Showing papers on "Noise (electronics) published in 2019"

Phase-change heterostructure enables ultralow noise and drift for memory operation

Abstract: Artificial intelligence and other data-intensive applications have escalated the demand for data storage and processing. New computing devices, such as phase-change random access memory (PCRAM)-based neuro-inspired devices, are promising options for breaking the von Neumann barrier by unifying storage with computing in memory cells. However, current PCRAM devices have considerable noise and drift in electrical resistance that erodes the precision and consistency of these devices. We designed a phase-change heterostructure (PCH) that consists of alternately stacked phase-change and confinement nanolayers to suppress the noise and drift, allowing reliable iterative RESET and cumulative SET operations for high-performance neuro-inspired computing. Our PCH architecture is amenable to industrial production as an intrinsic materials solution, without complex manufacturing procedure or much increased fabrication cost.

Printed subthreshold organic transistors operating at high gain and ultralow power.

Abstract: Overcoming the trade-offs among power consumption, fabrication cost, and signal amplification has been a long-standing issue for wearable electronics. We report a high-gain, fully inkjet-printed Schottky barrier organic thin-film transistor amplifier circuit. The transistor signal amplification efficiency is 38.2 siemens per ampere, which is near the theoretical thermionic limit, with an ultralow power consumption of 60 decibels and noise voltage of <0.3 microvolt per hertz1/2 at 100 hertz.

Overcoming Noise in Entanglement Distribution

Abstract: Photons entangled in high dimensions are more resilient to noise, making them ideal for quantum communication applications.

Analysis, Design, and Implementation of Accurate ZVS Angle Control for EV Battery Charging in Wireless High-Power Transfer

Abstract: To acquire high efficiency and reduce electromagnetic interference in wireless high-power charging for electric vehicles (EVs), it is of great importance to realize accurate zero voltage switching angle (ZVSA) control of the inverter. However, the traditional zero-crossing detection cannot be applied in high power because of considerable noise and poor accuracy in wide power range applications. In this paper, to suppress the noise in high power, a current hysteresis comparator is adopted, and an enhanced phase detection methodology is proposed to measure the phase of resonant current by using a reference signal produced by a processor. Meanwhile, to improve the accuracy of ZVSA, a uniform time delay compensation method (UTDCM) by considering the whole time delays synthetically is proposed, and a uniform time delay equation can be obtained to guarantee the high accuracy of phase detection, especially in the wide power range. Finally, a novel control strategy with the ZVSA loop based on UTDCM is proposed for battery charging in wireless high-power transfer system. A 500-W wireless power transfer prototype is built to verify the accuracy of ZVSA based on UTDCM and the system efficiency can achieve 94.17% with $k$ = 0.22.

Environment-Assisted Quantum Transport in a 10-qubit Network

Abstract: The way in which energy is transported through an interacting system governs fundamental properties in nature such as thermal and electric conductivity or phase changes. Remarkably, environmental noise can enhance the transport, an effect known as environment-assisted quantum transport (ENAQT). In this Letter, we study ENAQT in a network of coupled spins subject to engineered static disorder and temporally varying dephasing noise. The interacting spin network is realized in a chain of trapped atomic ions, and energy transport is represented by the transfer of electronic excitation between ions. With increasing noise strength, we observe a crossover from coherent dynamics and Anderson localization to ENAQT and finally a suppression of transport due to the quantum Zeno effect. We find that in the regime where ENAQT is most effective, the transport is mainly diffusive, displaying coherences only at very short times. Further, we show that dephasing characterized by non-Markovian noise can maintain coherences longer than white noise dephasing, with a strong influence of the spectral structure on the transport efficiency. Our approach represents a controlled and scalable way to investigate quantum transport in many-body networks under static disorder and dynamic noise.

