The presence of frequency response mismatches (FRMs) in time-interleaved (TI) systems can severely degrade system performance. In addition, it is difficult to represent FRMs in generalized TI systems using low-order polynomials or physical circuits, which complicates the design of calibration methods. In this study, first, we propose a digital time-interleaved (DTI) structure to establish a relationship between the TI system and a periodic time-varying filter. The DTI structure uses less resources in time-varying filter implementation than the method that utilizing filters and multipliers. We also develop a cascaded calibration model and its equivalent noncascaded form based on the DTI structure. The equivalent noncascaded form uses only one time-varying filter rather than cascades multiple time-varying filters, which is a significant advantage because it can improve the calibration performance without increasing hardware resources during implementation. Furthermore, a filtering process was included in the frequency domain, rather than in the time domain, to cope with the challenges of designing an arbitrary frequency response filter. Simulations based on a four-channel generalized frequency response TI system showed that the proposed method achieved more than 45-dB spur-free dynamic range (SFDR) improvements if measurements of frequency responses are unbiased. Also, more than 60-dB SFDR can be achieved even if a ±5% estimation bias in the measurement of frequency responses. Errors between calibration frames were also minimized by introducing an overlapping frame technique, which ensured that the algorithm could calibrate large data quantities with high precision. Calibration was also implemented in a real four-channel 10 gigabit sampling per second (GSPS) system. Results indicated that the spurious-free dynamic range increased from 47.27 to 62.21 dB at a 5-GHz bandwidth after calibration.

The band interleaved data acquisition system (BI-DAS) is an attractive structure to improve the bandwidth of the acquisition system. However, the non-ideal characteristic of the spectrum analysis filter in BI-DAS results in an overlapping frequency band between two adjacent frequency sub-bands. Phase misalignment (PM) between two sub-bands in the overlapping band may cause those signals canceled or partially canceled to each other when sub-bands’ signal are merged. In this paper, a compensation module with a digital all-pass filter (APF) is proposed for the PM of the overlapping bands in BI-DASs. Based on this compensation module, a hybrid Particle Swarm Optimization (PSO) algorithm, along with the Levenberg-Marquardt (LM) algorithm is proposed to design coefficients of the compensation module. The compensation module and corresponding method proposed in this paper are verified in a BI-DAS with 20Gsps sampling rate and 5.5GHz bandwidth. The experimental results show that the proposed compensation module can effectively compensate the PM between the sub-bands in the overlapping band. The proposed hybrid PSO-LM (HPSOLM) algorithm combines the flexibility and reliability inherent in the PSO with the fast convergence and precision of the LM algorithm. It can effectively design the compensation module with stable APF while consuming less time and obtaining better compensation results than the conventional PSO method.

Time interleaving (TI) technique is widely used in acquisition systems to improve the sampling rate. However, as a parallel sampling structure, it inevitably brings in channel mismatches, such as the offset mismatch, gain mismatch, and time mismatch. Moreover, the gain mismatch and time mismatch are frequency-dependent, which means that the gain mismatch and time mismatch will be different when the signal frequency changes. This is because the gain and time mismatches are the special circumstances of frequency response mismatches. In this paper, a frequency response mismatch estimation method in TI acquisition systems is proposed and analyzed. First, the two kinds of mismatch models are compared to find the relationship between frequency response mismatches and the gain and time mismatches. Then, a mismatch estimation method that can estimate mismatches when the analog bandwidth exceeds the sampling rate of a single channel in a time interleaving analog to digital converter is proposed. Sinusoids with different frequencies are utilized to convert the question of estimating frequency response mismatches to acquiring the mismatch coefficients at a series of frequency points. Furthermore, a semi-automatic estimation technique is proposed to reduce the operation time, and a 10 GSPS eight-channel TI system is introduced. Simulations show the accuracy and effectiveness of the proposed method. At last, the frequency response mismatches are calibrated by using the estimated parameters. The calibration improves the performance of an eight-channel TI system from the original spurious free dynamic range of 27.6639 to 56.7029 dB and signal-to-noise ratio of 25.5468 to 32.7667 dB. The calibration result demonstrates the usefulness of the proposed method.

A novel mismatch correction strategy is proposed for bandwidth-interleaved (BI) acquisition system with overlapping band. In the proposed strategy, mismatch errors due to the nonuniformity among different subbands are considered as phase misalignment and magnitude distortion, which are estimated and corrected separately. Taking advantage of the characteristics of overlapping band, phase misalignment is estimated by homomorphic correlation analysis of the signal in the overlapping band and compensated before subband merging. Magnitude distortion is compensated by an FIR filter designed with frequency sampling method after subband merging. Compared with other conventional methods, this strategy can realize nearly perfect reconstruction (NPR) without transfer function to be known or any additional hardware. The proposed strategy has been validated via simulations of a BI system with 2GHz bandwidth.

There is a contradiction between the estimation range and estimation accuracy of the most carrier frequency offset (CFO) estimation algorithms. In order to solve the dilemma, this paper proposes an improved Fast Fourier Transform (FFT) CFO estimation method based on Twice FFT Matrix Algorithm (TFMA). The idea of the method is to ameliorate the frequency resolution highly by enlarging the size of FFT, without sacrificing the estimation range. By the application of TFMA, the calculation resource consumption is decreased largely compared with the direct implementation of large-size FFT in the field programmable gate array (FPGA). Therefore, the approach can be used to estimate the large CFO of the high-order modulation signals accurately and effectively. The experiment results verify that the method can complete the estimation of the small or large CFO precisely, thus the contradiction above has been solved properly. Moreover, TFMA has been realized on the hardware platform of FPGA.