Frequency Response Mismatch Research Articles

Hadamard transformation based frequency response mismatch calibration for a 4-channel TIADC

The time-interleaved analog-to-digital converter (TIADC) is one of the most effective solutions for improving the sampling rate of acquisition systems. However, the frequency response mismatch between channels can seriously degrade the performance of the system. In this paper, we propose a calibration method for frequency response mismatches in 4-channel TIADC systems. Following the construction of a four-channel TIADC model using a four-order Hadamard matrix, the error signals were extracted using three time-invariant filters and subsequently subtracted from the output to complete the calibration. It uses the Hadamard transform instead of the complex exponential modulator used in conventional time-varying filter methods, which can further simplify the signal processing without the necessity of complicated calculations. We have employed a stimulated four-channel TIADC system to validate the effectiveness of the proposed calibration technique. Moreover, in a commercial 12.5 GSPS four-channel TIADC system, it is also demonstrated that this approach is effective in improving the spurious-free dynamic range of the system.

Efficient Parallel Polynomial-Based Compensation Structure for Frequency Response Mismatch in Two-Channel TI-ADCs

Efficient Parallel Polynomial-Based Compensation Structure for Frequency Response Mismatch in Two-Channel TI-ADCs

Calibration of frequency response mismatches in time‐interleaved analog‐to‐digital converter based on adaptive method

AbstractThe time‐interleaved analog‐to‐digital converter (TIADC) system could achieve high sampling rate effectively, but the frequency response inconsistency among channels will introduce frequency response mismatches, which will seriously degrade the signal quality. In this paper, a novel multi‐channel frequency response mismatches adaptive calibration method is proposed. The frequency response of the compensation filter is expanded into a polynomial of a digital differentiator, and the least mean square adaptive strategy is used to calibrate frequency response mismatches. It does not require measuring the channel frequency responses in advance and uses digital post‐processing technology to effectively compensate the frequency response of the multi‐channel TIADC system and improve the spurious‐free dynamic range. The experimental results verify the effectiveness of the algorithm.

A Novel Method for Microphone Channel Frequency Response Calibration Based on Newton Algorithm

Microphone arrays are widely applied in practical applications. In an array, each channel conventionally contains an acoustic sensor and a following signal conditioning circuit (SCC). Frequency response mismatches among channels will adversely affect array’s overall performance. Existing calibration methods provide promising results; however, their accuracy varies considerably across full frequency band and the passband bandwidth shrinkage problem also arises. To address these problems, we propose a novel calibration method based on Newton algorithm. The proposed method cascades calibration filters after channel output signals allowing the frequency response calibration to be equivalent to the optimization of calibration filter coefficients. First, all uncalibrated channels’ bandwidths are analyzed using a chirp calibration signal, resulting in appropriate construction of the desired output. Next, a spectrum mean square error criterion between each channel output and the desired signal is utilized to formulate the frequency response mismatch. Finally, we employ Newton algorithm to design the calibration filter coefficients corresponding to each channel. Explicit mathematical derivation is provided. Since the cost function is quadratic, expressions of the constant Hessian matrix and its inverse are derived. Furthermore, the inverse Hessian can be efficiently computed using spectral coefficients of channel outputs. Simulation results reveal that the proposed method significantly outperforms the state-of-the-art calibration approaches in terms of calibration accuracy, calibrated passband bandwidth performance, and convergence rate. Real-world experiments also verify its effectiveness.

Feedback Controller Optimization for Active Noise Control Headphones Considering Frequency Response Mismatch between Microphone and Human Ear

This paper presents an investigation on the feedback controller design for active noise control headphones under the condition that the frequency responses of the primary and secondary paths corresponding to the feedback microphone do not match to the ones corresponding to the human ear. The influence of such mismatches on the performance are analyzed first, and then an optimization method is proposed to enhance the comprehensive performance at the human ear. In the proposed method, the feedback loop is constructed directly with the feedback microphone and any extra filters of the virtual sensing techniques are avoided. Cascade biquad filters are used as the controller, which is in accordance with current applications. A differential evolution algorithm was used to solve the proposed optimization problem, and the optimal parameters of the controller were found. It has been shown by the experimental results that, at the dummy head ear position, good noise reduction performance could be obtained at the low frequency band with limited noise enhancement for high frequencies, even if large frequency response mismatches exist.