Measurement of the activation energies of oxygen ion diffusion in yttria stabilized zirconia by flicker noise spectroscopy

Abstract: The low-frequency noise in a nanometer-sized virtual memristor consisting of a contact of a conductive atomic force microscope (CAFM) probe to an yttria stabilized zirconia (YSZ) thin film deposited on a conductive substrate is investigated. YSZ is a promising material for the memristor application since it is featured by high oxygen ion mobility, and the oxygen vacancy concentration in YSZ can be controlled by varying the molar fraction of the stabilizing yttrium oxide. Due to the low diameter of the CAFM probe contact to the YSZ film (∼10 nm), we are able to measure the electric current flowing through an individual filament both in the low resistive state (LRS) and in the high resistive state (HRS) of the memristor. Probability density functions (Pdfs) and spectra of the CAFM probe current in both LRS and HRS are measured. The noise in the HRS is found to be featured by nearly the same Pdf and spectrum as the inner noise of the experimental setup. In the LRS, a flicker noise 1/fγ with γ ≈ 1.3 is observed in the low-frequency band (up to 8 kHz), which is attributed to the motion (drift/diffusion) of oxygen ions via oxygen vacancies in the filament. Activation energies of oxygen ion motion determined from the flicker noise spectra are distributed in the range of [0.52; 0.68] eV at 300 K. Knowing these values is of key importance for understanding the mechanisms of the resistive switching in YSZ based memristors as well as for the numerical simulations of memristor devices.

Measurement of quantum back action in the audio band at room temperature

Abstract: Quantum mechanics places a fundamental limit on the precision of continuous measurements. The Heisenberg uncertainty principle dictates that as the precision of a measurement of an observable (for example, position) increases, back action creates increased uncertainty in the conjugate variable (for example, momentum). In interferometric gravitational-wave detectors, higher laser powers reduce the position uncertainty created by shot noise (the photon-counting error caused by the quantum nature of the laser) but necessarily do so at the expense of back action in the form of quantum radiation pressure noise (QRPN)1. Once at design sensitivity, the gravitational-wave detectors Advanced LIGO2, VIRGO3 and KAGRA4 will be limited by QRPN at frequencies between 10 hertz and 100 hertz. There exist several proposals to improve the sensitivity of gravitational-wave detectors by mitigating QRPN5–10, but until now no platform has allowed for experimental tests of these ideas. Here we present a broadband measurement of QRPN at room temperature at frequencies relevant to gravitational-wave detectors. The noise spectrum obtained shows effects due to QRPN between about 2 kilohertz and 100 kilohertz, and the measured magnitude of QRPN agrees with our model. We now have a testbed for studying techniques with which to mitigate quantum back action, such as variational readout and squeezed light injection7, with the aim of improving the sensitivity of future gravitational-wave detectors. Future gravitational-wave detectors are expected to be limited by quantum back action, which is now found in the audio band in a low-loss optomechanical system.

Reservoir computing with the frequency, phase, and amplitude of spin-torque nano-oscillators

Abstract: Spin-torque nano-oscillators can emulate neurons at the nanoscale. Recent works show that the non-linearity of their oscillation amplitude can be leveraged to achieve waveform classification for an input signal encoded in the amplitude of the input voltage. Here, we show that the frequency and phase of the oscillator can also be used to recognize waveforms. For this purpose, we phase-lock the oscillator to the input waveform, which carries information in its modulated frequency. In this way, we considerably decrease the amplitude, phase, and frequency noise. We show that this method allows classifying sine and square waveforms with an accuracy above 99% when decoding the output from the oscillator amplitude, phase, or frequency. We find that recognition rates are directly related to the noise and non-linearity of each variable. These results prove that spin-torque nano-oscillators offer an interesting platform to implement different computing schemes leveraging their rich dynamical features.

Thermorefractive noise in silicon-nitride microresonators

Abstract: Thermodynamic noise places a fundamental limit on the frequency stability of dielectric optical resonators. Here, we present the characterization of thermorefractive noise in photonic-chip-based silicon-nitride (${\text{Si}}_{3}{\text{N}}_{4}$) microresonators and show that thermorefractive noise is the dominant thermal noise source in the platform. We employed balanced homodyne detection to measure the thermorefractive noise spectrum of microresonators of different diameters. The measurements are in good agreement with theoretical models and finite element method simulations. Our characterization sets quantitative bounds on the scaling and absolute magnitude of thermal noise in photonic-chip-based microresonators. An improved understanding of thermorefractive noise can prove valuable in the design considerations and performance limitations of future photonic integrated devices.

