Phase Error Calibration Research Articles

Expansion–compression variance-component-based autofocusing method for joint radar coincidence imaging and gain–phase error calibration

Radar coincidence imaging (RCI) is a super-resolution staring technique based on the innovative idea of random radiation and wavefront random modulation. To reconstruct the target, sparsity-driven methods are commonly used in RCI, while the prior knowledge of the imaging model requires to be known accurately. However, model error generally exists, which induces the inaccuracy of the model and defocuses the image. We focus on sparsity-driven RCI in the presence of gain–phase error and propose an autocalibration expansion–compression variance-component (AC-ExCoV)-based autofocusing method in a sparse Bayesian learning framework. The algorithm determines the gain–phase error as a part of the RCI process by reconstructing the target and compensating the gain–phase error iteratively. To probabilistically formulate the target reconstruction problem, a probabilistic model is utilized to fully exploit the sparse prior, and then solved using ExCoV. Meanwhile, the gain–phase error is estimated and calibrated to obtain a high-resolution focused image. The AC-ExCoV algorithm demands no prior knowledge about the sparsity or measurement-noise level with significant superiority in computational complexity. Simulation results show that the proposed algorithm obtains a well-focused target image with high reconstruction accuracy.

Digital Calibration Method for High Resolution in Analog/RF Designs

Transistor random mismatch continuously poses challenges for analog/RF circuit design for achieving high accuracy and high yield as the process technology advances. Existing statistical element selection (SES) design method can improve transistor matching property, but it falls short of being a general calibration method due to its limited calibration range. In this dissertation, we propose a high resolution digital calibration method, called extended statistical element selection (ESES). As compared to the SES method, the ESES method not only provides wider calibration range, but also it results in higher calibration yield with same calibration resolution target. Two types of ESES based calibration application in analog/RF circuits are also proposed. One is current source calibration and the other is phase/delay calibration. To verify this proposed digital calibration method in circuit implementation, we designed, fabricated and tested a wideband harmonic rejection receiver design. The receiver utilizes ESES-based gain and phase error calibration for improving harmonic rejection ratios. With the high calibration resolution provided by the ESES method, after calibration, we achieved best-in-class harmonic rejection ratios. To extend the application of the proposed method, we further designed a current-steering D/A data converter (CS-DAC). The CS-DAC utilizes ESES-based amplitude and timing error calibration for improving linearity performance. Simulation results showed that we can achieve more than one order of magnitude linearity improvement after performing ESES-based calibration in the CS-DAC.

An Eigenstructure Method for Estimating DOA and Sensor Gain-Phase Errors

In this paper, we consider the problem of direction of arrival (DOA) estimation in the presence of sensor gain-phase errors. Under some mild assumptions, we propose a new DOA estimation method based on the eigendecomposition of a covariance matrix which is constructed by the dot product of the array output vector and its conjugate. By combining the new DOA estimation with the conventional gain-phase error estimation, a method is proposed to simultaneously estimate the DOA and gain-phase errors without joint iteration. Theoretical analysis shows that the proposed method performs independently of phase errors and thus behaves well regardless of phase errors. However, the resolution capability of the proposed method is lower than that of the method in [A. J. Weiss and B. Friedlander, “Eigenstructure methods for direction finding with sensor gain and phase uncertainties,” Circuits Systems Signal Process., vol. 9, no. 3, pp. 271-300, 1990], named as the WF method. In order to improve the resolution capability and maintain phase error independence, a combined strategy is developed using the proposed and WF methods. The advantage of the proposed methods is that they are independent of phase errors, leading to the cancellation of phase error calibration during the operation life of an array. Moreover, the proposed methods avoid the problem of suboptimal convergence which occurs in the WF method. The drawbacks of the proposed methods are their high computational complexity and their requirement for the condition that at least two signals are spatially far from each other, and they are not applicable to a linear array. Simulation results verify the effectiveness of the proposed methods.

Phase Error Calibration Technique for Rotary Traveling Wave Oscillators

Phase error calibration technique that is suitable for an RTWO is presented. By introducing non-uniform capacitors in the distributed resonator, the phase relationships among multiphase outputs available from the RTWO are adjusted to compensate for physical asymmetries. To have a better understanding of the proposed method, we develop a model in which the RTWO is described as injection locked multiple SWOs. The proposed model reveals possible modes of oscillation, their stability, and provides better design insight. The prototype is fabricated in a 110 nm RF-CMOS process, demonstrating more than 10° phase control range at the vicinity of 3 GHz oscillation frequency.

Study of terahertz interferometric imaging using optical techniques

Principles of terahertz (THz) interferometric synthetic aperture imaging with heterodyne and optical techniques are presented. A THz interferometric experiment based on optical up-conversion is set up. The received THz signal is modulated into an optical carrier and transmitted in a fiber. To simulate phase differences between two THz receivers, the output of receiver is divided and a phase shifter is placed before electro-optical modulation (EOM). Interferometric spectra of these modulated optical signals are examined at different phase shifts. Otherwise, carrier suppression and phase error calibration are discussed for THz interferometric synthetic aperture imaging.

A Low-Jitter Polyphase-Filter-Based Frequency Multiplier With Phase Error Calibration

A new low-jitter polyphase-filter-based frequency multiplier incorporating a phase error calibration circuit to reduce the phase errors is presented. Designing with a multiplication ratio of eight, it has been fabricated in a 0.13-mum CMOS process. For input frequency of 25 MHz, the measured jitter is 2.46 ps (rms) and plusmn9.33 ps (pk-pk) at 200-MHz output frequency, while achievable maximum static phase error of the calibration circuit is 2.4 ps. The calibration leads to the normalized rms jitter of 0.049%.

Theoretical analyses of gain and phase error calibration with optimal implementation for linear equispaced array

In array signal processing, high-resolution direction-of-arrival (DOA) estimation algorithms are known to be sensitive to system errors. In practice, the system should be properly calibrated before DOA estimation. In this paper, a calibration method of gain and phase errors of linear equispaced arrays (LEAs) is considered. A class of simplified calibration algorithms based on different diagonal lines of the covariance matrix is proposed. The statistical performance analyses of the calibration algorithms due to finite data perturbations are presented. Expressions for average bias (Abias) and square root of average variance (SRAV) of the calibration algorithms are derived using first-order approximation. These statistical and computer simulation results reveal and explain why the more diagonal lines that are used for gain and phase error estimations, the more inferior performance that may be obtained. Based on this conclusion, the simple and optimal gain and phase error calibration algorithms for such model are obtained.