Noise Amplification Factor Research Articles

BDS-3 full-frequency precise point positioning: models and performance comparison

With the BDS-3 six-frequency integration, there are more choices to implement the precise point positioning (PPP) technology. To take full advantage of the multi-frequency combination, six typical BDS-3 six-frequency PPP models using uncombined observation (UC), five dual-frequency ionospheric-free (IF) combinations (IF2), four triple-frequency IF combinations (IF3), three four-frequency IF combinations (IF4), two five-frequency IF combinations (IF5), and a single six-frequency IF combination (IF6) were constructed and compared. The results indicate that the positioning accuracies of the six models are similar. The static positioning accuracies reach 4, 3–5, and 12–14 mm in the east, north, and up directions, respectively, while the kinematic positioning accuracies are 24–26, 16–17, and 42–43 mm, respectively. Regarding the convergence times, the UC model is slightly worse than the five IF combined models, except for some cases in the up direction. In the static mode, benefiting from the smallest noise amplification factor, the average convergence times of the IF6 model are the shortest, reaching 12.1, 5.5, and 13.4 min in the three directions, respectively, and are 7%, 15%, and 6% shorter than those of the UC model. In the kinematic mode, with the combination of more signals into a single IF combination, the noise level of the IF combined observables gradually decreases, but the convergence times gradually increase. The kinematic average convergence times of the IF2 model are 15.3, 3.6, and 18.0 min in the three directions, which are 6%, 22%, and 10% and 1%, 16%, and 20% shorter than those of the UC and IF6 models, respectively. In addition, the observation residuals, and the estimates of inter-frequency bias, tropospheric zenith wet delay, and receiver clock offsets from different models were compared and analyzed. The specific selection of the model should be based on actual situations.

Generalized echo squeezing protocol with near-Heisenberg-limit sensitivity and strong robustness against detection noise and variation in squeezing parameter

We present a generalized echo squeezing protocol (GESP) as a generalization of the Schr\"odinger cat state protocol (SCSP) with the value of the squeezing parameter being an arbitrary number rather than pi/2. We show analytically that over a broad range of the squeezing parameter the sensitivity reaches the Heisenberg limit (HL) within a factor of root-2. For a large number of particles, N, this plateau interval is almost the whole range from zero to pi/2, and the sensitivity is independent of the parity of N. Therefore, it is possible to operate a sensor over a wide interval of the squeezing parameter without changing the sensitivity. This is to be contrasted with the conventional echo squeezing protocol (CESP) which only works for a very small interval. In contrast to the CESP, the sensitivity of the GESP is close to the quantum Cram\'er-Rao bound over the whole range of the squeezing parameter. The enhancement in sensitivity for the GESP is due to a combination of two parameters: the phase magnification factor (PMF) and the noise amplification factor (NAF). As the value of the squeezing parameter increases, both PMF and NAF increase, keeping the ratio of PMF/NAF constant, yielding an enhancement of sensitivity at the HL within a factor of root-2. Thus, the robustness of the GESP against excess noise easily exceeds that of the CESP for a broad range of values of the squeezing parameter. As such, in the context of an experimental study, it should be possible to achieve a net enhancement in sensitivity higher than that for the CESP, under typical conditions where the excess noise exceeds the unsqueezed quantum projection noise. Finally, we consider the fragility of the GESP against collisions with background particles, and show how a balance between the fragility and the robustness against excess noise would in practice determine the optimal choice of parameters for the GESP.

