Impulse Response Estimation Research Articles

The existence and uniqueness of solutions for kernel-based system identification

The notion of reproducing kernel Hilbert space (RKHS) has emerged in system identification during the past decade. In the resulting framework, the impulse response estimation problem is formulated as a regularized optimization defined on an infinite-dimensional RKHS consisting of stable impulse responses. The consequent estimation problem is well-defined under the central assumption that the convolution operators restricted to the RKHS are continuous linear functionals. Moreover, according to this assumption, the representer theorem hold, and therefore, the impulse response can be estimated by solving a finite-dimensional program. Thus, the continuity feature plays a significant role in kernel-based system identification. We show that this central assumption is guaranteed to be satisfied in considerably general situations, namely when the input signal is bounded, the kernel is an integrable function, and in the case of continuous-time dynamics, continuous. Furthermore, the strong convexity of the optimization problem and the continuity property of the convolution operators imply that the kernel-based system identification admits a unique solution. Consequently, it follows that kernel-based system identification is a well-defined approach.

Research on the Relationship between Apple Stock Price and Changes in Exchange Rate: Evidence from Fed’s Rate Hike

The Fed’s Rate Hike changes the exchange rate, which would fluctuate the stock price. This paper uses VAR model and ARMA-GARCH model to determine the relationship between the exchange rate change and Apple stock price from January 2022 to July 2022. The impulse-response estimation suggests that the exchange rate seems to be a slight short-term external shock, and the ARMA-GARCH regression implies that the exchange rate affects the stock price significantly, which is lagging as well.

Online Input Signal Design for Kernel-Based Impulse Response Estimation

This article considers online input signal design for kernel-based estimation of impulse responses where the input signal is designed one bit at a time while simultaneously performing the identification. A method referred to as the direct spectrum shaping (DSS) method is proposed based on the biased Cramér–Rao lower bound, combined with detailed analysis of two popular choices of kernels. With no gradient computations, the DSS technique is able to achieve comparable accuracy but with a significant reduction in computational times by a factor of more than 370 compared with the existing Bayesian A-optimality (BAO) technique. The BAO technique, in general, attains higher estimation accuracy for oscillatory systems whereas the DSS approach is superior for systems with smoother impulse responses. The DSS method possesses further advantages of simplicity of implementation and low crest factor due to the signal being binary. An application example on a simulated curing oven in the glove manufacturing industry illustrates the potential impact of the DSS method.

Deep Learning Channel Estimation for OFDM 5G Systems with Different Channel Models

At cellular wireless communication systems, channel estimation (CE) is one of the key techniques that are used in Orthogonal Frequency Division Multiplexing modulation (OFDM). The most common methods are Decision‐Directed Channel Estimation, Pilot-Assisted Channel Estimation (PACE) and blind channel estimation. Among them, PACE is commonly used and has a steadier performance. Applying deep learning (DL) methods in CE is getting increasing interest of researchers during the past 3 years. The main objective of this paper is to assess the efficiency of DL-based CE compared to the conventional PACE techniques, such as least-square (LS) and minimum mean-square error (MMSE) estimators. A simulation environment to evaluate OFDM performance at different channel models has been used. A DL process that estimates the channel from training data is also employed to get the estimated impulse response of the channel. Two channel models have been used in the comparison: Tapped Delay Line and Clustered Delay Line channel models. The performance is evaluated under different parameters including number of pilots (64 pilots or 8 pilots), number of subcarriers (64), the length of cyclic prefix (16 or 0 samples) and carrier frequency (4 GHz) through computer simulation using MATLAB. From the simulation results, the trained DL estimator provides better results in estimating the channel and detecting the transmitted symbols compared to LS and MMSE estimators although, the complexity of the proposed LSTM estimator exceeds the equivalent LS estimator. Furthermore, the DL estimator also demonstrates its effectiveness with various pilot densities and with different cyclic prefix periods.

QT Interval Adaptation to Heart Rate Changes in Atrial Fibrillation as a Predictor of Sudden Cardiac Death.

