Noise Power Estimation Research Articles

Effective Energy Detection for IoT Systems Against Noise Uncertainty at Low SNR

This paper deals with spectrum sensing for cognitive radio-based Internet of Things (IoT) systems and their coexistence with Long Term Evolution (LTE) systems. Due to the sparsity of the covariance matrix of IoT/LTE signals, we reveal that the likelihood ratio test approximates to energy detection (ED) at low signal to noise ratio. However, the noise (power) uncertainty can degrade the performance of ED severely, especially when low-cost IoT devices are employed for spectrum sensing. To tackle this issue, we derive the relationship among noise power, total power, and autocorrelation coefficient of received signals, and propose an unbiased estimator of noise power without the knowledge of the presence/absence of IoT/LTE signals. We then design a new ED with multiple estimates of noise power from historical and current sensing data, and analyze its theoretical performance. Numerical results are provided to verify the theoretical results and demonstrate the superior performance of the proposed detector. It is shown that, by exploiting sufficient historical sensing data, the performance of the proposed ED can closely approach that of the ideal ED.

Nonlinear distortion estimation in dual-carrier PM-QPSK signals for uncompensated fiber links

Abstract Kerr nonlinearity is particularly detrimental in coherent optical communications over long-haul, sub-sea and transatlantic links. The correct and accurate determination of the penalty due to fiber nonlinearity is critical for estimating the link capacity and optical signal to noise ratio margins. Two distinct approaches for calculating the power in the nonlinear field are proposed. The first approach utilizes the nonlinear variance at the decision gate after coherent detection, while the second attempts to extract the electrical field of the nonlinear interference noise. Subsequently, the power spectral density of the nonlinear interference noise is integrated to estimate the nonlinear power within a pre-defined signal-to-nose ratio criterion. Based on the assumptions in this study, a temporal resolution of 16 samples per symbol or (6.25 ps) is required to achieve a signal-to-noise ratio sensitivity of 40 dB on the nonlinear power estimate for a 10 Gbaud signal. Furthermore, a minimum pattern length of 128 symbols is required to obtain an adequate estimate of the nonlinear noise power within 30 dB signal-to-noise ratio for two adjacent wavelength-division-multiplexed (WDM) channels. The influence of the pulse shaping roll-off factor and number of WDM channels on the required pattern length and the nonlinear power estimation is also investigated.

Improved order-statistics-based noise power estimator

This paper proposes an Order-Statistics (OS) based method for the robust estimation of the noise power. By deriving the analytic expression of the OS method, one deduces appropriate weighting coefficient which minimizes the Mean Squared Error (MSE) of the noise power estimate. The derived method, referred to as improved Order-Statistics (iOS), has an MSE close to the optimal one while preserving the robustness of the standard OS method against outliers or strong interferences. Simulation results are provided to illustrate the iOS performance in terms of MSE in both homogeneous and heterogeneous cases.

Performance Analysis of CFAR Detector Based on Censored Mean and Cell Average

It is proposed in this paper that a new constant false alarm rate detector based on censored mean and cell average. The detector takes the mean value of censored mean and cell average as noise or clutter power estimation. Under homogeneous background and Swerling II target models, The detection probability analytic expressions and the false alarm probability analytic expressions of the detector are derived. In homogeneous background and multiple interfering targets situation, the detection performance of the detector is analyzed. Compared with the classical detectors, such as the cell average detector, the greatest of detector and the smallest of detector, the new detector has better detection performance both in homogeneous background and in multiple interfering targets situation.

Reliable OFDM Receiver With Ultra-Low Resolution ADC

The use of low-resolution analog-to-digital converters (ADCs) can significantly reduce power consumption and hardware cost. However, their resulting severe nonlinear distortion makes reliable data transmission challenging. For orthogonal frequency division multiplexing (OFDM) transmission, the orthogonality among subcarriers is destroyed. This invalidates conventional OFDM receivers relying heavily on this orthogonality. In this study, we move on to quantized OFDM (Q-OFDM) prototyping implementation based on our previous achievement in optimal Q-OFDM detection. First, we propose a novel Q-OFDM channel estimator by extending the generalized Turbo (GTurbo) framework formerly applied for optimal detection. Specifically, we integrate a type of robust linear OFDM channel estimator into the original GTurbo framework and derive its corresponding extrinsic information to guarantee its convergence. We also propose feasible schemes for automatic gain control, noise power estimation, and synchronization. Combined with the proposed inference algorithms, we develop an efficient Q-OFDM receiver architecture. Furthermore, we construct a proof-of-concept prototyping system and conduct over-the-air (OTA) experiments to examine its feasibility and reliability. This is the first work that focuses on both algorithm design and system implementation in the field of low-resolution quantization communication. The results of the numerical simulation and OTA experiment demonstrate that reliable data transmission can be achieved.

