Blind calibration of timing offsets for four-channel time-interleaved ADCs

In this paper, we describe a blind calibration method for timing mismatches in a four-channel time-interleaved analog-to-digital converter (ADC). The proposed method requires that the input signal should be slightly oversampled. This ensures that there exists a frequency band around the zero frequency where the Fourier transforms of the four ADC subchannels contain only three alias components, instead of four. Then the matrix power spectral density (PSD) of the ADC subchannels is rank deficient over this frequency band. Accordingly, when the timing offsets are known, we can construct a filter bank that nulls the vector signal at the ADC outputs. We employ a parametrization of this filter bank to develop an adaptive null steering algorithm for estimating the ADC timing offsets. The null steering filter bank employs seven fixed finite-impulse response filters and three unknown timing offset parameters which are estimated by using an adaptive stochastic gradient technique. A convergence analysis is presented for the blind calibration method. Numerical simulations for a bandlimited white noise input and for inputs containing several sinusoidal components demonstrate the effectiveness of the proposed technique.