Optimal Signal-to-noise Ratio Research Articles

Quick recipes for gravitational-wave selection effects

Accurate modeling of selection effects is a key ingredient to the success of gravitational-wave astronomy. The detection probability plays a crucial role in both statistical population studies, where it enters the hierarchical Bayesian likelihood, and astrophysical modeling, where it is used to convert predictions from population-synthesis codes into observable distributions. We review the most commonly used approximations, extend them, and present some recipes for a straightforward implementation. These include a closed-form expression capturing both multiple detectors and noise realizations written in terms of the so-called Marcum Q-function and a ready-to-use mapping between signal-to-noise ratio (SNR) thresholds and false-alarm rates from state-of-the-art detection pipelines. The bias introduced by approximating the matched filter SNR with the optimal SNR is not symmetric: sources that are nominally below threshold are more likely to be detected than sources above threshold are to be missed. Using both analytical considerations and software injections in detection pipelines, we confirm that including noise realizations when estimating the selection function introduces an average variation of a few %. This effect is most relevant for large catalogs and specific subpopulations of sources at the edge of detectability (e.g. high redshifts).

Optimization of received signal strength in visible light communication using the combination of heuristic algorithms

SummaryLEDs are a prominent technique for a pervasive communication system using visible light communication (VLC), since LED includes long life expectancy, fast switching, and being visible light and is less expensive, which is safe for the human body, though still many technical problems presented to be addressed, especially in an indoor environment. Due to this, the major aim of this task is to afford a hybridized optimization algorithm that is highly suitable for enabling the signal to noise ratio (SNR) and received signal strength (RSS) maximization in VLC. Here, the coordinate of each point of the receiver photo detector in the VLC system is tuned by the new hybridized algorithm. The fusion of two optimization algorithms like Deer Hunting Optimization Algorithm (DHOA) and Dragonfly Algorithm (DA) termed as Fitness‐oriented Dragonfly‐based DHOA (FD‐DHOA) is used to attain the objective concerning the RSS or received power and SNR. The proposed model tries to attain maximum RSS and SNR at the receiver instead of calculating it at every angle. Moreover, the experimental analysis proves that the developed model validates the orientation that generates an optimum RSS and SNR value at the receiver.

Computational methods for the estimation of ideal current patterns in realistic human models.

To introduce a method for the estimation of the ideal current patterns (ICP) that yield optimal signal-to-noise ratio (SNR) for realistic heterogeneous tissue models in MRI. The ICP were calculated for different surfaces that resembled typical radiofrequency (RF) coil formers. We constructed numerical electromagnetic (EM) bases to accurately represent EM fields generated by RF current sources located on the current-bearing surfaces. Using these fields as excitations, we solved the volume integral equation and computed the EM fields in the sample. The fields were appropriately weighted to calculate the optimal SNR and the corresponding ICP. We demonstrated how to qualitatively use ICP to guide the design of a coil array to maximize SNR inside a head model. In agreement with previous analytic work, ICP formed large distributed loops for voxels in the middle of the sample and alternated between a single loop and a figure-eight shape for a voxel 3-cm deep in the sample's cortex. For the latter voxel, a surface quadrature loop array inspired by the shape of the ICP reached of the optimal SNR at 3T, whereas a single loop placed above the voxel reached only of the optimal SNR. At 7T, the performance of the two designs decreased to and , respectively, suggesting that loops could be suboptimal at ultra-high field MRI. ICP can be calculated for human tissue models, potentially guiding the design of application-specific RF coil arrays.

Design of spread spectrum communication system based on multipath signal synthesis

AbstractA low‐complexity anti‐multipath interference spread spectrum communication system is proposed to address shortcomings in traditional anti‐multipath technology, such as complex structures and high resource consumption. The system utilizes a fast Fourier transform to capture pseudo‐noise code signals and simultaneously detect multipath signals. Moreover, the signal‐to‐noise ratio (SNR) of each path signal is calculated, and the multipath signal is synthesized through the designed optimal SNR synthesis method to improve the SNR of the demodulated signal to reduce the bit error rate. MATLAB is used to perform functional simulations of the system to verify its feasibility. The simulation results show that the system can successfully detect and synthesize multipath signals and achieve lower communication error rates than traditional code division multiple access (CDMA) systems.