The clinical significance of QT interval adaptation to heart rate changes has been poorly investigated in atrial fibrillation (AF), since QT delineation in the presence of f-waves is challenging. The objective of the present study is to investigate new techniques for QT adaptation estimation in permanent AF. A multilead strategy based on periodic component analysis, to emphasize T-wave periodicity, is proposed for QT delineation. QT adaptation is modeled by a linear, time-invariant filter, which describes the dependence between the current QT interval and the preceding RR intervals, followed by a memoryless, nonlinear, function. The QT adaptation time lag is determined from the estimated impulse response. Using simulated ECGs in permanent AF, the transformed lead was found to offer more accurate QT delineation and time lag estimation than did the original ECG leads for a wide range of f-wave amplitudes. In a population with chronic heart failure and permanent AF, the time lag estimated from the transformed lead was found to have the strongest, statistically significant association with sudden cardiac death (SCD) (hazard ratio = 3.49). Periodic component analysis provides more accurate QT delineation and improves time lag estimation in AF. A prolonged QT adaptation time lag is associated with a high risk for SCD. SCD risk markers originally developed for sinus rhythm can also be used in AF, provided that T-wave periodicity is emphasized. The time lag is a potentially useful biomarker for identifying patients at risk for SCD, guiding clinicians in adopting effective therapeutic decisions.

Public debt and state-dependent effects of fiscal policy in the euro area

We investigate public debt related state dependencies of fiscal policy shocks for fifteen euro area economies during the period from 2000:Q1 to 2019:Q4. Our estimated impulse response functions suggest that the impact of fiscal policy shocks varies depending on the level of public debt characterizing an economy. Macroeconomic variables, notably output and consumption, go up in response to a positive government spending shock in the high-debt cross-sectional state, and these responses are distinctly different from those in the low-debt state. Using an extended model that considers both cross-sectional and time-serial high- and low-debt states we find that, for euro area economies, cross-sectional debt variation is more important than time-serial debt variation in driving differences in the responses of macroeconomic variables to government spending shocks.

Euro area monetary asset demand and Divisia aggregates**

Monetary asset user costs are functions of spreads between a benchmark rate of return and the own rates of return on the monetary assets. We analyze the impact of the benchmark rate on a Euro area Divisia M2 aggregate, on estimated elasticities of substitution, and on estimated impulse response functions. Substitution in response to changes in the user cost of M1 is generally elastic, but we find evidence of inelastic substitution along other dimensions. When a loan rate is used as the benchmark, substitution in response to changes in the user costs of the two components of M2-M1 is inelastic throughout the sample and the corresponding elasticity estimates are near their lowest levels during the pandemic. This is strong evidence that Divisia monetary aggregates are preferable to conventional monetary aggregates. Annual growth rates of simple sum and Divisia M2 monetary aggregates differ significantly in some periods, but not during the pandemic. Estimated impulse response functions using both Divisia and simple sum money measures indicate that money shocks have positive and statistically significant effects on real output. The response of the price level to a money shock tends to be more persistent when the models are estimated using Divisia aggregates. .

Performance Analysis of an MLS-Based Interface for Impulse Response Estimation of Resistive and Capacitive Sensors

This paper presents a performance analysis of a system for electrochemical impedance spectroscopy (EIS). The system, composed by an analog front-end (AFE) and a custom microcontroller (MCU) board, performs the impulse response (IR) measurement of linear and time-invariant (LTI) systems with pseudo-random excitation signals. As a novelty, a specific AFE for the interfacing of two-terminal resistive and capacitive sensors is covered in detail. The paper proposes, for the first time, a mathematical model to predict the impact of the main noise sources in the measured IR. Thanks to the proposed approach, the AFE and the system’s parameters can be properly designed in order to reduce the error, thus, minimizing the energy-per-error figure of merit (FOM) as well. The AFE is realized as discrete-components circuit and it has been included in a custom MCU-based measurement system as an expansion module. The predicted results from the mathematical model, in terms of noise power, SNR, and measurement error are validated through system-level simulation and experimental measurements. The system performs the IR measurement with 1023 points, showing root-mean-square (RMS) measurement errors of 1% and 1.4% for the tested ADC sampling frequencies of 62.5 kHz and 125 kHz, respectively. These lead to excellent FOM values of 128.9 mJ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\cdot $ </tex-math></inline-formula> % <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and 252.6 mJ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\cdot $ </tex-math></inline-formula> % <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> that outstand the state of the art.

