Method for array gain and phase uncertainties calibration based on ISM and ESPRIT

A new method for array calibration of array gain and phase uncertainties, which severely degrade the performance of spatial spectrum estimation, is presented. The method is based on the idea of the instrumental sensors method （ISM）, two well-calibrated sensors are added into the original array. By applying the principle of estimation of signal parameters via rotational invariance techniques （ESPRIT）, the direction-of-arrivals （DOAs） and uncertainties can be estimated simultaneously through eigen-decomposition. Compared with the conventional ones, this new method has less computational complexity while has higher estimation precision, what＇s more, it can overcome the problem of ambiguity. Both theoretical analysis and computer simulations show the effectiveness of the proposed method.

Study on fast calibration of a ULA's gain and phase error

Array calibration is important in engineering practice. In this paper, fast calibration methods for a ULA's gain and phase errors both in far and near fields are proposed. In the far field, using a single sound source without exact orientation, this method horizontally rotates the array exactly once, performs eigen value decomposition for the covariance matrix of received data, then computes the gain and phase error according to the formulas. In the near field, using the same single sound source, it is necessary to rotate the array horizontally at most three times, build equations according to geometric relations, then solve them. Using the formula proposed in this paper, spherical waves are modified into plane waves. Then eigen values decomposition is performed. These two calibration methods were shown to be valid by simulation and are fast, accurate and easy to use. Finally, an analysis of factors influencing estimation precision is given.

Sensor array calibration for uniform rectangular array in presence of mutual coupling and sensor gain-and-phase errors

The sensor array calibration methods tailored to uniform rectangular array(URA)in the presence of mutual coupling and sensor gain-and-phase errors were addressed.First,the mutual coupling model of the URA was studied,and then a set of steering vectors corresponding to distinct locations were numerically computed with the help of several time-disjoint auxiliary sources with known directions.Then,the optimization modeling with respect to the array error matrix(defined by the product of mutual coupling matrix and sensor gain-and-phase errors matrix)was constructed.Two preferable algorithms(called algorithm I and algorithm II)were developed to minimize the cost function.In algorithm I,the array error matrix was regarded as a whole parameter to be estimated,and the exact solution was available.Compared to some existing algorithms with the similar computation framework,algorithm I can make full use of the potentially linear characteristics of URA's error matrix,thus,the calibration precision was obviously enhanced.In algorithm II,the array error matrix was decomposed into two matrix parameters to be optimized.Compared to algorithm I,it can further decrease the number of unknowns and,thereby,yield better estimation accuracy.However,algorithm II was incapable of producing the closed-form solution and the iteration operation was unavoidable.Simulation results validate the excellent performances of the two novel algorithms compared to some existing calibration algorithms.

An Improved Calibration Method of Grating Projection Measurement System

In the traditional fringe projection profilometry system,the projector and the camera light center are both spatially virtual points.The spatial position relationships specified in the model are not easy to obtain,leading to inaccurate system parameters and affectingmeasurement accuracy.This paper proposes a method for solving the system parameters of the fringe projection profilometry system,and the spatial position of the camera and projector can be adjusted in accordance with the obtained calibration parameters.The steps are as follows:First,in accordance with the conversion relationship of the coordinate system in the calibration process,the calculation formula of the vertical distance from the camera light center to the reference plane and the calculation formula of the distance between the projector and the camera light center are given respectively.Secondly,according to the projector calibration principle,the position of the projector light axis perpendicular to the reference plane is gained by comparing the parallel relationship between the reference plane coordinate system and the projector coordinate system’s Z-axis.Then,in order to fulfill the position restriction that the line between the projector light center and the camera light center must be parallel to the reference plane,the camera’s spatial location is adjusted so that the vertical distance between it and the reference plane tends to that between the projector light center and the reference plane.And finally,the three-dimensional(3D)reconstruction of the target object can be finished using the phase height model’s system parameters once the aforementioned position limitations are put into practice.Experimental results demonstrate that the method improves the measurement accuracy,and verifies that it is effective and available in 3D shape measurement.

Calibration method for electrode gains in an axially symmetric stripline BPM

The four electrodes in the stripline beam position monitor(BPM) for Hefei Light Source(HLS II) storage ring are of axially symmetric type. We have derived a new calibration method of electrode gains for this type stripline BPM. The gain fit error of different data grids was analyzed, and the ±5 mm by ±5 mm grid is the best.The electrode gains of two stripline BPMs(HLS II SR-BD-STLB1 and HLS II SR-BD-STLB2) were obtained based on offline calibrated data. The results show that data after fitting gains are improved, with the electrode gains being between 0.94 and 1.15.

