Signal-to-noise Ratio Estimation Research Articles

Maximum Likelihood Estimation of SNR for Diffusion-Based Molecular Communication

We investigate the problem of estimation of a signal-to-noise ratio (SNR) measure for diffusion-based molecular communication (DMC) systems. Considering molecular concentration-encoded signal with residual noise, we present the SNR estimation using maximum likelihood principle with sampled observations. Moreover, we derive the Cramer–Rao lower bound and assess the performance of our proposed estimator in terms of its mean square error. Our analysis helps in designing a reliable DMC system with a memoryless receiver nanomachine.

On the Equivalence of Maximum SNR and MMSE Estimation: Applications to Additive Non-Gaussian Channels and Quantized Observations

The minimum mean-squared error (MMSE) is one of the most popular criteria for Bayesian estimation. Conversely, the signal-to-noise ratio (SNR) is a typical performance criterion in communications, radar, and generally detection theory. In this paper, we first formalize an SNR criterion to design an estimator, and then we prove that there exists an equivalence between MMSE and maximum-SNR estimators, for any statistics. We also extend this equivalence to specific classes of suboptimal estimators, which are expressed by a basis expansion model (BEM). Then, by exploiting an orthogonal BEM for the estimator, we derive the MMSE estimator constrained to a given quantization resolution of the noisy observations, and we prove that this suboptimal MMSE estimator tends to the optimal MMSE estimator that uses an infinite resolution of the observation. Besides, we derive closed-form expressions for the mean-squared error (MSE) and for the SNR of the proposed suboptimal estimators, and we show that these expressions constitute tight, asymptotically exact, bounds for the optimal MMSE, and maximum SNR.

Analysis and Modeling of Imperfections in Multi-Bit Per Stage Pipelined ADCs

In this paper, an approach to estimate signal to noise ratio (SNR) and effective number of bits (ENOB) in nonideal multi-bit stages of pipelined analog to digital converters (ADCs) is presented. The most significant error sources in multistage ADCs are the capacitor mismatch and the finite and imprecise gain of amplifier. Output voltage of each stage in pipelined ADC is modeled by an ideal and a nonideal output, where nonideal output is the error due to circuit imperfections in each stage. Using an appropriate model, the SNR and ENOB due to circuit nonidealities and in terms of standard deviation of random errors are calculated. Simulation results show the accuracy of the analytical proposed approach in estimation of SNR and ENOB in multi-bit per stage pipelined converters.

신호 대 잡음비 추정 방법을 이용한 다중 주파수 밴드 잡음 억제 시스템

본 논문은 밀접한 간격의 두 개의 마이크 배열 환경에서 SNR(Signal-to-Noise Ratio) 추정을 통한 잡음 억제 방법을 제안한다. 기존의 방법은 전 밴드에서 간섭 함수 기반의 SNR 추정을 통해 이득 함수를 얻는 잡음 억제 방법을 사용한다. 그러나 이 방법은 잡음으로 인한 손상이 모든 특징 벡터 성분에 영향을 미쳐 성능을 저하시키는 문제점을 가지고 있다. 따라서 주파수 영역의 신호를 N개의 다중 주파수 밴드로 구분하고 각 밴드별로 간섭 함수 기반의 SNR 추정을 통한 이득 함수를 얻는 잡음 억제 방법을 제안한다. 제안하는 방법의 성능평가는 ITU-T(International Telecommunications Union Telecommunication)에서 제공되는 객관적인 품질 평가 방법인 PESQ(Perceptual Evaluation of Speech Quality)로 비교하여 나타내었다. This paper proposes a noise suppression method through SNR (Singal-to Noise Ratio) estimation in the two microphone array environment of close spacing. The conventional method uses a noise suppression method for a gain function obtained through the SNR estimation based on coherence function from full band. However, this method cause performance decreased by the noise damage that affects all the feature vector component. So, we propose a noise suppression method that allocates a frequency domain signal into N constant multi frequency band and each frequency band gets a gain function through SNR estimation based on coherence function. Performance evaluation of the proposed method is shown by comparison with PESQ (Perceptual Evaluation of Speech Quality) value which is an objective quality evaluation method provided by the ITU-T (International Telecommunications Union Telecommunication).

Signal‐to‐noise ratio mismatch in polar codes

Theoretically, the accurate signal-to-noise ratio (SNR) is necessary when using a successive cancelation (SC) or belief propagation (BP) decoder for polar codes. However, the effect of an SNR mismatch on the bit error rate performance of polar codes has not been addressed yet. The sensitivity of polar decoding with SC and BP decoders to the mismatch of SNR is studied. Theoretical and simulation results show that an estimation of SNR is not necessary for polar codes from a practical point of view.