Frequency Response Mismatch Calibration in Generalized Time-Interleaved Systems

Frequency Response Mismatch Calibration in Generalized Time-Interleaved Systems

Frequency response mismatch calibration in 2-channel time-interleaved oscilloscopes.

The time-interleaved (TI) structure has been widely implemented in high speed, wideband data acquisition systems to increase the system sampling rate. However, the frequency responses of each sub-sampling path are not identical. This is named frequency response mismatches (FRMs). In TI-based printed circuit board level systems, due to the impact of the parasitic parameters, the FRMs are more complicated than the mismatches in TI analog-to-digital converters (TIADCs), which degrade the system performance severely. Therefore, the FRM calibration in 2-channel TI acquisition systems with two features is researched. The first one is that the TI system has a larger mismatch range than in most previous research. The second one is that the channel frequency response uses the general model. The calibration structure is established by the analysis of the digital TI model, which implements the TI operation in the digital domain to reconstruct the mismatches in the time domain. Furthermore, the problem of designing an arbitrary frequency response filter is transformed to the question of designing a three-stage cascaded filter group, which gives a method to realize the arbitrary frequency response in a real system. An oscilloscope prototype is proposed to verify the calibration performance. The simulation and experiment show the following: (i) Even though it uses the general frequency response and the FRMs are significant, the proposed method is still effective. (ii) The mismatch range of magnitude and phase responses is highly suppressed, and the spurious-free dynamic range is improved by 16.26 dB after calibration of the prototype.

A fast Fourier transform based method to estimate frequency response mismatches in time interleaved systems.

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.

Distributed Frequency Response Calibration Based on Consensus Strategy in Microphone Array

Frequency response mismatches among microphones inevitably result in performance deterioration of signal processing algorithms for microphone arrays. A frequency response calibration method based on the consensus strategy is proposed in this article. Adaptive calibration filters concatenated with microphone channels are first introduced to compensate for the frequency response mismatches among microphones. Then, the frequency response mismatch problem is formulated as the minimization of a cost function measuring the spectrum mismatches among neighboring microphone channel outputs. Finally, the consensus strategy is used to design the calibration filter in each microphone channel. By using the consensus strategy, the proposed frequency response calibration method is robust to the room impulse response and noise differences among microphones. The proposed method outperforms gain calibration methods and the centralized frequency response calibration method. Experimental results reveal the validity of the proposed method.

Frequency Response Analytical Calibration Based on Spectral Flatness for Microphone Arrays

Many audio processing tasks using microphone arrays suffer from the impact of frequency response mismatch among microphones. To mitigate this problem, a frequency response analytical calibration method based on spectral flatness for microphone arrays is proposed in this article. Specifically, the dynamic calibration model, including two geometric states, is first applied to arrange the uncalibrated microphones. Then, the calibration signals corresponding to two geometric states are synchronized by estimating the time difference of arrival (TDoA). Next, a filter design method is presented in the frequency domain, from which the coefficients of calibration filters can be derived as closed-form solutions. Furthermore, a noise reduction approach via the spectral subtraction technique is given to cope with the adverse effect of noises. Finally, the ripples introduced by calibration filters are further suppressed through a spectral flatness-based criterion. Simulation and real-world experimental results illustrate that the proposed method can effectively compensate both the gain and phase errors among microphones in noisy and reverberant environments.