Analysis of the Dynamic Relationships among Renewable Energy Consumption, Economic Growth, Financial Development, and Carbon Dioxide Emission in Five Sub-Saharan African Countries

This research investigates the relationships among renewable energy consumption, economic growth, and financial development in five sub-Saharan African nations utilizing panel data from 2000 to 2020. Econometric methods are used to ascertain the existence or absence of cross-sectional dependence and the short-run and long-run connections between the following factors: Pesaran cross-sectional dependence (CD) and cross-sectionally augmented IPS (CIPS) unit root tests, pooled mean group (PMG), and dynamic ordinary least squares (DOLS) estimations. The presence of cross-sectional dependence is found and represented with the CIPS unit root test. No significant short-run relationship is found between the variables of the study, yet a significant long-run relationship is present among them. A positive relationship exists between CO2 emissions and financial development, while financial development and renewable energy consumption are found to have negative relationships with CO2 emissions. The study also supports the scale effect of the environmental Kuznets curve hypothesis. Additionally, no causality is found among the variables, and impulse response and variance decomposition estimation are carried out to recommend future effects. Policy implications of findings are discussed, with accompanying suggestions.

Coalitions in international relations and coordination of agricultural trade policies

PurposeThe author attempts to examine the existence and pattern of coalitions in international relations across countries, and investigates whether international relations of coalition partners influence a country's enaction of agricultural non-tariff measures (NTMs).Design/methodology/approachThe author adopts a machine learning technique to identify international relation coalition partnerships and use network analysis to characterize the clustering pattern of coalitions with high-frequent records of global event data. The author then constructs a monthly dataset of agricultural NTMs against China and international relations with China of each importer and its coalition partners, and designs a panel structural vector autoregressive (PSVAR) model to estimate impulse response functions of agricultural NTMs with regard to international relation shocks.FindingsThe author finds countries to establish coalition partnerships. Two major clusters of coalitions are noted, with one composed of coalitions primarily among “North” countries and the other of coalitions among “South” countries. The United States is found to play a pivotal role by connecting the two clusters. The PSVAR estimation reveals reductions of NTMs against China following improved international relations with China of both the importer and its coalition partners. NTM responses are more substantial for measures that are trade restrictive. These results confirm that coalitions in international relations lead to coordination of agricultural NTMs.Originality/valueThe author provides international political insights into agricultural trade policymaking by showing interactions of NTM enaction across countries in the same coalition of international relations. These insights offer useful policy implications to predict and cope with hidden barriers to agricultural trade.

The fiscal cost of conflict: Evidence from Afghanistan 2005–2017

I use a novel monthly panel of provincially-collected central government revenues and conflict fatalities to estimate government revenues lost due to conflict in Afghanistan since 2005. Headline estimates are large, implying total revenue losses of $3bn since 2005 and that gains from peace would have been about 6 percent of GDP per year. That this is larger than estimates in cross-country studies reflects the uncommon intensity of the conflict in Afghanistan. The key challenge to identification is omitted variable bias, which I address by extending Powell’s (2021) generalized synthetic control method to a dynamic setting. This allows estimation of impulse response functions robust to a broad class of omitted variables bias.

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Identifying factor‐augmented vector autoregression models via changes in shock variances

SummaryThis study proposes a method to identify factor‐augmented vector autoregression models without imposing uncorrelatedness or any timing restrictions among observed and unobserved factors in the vector autoregression system. To this end, we utilize changes in unconditional shock variances following Rigobon (2003). The proposed method can incorporate both observed and unobserved factors in the structural vector autoregression system and allows the contemporaneous matrix to be fully unrestricted. We derive the asymptotic distribution of the impulse response estimator and consider a bootstrap inference method. We also provide two diagnostic tools: a test for the identification condition and a class of overidentifying restrictions tests. A Monte Carlo experiment shows that the asymptotic and bootstrap methods yield a satisfactory coverage rate when the shock of an observed factor is analyzed, although the bootstrap method is more accurate. We apply the proposed method to an empirical example for the effects of U.S. monetary policies on asset prices. A contractionary monetary policy shock induces positive and hump‐shaped interest rate responses along the maturity dimension and negative but insignificant stock price responses.

