Signal-to-noise Ratio Cases Research Articles

Exposure-Referred Signal-to-Noise Ratio for Digital Image Sensors

The signal-to-noise ratio (SNR) is a fundamental tool to measure the performance of an image sensor. However, confusions sometimes arise between the two types of SNRs. The first one is the output-referred SNR which measures the ratio between the signal and the noise seen at the sensor&#x2019;s output. This SNR is easy to compute, and it is linear in the log-log scale for most image sensors. The second SNR is the exposure-referred SNR, also known as the input-referred SNR. This SNR considers the noise at the input by including a derivative term to the output-referred SNR. The two SNRs have similar behaviors for sensors with a large full-well capacity. However, for sensors with a small full-well capacity, the exposure-referred SNR can capture some behaviors that the output-referred SNR cannot. While the exposure-referred SNR has been known and used by the industry for a long time, a theoretically rigorous derivation from a signal processing perspective is lacking. In particular, while various equations&#x00A0;can be found in different sources of the literature, there is currently no paper that attempts to assemble, derive, and organize these equations&#x00A0;in one place. This paper aims to fill the gap by answering four questions: (1) How is the exposure-referred SNR derived from first principles? (2) Is the output-referred SNR a special case of the exposure-referred SNR, or are they completely different? (3) How to compute the SNR efficiently? (4) What utilities can the SNR bring to solving imaging tasks? New theoretical results are derived for image sensors of <i>any</i> bit-depth and full-well capacity.

Improved CEM for Speech Harmonic Enhancement in Single Channel Noise Suppression

The periodic nature of voiced speech is often exploited to restore speech harmonics and to increase inter-harmonic noise suppression. In particular, a recent paper proposed to do this by manipulating the speech harmonic frequencies in the cepstral domain. The manipulations were carried out on the cepstrum of the excitation signal, obtained by the source-filter decomposition of speech. This method was termed Cepstral Excitation Manipulation (CEM). In this contribution we further analyse this method, point out its inherent weakness and propose means to overcome it. First of all, it will be shown by both illustrative examples and theoretical analysis that the existing method underestimates the excitation, especially at low signal to noise ratio (SNR) conditions. This inherent weakness leads to speech harmonic weakening and vocoding due to the insufficient noise suppression in the inter-harmonic regions. Then, we propose two modifications to improve the robustness and performance of CEM in low SNR cases. The first modification is to use an instantaneous amplifying factor adapted to the signal, instead of a pre-defined constant, for the excitation cepstrum. The second modification is to smooth the excitation cepstrum to preserve additional fine structure, instead of discarding it. These modifications result in better preservation of speech harmonics, more refined fine structure and higher inter-harmonic noise suppression. Experimental evaluations using a range of standard instrumental metrics conclusively demonstrate that our proposed modifications clearly outperform the existing method, especially in extremely noisy conditions.

A Time-Frequency Joint Time-Delay Difference Estimation Method for Signal Enhancement in the Distorted towed Hydrophone Array

To acquire the enhanced underwater ship-radiated noise signal in the presence of array shape distortion in a passive sonar system, the phase difference of the line-spectrum component in ship-radiated noise is often exploited to estimate the time-delay difference for the beamforming-based signal enhancement. However, the time-delay difference estimation performance drastically degrades with decreases of the signal-to-noise ratio (SNR) of the line-spectrum component. Meanwhile, although the time-delay difference estimation performance of the high-frequency line-spectrum components is generally superior to that of the low-frequency one, the phase difference measurements of the high-frequency line-spectrum component often easily encounter the issue of modulus 2π ambiguity. To address the above issues, a novel time-frequency joint time-delay difference estimation method is proposed in this paper. The proposed method establishes a data-driven hidden Markov model with robustness to phase difference ambiguity by fully exploiting the underlying property of slowly changing the time-delay difference over time. Thus, the phase difference measurements available for time-delay difference estimation are extended from that of low-frequency line-spectrum components in a single frame to that of all detected line-spectrum components in multiple frames. By jointly taking advantage of the phase difference measurements in both time and frequency dimensions, the proposed method can acquire enhanced time-delay difference estimates even in a low SNR case. Both simulation and at-sea experimental results have demonstrated the effectiveness of the proposed method.

