Signal-to-noise Ratio Expression Research Articles

Energy Minimization for In-Band Full-Duplex Relaying Using an Amplify-and-Forward UAV Relay

This paper investigates an in-band full-duplex (IBFD) relaying, where a fixed-wing unmanned aerial vehicle (UAV) is dispatched as an amplify-and-forward relay to forward data from a source to a destination. By considering ideal and practical IBFD cases, new received signal-to-noise ratio (SNR) expressions at the destination are derived. Armed with the newly derived SNR expressions and the existing one in literature, three different lower-bounds of the size of data received by the destination are calculated. Using the three lower-bounds of the size of data, an optimization problem corresponding to energy minimization of the IBFD relaying system subject to a total data-bit constraint in addition to a mission completion time (MCT) constraint is solved, leading to three sets of solutions. Computer simulation experiments are conducted and the accuracy of the derived SNR expressions and the three sets of solutions of the optimization problem are compared. The results demonstrated that the newly derived SNR expressions are more accurate than the existing one in literature and are more suitable to be utilized for energy minimization, and the proposed optimization method can complete the relaying task with the minimum energy and MCT. When the residual loop-interference channel power is equal to -100dB, the scheme of ideal IBFD only consumes up to 2.5% of the energy of the compared schemes regardless of the value of the total data-bit constraint.

Modular extremely large-scale array communication: Near-field modelling and performance analysis

This paper investigates the wireless communication with a novel architecture of antenna arrays, termed modular extremely large-scale array (XL-array), where array elements of an extremely large number/size are regularly mounted on a shared platform with both horizontally and vertically interlaced modules. Each module consists of a moderate/flexible number of array elements with the inter-element distance typically in the order of the signal wavelength, while different modules are separated by the relatively large inter-module distance for convenience of practical deployment. By accurately modelling the signal amplitudes and phases, as well as projected apertures across all modular elements, we analyse the near-field signal-to-noise ratio (SNR) performance for modular XL-array communications. Based on the non-uniform spherical wave (NUSW) modelling, the closed-form SNR expression is derived in terms of key system parameters, such as the overall modular array size, distances of adjacent modules along all dimensions, and the user's three-dimensional (3D) location. In addition, with the number of modules in different dimensions increasing infinitely, the asymptotic SNR scaling laws are revealed. Furthermore, we show that our proposed near-field modelling and performance analysis include the results for existing array architectures/modelling as special cases, e.g., the collocated XL-array architecture, the uniform plane wave (UPW) based far-field modelling, and the modular extremely large-scale uniform linear array (XL-ULA) of one-dimension. Extensive simulation results are presented to validate our findings.

Development and verification of the signal to noise ratio for a layer of turbulence in a multi-layer atmosphere.

Wide-field image correction in systems that look through the atmosphere generally requires a tomographic reconstruction of the turbulence volume to compensate for anisoplanatism. The reconstruction is conditioned by estimating the turbulence volume as a profile of thin homogeneous layers. We present the signal to noise ratio (SNR) of a layer, which quantifies how difficult a single layer of homogeneous turbulence is to detect with wavefront slope measurements. The signal is the sum of wavefront tip and tilt variances at the signal layer, and the noise is the sum of wavefront tip and tilt auto-correlations given the aperture shape and projected aperture separations at all non-signal layers. An analytic expression for layer SNR is found for Kolmogorov and von Kármán turbulence models, then verified with a Monte Carlo simulation. We show that the Kolmogorov layer SNR is a function of only layer Fried length, the spatio-angular sampling of the system, and normalized aperture separation at the layer. In addition to these parameters, the von Kármán layer SNR also depends on aperture size, and layer inner and outer scales. Due to the infinite outer scale, layers of Kolmogorov turbulence tend to have lower SNR than von Kármán layers. We conclude that the layer SNR is a statistically valid performance metric to be used when designing, simulating, operating, and quantifying the performance of any system that measures properties of layers of turbulence in the atmosphere from slope data.

Restricting passive attacks in 6G vehicular networks: a physical layer security perspective

Modern wireless technologies confirm the massive connectivity with sufficient data rate in intelligent transportation systems. Passive attacks may compromise the user’s transmission with increased amenities. Physical layer security can protect transmissions. The paper investigates outage probability (OP) and secrecy outage probability (SOP) for 6G enabled vehicular networks with passive eavesdroppers. The work considers the vehicular to infrastructure scenario with re configurable intelligent surfaces (RIS) instead of power-hungry roadside units. The vehicles and passive eavesdroppers are equipped with dual antennas. Specifically, for 6G vehicular networks, this work presents the analytical expressions for the received signal-to-noise ratio (SNR). We derive first-order secrecy metrics, such as outage probability and secrecy outage probability, from SNR expressions. We have derived SNR expressions for two initial receiver locations (near and far from the legitimate). Due to their robustness towards road parameters and signal parameters, the developed expressions aid in designing and simulating secrecy systems. We conclude that RIS can be more effective than regular access points because no major fluctuations have been observed in secrecy metrics under the influence of RIS.