A Precise Calibration Method on Phase Center of Uplink Antenna Array Considering Its Actual Pointing

With regard to the inferior techniques and low accuracy of phase center calibration of an antenna array, this paper proposes a new calibration method considering the actual antenna pointing by introducing a precise engineering surveying technique to measure the real state of antennas. First, an industrial photogrammetric system is utilized to obtain the coordinates of points on antenna panels in different postures, and the actual pointing of the mechanical axis is obtained via least-squares fitting. Then, based on this, the coordinates of antenna rotation center are obtained by seeking the intersection of mechanical axes via using the matrix method. Finally, the mechanical axis in arbitrary postures is estimated based on the inverse-angle weighting interpolation method, and the reliable phase center is obtained by moving a fixed length from the projective center along the mechanical axis. An uplink antenna array including three ? 3 m antennas is taken as experimental object, and all photogrammetric coordinate systems are unified by the engineering control network, with each antenna phase center precisely calibrated via the proposed method. The results of electrical signal synthesis indicate that this method can effectively overcome the influence of gravity deformation and mechanical installation error, and enhance the synthetic signal magnitude of the uplink antenna array.

Impact of Phase Noise on TDMS Based Calibration for Spaceborne Multi-Beam Antennas

For spaceborne multi-beam antennas(MBAs), time division multiplexed switching(TDMS) based calibration receiver can reduce implementation costs effectively and is very suitable for large-scale applications. However, in practice, random phase noise imposed by noisy local oscillators can cause significant performance degradation in TDMS-based calibration systems. Characterization of phase noise effects is therefore crucial for practical applications. In this paper, we analyze the impact of phase noise on the calibration performance for a MBA system. Specifically, we derive the relationship between the probability of correct amplitude/phase estimation and various practical factors involving the signal-to-noise ratio(SNR), the standard deviation of phase noise, the given tolerance region, and the length of the spreading code. The results provide high efficiency for evaluating the calibration performance of the MBAs based on TDMS, especially for precisely anticipating the impact of phase noise. Finally, the accuracy of the derived results is assessed by simulations in different scenarios.

Experimental demonstration of a fast calibration method for integrated photonic circuits with cascaded phase shifters

With the development of research on integrated photonic quantum information processing,the integration level of the integrated quantum photonic circuits has been increasing continuously,which makes the calibration of the phase shifters on the chip increasingly difficult.For the calibration of multiple cascaded phase shifters that is not easy to be decoupled,the resources consumed by conventional brute force methods increase exponentially with the number of phase shifters,making it impossible to calibrate a relatively large number of cascaded phase shifters.In this work,we experimentally validate an efficient method for calibrating cascaded phase shifters that achieves an exponential increase in calibration efficiency compared to the conventional method,thus solving the calibration problem for multiple cascaded phase shifters.Specifically,we experimentally calibrate an integrated quantum photonic circuit with nine cascaded phase shifters and achieve a high-precision calibration with an average fidelity of 99.26%.

Novel cued search strategy based on information gain for phased array radar

A search strategy based on the maximal information gain principle is presented for the cued search of phased array radars. First, the method for the determination of the cued search region, arrangement of beam positions, and the calculation of the prior probability distribution of each beam position is discussed. And then, two search algorithms based on information gain are proposed using Shannon entropy and Kullback-Leibler entropy, respectively. With the proposed strategy, the information gain of each beam position is predicted before the radar detection, and the observation is made in the beam position with the maximal information gain. Compared with the conventional method of sequential search and confirm search, simulation results show that the proposed search strategy can distinctly improve the search performance and save radar time resources with the same given detection probability.

Phase-dependent inversionless gain in a four-level atomic system with a closed interaction loop

A four-level atomic system with a closed interaction loop connected by two coherent driving fields and a microwave field is investigated. The results show that inversionless gain can be achieved on a higher frequency transition outside the closed interaction loop, and the gain behaviour can be modulated by the phase of the closed loop as well as the amplitude of the microwave field. The phase sensitivity property in such a scheme is similar to that in an analogous configuration with spontaneously generated coherence, but it is beyond the rigorous condition of near-degenerate levels with non-orthogonal dipole moments. Therefore this scheme is much more convenient in experimental realization.

