Cramer Rao Lower Bound for Blind Timing Offset Estimation of a Two-Channel Time-Interleaved A/D Converter

This paper discusses the statistical efficiency of a blind calibration method presented for estimating the timing offset between branches of a two-channel time-interleaved analog to digital converter (ADC). For a slightly oversampled signal, this method transforms the calibration problem into a conventional adaptive time-delay estimation problem by lowpass filtering the ADC ouputs. To evaluate the optimality of this approach, two Cramer Rao lower bounds (CRLBs) are derived. The first is applicable to all blind calibration algorithms, and the second to methods that rely on low-pass filtered ADC outputs. Since the time-delay estimation method is asymptotically efficient with respect to its CRLB at high SNR, its efficiency for the original calibration problem depends on whether the two CRLBS are close to each other. For a wideband WGN input, we obtain a condition expressed in terms of the ADC resolution and signal oversampling factor that ensures that the two CRLBs are near each other. Numerical simulations demonstrate the efficiency of the calibration method for an ADC SNR of 70 dB and oversampling factor of 15%.