Benefits of BDS-3 B1C/B1I/B2a triple-frequency signals on precise positioning and ambiguity resolution

BDS-3 currently has 28 operational satellites in orbit, of which 27 IGSO/MEO satellites provide open services on five frequencies simultaneously. In particular, the linear combinations of the BDS-3 B1C/B1I/B2a signals have significant benefits in reducing the influence of ionospheric delay error as well as improving ambiguity estimation and positioning accuracy. The presented optimal ionosphere-free combination (242, 218, − 345) and ionosphere-reduced combination (2, 2, − 3) can improve the measurement accuracy by about 20% compared to the BDS-3 B1C/B2a or GPS L1/L5 dual-frequency combination. The ionosphere-reduced combination (2, 2, − 3) with a wavelength of 10.9 cm is almost immune to the ionospheric delay error and has a smaller noise amplification factor compared to the existing dual-frequency combinations. Therefore, its combined ambiguities can be fixed directly even in the case of a long baseline, which can simplify the traditional precise positioning process based on the ionosphere-free combination. The numerical results of BDS-3 real data show that the triple-frequency ionosphere-free or ionosphere-reduced combinations can improve the single-point positioning accuracy by 16–20% and the phase differential positioning accuracy by 7–9%, respectively. The ambiguity resolution of the ionosphere-reduced combination (2, 2, − 3) is achieved with a fixing rate of 88.4% over long baseline up to 1600 km. The presented ionosphere-free and ionosphere-reduced combinations are also very promising to be applied in current PPP applications to simplify the ambiguity fixing process as well as improve positioning accuracy and shorten convergence time.

Stochastic resonance in multi-stable system driven by Lévy noise

In this paper, the stochastic resonance (SR) of a multi-stable system driven by Lévy noise is investigated by the mean signal-to-noise ratio gain (SNR-GM). The characteristics for resonant output of multi-stable system, governed by the system parameters (a and c), the noise amplification factor D of Lévy noise are investigated under different values of stability index α and asymmetry parameter β of Lévy noise. The results reveal that the parameter α is closer to 1, the amplitude of SNR-GM versus system parameter a (or c) is larger. The interval of SR presents a trend that the curve of SNR-GM shifts to the right with the increase of α especially when α > 1. In addition, the SNR-GM for different values of system parameter a (or c) exhibits a tendency to move to the left with the increase of system parameter c (or a). Finally, the simulation results prove that the proposed multi-stable model has better advantage than bistable system and monostable system in signal enhancement and SNR-GM performance.

ОБОСНОВАНИЕ ОПТИМАЛЬНОСТИ ОПЕРАЦИИ ДЕЛЕНИЯ ОЦЕНОК ШУМОВЫХ ТЕМПЕРАТУР НА СМЕЖНЫХ ИНТЕРВАЛАХ НАБЛЮДЕНИЯ В РАДИОМЕТРЕ С НЕСТАБИЛЬНЫМ КОЭФФИЦИЕНТОМ УСИЛЕНИЯ

В статье обоснована оптимальность операции деления оценок шумовых температур на смежных интервалах наблюдения в радиометре с нестабильным коэффициентом усиления. Задача раздельной оптимизации статистических оценок шумовых температур случайных процессов, наблюдаемых на двух смежных интервалах времени равной длительности при открытом и закрытом входе модуляционного радиометра с нестабильным коэффициентом усиления, решена методом максимального правдоподобия. Показано, что одной из существенных операций синтезированного алгоритма первичной обработки сигналов является операция деления оценок их средних мощностей, измеренных на соседних временных интервалах. Выведены аналитические выражения для предельных погрешностей оценок шумовой температуры исследуемого источника и нестабильности коэффициента усиления. Эти погрешности зависят от времени наблюдения, ширины полосы рабочих частот по входу, отношения сигнал/шум и нестабильности коэффициента усиления. Полученный алгоритм обработки сигналов целесообразно реализовывать в радиометрах, в состав додетекторных трактов которых входят недорогие низкостабильные усилители.

