Cumulant statistical adaptation of non-linear post conversion correction for TI-ADCs

Practical implementations of post conversion correction of time interleaved analog to digital converters (TI-ADCs) is of particular interest to the test and measurement community due to the demand for large instantaneous bandwidths and high dynamic ranges required by many fields. Ideally TIADCs allow for an increased sampling rate while maintaining the performance of the individual converters. In practice this is harder to achieve. Ultra wideband communications as well as direct conversion applications in RADAR also benefit from practical implementations of TI-ADCs. One such method proposed in this paper is based upon the work that was presented last year by the authors at Autotest 14 where an adaptive linear combination of nonlinear filters placed in the channels can ideally suppress the mismatches when driven by an ideal error signal. Here it is proposed that the structure can be driven by an approximate cumulant statistical adaptation these results are compared to an implementation of a non-ideal error signal generated using interpolation techniques. Various cumulants are discussed from the 1st to 8th order. These statistics are calculated using Boxcar FIR filter moving average approximations in place of averages over the entire dataset. A single channel is used as a reference and is interpolated to generate the reference samples for the second channel. This paper presents the implementation and results of the practical design applied to a behavioral TIADC model. The model is based upon off the shelf performance of 14 bit 80MSPS converters that suggest the performance of the intended implemented system and has been presented in prior works by the authors, allowing for evaluation of the new correction method in a realistic scenario. Results show that the cumulant based channelized correction scheme can suppress linear and nonlinear mismatch spurs by a significant amount, on average 35 dB up to ideal suppression in the sinusoidal input case. When a wideband QPSK input is used during adaptation, between 6dB and 20dB suppression is achieved. Design considerations will be presented including how to choose initial conditions, step size, the cumulant statistic used and adaptation time for implementations in the 2 and 4 TIADC case.