Simultaneous Wireless Power and Data Transfer System With Full-Duplex Mode Based on Double-Side LCCL and Dual-Notch Filter

The data transmission is always necessary for wireless power transfer systems, and however, the interference between power and data is the major problem for the full-duplex simultaneous wireless power and data transfer (SWPDT) system. To solve this problem, in this article, a novel SWPDT system based on the double-side <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCCL</i> and dual-notch filter is proposed. In the power transfer channel, by the double-side <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCCL</i> topology, the high impedance of power branches at the data carrier frequency reduces the power interference largely. In the data transfer channel, the dual-notch filter is utilized to separate the data carriers and realize the full-duplex communication, which could reduce the ipsilateral data interference and improve the signal-to-noise ratio (SNR). The transfer functions of data transmission are derived by the analysis on the impedance of each part. Since the interferences of power and ipsilateral data source are analyzed, the expression of SNR could be derived and the corresponding factors to improve the SNR are discussed. An optimization of data transfer channel to maximize the SNR is proposed by shifting the dual-notch filter and transformers. The experimental setup with 400-W output power and 200-kb/s data rate is conducted to verify the feasibility of the proposed SWPDT system and the correctness of the design method.

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.

Waveform Design for High-Order QAM Faster-Than-Nyquist Transmission in the Presence of Phase Noise

The state-of-the-art radio-frequency (RF) devices limit the deployment of extremely high-order quadrature amplitude modulation (QAM) formats (e.g., 16384-QAM) to meet the high-capacity demand on microwave backhaul links. This paper turns to faster-than-Nyquist (FTN) transmission using lower-order constellations and lower-cost RF devices as a solution to the demand. To realize low-complexity interference cancellation, we pre-equalize the FTN-induced inter-symbol interference at the transmitter by using Tomlinson-Harashima precoding (THP), while at the receiver suppressing the phase noise (PHN) generated by the RF local oscillators with pilot symbol assisted approaches. However, the THP may distort the pilots, which degrades the performance of PHN compensation. To resolve this problem, we propose two pilot designs that are distortion-free to precisely estimate the PHN samples. Moreover, we derive a closed-form expression of the symbol detection signal-to-noise ratio (SNR), in terms of the THP-FTN waveform parameters. With the SNR expression, a waveform optimization procedure is developed to maximize the SNR and enhance the achievable FTN capacity. The proposed scheme is validated in the simulated platform of 4096-QAM microwave link. The results demonstrate that the FTN signaling achieves the system capacity equivalent to that of the 16384-QAM Nyquist signaling with an SNR gain of 5.8 dB.

Information Leakages in Code-based Masking: A Unified Quantification Approach

This paper presents a unified approach to quantifying the information leakages in the most general code-based masking schemes. Specifically, by utilizing a uniform representation, we highlight first that all code-based masking schemes’ side-channel resistance can be quantified by an all-in-one framework consisting of two easy-tocompute parameters (the dual distance and the number of conditioned codewords) from a coding-theoretic perspective. In particular, we use signal-to-noise ratio (SNR) and mutual information (MI) as two complementary metrics, where a closed-form expression of SNR and an approximation of MI are proposed by connecting both metrics to the two coding-theoretic parameters. Secondly, considering the connection between Reed-Solomon code and SSS (Shamir’s Secret Sharing) scheme, the SSS-based masking is viewed as a particular case of generalized code-based masking. Hence as a straightforward application, we evaluate the impact of public points on the side-channel security of SSS-based masking schemes, namely the polynomial masking, and enhance the SSS-based masking by choosing optimal public points for it. Interestingly, we show that given a specific security order, more shares in SSS-based masking leak more information on secrets in an information-theoretic sense. Finally, our approach provides a systematic method for optimizing the side-channel resistance of every code-based masking. More precisely, this approach enables us to select optimal linear codes (parameters) for the generalized code-based masking by choosing appropriate codes according to the two coding-theoretic parameters. Summing up, we provide a best-practice guideline for the application of code-based masking to protect cryptographic implementations.

Predicting the noise in hybrid (phase and attenuation) x-ray images acquired with the edge illumination technique.

