Signal Extraction Problem Research Articles

A Novel Full-Duplex Primary Signal Extraction Method Based on Polarization Vector Distance in Cognitive Radio Networks

In this paper, a polarization vector distance based signal extraction (PVD-SE) method for full-duplex primary users (FD-PUs) oriented cognitive radio networks (CRN) is studied. The problem of primary signal extraction in FD-PUs oriented CRN boils down to a finite hypotheses testing problem. Based on the orientation and magnitude difference of the signal samples from different FD-PUs, the proposed PVD-SE method can efficiently detect each PU’s signal space by calculating polarization vector distance (PVD) between any two samples. It is found that the samples from the same PU experience relatively smaller PVD in comparison with those from different FD-PUs. As a result of the Gaussian distributed noise, the resulting PVD is non-central chi-squared distributed, which depends on the modified Bessel function of the first kind without closed-form expressions. Using large argument (LA) and small argument closed-form approximations of modified Bessel functions, the optimal extraction threshold that minimizes the extraction error probability is investigated, and analytical expressions of optimal threshold under the LA assumption are derived for amplitude modulated and non-amplitude modulated primary signals. The presented analytical results are verified by Monte Carlo simulation and the performance of PVD-SE is validated.

Monetary Misperceptions: Optimal Monetary Policy Under Incomplete Information

Inflation targeting is strictly suboptimal when economic actors have incomplete information about the state of the economy. Nominal income targeting is approximately optimal, and exactly optimal under certain parameterizations. We derive this result in a “Lucas islands” monetary misperceptions model built from explicit microfoundations. Agents have knowledge of local productivity and money supply conditions, but must perform a signal extraction problem each period to estimate the aggregate productivity shock and the aggregate money supply shock. Without full information, agents cannot perfectly distinguish between relative price shocks and aggregate shocks, causing monetary policy to affect the real economy. Since the model is built from agents optimizing from first principles, we are able to take a second-order welfare approximation and ask what monetary policy rule is optimal. In contrast to sticky price or sticky information models, inflation and price level targeting are always suboptimal, as price level variation provides useful information to agents. Under log utility, nominal income targeting is optimal.

Numerical relativity and gravitational wave astronomy

The first direct detection of gravitational wave has been realized by LIGO 100 years after Einstein’s theoretical prediction. It opens a new window for human to observe our Universe and initiates the age of Gravitational Wave Astronomy. The data analysis of gravitational wave detection is a typically signal extraction problem and the matched filtering technique has shown to be an optimal method in extracting weak signal buried in strong Gaussian noises. Matched filtering requires the accurate gravitational waveforms. It is also essential for the parameter estimation of the gravitational wave source, with which the GW150914 was recognized as a binary of 29 and 36 solar masses black holes merging about 1.3 billion light years away. Nowadays, other laser interferometric gravitational wave detectors such as Virgo, KAGRA and the third LIGO in the India, IndIGO, are under construction. The space-borne detection projects including eLISA, Taiji and TianQin are also in progress. The pulsar timing approach with FAST, SKA and other radio telescope arrays to detect gravitational wave are also in the rapid development. It is foreseeable the gravitational wave astronomy in the wide frequency band from 10–10 to 1000 Hz will be realized in the near future. As such, the matched filtering plays an important role, and correspondingly the theoretical research of gravitational wave source models becomes urgent and important. For astrophysical realistic objects without symmetries in general, the analytical treatment of Einstein equation becomes nearly intractable. The numerical relativity then becomes an essential method and tool for solving the Einstein equation. We briefly introduce the state of art research of numerical relativity in the viewpoint of gravitational wave astronomy.

Dissecting Interbank Risk

This paper analyses interbank risk using the information content of basis swap (BS) spreads, floating-to-floating interest rate swaps whose payments are associated with euro deposit rates for alternative tenors. We propose an empirical model to decompose BS quotes into persistent and transitory components. To estimate both unobservable constituents of BS spreads, we solve a signal extraction problem using a particle filter. Our empirical findings show that changes in systemic risk are associated with regime shifts. Shocks to aggregate liquidity are also important for describing persistent changes in BS spreads. Sovereign risk and risk aversion are relevant factors explaining transitory fluctuations.