Spiking activities in chain neural network driven by channel noise with field coupling

Abstract: The distribution of electromagnetic field in both intracellular and extracellular environments can be changed by fluctuations in the membrane potential, and the effects of electromagnetic induction should be considered in dealing with neuronal electrical activities, wherein field coupling plays a very important role in signal exchange between neurons. In this paper, basing on an improved electromagnetic induction model, a chain network is designed to investigate the responses of the neural system to channel noise under field coupling. Both the synchronization factor and coefficient of variation are numerically simulated, and it is found that (i) the weak field coupling strength is conducive to the regularity of discharge patterns in the neuronal network; (ii) the synchronization of neural spikes can be enhanced by selecting a suitable coupling intensity; and (iii) in the presence of the weak noise intensity, the discharge mode of neuron is easily affected by the inducing coefficient. Our results show that the regularity of discharge patterns in a stochastic neural network depends on the field coupling intensity, which reflects the importance of field coupling in the selection of neural discharge modes.

Robust and Resource-Efficient Microwave Near-Field Entangling ^{9}Be^{+} Gate.

Abstract: Microwave trapped-ion quantum logic gates avoid spontaneous emission as a fundamental source of decoherence. However, microwave two-qubit gates are still slower than laser-induced gates and hence more sensitive to fluctuations and noise of the motional mode frequency. We propose and implement amplitude-shaped gate drives to obtain resilience to such frequency changes without increasing the pulse energy per gate operation. We demonstrate the resilience by noise injection during a two-qubit entangling gate with $^{9}{\mathrm{Be}}^{+}$ ion qubits. In the absence of injected noise, amplitude modulation gives an operation infidelity in the ${10}^{\ensuremath{-}3}$ range.

Multireference Alignment Is Easier With an Aperiodic Translation Distribution

Abstract: In the multireference alignment model, a signal is observed by the action of a random circular translation and the addition of Gaussian noise. The goal is to recover the signal’s orbit by accessing multiple independent observations. Of particular interest is the sample complexity, i.e., the number of observations/samples needed in terms of the signal-to-noise ratio (SNR) (the signal energy divided by the noise variance) in order to drive the mean-square error to zero. Previous work showed that if the translations are drawn from the uniform distribution, then, in the low SNR regime, the sample complexity of the problem scales as $\omega (1/ \mathrm {SNR}^{3})$ . In this paper, using a generalization of the Chapman–Robbins bound for orbits and expansions of the $\chi ^{2}$ divergence at low SNR, we show that in the same regime the sample complexity for any aperiodic translation distribution scales as $\omega (1/ \mathrm {SNR}^{2})$ . This rate is achieved by a simple spectral algorithm. We propose two additional algorithms based on non-convex optimization and expectation–maximization. We also draw a connection between the multireference alignment problem and the spiked covariance model.

Quantum phase estimation of multiple eigenvalues for small-scale (noisy) experiments

Abstract: Quantum phase estimation (QPE) is the workhorse behind any quantum algorithm and a promising method for determining ground state energies of strongly correlated quantum systems. Low-cost QPE techniques make use of circuits which only use a single ancilla qubit, requiring classical post-processing to extract eigenvalue details of the system. We investigate choices for phase estimation for a unitary matrix with low-depth noise-free or noisy circuits, varying both the phase estimation circuits themselves as well as the classical post-processing to determine the eigenvalue phases. We work in the scenario when the input state is not an eigenstate of the unitary matrix. We develop a new post-processing technique to extract eigenvalues from phase estimation data based on a classical time-series (or frequency) analysis and contrast this to an analysis via Bayesian methods. We calculate the variance in estimating single eigenvalues via the time-series analysis analytically, finding that it scales to first order in the number of experiments performed, and to first or second order (depending on the experiment design) in the circuit depth. Numerical simulations confirm this scaling for both estimators. We attempt to compensate for the noise with both classical post-processing techniques, finding good results in the presence of depolarizing noise, but smaller improvements in 9-qubit circuit-level simulations of superconducting qubits aimed at resolving the electronic ground state of a H-4-molecule.

6 Gbps real-time optical quantum random number generator based on vacuum fluctuation.

Abstract: We demonstrate a 6 Gbps real-time optical quantum random number generator by measuring vacuum fluctuation. To address the common problem that speed gap exists between fast randomness generation and slow randomness extraction in most high-speed real-time quantum random number generator systems, we present an optimized extraction algorithm based on parallel implementation of Toeplitz hashing to reduce the influence of classical noise due to the imperfection of devices. Notably, the real-time rate of randomness extraction we have achieved reaches the highest speed of 12 Gbps by occupying less computing resources, and the algorithm has the ability to support hundreds of Gbps randomness extraction. By assuming that the eavesdropper with complete knowledge of the classical noise, our generator has a randomness generation speed of 6.83 Gbps and this supports the generation of 6 Gbps information-theoretically provable quantum random numbers, which are output in real-time through peripheral component interconnect express interface.