2.7-4.0 GHz PLL with dual-mode auto frequency calibration for navigation system on chip

A 2.7-4.0 GHz dual-mode auto frequency calibration(AFC) fast locking PLL was designed for navigation system on chip(SoC). The SoC was composed of one radio frequency(RF) receiver, one baseband and several system control parts. In the proposed AFC block, both analog and digital modes were designed to complete the AFC process. In analog mode, the analog part sampled and detected the charge pump output tuning voltage, which would give the indicator to digital part to adjust the voltage control oscillator(VCO) capacitor bank. In digital mode, the digital part counted the phase lock loop(PLL) divided clock to judge whether VCO frequency was fast or slow. The analog and digital modes completed the auto frequency calibration function independently by internal switch. By designing a special switching algorithm, the switch of the digital and analog mode could be realized anytime during the lock and unlock detecting process for faster and more stable locking. This chip is fabricated in 0.13 μm RF complementary metal oxide semiconductor(CMOS) process, and the VCO supports the frequency range from 2.7 to 4.0 GHz. Tested 3.96 GHz frequency phase noise is -90 d Bc/Hz@100 k Hz frequency offset and -120 d Bc/Hz@1 MHz frequency offset. By using the analog mode in lock detection and digital mode in unlock detection, tested AFC time is less than 9 μs and the total PLL lock time is less than 19 μs. The SoC acquisition and tracking sensitivity are about-142 d Bm and-155 d Bm, respectively. The area of the proposed PLL is 0.35 mm^2 and the total SoC area is about 9.6 mm^2.

A pressure calibration method for a portable wide-access “panoramic” cell

A simple and convenient pressure calibration method is developed for a newly designed portable wide-access ＇panoramic＇ cell. This cell is adapted to angle-dispersive-mode high-pressure in situ neutron diffraction of reactor neutron sources. This pressure calibration method has established a relationship between the cell pressure and the anvil displace- ment （gasket compression） based on the fixed-point calibration technique. By employing TiZr gasket with a thickness of 3 mm and WC anvil with a culet of 4 mm diameter, the average anvil displacements are 1.31 mm and 2.22 mm for Bi phase transitions （2.55 GPa and 7.7 GPa）, and 1.85 mm for Ba phase transitions （5.5 GPa）, respectively. In this pressure range, the pressure increases quickly with decreasing gasket thickness, and undergoes a linear increase with the anvil displacement. By extrapolating the calibration curve, the cell pressure will achieve 10 GPa when the anvil displacement is around 2.5 ram.

TWO NEW TYPES OF MICROWAVE RADIOMETER: A COMPUTER GAIN COMPENSATIVE DESIGN AND A REAL-TIME CALIBRATED DESIGN

Long term stability is the main factor that influences the minimum detectable signal of microwave radiometers. Two new types of microwave radiometer were studied: a computer gain compensative microwave radiometer and a real-time calibrated microwave radiometer. The long term stability of both designs was optimal because they were insensitive to system gain fluctuations. The continuous calibrated microwave radiometer was also insensitive to system noise fluctuations. The minimum detectable signals were 0.13 and 0.19K respectively under an integration time of 0.6s.

the phase-dependent gain without inversion in a Doppler broadened open four-level system

It is shown that in a Doppler broadened open N-type four-level atomic system with spontaneously generated coherence （SGC）, the gain without inversion （GWI） is very sensitive to the variation of the relative phase between the probe field and the driving field; the atomic exit rate （R0） and the ratio （S） of the atomic injection rates have a considerable modulation effect on the phase-dependent GWI. GWI first increases and then decreases with R0 increasing; in a certain value range of S, GWI increases monotonically with S increasing; by adjusting the values of R0 and S, in an open system a much larger GWI can be obtained than in the corresponding closed system [2011 Phys. Rev. A 83 043805]. The modulation effects of R0 and S on the phase-dependent GWI in the case with the counter-propagating probe and driving fields are stronger than those in the co-propagating case, GWI in the co-propagating case is much larger than that in the counter-propagating case.

A FAST FOREGROUND DIGITAL CALIBRATION TECHNIQUE FOR PIPELINED ADC

Digital calibration techniques are widely developed to cancel the non-idealities of the pipelined Analog-to-Digital Converters (ADCs). This letter presents a fast foreground digital calibration technique based on the analysis of error sources which influence the resolution of pipelined ADCs. This method estimates the gain error of the ADC prototype quickly and calibrates the ADC simultaneously in the operation time. Finally, a 10 bit, 100 Ms/s pipelined ADC is implemented and calibrated. The simulation results show that the digital calibration technique has its efficiency with fewer operation cycles.

An in situ Digital Background Calibration Algorithm for Multi-Channel R-βR Ladder DACs

The R-2R resistor ladder is one of the best topologies for implementing compact-sized digital-to-analog converter(DAC)arrays in implantable neuro-stimulators.However,it has a limited resolution and considerable inter-channel variation due to component mismatches.To avoid losing analog information,we present sub-radix-2 DAC implemented by the R-βR resistor ladder in this paper.The digital successive approximation register(DSAR)algorithm corrects the transfer function of DACs based on their actual bit weights.Furthermore,a low-cost in situ adaptive bit-weight calibration(ABC)algorithm drives the analog output error between two DACs to zero by adjusting their bit weights automatically.The simulation results show that the proposed algorithm can calibrate the non-linear transfer function of each DAC and the gain error among multiple channels in the background.