Differential signal extraction for continuous wave mud pulse telemetry

Continuous wave mud pulse telemetry system with a transmission rate of more than 12bps, is an irreplaceable high-speed data transmission technology for Measurement While Drilling (MWD) and Logging While Drilling (LWD) instruments used in modern oil drilling services. However, the valid signal is difficult to be obtained because of the disturbing of pump noise in the data transmission. Here, a differential signal extraction method for continuous wave mud pulse generator is applied to extract the effective mud pulse signal from pump noise. It utilizes dual sensor and a differential algorithm to extract the signal. To verify this method, the robustness was analyzed in the numerical simulation. In the actual test, a continuous wave mud pulse generator was designed, and a hydraulic circulation laboratory was built. The Signal to Noise Ratio (SNR) was risen from −13dB up to 25dB. The experimental results demonstrated the effectiveness of the designed mud pulse generator, and proved that this method can be a feasible way to solve the problem of signal extraction from pump noise.

Monetary policy regimes and the forward bias for foreign exchange

This paper provides a theoretical discussion of the forward premium anomaly. We reformulate the well-known Lucas (1982) model by allowing for the existence of monetary policy regimes. The monetary supply is viewed as having two stochastic components: (a) a persistent component that reflects the preferences of the central bank regarding the long-run money supply or inflation target, and (b) a transitory component that represents short-lived interventions. To generate agents’ forecasts, we consider two scenarios: (a) consumers can distinguish the permanent and the transitory components of the money supply (complete information), and (b) consumers face a signal-extraction problem to disentangle permanent and transitory components of the money supply (incomplete information). We simulate the model from a careful estimate of the parameters involved in the model. Numerical simulations reveal that, under complete information, forward unbiasedness cannot be rejected at conventionally significant levels. However, when learning about monetary policy is incorporated, the forward bias can be reproduced without artificially assuming an unreasonable degree of risk aversion.

Towards a New Keynesian Theory of the Price Level

Modifying the standard New-Keynesian model to replace firms’ full information and sticky prices with flexible prices and dispersed information, and imposing mild and plausible restrictions on the monetary authority’s decision rule, produces the striking results that (i) there exists a unique and globally stable steady-state rate of inflation, despite the possibility of a lower bound on nominal interest rates; and (ii) in the vicinity of steady-state, the price level is determinate (and not just the rate of inflation), despite the central bank targeting inflation. The specification of firms’ signal extraction problem under dispersed information removes the need to make use of Blanchard-Kahn conditions to solve the model, thereby removing the need to adhere to the Taylor principle and consequently circumventing the critique of Cochrane (2011). The model admits a determinate, stable solution with no role for sunspot shocks when the monetary authority responds by less than one-for-one to changes in expected inflation, including under an interest rate peg. An extension to include incomplete information on the part of the central bank permits the consideration of (rational) errors of judgement on the part of policymakers and provides a theoretical basis for inertial policymaking without interest rate smoothing, in support of Rudebusch (2002, 2006).

Towards a New Keynesian Theory of the Price Level

Modifying the standard New-Keynesian model to replace firms' full information and sticky prices with flexible prices and dispersed information, and imposing mild and plausible restrictions on the monetary authority's decision rule, produces the striking results that (i) there exists a unique and globally stable steady-state rate of inflation, despite the possibility of a lower bound on nominal interest rates; and (ii) in the vicinity of steady-state, the price level is determinate (and not just the rate of inflation), despite the central bank targeting inflation. The specification of firms' signal extraction problem under dispersed information removes the need to make use of Blanchard-Kahn conditions to solve the model,thereby removing the need to adhere to the Taylor principle and consequently circumventing the critique of Cochrane (2011). The model admits a determinate, stable solution with no role for sunspot shocks when the monetary authority responds by less than one-for-one to changes in expected inflation,including under an interest rate peg. An extension to include incomplete information on the part of the central bank permits the consideration of (rational) errors of judgement on the part of policymakers and provides a theoretical basis for inertial policymaking without interest rate smoothing, in support of Rudebusch (2002, 2006.