Josephson-based Threshold Detector for Lévy-Distributed Current Fluctuations

Abstract: What is that noise? The authors discuss the switching to the resistive state of a current-biased Josephson junction affected by non-Gaussian (i.e. L\'evy) stochastic fluctuations. Their theoretical study reveals the strong dependence of the features of switching-current distributions on peculiar parameters of the noise statistic. This phenomenon points the way to direct experimental investigation of $\ensuremath{\alpha}$-stable L\'evy noise features, or to determine the L\'evy component properties of an unknown noise source, for $e.g.$ improved telecommunication, or fault diagnosis in engineering, never mind the titular superconducting electronics.

Petermann-factor limited sensing near an exceptional point

Abstract: Non-Hermitian Hamiltonians describing open systems can feature singularities called exceptional points (EPs). Resonant frequencies become strongly dependent on externally applied perturbations near an EP which has given rise to the concept of EP-enhanced sensing in photonics. However, while increased sensor responsivity has been demonstrated, it is not known if this class of sensor results in improved signal-to-noise performance. Here, enhanced responsivity of a laser gyroscope caused by operation near an EP is shown to be exactly compensated by increasing sensor noise in the form of linewidth broadening. The noise, of fundamental origin, increases according to the Petermann factor, because the mode spectrum loses the oft-assumed property of orthogonality. This occurs as system eigenvectors coalesce near the EP and a biorthogonal analysis confirms experimental observations. Besides its importance to the physics of microcavities and non-Hermitian photonics, this is the first time that fundamental sensitivity limits have been quantified in an EP sensor.

Non-Gaussian noise spectroscopy with a superconducting qubit sensor

Abstract: Accurate characterization of the noise influencing a quantum system of interest has far-reaching implications across quantum science, ranging from microscopic modeling of decoherence dynamics to noise-optimized quantum control. While the assumption that noise obeys Gaussian statistics is commonly employed, noise is generically non-Gaussian in nature. In particular, the Gaussian approximation breaks down whenever a qubit is strongly coupled to discrete noise sources or has a non-linear response to the environmental degrees of freedom. Thus, in order to both scrutinize the applicability of the Gaussian assumption and capture distinctive non-Gaussian signatures, a tool for characterizing non-Gaussian noise is essential. Here, we experimentally validate a quantum control protocol which, in addition to the spectrum, reconstructs the leading higher-order spectrum of engineered non-Gaussian dephasing noise using a superconducting qubit as a sensor. This first experimental demonstration of non-Gaussian noise spectroscopy represents a major step toward demonstrating a complete spectral estimation toolbox for quantum devices.

Quantum stochastic resonance in an a.c.-driven single-electron quantum dot

Abstract: In stochastic resonance, the combination of a weak signal with noise leads to its amplification and optimization1. This phenomenon has been observed in several systems in contexts ranging from palaeoclimatology, biology, medicine, sociology and economics to physics1–9. In all these cases, the systems were either operating in the presence of thermal noise or were exposed to external classical noise sources. For quantum-mechanical systems, it has been theoretically predicted that intrinsic fluctuations lead to stochastic resonance as well, a phenomenon referred to as quantum stochastic resonance1,10,11, but this has not been reported experimentally so far. Here we demonstrate tunnelling-controlled quantum stochastic resonance in the a.c.-driven charging and discharging of single electrons on a quantum dot. By analysing the counting statistics12–16, we demonstrate that synchronization between the sequential tunnelling processes and a periodic driving signal passes through an optimum, irrespective of whether the external frequency or the internal tunnel coupling is tuned. Quantum stochastic resonance, in which the quantum fluctuation represents the noise needed to amplify an otherwise weak signal, is reported in the charging and discharging of a single-electron quantum dot.