Robust Adaptive Beamforming based on Automatic Variable Loading in Array Antenna

Diagonal loading technology is widely used in array antenna beamforming because of its simple method, low computational complexity and the ability to improve the robustness of beamformer. On this basis, this paper proposes a robust adaptive beamforming method based on automatic variable loading technology. The automatic variable loading matrix (AVLM) of the method is composed of two parts. The non-uniform loading matrix dominants when the input signal-to-noise ratio (SNR) is small, effectively control the influence of noise disturbance without affecting the ability of array antenna to suppress interference. The variable diagonal loading matrix dominants when the input SNR is high to improve the output performance of array antenna. Simulated results show that compared to other methods, the proposed method has better output performance for both low and high input SNR cases.

High-Resolution Time Delay Estimation Algorithms Through Cross-Correlation Post-Processing

Conventional cross-correlation (CC) and matched filter (MF) algorithms fail to resolve the multipath signals in cases when they are spaced within a Rayleigh resolution limit. Further post-processing of the CC outputs is necessary to improve the performance of CC. In this work, we propose two high-resolution time delay estimation algorithms by post-processing of the CC outputs. The first method applies a Richardson-Lucy deconvolution algorithm used in image deblurring to the CC outputs (Dec-CC). The proposed Dec-CC algorithm yields narrow beams to improve the estimation resolution and accuracy and achieve excellent performance in low signal-to-noise ratio (SNR) environments. The second method reformulates CC as a sparse signal recovery (SSR) problem and estimates time delay via weighted L1 norm minimization (CC-WL1). CC-WL1 also performs excellently for low SNR cases. Simulation results show that the proposed Dec-CC and CC-WL1 algorithms outperform other counterparts.

Nonlinear AVA Inversion Based on a Novel Quadratic Approximation for Fluid Discrimination

Fluid discrimination plays an important role in reservoir exploration and development. At present, the fluid factors used for fluid discrimination are estimated by linear AVA inversion methods based on the linear approximations of the Zoeppritz equations. However, the Zoeppritz equations show that the relationship between prestack AVA reflection coefficients and reservoir parameters is highly nonlinear. Therefore, inversion methods based on linear approximations will seriously influence the nonuniqueness and uncertainty of inversion results. In this paper, a nonlinear inversion based on the quadratic approximation is carried out to reduce the nonuniqueness and uncertainty of fluid factor. Firstly, in order to directly invert the fluid factor, a novel quadratic approximation in terms of the fluid factor (ρf), shear modulus, and density on both sides of the reflection interface is derived based on poroelasticity theory. Then, a nonlinear inversion objective function is constructed using the novel quadratic approximation in a Bayesian framework, and the Gauss-Newton method is adopted to minimize this objective function. The synthetic data example shows that the new method can obtain reasonable fluid factor inversion results even in low SNR (signal-to-noise ratio) case. Finally, the proposed method is also applied to field data which shows that it can effectively discriminate reservoir fluids.

Closed expression of source signal's DOA information in sensor array

In this study, a novel closed expression of direction of arrival (DOA) information (DI) in a single-source scenario is proposed, which is more convenient than the theoretical expression to evaluate the performance of DOA estimation. Firstly, the authors give a uniform linear array system model, where the DI is expressed as the mutual information between the source and the received signal with complex additive white Gaussian noise. Then the posterior probability density function of DOA is deduced. Moreover, by dividing the integral interval into a signal part and a noise part, a novel closed approximate expression of DI is derived. It contains the posteriori entropy in low and high signal-to-noise ratio (SNR) cases and the normalised probability. The normalised probability is obtained through a normalisation procedure on the basis of the correlation functions. As special cases, the closed expression of DI in low and high SNR cases is given and some interesting relationships between physical quantities are revealed. Finally, numerical results are presented to verify the effectiveness of the proposed approximate closed expression.