Performance Analysis of Optimal Combinations for Triple-Frequency BDS

A theoretical and experimental investigation on the BeiDou Navigation Satellite System triple-frequency combination theory is presented. The optimal combination strategies under different application circumstances are given in consideration of the combination wavelength, noise, and ionosphere amplification factor as the main criteria. On this basis, the performance of BeiDou Navigation Satellite System triple-frequency optimal combinations, in regard to ambiguity resolution and relative positioning accuracy, is verified by four static tests with baseline lengths of 4.8, 12.4, 20, and 36.8 km, respectively. Finally, a few suggestions about the optimal phase combinations used in relative navigation applications are given.

An Inter-Group Swapping Based Resource Scheduling Scheme for Quasi-Single Frequency Multi-beam Mobile Satellite System

A resource scheduling scheme is proposed in this paper for multi-beam satellite system to eliminate downlink interference as well as to overcome the noise amplification problem caused by Tomlinson-Hiroshima preceding. Firstly, to analyze the noise amplification problem, Tomlinson-Hiroshima preceding (THP) is discussed. Secondly, an inter-group swapping based resource scheduling scheme is proposed to according to the principle of minimizing the maximum noise amplification factor of the same frequency users. Finally, simulations are executed to validate the proposed scheme, which suggest that compared to no-swapping scheme, the proposed scheme can successfully reduce the ratio of low SINR users and improve the minimum signal to interference and noise ratio(SINR).

E.429 - Quality assurance of phased array coils: Analysis of the noise amplification factor distribution

E.429 - Quality assurance of phased array coils: Analysis of the noise amplification factor distribution

BDS triple-frequency carrier-phase linear combination models and their characteristics

An investigation has been made on the models and characteristics of triple-frequency carrier-phase linear combinations for the BeiDou Navigation Satellite System (BDS). Based on the three frequencies of the BDS, three categories of combinations are developed: ionosphere-free combinations (i.e., those that eliminate the ionospheric effect), minimum-noise combinations (those that mitigate the effects of thermal noise and multiple paths), and troposphere-free combinations (those that mitigate tropospheric effects). Both the ionosphere-free and troposphere-free combinations can be expressed as planes, whereas the minimum-noise combinations can be expressed as a line. The relationships between these three categories of linear combinations are investigated from the perspective of geometry. The angle between the troposphere-free plane and ionosphere-free plane is small, while the angles between the troposphere-free plane and the minimum-noise line, and between the ionosphere-free plane and the minimum-noise line, are large. Specifically, the troposphere-free plane is orthogonal to the minimum- noise line. By introducing the concepts of lane number and integer ionosphere number, the characteristics of the long-wavelength integer combinations and ionosphere-free integer combinations are investigated. The analysis indicates that the longest wavelength that can be formed for integer combinations is 146.53 m, and the ionosphere-free integer combinations all have large noise amplification factors. The ionosphere-free integer combination with minimum noise amplification factor is (0, 62, 59). According to the lane number, integer ionosphere number, and noise amplification factor, optimal integer combinations with different characteristics are presented. For general short baselines and long baselines, three independent integer combinations are suggested.

Precise Point Positioning using Triple-Frequency GPS Measurements

Precise Point Positioning (PPP) performance is improving under the ongoing Global Positioning System (GPS) modernisation program. The availability of the third frequency, L5, enables triple-frequency combinations. However, to utilise the modernised L5 signal along with the existing GPS signals, P1-C5 differential code bias must be determined. In this paper, the global network of Multi-Global Navigation Satellite System Experiment (MGEX) stations was used to estimate P1-C5 satellites differential code biases $(DCB_{P1 - C5}^S )$. Mathematical background for triple-frequency linear combinations was provided along with the resultant noise and ionosphere amplification factors. Nine triple-frequency linear combinations were chosen, based on different criteria, for processing the modernised L5 signal along with the legacy GPS signals. Finally, test results using real GPS data from ten MGEX stations were provided showing the benefits of the availability of the third frequency on PPP solution convergence time and the precision of the estimated parameters. It was shown that triple-frequency combinations could improve the PPP convergence time and the precision of the estimated parameters by about 10%. These results are considered promising for using the modernised GPS signals for precise positioning applications especially when the fully modernised GPS constellation is available.