Waveform Selection Based on Discrete Prolate Spheroidal Sequences for Near-Optimal SNRs for Photoacoustic Applications

Waveform engineering is an important topic in imaging and detection systems. Waveform design for the optimal Signal-to-Noise Ratio (SNR) under energy and duration constraints can be modelled as an eigenproblem of a Fredholm integral equation of the second kind. SNR gains can be achieved using this approach. However, calculating the waveform for optimal SNR requires precise knowledge of the functional form of the absorber, as well as solving a Fredholm integral eigenproblem which can be difficult. In this paper, we address both those difficulties by proposing a Fourier series expansion method to convert the integral eigenproblem to a small matrix eigenproblem which is both easy to compute and gives a heuristic view of the effects of different absorber kernels on the eigenproblem. Another important result of this paper is to provide an alternate waveform, the Discrete Prolate Spheroidal Sequences (DPSS), as the input waveform to obtain near optimal SNR that does not require the exact form of the absorber to be known apriori.

Optimal radar waveform design for determining perforations in the oil well production zone

Radar systems model the emission medium simply as a delay and attenuation, assuming that the received signal from a point target is identical to the transmitted signal. However, when it comes to oil well walls, which are long metal cylinders, they exhibit frequency-selective behaviour and have a specific frequency response. If the transmitted waveform exceeds the channel's bandwidth, no signal is received. A low channel bandwidth results in reduced signal resolution, making it challenging to locate oil well perforations. Therefore, this paper aims to discuss the properties of the optimal waveform in terms of both signal-to-noise ratio (SNR) and resolution objectives. Additionally, it investigates conventional radar waveforms to determine which one performs best in an oil well context. The study reveals that achieving the optimum SNR and the highest resolution simultaneously is not possible, and a trade-off must be considered during waveform design.

Application of single photon counter module in weak signal detection for RF chip scanning using a quantum near field probe

AbstractDiamond based quantum sensing for on‐chip electromagnetic field imaging is an emerging field. While smaller diamond probes offer higher spatial resolution, their lower fluorescence intensity poses a challenge for the traditional Avalanche Photo Diode. In this work, we propose a tapered fiber diamond probe containing Nitrogen‐vacancy center and utilize a single photon counter module as the detector. A time domain differential pulse sequence is introduced to suppress noise caused by laser intensity fluctuation. By analyzing the relationship between the signal‐to‐noise ratio (SNR) and parameters of differential pulse sequence, we derived the formula of SNR and the basic cycle (), and obtained the optimal SNR in the same measurement time through trade‐off between two different kinds of noise. The technique was applied to a waveguide microstrip filter chip, accurately imaging the current density distribution. Our results have potential applications in on‐chip testing and failure analysis.

Secrecy outage probability and limiting threshold criteria in an optimal SNR regime by maximizing desired transfer rate

In this paper, the optimum secrecy probability has been calculated using a reduction function that optimizes the transfer rate of the user's signal for a given average broadcast power while minimizing the transfer rate of the eavesdropper's signal to ensure safe transmission. In this work, the signal-to-noise ratio (SNR) of the eavesdropper signal and the received signal are accurately estimated using matrix theory. These approximated SNRs have been studied in relation to the outage probability. By making three distinct assumptions about channel correlation, it has been possible to determine the precise secrecy outage probability. In correlated multi-antenna transmit and receive channels, this research investigates the secrecy performance of three popular diversity combining strategies—maximum ratio combining (MRC), selection combining (SC), and equal gain combining (EGC). In this research, we consider a Rayleigh fading channel with overhead communication between the transmitter and recipient. In this research, we also propose a limiting bounds condition to improve the limits on the outage probability for the Rayleigh fading environment using the three diversity combining methods. Our restricting distribution is threshold-based in order to generate precise limits on the probability of secrecy outage. An application case has been presented which discusses the impact of the proposed model for device to device communication application scenario. Our findings demonstrate that channel correlation substantially influences the probability of a secrecy outage.

IDBD-Based Beamforming Algorithm for Improving the Performance of Phased Array Radar in Nonstationary Environments

Adaptive array processing technology for a phased array radar is usually based on the assumption of a stationary environment; however, in real-world scenarios, nonstationary interference and noise deteriorate the performance of the traditional gradient descent algorithm, in which the learning rate of the tap weights is fixed, leading to errors in the beam pattern and a reduced output signal-to-noise ratio (SNR). In this paper, we use the incremental delta-bar-delta (IDBD) algorithm, which has been widely used for system identification problems in nonstationary environments, to control the time-varying learning rates of the tap weights. The designed iteration formula for the learning rate ensures that the tap weights adaptively track the Wiener solution. The results of numerical simulations show that in a nonstationary environment, the traditional gradient descent algorithm with a fixed learning rate has a distorted beam pattern and reduced output SNR; however, the IDBD-based beamforming algorithm, in which a secondary control mechanism is used to adaptively update the learning rates, showed a similar beam pattern and output SNR to a traditional beamformer in a Gaussian white noise background; that is, the main beam and null satisfied the pointing constraints, and the optimal output SNR was obtained. Although the proposed algorithm contains a matrix inversion operation, which has considerable computational complexity, this operation could be replaced by the Levinson-Durbin iteration due to the Toeplitz characteristic of the matrix; therefore, the computational complexity could be decreased to O(n), so additional computing resources are not required. Moreover, according to some intuitive interpretations, the reliability and stability of the algorithm are guaranteed.