Secrecy Performance Analysis of UAV Assisted Relay Transmission for Cognitive Network With Energy Harvesting

The unmanned aerial vehicle (UAV) assisted transmission can significantly improve the spectrum efficiency and coverage of the wireless communication network. The paper proposed a cooperative secrecy transmission mechanism, which can take advantage of transmitter signal of primary user (PU) as a dedicated radio frequency (RF) source with decode and forward (DF) UAV selection and energy harvesting (EH) under cognitive network. Specifically, the transmitting signal of PU in the cognitive network can be viewed and used as energy to drive secondary user (SU) nodes and multi-relay nodes to send signals. It was worth noting that the DF UAV relay may bring about the unexpected noise and decrease the received signal to noise ratio (SNR), therefore, the multiple UAV assisted relays selected with secrecy capacity maximization criteria under cognitive network was proposed and investigated in detail, where the destination node equipped with multiple antennas and adopted the optimal antenna selection receiver. Moreover, By using the function analysis method, the closed expressions of the system secrecy outage probability (SOP) and the probability of non-zero secrecy capacity were calculated and derived accurately. Furthermore, the asymptotic expressions of the UAV assisted relay system under the large SNR cases were analyzed in detail, where the expressions of secrecy diversity order and secrecy diversity gain of the UAV assisted relay cognitive system were obtained thoroughly. Simulation results verified the effectiveness of the proposed mechanism and the correctness of the calculation.

Comparison of Geometrically Shaped 32-QAM and Probabilistically Shaped 32-QAM in a Bandwidth-Limited IM-DD System

We use the generalized pair-wise optimization (PO) algorithm to optimize the geometrically shaped 32-ary quadrature amplitude modulation (GS-32-QAM) constellation and adopt the probabilistic fold shaping (PFS) scheme to generate the probabilistically shaped 32-QAM (PS-32-QAM) format. We present a detailed comparison among the application of GS-32-QAM, PS-32-QAM and uniform 32-QAM in an intensity modulation/direct detection (IM/DD) system with a bandwidth-limited digital-to-analog converter (DAC). We experimentally demonstrate the 32-QAM discrete Fourier transform-spread (DFT-S) discrete multi-tone (DMT) signal transmission over 1-km standard single mode fiber (SSMF) in an IM/DD system with a net data rate of 108.29-Gb/s/λ, and achieve 0.6 dB and 0.9 dB receiver sensitivity gain using PS and GS constellations, respectively. In the high signal to noise ratio (SNR) case with a net bit rate of 69.61-Gb/s/λ, the PS-32-QAM DMT signal can provide the receiver sensitivity gain of 0.5 dB while the receiver sensitivity gain of the GS-32-QAM DMT signal is 0.4 dB, compared to the uniform 32-QAM DMT signal. Although PS-32-QAM achieves better receiver sensitivity gain than GS-32-QAM in the high SNR case, the proposed GS-32-QAM format outperforms PS-32-QAM in the low SNR case.

Impulsive Modelling of Noise for OFDM Systems in Power Line Communication: A Necessity or a Redundant Task?

In Power Line Communication, variations in the characteristics of power lines and additive noise reduce the efficiency of Orthogonal Frequency Division Multiplexing (OFDM), and that makes channel estimation essential. The earlier estimation techniques in the literature assume channel noise is Gaussian as in the wireless communication, whereas the recent ones model the corrupted noise more realistic, impulsive, which results in complicated receivers. This study judges the need of impulsive noise modelling and complex receivers. The performances of two Maximum A-Posteriori (MAP) channel estimators proposed for additive Gaussian noise and impulsive noise are compared under impulsive noise. The channel data used in the simulations is taken from the literature and impulsive noise is modelled by Middleton Class A distribution. The results show that the MAP estimator, which assumes Gaussian noise instead of impulsive, has better performance. The MAP estimator which assumes impulsive noise has a satisfactory performance under weak impulsive noise and low Signal to Noise Ratio (SNR) only, otherwise its performance is low, close to Maximum Likelihood estimator performance. The estimator designed for Gaussian noise has a better performance even under heavy impulsive noise and this distinction is clearer for low SNR cases.