Adaptive Frequency Response Calibration Method for Microphone Arrays

Frequency response mismatch among microphones inevitably leads to performance deterioration of signal processing algorithms of microphone arrays, especially for distributed microphone networks. An adaptive frequency response calibration method for microphone arrays based on frequency domain least mean square (FLMS) algorithm is proposed in this paper. Adaptive calibration filters are first introduced to calibrate the frequency response mismatch among microphones, which are concatenated with microphone channels. Then, the frequency response mismatch problem is formulated with a combined spectrum mean square error criterion of pairwise microphone outputs, and an unit-norm constraint is imposed to avoid undesired solutions. Finally, FLMS algorithm is used to design the calibration filter in each microphone channel. This method achieves good frequency response calibration performance even under severe ambient noise and reverberation conditions. Experimental results reveal the validity of the proposed method.

An Adaptive Blind Calibration Technique for Frequency Response Mismatches in M-Channel Time-Interleaved ADCs

This brief proposes a novel adaptive architecture for blind estimation and calibration of the frequency response mismatches in an M-channel time-interleaved analog-to-digital converter (TI-ADC). Based on the basis functions generated from the measured TI-ADC output, the mismatch errors could be reconstructed blindly and subtracted from the TI-ADC output adaptively. The advantage of the proposed technique is that it only needs to know the measured output signal without requiring any additional information and it is applicable to any channel TI-ADCs. Specially, the calibration structure only needs several differentiators with fixed coefficients without requiring a bank of adaptive FIR filters. In addition, the numerical simulations have been presented to demonstrate the effectiveness and superiority of the proposed technique, which shows that the proposed technique can improve the SNR and SFDR by over 25 dB.

Deconvolution using CLEAN-SC for acoustic source identification with spherical microphone arrays

The point spread function (PSF) based deconvolution algorithms may fall short due to the inconformity between the actual beam pattern of acoustic sources and the theoretical PSF. CLEAN-SC, originally developed for delay and sum beamforming with planar microphone arrays, can circumvent the inconformity. This paper devotes to adapting CLEAN-SC to spherical harmonics beamforming (SHB). The core of adapting CLEAN-SC to SHB is to express the output of SHB in the spatial domain as a specific form of matrix operation completely. We solve the issue and establish CLEAN-SC with spherical microphone arrays. Its performance is analyzed and compared with PSF based CLEAN. CLEAN-SC with spherical microphone arrays can improve spatial resolution and suppress sidelobes more effectively, as well as quantify the sound pressure contribution accurately. Moreover, it has better convergence, higher computational efficiency, and stronger robustness to interference such as background noise and frequency response mismatch of microphone and measurement channel. This study provides an alternative approach for acoustic source identification in three-dimensional space.

Efficient real-time blind calibration for frequency response mismatches in two-channel TI-ADCs

Efficient real-time blind calibration for frequency response mismatches in two-channel TI-ADCs

Frequency-response mismatch effects in Johnson noise thermometry

Johnson noise thermometry is of considerable interest at present due to the planned redefinition of the kelvin in 2019, and several determinations of the Boltzmann constant have recently been published in support of the redefinition. To determine the Boltzmann constant by noise thermometry, the thermal noise from a sensing resistor at the triple point of water is compared to a pseudo-random noise with a calculable power spectral density traceable to quantum electrical standards. In all the measurements to date, the two dominant sources of measurement uncertainty are strongly influenced by a single factor: the frequency-response mismatch between the sets of leads connecting the thermometer to the two noise sources. In the most recent determination at the National Institute of Metrology, China, substantial changes were made to the connecting leads to reduce the mismatch effects. The aims of this paper are, firstly, to describe and explain the rationale for the changes, and secondly, to better understand the effects of the least-squares fits and the bias-variance compromise in the analysis of measurements affected by the mismatch effects. While significant improvements can be made to the connecting leads to lessen the effects of the frequency-response mismatch, the efforts are unlikely to be rewarded by a significant increase in bandwidth or a significant reduction in uncertainty.