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These simplifying assumptions, or variants of them, are familiar in the literature, but they are not enough for the purposes of this paper. Instead, Hassan and Mertens also reverse engineer the demand of the noise traders in such a way that they can guarantee that the information-aggregation and the signal-extraction problems in that market remain Gaussian, and highly manageable, despite the accommodation of rich preferences and rich dynamics in consumption and wealth.

Signal extraction for GPS deformation monitoring in mining survey

The basic signal model of deformation monitoring with GPS was introduced and the main problems of GPS deformation monitoring in mining area were discussed. For the problem of noise signal extraction in GPS deformation monitoring, the Kalman-EMD method was proposed to obtain the effective deformation signal. The reliability and effectiveness of the methodology were tested and verified by analog signal. The results of experiment in Mongolia show that the accuracy of the proposed GPS deformation monitoring model is equivalent to that of level method.

An improved filter-u least mean square vibration control algorithm for aircraft framework.

Active vibration control of aerospace vehicle structures is very a hot spot and in which filter-u least mean square (FULMS) algorithm is one of the key methods. But for practical reasons and technical limitations, vibration reference signal extraction is always a difficult problem for FULMS algorithm. To solve the vibration reference signal extraction problem, an improved FULMS vibration control algorithm is proposed in this paper. Reference signal is constructed based on the controller structure and the data in the algorithm process, using a vibration response residual signal extracted directly from the vibration structure. To test the proposed algorithm, an aircraft frame model is built and an experimental platform is constructed. The simulation and experimental results show that the proposed algorithm is more practical with a good vibration suppression performance.

Minimum Mutual Information-Based Linearly Constrained Broadband Signal Extraction

In this contribution, the problem of broadband acoustic signal extraction is treated as a specific source separation problem, where the desired signal components are to be separated from all remaining undesired components. For this, we exploit the generic TRIple-N Independent component analysis for CONvolutive mixtures (TRINICON) framework. The TRINICON optimization criterion is complemented with linear constraints leading to the Linearly Constrained Minimum Mutual Information (LCMMI) criterion for desired signal extraction. A general linearly constrained update rule for iterative filter optimization is derived, which can efficiently be realized in a novel Minimum Mutual Information (MMI)-Generalized Sidelobe Canceler (GSC). The general treatment of the signal extraction problem using an MMI criterion provides several advantages: Firstly, new insights into the signal extraction problem can be derived by establishing links to both the original GSC and the Multichannel Wiener Filter (MWF). Secondly, by exploiting fundamental properties characteristic for speech and audio signals, complicated and often unreliable Voice Activity Detection (VAD)-based control mechanisms become unnecessary. Thirdly, the overall realization requires only prior information of the desired source position. An evaluation of the MMI-GSC for the double-talk situation with two concurrently active speech sources under reverberant and noisy conditions demonstrates the effectiveness of this novel approach.

Analytical tools for single-molecule fluorescence imaging in cellulo

Recent technological advances in cutting-edge ultrasensitive fluorescence microscopy have allowed single-molecule imaging experiments in living cells across all three domains of life to become commonplace. Single-molecule live-cell data is typically obtained in a low signal-to-noise ratio (SNR) regime sometimes only marginally in excess of 1, in which a combination of detector shot noise, sub-optimal probe photophysics, native cell autofluorescence and intrinsically underlying stochasticity of molecules result in highly noisy datasets for which underlying true molecular behaviour is non-trivial to discern. The ability to elucidate real molecular phenomena is essential in relating experimental single-molecule observations to both the biological system under study as well as offering insight into the fine details of the physical and chemical environments of the living cell. To confront this problem of faithful signal extraction and analysis in a noise-dominated regime, the 'needle in a haystack' challenge, such experiments benefit enormously from a suite of objective, automated, high-throughput analysis tools that can home in on the underlying 'molecular signature' and generate meaningful statistics across a large population of individual cells and molecules. Here, I discuss the development and application of several analytical methods applied to real case studies, including objective methods of segmenting cellular images from light microscopy data, tools to robustly localize and track single fluorescently-labelled molecules, algorithms to objectively interpret molecular mobility, analysis protocols to reliably estimate molecular stoichiometry and turnover, and methods to objectively render distributions of molecular parameters.