Detection performance analysis of hybrid MIMO radar

This study focuses on the detection performance analysis of a notional hybrid MIMO radar, which can be seen as a combination of the phased-array and distributed MIMO radars. The signal model of the proposed hybrid MIMO radar is re-derived using the Rayleigh target model. In the sense of Neyman–Person principle, the optimal detector is developed. Then, the detection performance bound is derived based on the relative entropy. Theoretical derivation and numerical examples show that, for most common signal-to-noise ratio (SNR) cases, the detection performance of the hybrid MIMO is better than the conventional phased-array and MIMO radars. Furthermore, for the high SNR case, the proposed system configuration with larger number of sub-arrays performs better detections, while in the low SNR case, that with smaller number of sub-arrays performs better detections.

New fast multi‐user beam training scheme based on compressed sensing theory for millimetre‐wave communication

Compensating for the considerable propagation loss, millimetre-wave communication systems adopt large antenna arrays and beamforming technologies to obtain high antenna gains. The beamforming training is rather time-consuming especially in multi-user cases. To reduce the training overhead, a new fast multi-user training scheme based on Compressed Sensing theory is proposed. This scheme includes a multi-user training algorithm and a corresponding semi-fixed semi-random codebook design strategy. The base station (BS) simultaneously broadcasts the training pilots to all user equipments (UEs). Then all UEs independently conduct the proposed training algorithm from channel responses. Finally, all UEs send back the training results to the BS. Compared to the exhaustive search algorithm's training overhead ξ = K r K t , the cost of the proposed scheme is only O ( ξ ) = log ⁡ ( K r K t ) , where K r and K t denote the number of beam patterns in the receiver and the transmitter. Simulation results show that the proposed scheme achieves excellent performance in high SNR (signal-to-noise ratio) cases with only 3 − 5 % performance difference from the theoretical bound. And in contrast with other Compressed Sensing schemes with random codebooks, the proposed scheme reduces the sensitivity to transmission SNR and improves approximately 3 dB performance in low SNR cases.

Multiuser precoding scheme and achievable rate analysis for massive MIMO system

We analyze the downlink multiuser precoding of massive multiple input multiple output (MIMO) system, where the base station (BS) has ideal channel state information (CSI) and adopts three types of different linear precoding schemes, i.e., maximum ratio transmission (MRT), zero-forcing (ZF), and minimum mean squared error (MMSE). Under a Rayleigh fading channel, we attain the exact expressions on the achievable rate for these three precoding schemes. Moreover, we provide several insights on the achievable rates and reveal the relation of the number of BS antennas, the number of users, and the input signal-to-noise ratio (SNR) with the achievable rates respectively. It is found in general that the achievable rate increases with the number of BS antennas and the input SNR. To be more specific, the MRT precoding scheme is much inferior to the ZF and MMSE precoding schemes and tends to be at a fixed rate at the high SNR case. On the contrary, the MRT precoding scheme outperforms ZF precoding schemes at the low SNR case. Moreover, the total achievable rate always does not increase with the number of users and the optimal number of users always exists for the ZF and MMSE precoding schemes.

Integrated ensemble noise-reconstructed empirical mode decomposition for mechanical fault detection

Abstract A new branch of fault detection is utilizing the noise such as enhancing, adding or estimating the noise so as to improve the signal-to-noise ratio (SNR) and extract the fault signatures. Hereinto, ensemble noise-reconstructed empirical mode decomposition (ENEMD) is a novel noise utilization method to ameliorate the mode mixing and denoised the intrinsic mode functions (IMFs). Despite the possibility of superior performance in detecting weak and multiple faults, the method still suffers from the major problems of the user-defined parameter and the powerless capability for a high SNR case. Hence, integrated ensemble noise-reconstructed empirical mode decomposition is proposed to overcome the drawbacks, improved by two noise estimation techniques for different SNRs as well as the noise estimation strategy. Independent from the artificial setup, the noise estimation by the minimax thresholding is improved for a low SNR case, which especially shows an outstanding interpretation for signature enhancement. For approximating the weak noise precisely, the noise estimation by the local reconfiguration using singular value decomposition (SVD) is proposed for a high SNR case, which is particularly powerful for reducing the mode mixing. Thereinto, the sliding window for projecting the phase space is optimally designed by the correlation minimization. Meanwhile, the reasonable singular order for the local reconfiguration to estimate the noise is determined by the inflection point of the increment trend of normalized singular entropy. Furthermore, the noise estimation strategy, i.e. the selection approaches of the two estimation techniques along with the critical case, is developed and discussed for different SNRs by means of the possible noise-only IMF family. The method is validated by the repeatable simulations to demonstrate the synthetical performance and especially confirm the capability of noise estimation. Finally, the method is applied to detect the local wear fault from a dual-axis stabilized platform and the gear crack from an operating electric locomotive to verify its effectiveness and feasibility.