To analyze the noise performance of the edge illumination phase-based x-ray imaging technique when applying "single-shot" phase retrieval. The latter consists in applying a sample-specific low-pass filter to the raw data, leading to "hybrid" images in which phase and attenuation contrast are merged with each other. The second objective is to compare the hybrid images with attenuation-only images based on their respective signal-to-noise ratio (SNR). Noise is propagated from the raw images into the retrieved hybrid images, yielding analytic expressions for the variances and noise power spectra of the latter. An expression for the relative SNR between hybrid and attenuation images is derived. A comparison with simulated data is performed. Experimental data are also shown and discussed in the context of the theory. The noise transfer into the retrieved hybrid images is strongly related to the setup and acquisition parameters, as well as the imaged sample itself. Consequently, the relative merit between hybrid and attenuation images also depends on these criteria. Generally, the hybrid approach tends to perform worse for highly attenuating samples, as the availability of phase contrast is outweighed by the loss of photons that is necessarily encountered in hybrid acquisitions. On the contrary, the hybrid approach can lead to a much better SNR for weakly attenuating samples, as here phase effects lead to much stronger contrast, outweighing the reduction in photon numbers. The analytic expressions inform the design of edge illumination setups that lead to minimum noise transfer into the retrieved hybrid images. We also anticipate our theory to guide the decision as to which imaging mode (hybrid or attenuation) to use in order to maximize SNR for a specific sample.

MIMO iterative receiver SNR estimation strategies for link to system interfacing

SummaryThis paper presents link to system (L2S) interfacing technique for multiple input and multiple output (MIMO) iterative receivers. In L2S interfacing, usually the post detection signal to noise ratio (SNR)‐based frame error rate lookup tables (LUT) are used to predict the link level performance of receivers. While L2S interfacing for linear MIMO receivers can be conveniently implemented, it is more challenging for MIMO iterative receivers due to unavailability of the closed form SNR expressions. In this paper, we propose three methods for post detection SNR estimation for MIMO iterative receivers. The first is based on the QR decomposition of the channel matrix, the second relies on the residual noise calculation based on the soft symbols, and the third exploits the closed form SNR expressions for linear receivers. A link to system interface model for iterative receivers is developed for evaluating the reference curves for different modulation and coding schemes, and results are validated by comparing the simulated and predicted frame error rates. It is shown that linear and residual noise‐based SNR approximations result in a very good prediction performance whereas the performance of QR decomposition‐based method degrades for higher order modulations and coding schemes.This paper presents link to system interfacing technique for MIMO iterative receivers. A link to system interface model for iterative receivers is developed for evaluating the reference curves for different modulation and coding schemes, and results are validated by comparing the simulated and predicted frame error rates. Three post detection SNR evaluation schemes have been proposed for link to system interfacing all of which give good prediction performance especially at lower order modulation.

ZF detectors for uplink distributed massive MIMO systems over Rayleigh‐inverse Gaussian composite fading channels

Massive multiple-input multiple-output (MIMO), together with distributed antenna systems has emerged as a promising technology in modern wireless networks because of their remarkable capacity potential and link reliability. The combined architecture, that is distributed massive MIMO (DM-MIMO) comprises of arbitrarily located multiple radio ports (RPs) each having more than one antennas and a base station containing asymptotically large number of antennas. At the outset, the instantaneous output signal to noise ratio (SNR) corresponding to individual subchannel is obtained for ZF detector. Subsequently, closed form expression of exact and high SNR approximated ergodic capacity are obtained in the context of DM-MIMO. The lower bound of ergodic capacity are then derived using a generalized approach, which may be applicable to all composite fading channels. Moreover, lower bound over all users are formulated in closed form considering large number of RPs located in a circular topology. In subsequent analysis, SER and OP characterization of the ZF detector over DM-MIMO channel is presented with tractable mathematical expressions. In addition to the per subchannel based SER, the global average SER is also evaluated for the considered configurations. Finally, the implications of model parameters on ZF detectors are analysed through a set of Monte-Carlo simulations.

A performance study on diversity receivers over κ-μ shadowed fading channels

In this study, N-branch selection combining (SC), dual-branch SC and dual-branch maximal ratio combining (MRC) receivers over κ-μ shadowed fading channels are investigated in terms of average bit error probability (BEP), outage probability (OP) and channel capacity (CC). Firstly, a cumulative distribution function (CDF) expression for instantaneous signal-to-noise ratio (SNR) at the output of the N-branch SC system over a κ-μ shadowed fading channel is derived. Based on the proposed CDF expression of output SNR for N-branch SC receiver, OP and approximate average BEP expressions are obtained. Secondly, the probability density function (PDF) expression for a dual-branch SC system over κ-μ shadowed channels is derived. Then, two different CC expressions of a dual-branch SC receiver are obtained by using the proposed PDF expression. Thirdly, a PDF expression for a dual-branch MRC system under κ-μ shadowed conditions is proposed and its CC expression with channel inversion with fixed rate for is derived. Effects of the fading parameters and the total number of branches on the system performance are examined with different scenarios. Finally, the obtained results from OP, average BEP and CC expressions are verified with numerical simulations.