Polynomial-Based Evaluation of the Impact of Aperture Phase Taper on the Gain of Rectangular Horns

The aperture phase taper due to quadratic phase errors in the principal planes of a rectangular horn imposes signifi-cant constraints on the on-axis far-field gain of the horn. The precise calculation of gain reduction involves Fresnel integrals;therefore, exact results are obtained only from numerical methods. However, in horns’ analysis and design, simple closed-form expressions are often required for the description of horn-gain. This paper provides a set of simple polynomial approximations that adequately describe the gain reduction factors of pyramidal and sectoral horns. The proposed formulas are derived using least-squares polynomial regression analysis and they are valid for a broad range of quadratic phase error values. Numerical results verify the accuracy of the derived expressions. Application examples and comparisons with methods in the literature demonstrate the efficacy of the approach.

Effect of stimulated Brillouin scattering on the gain saturation of distributed fiber Raman amplifier and its suppression by phase modulation

For distributed fiber Raman amplifiers（DFRAs）, stimulated Brillouin scattering（SBS） can deplete the pump once occurring and consequently generate gain saturation. On the basis of such a theory, theoretical gain saturation powers in DFRAs with various pump schemes are obtained by calculating SBS thresholds in them, and the experimental results show that they are in excellent agreement with the calculation results. The saturation power of the DFRA with a 300 m W forward pump is as low as 0 d Bm, which needs to be enhanced by phase modulation, and the effect is quantitatively studied. A simple model taking both modulation frequency and index into consideration is presented by introducing a correction factor to evaluate the effect of phase modulation on the enhancement of saturation power. Experimentally, it is shown that such a correction factor decreases as the modulation frequency increases and approaches zero when the modulation frequency becomes high enough. In particular, a phase modulation with a modulation frequency of 100 MHz and a modulation index of 1.380 can enhance the saturation power by 4.44 d B, and the correction factor is 0.25 d B, in which the modulation frequency is high enough. Additionally, the factor is 1.767 d B for the modulation frequency of 25 MHz. On this basis,phase modulations with various indexes and a fixed frequency of 25 MHz are adopted to verify the modified model, and the results are positive. To obtain the highest gain saturation power, the model is referable. The research results provide a guide for the design of practical DFRAs.

Calibration and Validation of the GR2M Hydrologic Model in the Kouilou-Niari Basin in Southwestern Congo-Brazzaville

The hydrologic simulation of a catchment area, described as the transformation of rainfall into runoff, generally uses hydrologic model. This work opts for the global conceptual hydrologic model GR2M, a monthly time step model, to study the Kouilou-Niari basin, the second most important ones of the Republic of Congo. This includes two parameters to model the hydrologic behavior of a catchment area. The choice of the conceptual model GR2M is justified by the reduced number of parameters and the monthly time scale. The objective of this study is to determine the characteristic parameters of the GR2M model, by a calibrating and a validating procedure. The use of these parameters enables to follow the evolution of the water resources from the climatic variables. It has been first carried out a characterization of some physical, geological and climatic factors governing the flow, by dealing with the main climatic variables which constitute the inputs of the hydrologic model. Then, a hydrologic rainfall-runoff modeling allows to calibrate and validate the model at monthly time scale. Taking into account the number of parameters involved in hydrologic processes and the complexity of the cathment area, this model gives acceptable results throughout the Kouilou-Niari basin. The values of the Nash-Sutcliffe criterion and those of the correlation coefficient obtained are greater than 80% in validation, which explains the performance and robustness of the GR2M model on this basin.

DOA estimation for mixed signals with gain-phase error array

Most of the direction of arrival(DOA) estimation methods often need the exact array manifold, but in actual applications,the gain and phase of the channels are usually inconsistent, which will cause the estimation invalid. A novel direction finding approach for mixed far-field and near-field signals with gain-phase error array is provided. Based on simplifying the space spectrum function by matrix transformation, DOA of far-field signals is obtained. Consequently, errors of the array are acquired according to the orthogonality of far-field signal subspace and noise subspace.Finally, DOA of near-field signals can be estimated. The method merely needs one-dimensional spectrum searching, so as to improve the computational efficiency on the premise of ensuring a certain accuracy, simulation results manifest the effectiveness of the method.