SNR Threshold-Based Relay Association and Random Phase Rotation for Cooperative Communication

In this study, a cooperative communication system that employs multiple decode-and-forward relay nodes (RNs), in which the associated/active RNs perform phase rotation of the regenerated signals before retransmitting them to a destination node (DN), is examined. In the first phase, i.e., communication from a source node to RNs, a received signal-to-noise ratio (SNR) threshold-based RN association method is proposed. The optimal SNR thresholds are designed to maximize the bit-error-rate (BER) performance at the DN under various communication environments, such as modulation types and channel code rates. Furthermore, the number of phase rotations (PRs) in a frame is examined. Intensive numerical results show that more PRs in a frame provide better BER performance at the DN, irrespective of the communication environments. This study provides a valuable guideline for designing practical cooperative networks with multiple decode-and-forward RNs with PRs.

Photoacoustics Waveform Design for Optimal Signal to Noise Ratio

Time-frequency analysis in waveform engineering can be applied to many detection and imaging systems, such as radar, sonar, and ultrasound to improve their Signal-to-Noise Ratio (SNR). Recently, photoacoustic imaging systems have attracted researchers’ attention. However, the SNR optimization problem for photoacoustic systems has not been fully addressed. In this paper, the one-dimensional SNR optimization of the photoacoustic response to an input waveform with finite duration and energy was considered. This paper applied an eigenfunction optimization approach to find the waveform for optimal SNR for various photoacoustic absorber profiles. SNR gains via the obtained optimal waveform were compared with simple square-pulse and pulsed sinusoidal waveforms in simulations. Results showed that by using the optimal waveform, SNR can be enhanced especially if the input wave duration is comparable with the absorber time profile duration. The optimal waveforms can achieve 5%–10% higher SNR than square pulses and over 100% higher SNR compared with pulsed sinusoids. The symmetry between time and frequency domains assures similar behavior when temporal durations of the input waveforms are too short or too long compared with the absorber.

Comparison of SNR gain between quantum illumination radar and classical radar.

It has been proved that quantum illumination (QI) radar has the quantum advantages in error-probability exponent. However, the error-probability exponent is not a recognized figure of merit in the radar literature, nor does it correspond in a straightforward manner to any such figure of merit. Signal to noise ratio (SNR) gain is an important criterion in radar theory. While, the theoretical analysis of quantum enhancement in SNR gain of QI radar has not been reported. In this paper, we compare the physical fundamental of matched filter (MF), which can achieve the optimal SNR gain under white noise in classical radar theory, and phase conjugation (PC) receiver. Furthermore, the quantum enhancement of SNR gain in QI radar is studied. It is shown that QI radar with practical receivers can achieve about 3dB quantum advantage in SNR gain. In addition, in the case of extremely weak signal, it can potentially achieve tens of dB enhancement in SNR gain compared with the MF based classical radar.

Comprehensive performance analysis of hybrid FSO/RF space–air–ground integrated network

Free space optics (FSO) communication due to its large optical carrier bandwidth offers better data rates close to gigabits per second (GBPS) compared to radio frequency (RF) communication and can support seamless ubiquitous high-speed broadband connectivity, which is a significant requirement for sixth-generation (6G) communication. It is also envisioned that the data transmission in 6G communication will be over space–air–ground integrated network (SAGIN) to provide broadband global mobile connectivity. Thus, our main aim in this paper is to investigate the performance of a dual-hop (DH) system model utilizing high-altitude platform station (HAPS) as a relay station with FSO communication for SAGIN scenario, which is expected to be featured in 6G communication. Despite various advantages, HAPS-based FSO satellite communication (SATCOM) is undermined by several factors such as atmospheric turbulence, pointing errors, and atmospheric attenuation. To improve the system performance in terms of capacity and reliability, hybrid FSO/RF communication with RF link as a backup is utilized between ground station (GS) and HAPS. Further, comprehensive end-to-end system performance is investigated by deriving unified closed-form expressions for outage probability and average symbol error rate (SER). We also obtain approximate upper bound expressions for ergodic capacity and outage capacity. The asymptotic expressions are also derived to obtain the diversity order. Here, FSO and RF links are modelled using generalized Malaga distribution with non-zero boresight pointing errors and shadowed κ−μ distribution, respectively. Further, the closed-form expressions for optimum switching threshold signal-to-noise ratio (SNR) are derived and the obtained optimal SNR values are verified using a numerical optimization technique. Finally, the results show that the proposed DH SAGIN-based hybrid FSO/RF SATCOM system is more reliable as well as achieves higher capacity compared to the FSO-based SATCOM systems.