Estimation and Mitigation of Channel Non-Reciprocity in Massive MIMO

Time-division duplex (TDD) based massive MIMO systems rely on the reciprocity of the wireless propagation channels when calculating the downlink precoders based on uplink pilots. However, the effective uplink and downlink channels incorporating the analog radio front-ends of the base station (BS) and user equipments (UEs) exhibit non-reciprocity due to non-identical behavior of the individual transmit and receive chains. When downlink precoder is not aware of such channel non-reciprocity (NRC), system performance can be significantly degraded due to NRC induced interference terms. In this work, we consider a general TDD-based massive MIMO system where frequency-response mismatches at both the BS and UEs, as well as the mutual coupling mismatch at the BS large-array system all coexist and induce channel NRC. Based on the NRC-impaired signal models, we first propose a novel iterative estimation method for acquiring both the BS and UE side NRC matrices and then also propose a novel NRC-aware downlink precoder design which utilizes the obtained estimates. Furthermore, an efficient pilot signaling scheme between the BS and UEs is introduced in order to facilitate executing the proposed estimation method and the NRC-aware precoding technique in practical systems. Comprehensive numerical results indicate substantially improved spectral efficiency performance when the proposed NRC estimation and NRC-aware precoding methods are adopted, compared to the existing state-of-the-art methods.

An Adaptive Blind Frequency-Response Mismatches Calibration Method for Four-Channel TIADCs Based on Channel Swapping

This brief proposes a novel adaptive blind calibration method to compensate for the frequency-response mismatches in four-channel time-interleaved analog-to-digital converters. By representing the frequency responses as a polynomial series in $j\omega$ , the mismatch parameters are estimated exploiting the filter-X least-mean square algorithm and the channel swapping technique. Mismatch-induced error signal is reconstructed by the proposed reconstruction structure using the estimated mismatch parameters. Numerical simulation results show that the proposed method is effective and efficient.

Digital correction of frequency‐response errors in bandwidth‐interleaved ADCs

A multichannel bandwidth-interleaved (BI) framework with digital back-end correction of mismatch errors is explored to simultaneously increase the sample-rate and bandwidth of the ADCs. In addition to the consideration of channel frequency-response mismatch and aliasing error associated with sampling, the autocorrelation matrix of magnitude response is introduced to evaluate the performance of overlapping cancellation between the nearby subbands. Simulation results and analytical calculations are provided to verify the efficacy of the proposed correction approach.

Digitally Enhanced Wideband I/Q Downconversion Receiver With 2-Channel Time-Interleaved ADCs

The interesting concept of employing in-phase/quadrature (I/Q) downconversion together with time-interleaved analog-to-digital converters allows digitizing very wide instantaneous radio-frequency (RF) bandwidths (BWs) and grants enhanced flexibility in accessing and processing the RF spectrum. Such a structure also inevitably suffers from performance degradation due to the analog components' nonidealities, e.g., frequency response mismatches (FRMs), that ultimately lead to spurious mismatch components that limit the system's dynamic range. Available solutions developed for I/Q mismatches or time-interleaving mismatches alone are not compatible for correcting the FRM spurs in such joint I/Q time-interleaved converter (IQ-TIC) architecture. This brief proposes novel blind FRM identification and correction solutions that are able to suppress all the associated spurs in the considered wideband IQ-TIC architecture. The proposed digital correction solutions are tested and verified using measured hardware data obtained from an experimental platform, exhibiting good FRM spur correction performance with instantaneous BW on the order of 800 MHz. These developments pave the way toward 5G radio communication devices and systems where instantaneous BWs on the order of 1 GHz are envisioned at centimeter- and millimeter-wave frequency bands.

A calibration method for frequency response mismatches in <i>M</i>-channel time-interleaved analog-to-digital converters

Frequency response mismatches (FRMs) in time-interleaved analog-to-digital converters (TIADCs) generate undesired spurs degrading the performance of TIADCs. This paper introduces a digital calibration method for the FRM in M-channel TIADCs (M-TIADCs). This method exploits fixed differentiator finite-impulse response (FIR) filters and the Hadamard transform to reconstruct the mismatch induced error signal. The mismatch parameters are estimated utilizing a short training signal and the least square (LS) method. Our method is simpler in terms of implementation compared with conventional methods as cumbersome time-varying filters, complex signal processing and front-end hardware modifications are avoided. Numerical simulation results demonstrate the efficacy and efficiency of the proposed method.