SSP based underwater CIR estimation with S-BiFPN

In underwater sensor networks (USN), channel impulse response (CIR) estimation based on sound speed profile (SSP) ensures link reliability. We propose a separate bi-directional feature pyramid network (S-BiFPN) that estimates the CIR using deep learning based on SSP. The proposed method enlarges the small variation of SSP by converting 1-dimension into 2-dimension, extracts various features using a fused feature map obtained from the separate paths, and estimates the CIR. Simulations are performed using the practically measured SSPs and CIRs, and the results show that the proposed method has the lowest mean square error (MSE) and a reasonable running time compared to conventional methods.

Online Acoustic System Identification Exploiting Kalman Filtering and an Adaptive Impulse Response Subspace Model

We introduce a novel algorithm for online estimation of Acoustic Impulse Responses (AIRs) which allows for fast convergence by exploiting prior knowledge about the fundamental structure of AIRs. The proposed method assumes that the variability of AIRs of an acoustic scene is confined to a low-dimensional manifold which is embedded in a high-dimensional space of possible AIR estimates. We discuss various approaches which exploit a training data set of AIRs, e.g., high-accuracy AIR estimates from the acoustic scene, to learn a local affine subspace approximation of the AIR manifold. The model is motivated by the idea of describing the generally nonlinear AIR manifold locally by tangential hyperplanes and its validity is verified for simulated data. Subsequently, we describe how the manifold assumption can be used to enhance online AIR estimates by projecting them onto an adaptively estimated subspace. Motivated by the assumption of manifolds being locally Euclidean, the parameters determining the adaptive subspace are learned from the nearest neighbor AIR training samples to the current AIR estimate. To assess the proximity of training data AIRs to the current AIR estimate, we introduce a probabilistic extension of the Euclidean distance which improves the performance for applications with non-white excitation signals. Furthermore, we describe how model imperfections can be tackled by a soft projection of the AIR estimates. The proposed algorithm exhibits significantly faster convergence properties in comparison to a high-performance state-of-the-art algorithm. Furthermore, we show an improved steady-state performance for speech-excited system identification scenarios suffering from high-level interfering noise and nonunique solutions.

Motion Estimation of Underwater Platforms Using Impulse Responses From the Seafloor

Autonomous underwater vehicles require accurate navigation. Techniques such as image registration using consecutive acoustic images from a sonar have shown promising results for this task. The implementation of such techniques using sonar images augmented with deep learning (DL) networks demonstrate high navigation accuracy; this is possible even with highly compressed images. The sonar images are estimates of sampled in time (with a ping period) magnitudes of channel impulse responses representing the underwater acoustic environment. More information about the environment is contained in (almost) continuous in time estimates of the channel impulse responses. Such estimates can be obtained using full-duplex technology. Rather than using sonar images, this paper investigates the use of channel impulse response estimates for underwater platform motion estimation. The proposed system uses a single projector and a small number of receiving transducers installed on the moving platform. A DL network is used to estimate the motion in two degrees of freedom (forward/backward and sideways), using two or more consecutive impulse response estimates as the input. To train the DL network, a specially designed simulator is used to model the underwater acoustic environment, populated with multiple objects spread on the seafloor. The proposed technique can significantly reduce the acoustic hardware and processing complexity of the DL network and obtain a higher accuracy of motion estimation, compared with techniques based on the processing of sonar images, e.g., the error achieved with the technique proposed in this paper is 1.7% of the maximum platform displacement, compared to 4% achieved with a technique using sonar images. The navigation accuracy is further illustrated by examples of estimation of complex trajectories.

BER Analysis and CS-Based Channel Estimation and HPA Nonlinearities Compensation Technique for Massive MIMO System

Massive Multiple Input Multiple Output (MIMO) system has gathered lately a huge interest from researchers and it has been known as a backbone technology for the 5th generation because it can greatly improve the capacity of wireless communication and it can potentially provide energy efficiency and security. Before ensuring the full advantages, massive MIMO system has to overcome many challenges. One of them is to accurate an exact estimation of the Channel Impulse response (CIR) between each transmit-receive antenna pair. The other problem arises when implementing such a system in presence of High Power Amplifiers (HPA) which imposes a nonlinear distortion on the transmitted signals. This paper proposes contributions in three key areas. Firstly, we investigate the nonlinear effects of memoryless HPA, which is modeled using Saleh model, by deriving its Bit Error Rate expression (BER) in massive MIMO Orthogonal Frequency Division Multiplexing (OFDM) system. Secondly, we highlight the necessity of providing the accurate channel characteristics by estimating it using Compressive Sensing (CS) techniques. Moreover, we propose also a CS compensation algorithm based on Orthogonal Matching Pursuit (OMP) to mitigate the nonlinear distortion in the receiver. The proposed CS-based compensation technique has been compared to the Neural Network (NN) pre and post compensation technique and it has shown a good performance not only in terms of BER but also in terms of complexity.