Communicating With Extremely Large-Scale Array/Surface: Unified Modeling and Performance Analysis

Wireless communications with extremely large-scale array (XL-array) correspond to systems whose antenna sizes are so large that conventional modeling assumptions, such as uniform plane wave (UPW) impingement, are no longer valid. This paper studies the mathematical modeling and performance analysis of XL-array communications. By deviating from the conventional modeling approach that treats the array elements as sizeless points, we explicitly model their physical area/aperture, which enables a unified modeling for the classical discrete antenna arrays and the emerging active continuous surfaces. As such, a generic array/surface model that accurately takes into account the variations of signal phase, amplitude and projected aperture across array elements is proposed. Based on the proposed model, a closed-form expression of the resulting signal-to-noise ratio (SNR) with the optimal single-user maximum ratio combining/transmission (MRC/MRT) beamforming is derived. The expression reveals that instead of scaling linearly with the antenna number <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> as in conventional UPW modeling, the SNR with the more generic model increases with <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> with diminishing return, which is governed by the collective properties of the array, such as the <i>array occupation ratio</i> and the physical sizes of the array along each dimension, while irrespective of the properties of the individual array element. In addition, we have derived an alternative insightful expression for the optimal SNR in terms of the <i>vertical</i> and <i>horizontal angular spans</i>, which are fully determined by the geometric angles formed by the array/surface and user location. Furthermore, we also show that our derived results include the far-field UPW modeling as a special case. One important finding during the study of far-field approximation is the necessity to introduce a new distance criterion to complement the classical Rayleigh distance, termed <i>uniform-power distance</i> (UPD), which concerns the signal amplitude/power variations across array elements, instead of phase variations as for Rayleigh distance. Extensive numerical results are provided to demonstrate the necessity of proper modeling for XL-array communications by comparing the proposed model with various benchmark models.

Enhancing critical resolution of a ghost imaging system by using a vortex beam.

In an imaging system, resolution and signal-to-noise ratio (SNR) are two important indexes to characterize imaging quality. Ghost imaging is a novel imaging method whose imaging resolution and SNR are affected by the speckle size. In this paper, the relation between speckle size and resolution as well as that between speckle size and SNR in the GI system is analyzed in detail. It is shown that the critical resolution, resolvable minimum-separation between two adjacent objects, is approximately equal to the speckle size (speckle diameter). There exists an optimum SNR when the speckle size is larger than the object size. Based on our conclusion, we propose a scheme to enhance the critical resolution of the GI system by using a vortex beam, and the enhancement ability under different topological charges is clearly presented, which can be quantized by a simple formula.

The Impact of Sparse Coding on Memory Lifetimes in Simple and Complex Models of Synaptic Plasticity

Models of associative memory with discrete state synapses learn new memories by forgetting old ones. In the simplest models, memories are forgotten exponentially quickly. Sparse population coding ameliorates this problem, as do complex models of synaptic plasticity that posit internal synaptic states, giving rise to synaptic metaplasticity. We examine memory lifetimes in both simple and complex models of synaptic plasticity with sparse coding. We consider our own integrative, filter-based model of synaptic plasticity, and examine the cascade and serial synapse models for comparison. We explore memory lifetimes at both the single-neuron and the population level, allowing for spontaneous activity. Memory lifetimes are defined using either a signal-to-noise ratio (SNR) approach or a first passage time (FPT) method, although we use the latter only for simple models at the single-neuron level. All studied models exhibit a decrease in the optimal single-neuron SNR memory lifetime, optimised with respect to sparseness, as the probability of synaptic updates decreases or, equivalently, as synaptic complexity increases. This holds regardless of spontaneous activity levels. In contrast, at the population level, even a low but nonzero level of spontaneous activity is critical in facilitating an increase in optimal SNR memory lifetimes with increasing synaptic complexity, but only in filter and serial models. However, SNR memory lifetimes are valid only in an asymptotic regime in which a mean field approximation is valid. By considering FPT memory lifetimes, we find that this asymptotic regime is not satisfied for very sparse coding, violating the conditions for the optimisation of single-perceptron SNR memory lifetimes with respect to sparseness. Similar violations are also expected for complex models of synaptic plasticity.

