Continuing Paper Notes: Linear LMS Compensation for Timing Mismatch in TIADCs

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Results:

  • Performance is quantified using the inverse of the SINAD.
  • Known Input Spectrum:
    1500 taps
    Input is filtered white noise, Butterworth 20th order wc cutoff
    JL -79 to -25 dB
    EO -62 to -35 dB
    PLH -90 to -39 dB
    FIR LMS -90 to -39 dB (best overall)

    150 taps FIR LMS clearly better (same performance), others have -70 and > dB

    15 taps FIR LMS clearly better (same performance), others have -54 and > dB

  • Unknown Input Spectrum
    150 taps, fixed nominal filter Butterworth lowpass 10th order cutoff 0.4Hz
    FIR LMS clearly better with nearly same performance, others have -88 and >
  • Periodic Input Signal
    150 taps, Butterworth lowpass input filter 20th order cutoff 0.4Hz
    FIR LMS clearly better -172.83 dB
    PLH -71.65 dB
    JL -30 dB
    EO -58.37 dB

Final Comments:

Each of the methods can be shown to be equivalent in certain cases but the FIR LMS seems to out perform on a wide scale because of the optimal derivation.

Official Reference:

Marelli, D.; Mahata, K.; Minyue Fu, “Linear LMS Compensation for Timing Mismatch in Time-Interleaved ADCs,” Circuits and Systems I: Regular Papers, IEEE Transactions on , vol.56, no.11, pp.2476-2486, Nov. 2009
URL:
http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=4785489&isnumber=5308577

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Paper Notes: Linear LMS Compensation for Timing ismatch in Time-Interleaved ADCS

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Authors: Damián Marelli, Kaushik Mahata and Minyue Fu

Year: November 2009

Idea: A compensation method which does not assume the input signal is bandlimited, however it has a stationary known power spectrum. (The spectrum power can also be estimated) Then compensation for timing mismatches are desiged in a statistically optimal sense.

Method:
Formulate the problem as a estimation problem. Do the estimation using a linear LMS criterion. Where the weights W are calculated to minimize the power if the reconstruction error signal.

Results:
Simulations only.

Notes:

  • Using LMS with knowledge on the spectrum. (Minimize the power of the reconstruction error signal)
  • Faster decay rate, reduces order
  • Optimization with order constraint possible
  • Proposed Wiener filter equiv filter bank compensation
  • Other methods mentioned: Eldar-Oppenheim, Johansson-Lowenborg, Prendergast-Levy-Hurst (PLH)

Look up:

  • Frobenius norm
  • Moore-Penrose pseudoinverse
  • Wiener smoother