A Family of MMSE-Based Decision Feedback Equalizers and Their Properties for FBMC/OQAM Systems

Filter bank multi-carrier based on offset quadrature amplitude modulation (FBMC/OQAM) suffers from inter-symbol interference and inter-subchannel interference in multi-path fading channels. By exploiting the special structures of the FBMC/OQAM signal and the resulting correlation matrix and assuming perfect estimation of channel and noise power, we study the properties of the decision feedback equalizer (DFE) designed by the minimum mean square error criterion. The study leads to efficient and mathematically equivalent computation of DFE coefficients. Consequently, the DFE requires a smaller complexity in computing the equalizer coefficients than the linear equalizer, while achieving a significant performance gain in highly frequency-selective channels. Building upon the proposed efficient computation of DFE, we develop DFE-based detectors—namely, two-stage DFE and multi-band DFE—so that a better detection performance can be obtained more efficiently. Complexity analysis and simulation results demonstrate the efficacy of the proposed computation method and the DFE-based detectors.

The impact of noise power estimation on speech intelligibility in cochlear-implant speech coding strategies

The advanced combination encoder (ACE™) is an established speech-coding strategy in cochlear-implant processing that selects a number of frequency channels based on amplitudes. However, speech intelligibility outcomes with this strategy are limited in noisy conditions. To improve speech intelligibility, either noise-dominant channels can be attenuated prior to ACE™ with noise reduction or, alternatively, channels can be selected based on estimated signal-to-noise ratios. A noise power estimation stage is, therefore, required. This study investigated the impact of noise power estimation in noise-reduction and channel-selection strategies. Results imply that estimation with improved noise-tracking capabilities does not necessarily translate into increased speech intelligibility.

Adaptive threshold to guarantee both detection and false alarm probabilities in multi-taper based spectrum sensing

The multi-taper spectrum (MTS) estimator enjoys a relatively low computational complexity and high estimation accuracy making it an attractive method for spectrum sensing in cognitive radio (CR) networks. However, it is difficult to guarantee both detection and false alarm probabilities when its design is based on fixed threshold, especially when the noise power fluctuates due to channel conditions. In this paper, a new adaptive threshold method to guarantee both detection and false alarm probabilities for MTS based spectrum sensing is proposed. By means of estimating noise power and signal power, the decision of adaptive threshold is able to adapt the noise fluctuation and achieve efficient trade-off between detection and false alarm probabilities. A closed form expression for the adaptive threshold is derived for both additive white Gaussian noise (AWGN) channel and multipath fading channel. Several metrics are employed to compare the performance of the proposed adaptive threshold method with that of the fixed threshold methods such as: error decision probability, detection probability, false alarm probability and throughput. The obtained results show that the proposed method achieves better spectrum efficiency and high throughput in comparison with the conventional fixed and adaptive threshold methods presented in the literature.

Direction of Arrival estimation by modified Orthogonal Propagator Method with linear prediction in low SNR scenarios

Abstract In propagator based methods for Direction of Arrival (DoA) finding, conventional approaches for eliminating the noise impact are based on signal enhancement or noise power estimation. In this paper, a new method is introduced from another point of view. When the noise is an additive spatially and temporally white Gaussian noise, theoretically, it only impacts the diagonal elements of the data covariance matrix. Firstly, the proposed method utilizes the principle of Linear Prediction (LP) to rebuild the denoised diagonal elements of the data covariance matrix. Then, the Orthogonal Propagator Method (OPM) is directly applied for DoA estimation. Compared with the conventional OPM-based methods, the proposed method is more robust to the noise, especially in low Signal to Noise Ratio (SNR) scenarios. Simulation examples are provided to demonstrate the performance of the proposed method.

OSNR and nonlinear noise power estimation for optical fiber communication systems using LSTM based deep learning technique.

The optical signal-to-noise ratio (OSNR) and fiber nonlinearity are critical factors in evaluating the performance of high-speed optical fiber communication systems. Recently, several deep learning based methods have been put forward to monitor OSNR of a fiber communication system. In this work, we propose a long short-term memory (LSTM) network based method to simultaneously estimate OSNR and nonlinear noise power caused by fiber nonlinearity. In the training step, LSTM network extracts the essential features in frequency domain of the input signal. Then, with the built model in the training step, the LSTM output the OSNR and nonlinear noise power of the signal under test. The simulation by VPI software is carried on a 5-channel long haul optical transmission system with the launched optical power of -3.0~ + 3.0dBm per channel. The results show that the test error of OSNR is less than 1.0dB with the reference OSNR from 15 to 30dB for QPSK, 16QAM and 64QAM signal. The test error of nonlinear noise power is less than 1.0dB for QPSK and 16QAM signal when the Laser linewidth is 6 KHz and 100 KHz respectively. The proposed method is a promising candidate for nonlinearity-insensitive OSNR and accurate nonlinear noise power estimation in multi-channel long haul optical fiber communication systems.