Performance of signal-to-noise ratio estimation for scanning electron microscope using autocorrelation Levinson-Durbin recursion model.

A new technique to quantify signal-to-noise ratio (SNR) value of the scanning electron microscope (SEM) images is proposed. This technique is known as autocorrelation Levinson-Durbin recursion (ACLDR) model. To test the performance of this technique, the SEM image is corrupted with noise. The autocorrelation function of the original image and the noisy image are formed. The signal spectrum based on the autocorrelation function of image is formed. ACLDR is then used as an SNR estimator to quantify the signal spectrum of noisy image. The SNR values of the original image and the quantified image are calculated. The ACLDR is then compared with the three existing techniques, which are nearest neighbourhood, first-order linear interpolation and nearest neighbourhood combined with first-order linear interpolation. It is shown that ACLDR model is able to achieve higher accuracy in SNR estimation.

Two-Stage Supervised Learning-Based Method to Detect Screams and Cries in Urban Environments

Smartphones can enable monitoring signs of distress as a human goes about his daily routine. Motivated by this possibility of 24x7 distress detection, we investigate detection of screaming and crying in urban environments, which we categorize into the contexts of indoors (home and office), outdoors, human conversation, large human gatherings, machinery, and audio from multimedia devices. Prior works are often restricted to specific environments or controlled settings. We propose a novel two-stage supervised learning based method, with tunable decision parameters for each stage, to achieve a desired true distress (scream and cry) detection rate (DR) and false alarm rate (FAR). We observe that the choice of the parameters is a function of the signal-to-noise ratio (SNR) of the distress signal, which is the ratio of the power of the distress signal to the power of the context audio. In the absence of SNR information, we show that a simple SNR estimation scheme performs well. Alternately, we show how the decision parameters can be selected based on the context estimated by the method. We show the results of testing the proposal over hundred hours of audio data recorded by the smartphones of ten volunteers as they went about their daily routines. Achieved performance is exemplified by a DR of 93.16% and a FAR of 4.76% at a SNR of 20 dB. The corresponding values for a SNR of 10 dB are 84.13% and 4.77%. Finally, we compare with, which also deals with audio event detection in noisy environments.

Signal‐to‐noise ratio estimation for DVB‐S2 based on eigenvalue decomposition

Signal-to-noise ratio (SNR) estimation is required in many receivers and systems of communications. In this study, the authors propose a novel SNR estimation method for DVB-S2 over additive white Gaussian noise channel. This is a non-data-aided, eigenvalue decomposition-based method. First, they use the even and odd component vectors of received signal to construct a novel 2 × 2 matrix, and propose an estimation variable using the standard condition number of this matrix. And then, they derive the relationship between this variable and SNR, and give the detailed expressions for SNR estimation on different modulations used in DVB-S2, including quadrature phase shift keying, 8PSK, 16 amplitude PSK (APSK) and 32APSK. Monte Carlo simulation results show the good estimation performance for different modulations. The proposed method is asymptotic unbiased and can be used for both constant and non-constant modulus constellations such as M-ary PSK, MAPSK and M-ary quadrature amplitude modulation.

Maximum Likelihood SNR Estimation of Hyper Cubic Signals Over Gaussian Channel

In this letter, we address the problem of closed-form data aided (DA) and non-data aided (NDA) maximum likelihood (ML) signal-to-noise ratio (SNR) estimation for hyper-cubic modulated signals over Gaussian channel. The requirement of high SNR is exploited to derive closed-form expression of unbiased NDA ML SNR estimator. Exact expressions for the DA and NDA Cramer-Rao lower bound (CRLB) on the variance of these estimators are also determined analytically. The Monte Carlo simulation method is used to compute the normalized mean squared error (NMSE) of the estimators, and the results show that the NMSEs approach the respective normalized CRLBs.

EM‐based SNR estimator for faster‐than‐Nyquist signalling system

Considering the intentionally introduced inter-symbol interference and coloured noise, proposed is a new signal-to-noise ratio (SNR) estimator based on the expectation–maximisation algorithm for the faster-than-Nyquist signalling system. The proposed SNR estimator can maximise the likelihood function by iteratively using the soft information from the channel decoder. Moreover, the new SNR estimator can be applied into high-order modulation. The performance of the proposed SNR estimator is verified and tested.

