backoff (to stay linear) • Oversampling factor = 8

36. Comparing PAR’s for DCT and DFT Comparable PAR for DFT-MCM and DCT-MCM Average Power tends to be Gaussian according to Central Limit Theorem

37. 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, Mobility • 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

38. 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

39. Thank you

40. 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

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