A Low-Noise Chopper Amplifier Designed for Multi-Channel Neural Signal Acquisition

Abstract: This paper proposed the design of a low-noise, low total harmonic distortion (THD) chopper amplifier for neural signal acquisition. A dc servo loop (DSL) based on active Gm-C integrator is proposed to reject the electrode-dc-offset (EDO). Architecture of a complementary input very low-transconductance (VLT) operational transconductance amplifier (OTA) was proposed and integrated in the active Gm-C integrator to improve the linearity as well as to reduce the noise, featuring a transconductance ranging from 45 pS to a few nS. The proposed amplifier was fabricated in a TSMC 0.18- $\mu \text{m}$ CMOS process, occupying an area of 0.2 mm 2, featuring a power consumption of $3.24~\mu \text{W}$ /channel under a 1.8-V supply voltage. The THD for a 5-mVpp input is lower than −61 dB. An input-referred thermal noise power spectral density (PSD) of 39 nV/ $\sqrt {\text {Hz}}$ is measured. The measured input-referred noise is $0.65~\mu \text {V}_{\text {rms}}$ in the 0.3–200-Hz frequency band and $2.14~\mu \text{V}_{\text {rms}}$ in the 200-Hz–5-kHz frequency band, respectively, leading to a noise-efficiency factor of 2.37 (0.3–200 Hz) and 1.56 (0.2 k–5 kHz). In addition, the high-pass corner frequency can be precisely configured and linearly adjusted with the external bias current from 0.35 to 54.5 Hz.

Strong convergence rates of semidiscrete splitting approximations for the stochastic Allen–Cahn equation

Abstract: This article analyzes an explicit temporal splitting numerical scheme for the stochastic Allen-Cahn equation driven by additive noise, in a bounded spatial domain with smooth boundary in dimension d ≤ 3. The splitting strategy is combined with an exponential Euler scheme of an auxiliary problem. When d = 1 and the driving noise is a space-time white noise, we first show some a priori estimates of this splitting scheme. Using the monotonicity of the drift nonlinearity, we then prove that under very mild assumptions on the initial data, this scheme achieves the optimal strong convergence rate O(δt 1 4). When d ≤ 3 and the driving noise possesses some regularity in space, we study exponential integrability properties of the exact and numerical solutions. Finally, in dimension d = 1, these properties are used to prove that the splitting scheme has a strong convergence rate O(δt).

Time-Frequency Based Phase-Amplitude Coupling Measure For Neuronal Oscillations.

Abstract: Oscillatory activity in the brain has been associated with a wide variety of cognitive processes including decision making, feedback processing, and working memory. The high temporal resolution provided by electroencephalography (EEG) enables the study of variation of oscillatory power and coupling across time. Various forms of neural synchrony across frequency bands have been suggested as the mechanism underlying neural binding. Recently, a considerable amount of work has focused on phase-amplitude coupling (PAC)- a form of cross-frequency coupling where the amplitude of a high frequency signal is modulated by the phase of low frequency oscillations. The existing methods for assessing PAC have some limitations including limited frequency resolution and sensitivity to noise, data length and sampling rate due to the inherent dependence on bandpass filtering. In this paper, we propose a new time-frequency based PAC (t-f PAC) measure that can address these issues. The proposed method relies on a complex time-frequency distribution, known as the Reduced Interference Distribution (RID)-Rihaczek distribution, to estimate both the phase and the envelope of low and high frequency oscillations, respectively. As such, it does not rely on bandpass filtering and possesses some of the desirable properties of time-frequency distributions such as high frequency resolution. The proposed technique is first evaluated for simulated data and then applied to an EEG speeded reaction task dataset. The results illustrate that the proposed time-frequency based PAC is more robust to varying signal parameters and provides a more accurate measure of coupling strength.

1/f noise in solid-state nanopores is governed by access and surface regions

Abstract: The performance of solid-state nanopores as promising biosensors is severely hampered by low-frequency 1/f noise in the through-pore ionic current recordings. Here, we develop a model for the 1/f noise in such nanopores, that, unlike previous reports, accounts for contributions from both the pore-cylinder, pore-surface, and access regions. To test our model, we present measurements of the open-pore current noise through solid-state nanopores of different diameters (1-50 nm). To describe the observed trends, it appears essential to include the access resistance in the modeling of the 1/f noise. We attribute a different Hooge constant for the charge carrier fluctuations occurring in the bulk electrolyte and at the pore surface. The model reported here can be used to accurately analyze different contributions to the nanopore low-frequency noise, rendering it a powerful tool for characterizing and comparing different membrane materials in terms of their 1/f noise properties.