Timing Acquisition and Error Analysis for Pulse-Based Terahertz Band Wireless Systems

Terahertz (THz) band communication is envisioned as a key technology to satisfy the increasing demand for ultrabroadband wireless systems, thanks to its ultrabroad bandwidth. Tailored for the unique properties of pulse-based communications in the THz band, two timing acquisition algorithms are proposed and analyzed thoroughly in this paper. First, a low-sampling-rate (LSR) synchronization algorithm is proposed, by extending the theory of sampling signals with finite rate of innovation in the communication context and exploiting the properties of the annihilating filter. The simulation results show that the timing accuracy at an order of ten picoseconds is achievable. In particular, the LSR algorithm has high performance with uniform sampling at $1/20$ of the Nyquist rate when the signal-to-noise ratio (SNR) is high (i.e., greater than 18 dB). Complementary to this, a maximum likelihood (ML) approach for timing acquisition is developed, which searches for the timing offsets by adopting a two-step acquisition procedure based on the ML criterion. The simulation results show that the ML-based algorithm is well suitable in the low SNR case with a half-reduced search space. For further evaluation, the error performance and the resulting bit-error-rate sensitivity to the timing errors in the LSR and the ML algorithms are both analytically and numerically studied. This paper provides very different and promising angles to efficiently and reliably solve the timing acquisition problem for pulse-based THz band wireless systems.

Improved Wideband DOA Estimation Using Modified TOPS (mTOPS) Algorithm

Test of orthogonality of projected subspaces (TOPS) estimates directions of arrival of wideband sources by exploiting orthogonality between signal and noise subspaces in spectral domain. TOPS performs well at mid signal-to-noise ratio (SNR) range, but fares poorly at high SNR and noise-free cases. The TOPS pseudospectrum often exhibits spurious peaks at all SNR levels. This paper attempts to explain the cause of poor performance, and proposes suitable modifications to extend the effectiveness of TOPS from low SNR to noise-free case. The proposed modified-TOPS (mTOPS) achieves reduction in spurious peaks by incorporating signal-subspace projection instead of null-space projection used in TOPS. It also uses trace as performance metric, instead of loss of rank used in TOPS. The effectiveness of mTOPS has been studied via simulations.

Robust and Efficient Frequency Estimator for Undersampled Waveforms Based on Frequency Offset Recognition.

This paper proposes an efficient frequency estimator based on Chinese Remainder Theorem for undersampled waveforms. Due to the emphasis on frequency offset recognition (i.e., frequency shift and compensation) of small-point DFT remainders, compared to estimators using large-point DFT remainders, it can achieve higher noise robustness in low signal-to-noise ratio (SNR) cases and higher accuracy in high SNR cases. Numerical results show that, by incorporating a remainder screening method and the Tsui spectrum corrector, the proposed estimator not only lowers the SNR threshold of detection, but also provides a higher accuracy than the large-point DFT estimator when the DFT size decreases to 1/90 of the latter case.