Convolutional autoencoder for exposure effects equalization and noise mitigation in optical camera communication.

In rolling shutter-based optical camera communication (OCC), the camera's exposure time limits the achievable reception bandwidth. In long-exposure settings, the image sensor pixels average the incident received power, producing inter-symbol interference (ISI), which is perceived in the images as a spatial mixture of the symbol bands. Hence, the shortest possible exposure configuration should be selected to alleviate ISI. However, in these conditions, the camera produces dark images with impracticable light conditions for human or machine-supervised applications. In this paper, a novel convolutional autoencoder-based equalizer is proposed to alleviate exposure-related ISI and noise. Furthermore, unlike other systems that use artificial neural networks for equalization and decoding, the training procedure is conducted offline using synthetic images for which no prior information about the deployment scenario is used. Hence the training can be performed for a wide range of cameras and signal-to-noise ratio (SNR) conditions, using a vast number of samples, improving the network fitting and the system decoding robustness. The results obtained in the experimental validation record the highest ISI mitigation potential for Manchester encoded on-off keying signals. The system can mitigate the ISI produced by exposure time windows that are up to seven times longer than the transmission symbol duration, with bit error rates (BER) lower than 10-5 under optimal SNR conditions. Consequently, the reception bandwidth improves up to 14 times compared to non-equalized systems. In addition, under harsh SNRs conditions, the system achieves BERs below the forward error correction limit for 1dB and 5 dB while operating with exposure times that are 2 and 4 times greater than the symbol time, respectively.

Low limit of detection of the AlGaN/GaN-based sensor by the Kelvin connection detection technique

The AlGaN/GaN-based sensor is a promising POCT (point-of-care-testing) device featuring miniaturization, low cost, and high sensitivity. BNP is an effective protein biomarker for the early diagnosis of HF (heart failure). In this work, a novel AlGaN/GaN device with the Kelvin connection structure and the corresponding detection technique was proposed. This technique can effectively suppress the background noise and improve the SNR (signal-to-noise ratio). A BNP detection experiment was carried out to verify the effectiveness of this technique. It is shown that compared with that of the traditional detection method, the LOD (limit of detection) was improved from 0.47 ng/mL to 1.29 pg/mL. The BNP detection experiment was also carried out with a traditional electrochemical Au-electrode sensor with the same surface functionalization steps. The AlGaN/GaN sensor showed a better LOD than the Au-electrode sensor. Moreover, the influence of AlGaN/GaN sensor package on background noise was investigated with the mechanism of the noise source revealed. Finally, based on the optimized package, the optimal SNR quiescent operating point of the AlGaN/GaN sensor was determined. By biasing the sensor at the optimal quiescent operating point and immobilizing the magnetic beads with anti-BNP on the gate of the AlGaN/GaN sensor, the LOD for BNP detection was further improved to 0.097 pg/mL.

Stochastic resonance in coupled star-networks with power-law heterogeneity

In this paper, the power-law heterogeneity of the coupling coefficients is proved to have an important influence on the output signal-to-noise ratio (SNR) of the central oscillator in coupled star-network. The network is described by dimensionless Langevin equations subjected to periodic forces and additive noise in a symmetric bistable potential. Creatively, a random variable with power-law-like distribution is constructed to model the heterogeneity of coupling coefficients. It is revealed that the degree of heterogeneity of coupling coefficients can be measured by the entropy of random variables. In numerical simulation, the output SNR of the central oscillator is obtained to divide the two-dimensional parameter space into four regions of resonance, non-resonance, sub-resonance and super-resonance. In each region, the monotonicity of output SNR curves is discussed to determine the optimal SNR and the corresponding power exponent. At last, an explanation of physical mechanism is given based on the stochastic resonance (SR) theory.

Measuring the primordial gravitational wave background in the presence of other stochastic signals

Standard methodologies for the extraction of the stochastic gravitational wave background (SGWB) from auto- or cross-correlation of interferometric signals often involve the use of a filter function.The standard optimal filter maximizes the signal-to-noise ratio (SNR) between the total SGWB and the noise.We derive expressions for the optimal filter and SNR in the presence of a target SGWB plus other unwanted components. We also generalize the methodology to the case of template-free reconstruction.The formalism allows to easily perform analyses and forecasts that marginalize over foreground signals, such as the typical ΩGW∝ f2/3 background arising from binary coalescence.We demonstrate the methodology with the LISA mission and discuss possible extensions and domains of application.