Optimal sampling for “Noquist” reduced-data cine magnetic resonance imaging

To analyze and optimize the signal-to-noise ratio (SNR) for the "Noquist" method for acceleration of cine magnetic resonance imaging in the presence of partially static field of view, designing practical methods for selection of optimal or near-optimal sample sets to allow reliable application of the method for variable image dimensions. To investigate the impact of the Noquist method and its experimental parameters on the SNR in the image reconstructed from reduced data, and to explore optimization of methods for highest SNR stability, three different optimization parameters have been selected: the condition of the forward matrix (R(cond)) as it defines the propagation of noise into the reconstructed image, and the maximum (Φ(maxD)) and the mean (Φ(meanD)) linear noise amplification factor of the dynamic field-of-view (FOV) region. As SNR in a Noquist reconstruction is often not uniform across the FOV and since dynamic regions may contain the part of the image more clinically relevant, primarily these noise levels are targeted for optimization. Using these three optimization parameters, three experiments were conducted: characterization of Noquist SNR properties as a function of important image size parameters; for sufficiently small image dimensions, employment of exhaustive search using lexicographical algorithms to visit all possibilities under the cine imaging constraint that equal numbers of views are acquired at each time point of the sequence; and, departing from an hypothetically optimal pattern, generation and evaluation of SNR characteristics of a series of random variations to that optimal pattern. The impact of favorable sparse data selection is illustrated, and SNR properties are characterized as a function of relevant acquisition parameters. Optimal data selection is investigated by exhaustive methods for small image sizes, and compared with algorithmic selection patterns. Observations from these experiments are confirmed by further studies on data selection for realistic image dimensions and an optimal selection algorithm is proposed. Sixty-four cases of small image sizes were analyzed through exhaustive search with a total of 527 984 141 matrix inversions called in the process, evaluating several SNR parameters for each case. An algorithm, named "Stairwell," that permits to design image dimensions with optimal SNR characteristics is presented, evaluated and compared with cases analyzed through exhaustive search. In 71.9% of the cases exhaustively studied, the Stairwell algorithm yielded optimal solutions. For no case did the deviation from optimum exceed 3.2% (R(cond)), 1.0% (Φ(meanD)), and 4.9% (Φ(maxD)). We have demonstrated SNR-optimality of the "Stairwell" selection algorithm for small image dimensions, and performed additional experiments which all support hypothesized optimality of the algorithm for any image dimensions that satisfy certain symmetry constraints for Noquist reduced-data cine MR imaging. Furthermore, we have presented overall SNR characteristics associated with use of the Noquist method by this algorithm for practical clinical image dimensions. Additionally, observations from our optimization experiments allow us to formulate recommendations for dimensioning Noquist image acquisition parameters which guarantee stable inversion. Moreover, these results allow prediction of the anticipated SNR properties of the reconstruction for given image dimensions (S,D,T), relative to SNR in a conventional full-grid acquisition.

A new unequal-weighted triple-frequency first order ionosphere correction algorithm and its application in COMPASS

As the introduction of triple-frequency signals in GNSS, the multi-frequency ionosphere correction technology has been fast developing. References indicate that the triple-frequency second order ionosphere correction is worse than the dual-frequency first order ionosphere correction because of the larger noise amplification factor. On the assumption that the variances of three frequency pseudoranges were equal, other references presented the triple-frequency first order ionosphere correction, which proved worse or better than the dual-frequency first order correction in different situations. In practice, the PN code rate, carrier-to-noise ratio, parameters of DLL and multipath effect of each frequency are not the same, so three frequency pseudorange variances are unequal. Under this consideration, a new unequal-weighted triple-frequency first order ionosphere correction algorithm, which minimizes the variance of the pseudorange ionosphere-free combination, is proposed in this paper. It is found that conventional dual-frequency first-order correction algorithms and the equal-weighted triple-frequency first order correction algorithm are special cases of the new algorithm. A new pseudorange variance estimation method based on the three carrier combination is also introduced. Theoretical analysis shows that the new algorithm is optimal. The experiment with COMPASS G3 satellite observations demonstrates that the ionosphere-free pseudorange combination variance of the new algorithm is smaller than traditional multi-frequency correction algorithms.