Accounting for errors in quantum algorithms via individual error reduction

Abstract: We discuss a surprisingly simple scheme for accounting (and removal) of error in observables determined from quantum algorithms. A correction to the value of the observable is calculated by first measuring the observable with all error sources active and subsequently measuring the observable with each error source reduced separately. We apply this scheme to the variational quantum eigensolver, simulating the calculation of the ground state energy of equilibrium H2 and LiH in the presence of several noise sources, including amplitude damping, dephasing, thermal noise, and correlated noise. We show that this scheme provides a decrease in the needed quality of the qubits by up to two orders of magnitude. In near-term quantum computing, where full fault-tolerant error correction is too expensive, this scheme provides a route to significantly more accurate calculations. The errors in quantum computing can be strongly reduced exploiting partial removal and subsequent estimation of the residual error. Matthew Otten and Stephen Gray from Argonne National Laboratory have devised a simple scheme that should be able to greatly reduce the practical requirements for quantum devices in terms of cleanliness of operation, both for computation and for some quantum sensing protocol. The approach requires being able to actively reduce, of a certain amount, each error source separately, and measure the quantity to be calculated separately each time. Then, the authors show that it is possible to combine these noisy measurements together and get a reliable estimation of the noiseless result. Numerical simulations prove that the scheme would work for many different types of noise.

Noise of supercontinuum sources in spectral domain optical coherence tomography

Abstract: In this paper, we investigate the effect of pulse-to-pulse fluctuations of supercontinuum sources on the noise in spectral domain optical coherence tomography (OCT) images. The commonly quoted theoretical expression for the OCT noise is derived for a thermal light source, which is not suitable if a supercontinuum light source is used. We therefore propose a new, measurement-based OCT noise model that predicts the noise without any assumptions on the type of light source. We show that the predicted noise values are in excellent agreement with the measured values. The spectral correlation evaluated for the photodetected signal when using a supercontinuum determines the shape of the OCT noise floor, which must be taken into account when characterizing the sensitivity roll-off of a supercontinuum-based OCT system. The spectral correlations using both conventional supercontinuum sources and low-noise all-normal dispersion supercontinuum sources are investigated, and the fundamental physical effects that cause these correlations are discussed.

Low-frequency spin qubit detuning noise in highly purified $^{28}$Si/SiGe

Abstract: The manipulation fidelity of a single electron qubit gate-confined in a $^{28}$Si/SiGe quantum dot has recently been drastically improved by nuclear isotope purification. Here, we identify the dominant source for low-frequency qubit detuning noise in a device with an embedded nanomagnet, a remaining $^{29}$Si concentration of only 60$\,$ppm in the strained $^{28}$Si quantum well layer and a spin echo decay time $T_2^{\text{echo}}=128\,\mu$s. The power spectral density (PSD) of the charge noise explains both the observed transition of a $1/f^2$- to a $1/f$-dependence of the detuning noise PSD as well as the observation of a decreasing time-ensemble spin dephasing time from $T_2^* \approx 20\,\mu$s with increasing measurement time over several hours. Despite their strong hyperfine contact interaction, the few $^{73}$Ge nuclei overlapping with the quantum dot in the barrier do not limit $T_2^*$, as their dynamics is frozen on a few hours measurement scale. We conclude that charge noise and the design of the gradient magnetic field is the key to further improve the qubit fidelity.

Multichannel Signal Detection Based on Wald Test in Subspace Interference and Gaussian Noise

Abstract: This paper investigates the problem of detecting a multichannel signal embedded in subspace interference and Gaussian noise The interference lies in a known subspace but with unknown coordinates, while the noise, in the general sense, consisting of thermal noise and clutter, has an unknown covariance matrix To estimate the covariance matrix, it is assumed that there are sufficient signal-free training data Two cases are considered, namely, the homogeneous environment (HE) and partially HE (PHE) The test and training data in the HE have the same noise covariance matrix, while the test and training data in the PHE share the same noise covariance matrix up to an unknown scaling factor We derive the corresponding Wald tests both in the HE and PHE Remarkably, these two detectors reject the clutter by using the sample covariance matrix, and then reject interference and integrate signal simultaneously through the oblique projection Numerical examples show that the two proposed detectors can provide better detection performance than existing detectors in some situations