## 1 Introduction  
The time-interleaved analog-to-digital converter (TIADC) is proposed to meet the fast increasing demand for a high sampling rate in modern mixed-signal processing systems, e.g., radar, communication and measurement equipment. The sampling rate of an \(M\)-channel TIADC (\(M\)-TIADC) is \(M\)-times the sampling rate of the sub-ADCs, and the resolution of the \(M\)-TIADC is the same as the resolution of sub-ADCs in the ideal case. However, due to non-ideal circuit implementations, spurious components arise because of the discrepancies among the sub-ADCs, distorting the sampled signal and degrading the effective resolution of the sub-ADCs. Therefore, calibration (compensation) methods are required to suppress the spurious components and restore the dynamic performance of sub-ADCs. A large number of papers devoted to estimation and compensation methods for TIADCs has been published during the past few decades. Most of them aim at the compensation methods for the linear mismatches, including gain, time-skew and frequency response mismatches [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20]. By comparison, relatively few papers have been published to address the nonlinear mismatches problem, which stems from the imperfection of front-end circuits, as well as the differential and integral nonlinearities of sub-ADCs [21; 22; 23; 24; 25; 26; 27; 28]. A study of differential nonlinearities (DNL) and integral nonlinearities (INL) in \(M\)-TIADC is presented in [22]. It is pointed out that the DNL and INL of a TIADC are smaller than the DNL and INL errors for individual sub-ADCs. The channel linearity mismatch effects in TIADCs are analyzed and simulated in [21], in which several distinct features of nonlinear mismatch are shown. A nonlinear hybrid filter banks model of TIADCs is proposed in [29], where the input-output relationship of TIADCs with nonlinear mismatches is formulated. Several methods are proposed following the analysis and model mentioned above. A method exploiting the inverse function of the INL of each sub-ADC is proposed in [30] to compensate for the INL mismatches in \(M\)-TIADCs. However, the inverse function can only be measured by interrupting the normal sampling operation. A randomization-based calibration method is presented in [31] with the cost of additional converters, which is also the main drawback of the methods exploiting reference channels [24]. A digital compensation method that relies on the foreground estimated nonlinearities is presented in [26], where a sinusoidal signal is employed as the training signal during the estimation procedure. A blind calibration method is proposed in [27; 28] for 2-TIADCs and extended in [25] for \(M\)-TIADCs. The bandwidth efficient (BWE) method proposed in [25] is able to calibrate the nonlinear mismatches in \(M\)-TIADCs, as long as the mismatch-induced error signals are present in the input-free band, which is generated by a slight oversampling. However, there are two major drawbacks of the BWE method. Firstly, it is not only resource consuming, but also cumbersome to generate the sinusoidal modulation sequences needed in the BWE method. Secondly, two sets of variable multipliers are exploited for modulation and for weighting, respectively, which means a large number of multipliers is required. These two drawbacks are overcome by the method proposed in this paper. In this paper, a blind calibration method exploiting the binary Hadamard sequences is proposed for nonlinear mismatches in \(M\)-TIADCs (\(M=1,2,4,8,...\)). Our method consumes much less hardware resources while maintaining the bandwidth efficiency and calibration performance of the BWE method. The sinusoidal modulation sequences in the BWE method are replaced by the binary Hadamard sequences in our approach, which brings the following two benefits. Firstly, the Hadamard sequences are much easier to generate compared with the sinusoidal sequences because there are only \(1\) and \(-1\) in the binary Hadamard sequences.