Performance and optimisation of agent compression and forwarding system for correlated sources

A system for the correlated Gaussian sources to perform compression forwarding via the multi-relay network in the additive white Gaussian noise channel is proposed in this study. The characteristic of the newly proposed system is that it is composed of two parts: an analogue sensor network from the sources to multiple relay nodes and a digital communication network from multiple relay nodes to the destination node. The sensors can only perform simple analogue signal transmission, but the encoder set up at each relay can carry out complex distributed source coding DSC and then send the coded digital signals to the destination node. In this study, the authors establish the rate–distortion function of DSC based on the Chief Executive Officer problem. Combined with the channel capacity theorem, an optimal power allocation scheme is first proposed. The quantisation signal-to-noise ratio (SNR) at the destination node is used to evaluate the performance of the system under different correlations between sources. For the case of independent sources, a closed-form expression for the quantisation SNR is derived and they compare the optimised agent compress-and-forward system with the traditional amplify-and-forward system to verify that the proposed system can achieve better SNR performance.

Generic blind spectrum sensing scheme for all optical-wavelength multi-user free space optical communications

Spectrum sensing is a fundamental component in multi-user free space optical communication systems. In order to avoid interference among the users, it is required to periodically sense the optical frequency spectrum to detect if the channel is occupied by active transceiver pairs. Spectrum sensing allows the user to continuously sense the optical spectrum within their operating range to detect the channels. In this paper, we propose a generic novel blind spectrum sensing scheme for an unknown optical signal over strong atmospheric turbulence channel. By generic, we mean that the proposed scheme is applicable to all optical wavelengths, i.e. ultraviolet (UV), visible light, and infrared. The proposed blind spectrum sensing scheme is based on the estimated signal-to-noise ratio (SNR) and the noise power, for which we have derived expressions from a statistical ratio of the received signal. The atmospheric turbulence is the main reason behind the signal fading in free space optical links as it causes fluctuations in the received signal intensity. To mitigate this adverse effect, the proposed scheme is equipped with a spatial diversity scheme in the form of switch-and-stay combining. We use Gamma–Gamma distribution to model both small-scale and large-scale turbulence fadings. From the estimated SNR and noise power expressions, we formulate the novel closed-form expressions for the probabilities of detection and false alarm mathematically. Numerical and simulation results based on randomly generated optical signals are presented to verify the effectiveness of the proposed scheme.

A Novel Blind Spectrum Sensing Technique for Multi-User Ultraviolet Communications in Atmospheric Turbulence Channel

One of the primary challenges in multi-user free space optical wireless systems is to periodically sense the optical frequency spectrum at the receiver to identify whether the channel is occupied by other transceiver pairs in order to avoid interference. Spectrum sensing enables the user to continuously monitor the channel prior to its access to the channel. In this paper, we propose a novel blind spectrum sensing scheme for an unknown ultraviolet signal over strong atmospheric turbulence channel, based on the estimated signal-to-noise ratio (SNR) and the noise power. We derive this estimated SNR and the noise power from a statistical ratio of the received signal. The turbulence effect causes fluctuations in the received signal intensity, resulting in power loss at the receiver. Taking this negative effect into account, the blind SNR-based spectrum sensing scheme is equipped with spatial diversity scheme in the form of switch-and-stay combining. The intensity fluctuations are modeled by a gamma-gamma distribution. Based on the estimated SNR and noise power expressions, novel closed-form expressions for the probability of detection and the probability of false alarm are derived. It is also found that sensing capability is enhanced with the diversity scheme.

Signal-to-noise ratio reduction due to oceanic turbulence in oceanic wireless optical communication links

The effect of oceanic turbulence on the signal-to-noise ratio (SNR) at the receiver of an oceanic wireless optical communication (OWOC) link is studied. To quantify such effect, the metric employed is the reduction in the SNR when oceanic turbulence is present. SNR reduction due to oceanic turbulence is formulated by subtracting the 10 log (SNR) evaluated at the receiver in the presence of turbulence from the 10 log (SNR) evaluated at the receiver in the absence of turbulence. Classical SNR formula which is function of the received optical power, noise and optical detector parameters is utilized. As the average received power, our earlier result that uses a Gaussian optical source field and a finite Gaussian receiver aperture in atmospheric turbulence is adapted for oceanic turbulence and such found average received power is inserted in the SNR expression. OWOC links that use collimated Gaussian optical sources at the transmitter and PIN photodiode, avalanche photodiode (APD) at the receiver, are analyzed. Results that present the variations of the SNR reduction due to oceanic turbulence against the changes in the source, oceanic turbulence and the optical receiver parameters are reported.