SENSE Performance of RF Coil Array at Ultra-High Fields

The geometrical noise amplification factor (g-factor) of an eight-channel receive-only coil array was studied for brain imaging at various field strengths. At 1.5, 3.0 and 7.0 Tesla, both experimental and simulation results were obtained and compared for verification purposes. Numerical simulations were further performed at 11.7, 14.0 and 21.0 Tesla. It was found that the most significant parallel imaging performance gain was achieved at an acceleration rate 4 and when the field strength is above 3.0 Tesla. However, the performance of parallel imaging plateaus above 11.7 Tesla plateaus due to highly correlated coil profiles.

Giant subthreshold amplification in synchronously pumped optical parametric oscillators

Synchronously pumped parametric oscillators have been shown to have subthreshold giant amplification of such a magnitude that a macroscopic, entirely noise-driven, signal is present at output even when the device is below threshold. In this paper we quantify the magnitude of the amplification factor in terms of some key device parameters. We use non-normal operator theory to find the noise amplification factor (Kreiss constant) and show that the signal amplitude is proportional to it. We also determine that the noise sensitivity depends in a nontrivial way on the group velocity of the three fields.

ERA-40-aided assessment of the atmospheric influence on satellite retrieval of Adriatic Sea surface temperature

The aim of this work is assessment of regional atmospheric influence on satellite derivation of Adriatic Sea surface temperature (SST). To this end the European Centre for Medium-Range Weather Forecast (ECMWF) ERA-40 reanalysis dataset has been employed to provide the temperature and humidity profiles and surface data, while the RTTOV 8.7 radiative transfer model was used to calculate the top-of-atmosphere brightness temperatures for the advanced very high-resolution radiometer (AVHRR) channels. Ten ERA-40 grid points over the Adriatic Sea were used in the analysis, providing 29,590, 00 UTC and 12 UTC, clear-sky profiles. Climatological analysis of the ERA-40 profiles demonstrated distinct seasonal variability over the Adriatic Sea. Seasonality noted in the temperature and specific humidity profiles also evinced in the atmospheric transmittance, thermal channels temperature deficit, and derived γ and ρ parameters. A multivariate analysis was applied to relate the simulated top-of-atmosphere brightness temperatures to the Adriatic SSTs in order to generate exploratory sets of SST retrieval coefficients. All derived coefficient sets exhibited smaller noise amplification factor than the global counterpart. A test comparison of satellite-derived SST with an 11-month in situ SST series showed than locally derived coefficients provide smaller scatter (improved precision), and skin-centred bias that requires additional adjustment. Almost identical SST residual and error metric was obtained with seasonally adjusted classical split-window coefficients and with coefficients explicitly accommodating water-vapor dependence. Comparison with data reinforces the notion that the atmosphere over the Adriatic may exhibit variability that cannot be fully accommodated by globally adjusted correction.