Estimation of Acoustic Channel Impulse Response at Low Frequencies Using Sparse Bayesian Learning for Nonuniform Noise Power

Sparse Bayesian learning (SBL) has been extended to estimate acoustic channel impulse responses (CIRs) at low frequencies, where matched filter (MF)-based CIR estimation suffers from low resolution due to a limited frequency band. In this study, the extended SBL was developed to account for nonuniform noise power in a signal model for the CIR via a formulation that considers inconsistent noise and multiple measurements, which cannot be handled in the conventional SBL. The extended SBL is applied to simulated and measured acoustic data and then compared with the MF and existing SBLs. With the advancement in the schemes, the time resolution and denoising are enhanced; especially, the results of the extended SBL on the simulated data show that it clearly distinguishes the two adjacent arrivals with moderate errors in the estimated time delays. Additionally, as a result of applying it to the measured array data, the extended SBL can achieve a high resolution in the CIR estimation, which retains assured arrivals with a single measurement, while some arrivals are weakened by the insufficient measurement for the extended SBL.

Do Exchange Rate and Inflation Matters to Nigerian Economy? New Evidence from Vector Autoregressive (VAR) Approach

Currency fluctuations and inflation are the natural norm for most major economies. Numerous factors influence economic growth, including a country’s exchange rate system performance, the outlook for inflation, and interest rate differentials. These are the most significant factors that hinder the economic growth of every nation. As a result, this analysis investigates the impact of exchange rate and inflation on Nigeria’s growth performance from 1986 to 2021. Impulse response and variance decomposition were estimated. The real gross domestic product (RGDP) was used as a proxy for growth performance, while the inflation rate (IFNR), real exchange rate (REXR), and interest rate (INTR) were also used as proxies. The results of impulse response and variance decomposition estimates in the short-run (third quarter) and long-run (tenth quarter) show that real exchange rate D(REXR), INTR, and IFNR all have a positive impact on RGDP variation, with values of 13.38%, 31.88%, and 22.40%, respectively, in the third quarter. In the long run (the 10th quarter), REXR contributed approximately 28.76% of the variation in RGDP. The interest rate contributed 24.14%, while the IFNR has contributed about 28.27% of the variation in RGDP in the long run. Therefore, summing the contributions of REXR, INTR, and INFR to RGDP, these variables contributed about 81.17% of the variation in RGDP in the long run. Hence, the research concluded that REXR, INTR, and IFNR have a positive effect on growth performance as proxied by RGDP in Nigeria within the period of the research. The research recommended that the government should provide a policy that will reduce the excess growth of aggregate demand (AD) in the economy, which will reduce inflationary pressure, in order to achieve the sustainable development goals (SDGs) of 2030 in Nigeria, which include restoring economic growth and macroeconomic stability through macroeconomic variables such as the exchange rate, inflation, and other significant variables.

Low-Complexity Joint CFO and Channel Estimation for RIS-Aided OFDM Systems

Accurate channel estimation is essential for achieving the performance gains offered by reconfigurable intelligent surface (RIS)-aided wireless communications. A variety of channel estimation methods have been proposed for such systems; however, none of the existing methods takes into account the effect of synchronization errors such as carrier frequency offset (CFO). In general, CFO can significantly degrade the channel estimation performance of orthogonal frequency division multiplexing (OFDM) systems. Motivated by this, we investigate the effect of CFO on channel estimation for RIS-aided OFDM systems. Furthermore, we propose a joint CFO and channel impulse response (CIR) estimation method for these systems. Simulation results demonstrate the effectiveness of our proposed method, and also demonstrate that the use of time-domain rather than frequency-domain estimation in this context results in an improvement in the mean-squared error (MSE) performance of channel estimation as well as in a significantly lower overall computational complexity.