The aggregation of dynamic relationships caused by incomplete information

We consider the aggregation of heterogeneous dynamic equations across a large population, as introduced by Granger (1980), where the dynamics arise because agents face a signal extraction problem caused by incomplete information. This weakens the independence assumptions used previously in the aggregation literature. We show that, under plausible assumptions, the differenced cross-section aggregate shows long term persistence even though every individual micro-series follows a random walk. As an example, estimates of the model’s micro-relations are made using US household panel data.

APPRAISAL METHODS FOR THE U.S. HOUSING MARKET

ABSTRACT We propose an ideal real estate appraisal procedure that would eliminate biases that exist in traditional appraisal methods. Throughout the exposition, the type of real estate we have in mind is residential property, and so we use the sales comparisons method. We treat appraisal as a simple form of signal extraction problem, taking into account informational constraints that are present. We treat the issue using filtering theory and discuss the recent advances in nonlinear filtering theory that enable one to treat the complicated circumstances characterizing the appraisal of property. Keywords real estate appraisal, filtering, signal extraction

Oil Price Dynamics and Monetary Policy in a Heterogeneous Monetary Union

Summary This paper analyzes the dynamic effects of oil price increases in a small two-country monetary union with asymmetric wage adjustment equations. Common oil price shocks lead during the adjustment process to temporary divergences in output and inflation and also to reversals in the relative cyclical position across the monetary union. We distinguish between three types of oil price shocks: (1) an unanticipated permanent shock, (2) an unanticipated temporary shock and (3) an anticipated permanent shock.We illustrate the macroeconomic effects of these shocks by means of dynamic simulations and examine the respective stabilization role of monetary policy. While permanent oil price hikes always lead to stagflation, temporary shocks are associated with deflation in the very short run as the reduction of real income lowers the demand for the domestically produced good. The implications for monetary policy are also shock-specific. Monetary policy faces a signal extraction problem as it needs to determine whether oil price shocks are transitory or permanent in order to make appropriate decisions not only about the strength, but also the direction of monetary policy.

Analysis and implementation of improved multi-input multi-output filtered-X least mean square algorithm for active structural vibration control

An improved multi-input multi-output filtered-X least mean square-based vibration control algorithm is proposed to solve the reference signal extraction problem for active vibration control system. The reference signal is constructed by the controller parameters and the vibration residual signal extracted directly from the vibrating structure, which is related to the external disturbance signal. Meanwhile, an FIR filter is adopted for online identification by adding white noise signal to the controller output as identification input signal; the identified model is substituted into the control algorithm, and the online secondary path identification is realized. Thus, the practical application problem of filtered-X least mean square algorithm is solved. The simulations and experiments show that the proposed algorithm is reliable and effective with good control performance. Copyright © 2013 John Wiley & Sons, Ltd.

Fitting survey expectations and uncertainty about trend inflation

Many studies document that the inflation rate is governed by persistent trend shifts and time-varying uncertainty about trend inflation. As both these quantities are unobserved, a forecaster has to learn about changes in trend inflation by a signal extraction procedure. I suggest that the forecaster uses a simple IMA(1,1) model because it is well suited to forecast inflation and it provides an efficient way to solve the signal extraction problem. I test whether this model provides a good fit for expectations from the Survey of Professional Forecasters. The model appears to be well suited to model observed inflation expectations if we allow for stochastic volatility. When I estimate the implied learning rule, results are supportive for the trend learning hypothesis. Moreover, stochastic volatility seems to influence the way agents learn over time. It appears that survey participants systematically adapt their learning behavior when inflation uncertainty changes.

Private Uncertainty and Multiplicity

This paper provides the conditions under which small enough private uncertainty on an aggregate endogenous state of the economy can invalidate uniqueness of the equilibrium. The main result is presented in a fully microfounded macroeconomic model where agents learn from arising prices. The findings apply to a broad class of static signal extraction problems where both fundamental correlation and pay-off externalities jointly contribute to a multiplicity of equilibria. The cases where only one of these two determinants is sufficient for a multiplicity are also isolated and discussed