Automatic modulation format/bit-rate classification and signal-to-noise ratio estimation using asynchronous delay-tap sampling

We propose a novel technique for automatic classification of modulation formats/bit-rates of digitally modulated signals as well as non-data-aided (NDA) estimation of signal-to-noise ratio (SNR) in wireless networks. The proposed technique exploits modulation format, bit-rate, and SNR sensitive features of asynchronous delay-tap plots (ADTPs) for the joint estimation of these parameters. Simulation results validate successful classification of three commonly-used modulation formats at two different bit-rates with an overall accuracy of 99.12%. Similarly, in-service estimation of SNR in the range of 0−30 dB is demonstrated with mean estimation error of 0.88 dB. The proposed technique requires low-speed asynchronous sampling of signal envelope and hence, it can enable simple and cost-effective joint modulation format/bit-rate classification and NDA SNR estimation in future wireless networks.

Harmonic Phase Estimation in Single-Channel Speech Enhancement Using Phase Decomposition and SNR Information

In conventional single-channel speech enhancement, typically the noisy spectral amplitude is modified while the noisy phase is used to reconstruct the enhanced signal. Several recent attempts have shown the effectiveness of utilizing an improved spectral phase for phase-aware speech enhancement and consequently its positive impact on the perceived speech quality. In this paper, we present a harmonic phase estimation method relying on fundamental frequency and signal-to-noise ratio (SNR) information estimated from noisy speech. The proposed method relies on SNR-based time-frequency smoothing of the unwrapped phase obtained from the decomposition of the noisy phase. To incorporate the uncertainty in the estimated phase due to unreliable voicing decision and SNR estimate, we propose a binary hypothesis test assuming speech-present and speech-absent classes representing high and low SNRs. The effectiveness of the proposed phase estimation method is evaluated for both phase-only enhancement of noisy speech and in combination with an amplitude-only enhancement scheme. We show that by enhancing the noisy phase both perceived speech quality as well as speech intelligibility are improved as predicted by the instrumental metrics and justified by subjective listening tests.

Improved signal‐to‐noise ratio estimation algorithm for asymmetric pulse‐shaped signals

The split-symbol moment estimation (SSME) algorithm is a conventional method to estimate the signal-to-noise ratio (SNR) in communication systems for M-ary phase shift keying signals. However, the conventional SSME is based on the assumption of symmetric pulse-shaping waveforms, and becomes no longer proper when the shaping pulse is asymmetric. In this study, the authors propose a modified SSME algorithm for asymmetric pulse-shaped signals, based on an odd-even symbol splitting approach. Simulation results show that the modified SSME outperforms the conventional SSME for both symmetric and asymmetric pulse-shaped signals in terms of SNR estimation accuracy.

Reduced Complexity SNR Estimation via Kolmogorov-Smirnov Test

Two complexity reducing schemes are proposed in this letter for the recently presented Kolmogorov-Smirnov (K-S) test based signal-to-noise ratio (SNR) estimator. The K-S test based SNR estimator can work properly over an extended SNR range for various multilevel constellations with limited signal samples, but involves considerably more add operations as a result for the huge amount of reference signals needed for matching operations. The proposed two complexity reducing schemes explore the order characteristic of the SNR matching pool to accelerate the searching procedure. For the situation under consideration, the computational complexities (numbers of add operation) of the two proposed schemes are about 1/5 and 1/20 of the original one respectively. Simulation results have verified these schemes' effectiveness.

Shrinkage‐based biased signal‐to‐noise ratio estimator using pilot and data symbols for linearly modulated signals

In diverse engineering problems including wireless communications, the estimate of the signal-to-noise ratio (SNR) is required. In this study, the authors develop a shrinkage-based SNR estimator in the data-aided and non-data-aided schemes for higher M-ary phase-shift-keying (M ≥ 8) and quadrature amplitude modulations. The observed Cramer-Rao lower bound is used as the variance of the expectation maximisation estimator to determine the optimal shrinkage factor. Simulation results show that the normalised mean-squared error of the proposed method is lower than that of the expectation maximisation method for low and moderate SNR conditions.

Compressed SNR-and-channel estimation for beam tracking in 60-GHz WLAN

Signal-to-noise ratio (SNR) and channel estimations are critical for 60-GHz communications to track the optimal transmission and reception beam pairs. However, the excessive pilot overhead for the estimations severely reduces system throughput in fast-rotation scenarios. In order to address this problem, we firstly demonstrate the potential sparseness property of 60-GHz channel in beam tracking; subsequently, via exploiting this property, we propose a novel compressed SNR-and-channel estimation. The estimation is conducted in a three-stage fashion, including the unstructured estimation, nonzero-tap detection, and structured estimation with nonzero- tap location. Numerical simulations show that, in the case of substantial reduction of the pilot overhead, the proposed estimator still reveals a significant improvement in terms of estimation performance over the scheme in IEEE 802.11ad. Furthermore, it is also demonstrated that the proposed SNR and channel estimators can approach the lower bounds in sparse channels so long as SNR exceeds 8 dB.