Stochastic resonance in an asymmetric bistable system driven by multiplicative and additive Gaussian noise and its application in bearing fault detection

The phenomenon of stochastic resonance (SR) in a new asymmetric bistable model is investigated. Firstly, a new asymmetric bistable model with an asymmetric term is proposed based on traditional bistable model and the influence of system parameters on the asymmetric bistable potential function is studied. Secondly, the signal-to-noise ratio (SNR) as the index of evaluating the model are researched. Thirdly, Applying the two-state theory and the adiabatic approximation theory, the analytical expressions of SNR is derived for the asymmetric bistable system driven by a periodic signal, unrelated multiplicative and additive Gaussian noise. Finally, the asymmetric bistable stochastic resonance (ABSR) is applied to the bearing fault detection and compared with classical bistable stochastic resonance (CBSR) and classical tri-stable stochastic resonance (CTSR). The numerical computations results show that:(1) the curve of SNR as a function of the additive Gaussian noise and multiplicative Gaussian noise first increased and then decreased with the different influence of the parameters a, b, r and A; This demonstrates that the phenomenon of SR can be induced by system parameters; (2) by parameter compensation method, the ABSR performs better in bearing fault detection than the CBSR and CTSR with merits of higher output SNR, better anti-noise and frequency response capability.

Stochastic resonance in a time polo-delayed asymmetry bistable system driven by multiplicative white noise and additive color noise

Stochastic resonance (SR) in a time polo-delayed asymmetry bistable system driven by multiplicative white noise and additive color noise is investigated in this paper. First, the effective potential function is deduced based on probability density approach theory, small delay approximation theory and colored noise approximation theory. Second, the mean first-passage time (MFPT) which plays an important role in investigating on particles escape rate is derived and we find that the effect of additive color noise is more observable than that of multiplicative white noise on MFPT. Finally, influences of different parameters on SR are studied by signal-to-noise ratio (SNR). The analytic expression of SNR is derived and three-dimensional graphs of SNR with different parameters are obtained. We conclude that time delay τ and time delay strength e can suppress SR and that asymmetric item r has a non-monotone effect on SR. The results also suggest that adjusting the additive noise intensity Q is more sensitive than that of the multiplicative noise intensity D in controlling SNR.

Stochastic Resonance in Second-Order Underdamped System With Exponential Bistable Potential for Bearing Fault Diagnosis

Stochastic resonance (SR) as effective approach for weak signal detection has been widely used in bearing fault signal diagnosis. In this paper, a new method was proposed to detect fault signals, which consists of an exponential bistable potential model generalized by using a harmonic Potential (HP) model, a Gaussian potential (GP) model and second-order underdamped system. As the classical bistable SR (CBSR) has the disadvantage of output saturation, which will suppress the optimal signal-to-noise ratio (SNR) of the system, therefore, underdamped SR with exponential potential (UESR) and underdamped SR with classical bistable potential (UCSR) are applied to detect fault signal, respectively. Under the adiabatic condition, the analytical expression of the SNR is calculated for the UESR system driven by Gaussian white noise and periodic signal. Then, the effects of system parameters and the damping factor on analytical expression of SNR as a function of noise intensity for different parameters are studied, respectively. Finally, the proposed method is applied to detect simulated fault signals and actual bearing fault signals. The experimental results show that the proposed UESR method is superior to the UCSR method in fault signal diagnosis, such as larger output SNR and higher spectrum peaks at fault characteristic frequencies.

Effects of combined harmonic and random excitations on a Brusselator model

We discuss the constructive role of combined harmonic and random excitation on stochastic resonance (SR) in a Brusselator model. We first numerically investigate SR determined by the Signal-to-Noise Ratio (SNR) in this model. Effects of different parameters on SR are described in detail. Our simulation results show that the intensity of the Gaussian colored noise and the amplitude of the periodic force can enhance SR. Moreover, an analytical framework is presented for the SNR of the Brusselator model, leading to a theoretical expression of SNR. We observe a good agreement between the theoretical and numerical results, and the effectiveness of the proposed theoretical method is verified. This theoretical analysis provides a global view on how the dynamics of a periodically forced system with noise changes in the vicinity of a Hopf bifurcation.