A Regression Approach to Single-Channel Speech Separation Via High-Resolution Deep Neural Networks

We propose a novel data-driven approach to single-channel speech separation based on deep neural networks (DNNs) to directly model the highly nonlinear relationship between speech features of a mixed signal containing a target speaker and other interfering speakers. We focus our discussion on a semisupervised mode to separate speech of the target speaker from an unknown interfering speaker, which is more flexible than the conventional supervised mode with known information of both the target and interfering speakers. Two key issues are investigated. First, we propose a DNN architecture with dual outputs of the features of both the target and interfering speakers, which is shown to achieve a better generalization capability than that with output features of only the target speaker. Second, we propose using a set of multiple DNNs, each intending to be signal-noise-dependent (SND), to cope with the difficulty that one single general DNN could not well accommodate all the speaker mixing variabilities at different signal-to-noise ratio (SNR) levels. Experimental results on the speech separation challenge (SSC) data demonstrate that our proposed framework achieves better separation results than other conventional approaches in a supervised or semisupervised mode. SND-DNNs could also yield significant performance improvements over a general DNN for speech separation in low SNR cases. Furthermore, for automatic speech recognition (ASR) following speech separation, this purely front-end processing with a single set of speaker-independent ASR acoustic models, achieves a relative word error rate (WER) reduction of 11.6% over a state-of-the-art separation and recognition system where a complicated joint back-end decoding framework with multiple sets of speaker-dependent ASR acoustic models needs to be implemented. When speaker-adaptive ASR acoustic models for the target speakers are adopted for the enhanced signals, another 12.1% WER reduction over our best speaker-independent ASR system is achieved.

Robust spectrum sensing algorithm based on free probability theory

AbstractIn low signal‐to‐noise ratio (SNR) cases, the performance of spectrum sensing algorithms cannot meet the practical needs, which is a major problem faced by spectrum sensing technology in current cognitive radio field. Now, existing algorithms based on random matrix theory (RMT) have high sensing performance, but they require a large number of samples, which are very difficult to satisfy in practice. Free probability theory (FPT) is a main branch of RMT. It describes the asymptotic behavior of large random matrices and portrays a strong link between two matrices and their sum or product matrices. FPT can also be utilized to the digital communication system that can be modeled by random matrices and has been applied to spectrum sensing in simplified ideal channels, for example, additive white Gaussian noise channel. The most pivotal issue and difficulty of the FPT‐based methods is to set up and solve the asymptotic freeness equation corresponding to a specific communication model. In this paper, FPT‐based spectrum sensing schemes are proposed for some typical wireless communication systems, such as multiple‐input multiple‐output system, Rayleigh multipath fading system, and orthogonal frequency division multiplexing system. It is shown that the asymptotic freeness behavior of random matrices and the property of Wishart distribution can be used to assist spectrum sensing for these typical systems with low SNR and very limited samples. Simulation results demonstrate that compared with the existing RMT‐based spectrum detection methods, for example, the maximum and minimum eigenvalue detectors, the proposed FPT‐based schemes offer superior detection performance and are more robust to low SNR cases, especially for a small sample of observations. Copyright © 2015 John Wiley &amp; Sons, Ltd.

Energy Efficiency Optimization With Interference Alignment in Multi-Cell MIMO Interfering Broadcast Channels

Characterizing the fundamental energy efficiency (EE) performance of multiple-input–multiple-output interfering broadcast channels (MIMO-IFBC) is important for the design of green wireless system. In this paper, we propose a new network architecture proposition based on EE maximization for Multi-Cell MIMO-IFBC within the context of interference alignment (IA). Particularly, EE is maximized subject to maximum power and minimum throughput constraints. We propose two schemes to optimize EE for different signal-to-noise ratio (SNR) regions. For high-SNR operating regions, we employ a grouping-based IA scheme to jointly cancel intra- and inter-cell interferences and thus transform the MIMO-IFBC to a single-cell MIMO scenario. A gradient-based power adaptation scheme is proposed based on water-filling power adaptation and singular value decomposition to maximize EE for each cell. For moderate SNR cases, we propose an approach using dirty paper coding (DPC) with the principle of multiple access channel and broadcast channel duality to perform IA while maximizing EE in each cell. The algorithm in its dual form is solved using a subgradient method and a bisection searching scheme. Simulation results demonstrate the superior performance of the proposed schemes over several existing approaches. It also shows that interference-nulling-based IA approaches outperform hybrid DPC-IA approach in high-SNR region, and the opposite occurs in low-SNR region.