Measuring the signal-to-noise ratio of a neuron

The signal-to-noise ratio (SNR), a commonly used measure of fidelity in physical systems, is defined as the ratio of the squared amplitude or variance of a signal relative to the variance of the noise. This definition is not appropriate for neural systems in which spiking activity is more accurately represented as point processes. We show that the SNR estimates a ratio of expected prediction errors and extend the standard definition to one appropriate for single neurons by representing neural spiking activity using point process generalized linear models (PP-GLM). We estimate the prediction errors using the residual deviances from the PP-GLM fits. Because the deviance is an approximate χ(2) random variable, we compute a bias-corrected SNR estimate appropriate for single-neuron analysis and use the bootstrap to assess its uncertainty. In the analyses of four systems neuroscience experiments, we show that the SNRs are -10 dB to -3 dB for guinea pig auditory cortex neurons, -18 dB to -7 dB for rat thalamic neurons, -28 dB to -14 dB for monkey hippocampal neurons, and -29 dB to -20 dB for human subthalamic neurons. The new SNR definition makes explicit in the measure commonly used for physical systems the often-quoted observation that single neurons have low SNRs. The neuron's spiking history is frequently a more informative covariate for predicting spiking propensity than the applied stimulus. Our new SNR definition extends to any GLM system in which the factors modulating the response can be expressed as separate components of a likelihood function.

Optimal Power Allocation for Channel Estimation in MIMO-OFDM System with Per-Subcarrier Transmit Antenna Selection

A novel hybrid channel estimator is proposed for multiple-input multiple-output orthogonal frequency- divi- sion multiplexing (MIMO-OFDM) system with per-subcar- rier transmit antenna selection having optimal power allo- cation among subcarriers. In practice, antenna selection information is transmitted through a binary symmetric control channel with a crossover probability. Linear mini- mum mean-square error (LMMSE) technique is optimal technique for channel estimation in MIMO-OFDM system. Though LMMSE estimator performs well at low signal to noise ratio (SNR), in the presence of antenna-to-subcar- rier-assignment error (ATSA), it introduces irreducible error at high SNR. We have proved that relaxed MMSE (RMMSE) estimator overcomes the performance degrada- tion at high SNR. The proposed hybrid estimator combines the benefits of LMMSE at low SNR and RMMSE estimator at high SNR. The vector mean square error (MSE) expres- sion is modified as scalar expression so that an optimal power allocation can be performed. The convex optimiza- tion problem is formulated and solved to allocate optimal power to subcarriers minimizing the MSE, subject to transmit sum power constraint. Further, an analytical expression for SNR threshold at which the hybrid estimator is to be switched from LMMSE to RMMSE is derived. The simulation results show that the proposed hybrid estimator gives robust performance, irrespective of ATSA error.

Cramér-Rao Bounds for SNR Estimation of Oversampled Linearly Modulated Signals

Most signal-to-noise ratio (SNR) estimators use the receiver matched filter output sampled at the symbol rate, an approach which does not preserve all information in the analog waveform due to aliasing. Thus, it is relevant to ask whether avoiding aliasing could improve SNR estimation. To this end, we compute the corresponding data-aided (DA) and nondata-aided (NDA) Cramér-Rao bounds (CRBs). We adopt a novel dual filter framework, which is shown to be information-preserving under suitable conditions and considerably simplifies the analysis. It is shown that the CRB can be substantially reduced by exploiting any available excess bandwidth, depending on the modulation scheme, the SNR range, and the estimator type (DA or NDA).

Binary mask estimation for noise reduction based on instantaneous SNR estimation using Bayes risk minimisation

The binary mask approach has been researched to suppress noise and improve speech intelligibility in noisy environments. An algorithm that estimates the binary mask for noise-corrupted speech based on the instantaneous signal-to-noise ratio (SNR) estimation is proposed. The instantaneous SNR estimation is performed by minimising the Bayes risk with a weighted cost function. In the experiments, white noise was used for the training of the SNR estimator and the binary mask estimation was performed for babble, factory, speech-shaped noise. The experimental results show that the proposed method yields substantial improvements in terms of classification accuracy for the binary mask estimation.