Water–fat separation with bipolar multiecho sequences

Multiecho sequences provide an efficient means to acquire multiple echoes in a single repetition, which has found applications in spectroscopy, relaxometry, and water-fat separation. By replacing the fly-back gradients in unipolar multiecho sequences with alternating readout gradients, bipolar multiecho sequences greatly reduce both echo-spacing and repetition interval. This offers many attractive advantages, such as shorter scan times, higher SNR efficiency, more robust field map estimation, reduced motion-induced artifacts, and less sensitivity to short T(2)*. However, the alternating readout gradients cause several technical problems, including delay effects and image misregistrations, which prevent direct application of existing water-fat separation methods. This work presents solutions to address these problems, including a post-processing method that shifts k-space data to correct k-space echo misalignment, an image warping method that utilizes a low-resolution field map to remove field-inhomogeneity-induced misregistration, and a k-space water-fat separation method that eliminates chemical-shift-induced artifacts in separated water and fat images. In addition, a noise amplification factor, which characterizes the noise present in separated images, is proposed to serve as a useful guideline for choosing imaging parameters or regularization parameters in the case of ill-conditioned separation. The proposed methods are validated both in phantoms and in vivo to enable reliable and SNR efficient water-fat separation with bipolar multiecho sequences.

A systematic investigation of optimal carrier-phase combinations for modernized triple-frequency GPS

The upcoming modernization of the GPS signals will allow for measurements on an additional third frequency L5 located at 1176.45 MHz. To take advantage of carrier-phase measurements on this new signal, the strategies for integer ambiguity resolution, required for centimeter-level accuracy, may need to be revised. The Least-squares Ambiguity Decorrelation Adjustment method remains perhaps the most powerful tool for finding the best combinations based on a complete decorrelation of the variance–covariance matrix related to the ambiguities. However, the computational load of that method plus the opportunity to comprehensively study the interaction of multiple frequencies suggest a reconsideration of approaches using predefined combinations between frequencies is not out of place. In this paper a systematic investigation is made of all possible triple-frequency geometry-free carrier-phase combinations which retain the integer nature of the ambiguities. The concept of the lane-number is presented to unambiguously describe the wavelength of a particular combination. The propagation of the observation noise and of the ionospheric bias on these combinations is presented. These noise and ionospheric amplification factors are analysed with respect to the resulting wavelength, in an effort to highlight optimal combinations characterized by a long wavelength, low noise and limited ionospheric impact.

Measuring the effect of field strength on noise amplification factor

AbstractAs shown previously, parallel imaging techniques should benefit significantly from higher field strengths due to a reduction in noise amplification (g) factor. The intent of this study was to measure directly the role of field strength in this reduction, comparing the measured g factors for two commercial eight‐channel head array coils of similar mechanical design at 3T and 7T using low and high permittivity phantoms. The results indicated that the lower g factors result primarily from the RF standing wave pattern and the greater spatial complexity of the coil sensitivities in high permittivity materials at high frequency, although the physical design of the array elements plays an important role in controlling the growth of noise amplification. A simplified method of g factor measurement for an array coil is also presented. © 2007 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 31B: 51–59, 2007

Optimal discrimination and classification of THz spectra in the wavelet domain

In rapid scan Fourier transform spectrometry, we show that the noise in the wavelet coefficients resulting from the filter bank decomposition of the complex insertion loss function is linearly related to the noise power in the sample interferogram by a noise amplification factor. By maximizing an objective function composed of the power of the wavelet coefficients divided by the noise amplification factor, optimal feature extraction in the wavelet domain is performed. The performance of a classifier based on the output of a filter bank is shown to be considerably better than that of an Euclidean distance classifier in the original spectral domain. An optimization procedure results in a further improvement of the wavelet classifier. The procedure is suitable for enhancing the contrast or classifying spectra acquired by either continuous wave or THz transient spectrometers as well as for increasing the dynamic range of THz imaging systems.

Noise amplification during supercontinuum generation in microstructure fiber.

Supercontinua generated by femtosecond pulses launched in microstructure fiber can exhibit significant low-frequency (<1-MHz) amplitude noise on the output pulse train. We show that this low-frequency noise is an amplified version of the amplitude noise that is already present on the input laser pulse train. Through both experimental measurements and numerical simulations, we quantify the noise amplification factor and its dependence on the supercontinuum wavelength and on the energy and duration of the input pulse. Interestingly, the dependence differs significantly from that of the broadband white-noise component, which arises from amplification of the input laser shot noise.