Detection of Pilot Contamination Attack based on Uncoordinated Frequency Shifts

Pilot contamination attack is an important activity of active eavesdropping conducted by a malicious user during channel training phase. This attack is potentially harmful to the physical layer security. In this paper, motivated by the fact that frequency asynchronism could introduce divergence of the transmitted pilot signals between intended user and attacker, we propose a new uncoordinated frequency shift (UFS) scheme for detecting pilot contamination attack in multiple antenna system. During the reverse training phase of the UFS scheme, the legitimate user Bob deliberately introduces multiple random frequency shifts in the publicly known pilot sequence. Since eavesdropper Eve has no knowledge of these random frequency shifts, it is almost impossible for her to pretend exactly like Bob. This provides the opportunity to detect the presence of Eve. An attack detection algorithm is then developed based on source enumeration method. Both the asymptotic performance analysis and numerical results are provided to verify the proposed detection scheme. The proposed scheme is also enhanced based on noise power estimation to cope with attacks from a multi-antenna Eve. Furthermore, the proposed UFS scheme is extended by introducing general parameterized phase shifts. It is demonstrated that the proposed UFS scheme can achieve comparable detection performance as the existing superimposed random sequence based scheme, without sacrifice of legitimate channel estimation performance.

Performance of Hybrid Sensing Method in Environment with Noise Uncertainty

The paper presents a novel hybrid spectrum sensing method used in cognitive radio and presents a hybrid detector (HD) which improves the sensing performance. The proposed HD takes advantage of the energy detection (ED) principle and a method based on Covariance Absolute Value (CAV), as well as on Cyclic Autocorrelation Function (CAF). The paper shows the limitations of using ED, resulting from the uncertainty of spectral density of noise power estimation, known as the SNR wall. The paper describes a system model and presents simulation results for the OFDM signal of a WiMAX-based communications system. The simulation results refer to an ideal environment with well-known parameters, and to an environment with uncertain spectral density of noise power estimation.

GNSS Interference Detection Using Statistical Analysis in the Time-Frequency Domain

This paper presents a precorrelation interference detection method based on statistical analysis in the time-frequency (TF) domain for global navigation satellite system signals. In particular, the short-time Fourier transform (STFT) is considered as the TF tool due to its linear property and low computational complexity. A goodness-of-fit (GoF) test is applied to each frequency slice in the spectrogram of the received signal, which approximately follows a chi-square distribution in the absence of interference. The expected probability density function (PDF) of the observed TF-domain samples can be computed based on an interference-free signal or the noise power estimate. Two versions of the proposed technique are presented: one based on the canonical STFT with the maximum overlap size, and the other based on the block-wise STFT using nonoverlapped samples. The canonical STFT-based method shows better detection capability at the expense of degraded false alarm performance caused by the PDF distortion in the canonical STFT samples. The block-wise STFT-based method alleviates the false alarm issue but slightly weakens the detection capability. Simulations show that the proposed canonical and block-wise STFT-based methods improve the detection performance for both narrow- and wideband interference in low jammer-to-noise ratio environments when compared with the existing GoF test applied to the time-domain samples.

A Spatial Filtering Based Gridless DOA Estimation Method for Coherent Sources

In this paper, we investigate a covariance matrix reconstruction approach (CMRA) for direction-of-arrival (DOA) estimation in correlated/coherent sources scenario. We incorporate a spatial filtering (SF) model into our recently developed method CMRA in order to enhance its adaptation ability. In particular, a sliding window scheme is proposed to estimate the number of sources, and an iterative procedure is provided to estimate the DOAs of the signals. Since the original CMRA provides inaccurate estimate of the noise power which is undesirable during iterations, a new update rule for the noise power is proposed. Moreover, we derive a fast implementation of the SF-CMRA to accelerate the DOA estimation in each iteration. The proposed methods are suitable for both uniform and sparse linear arrays and are able to provide accurate estimates of DOAs, signal powers, and noise power. We also show that the proposed algorithmic framework can be easily extended to other gridless DOA estimation methods for accuracy improvement. Simulation results are provided to illustrate the superiority of our proposed methods.

Noise Power Estimators in ISM Radio Environments: Performance Comparison and Enhancement Using a Novel Samples Separation Technique

Noise power estimation is central to efficient radio resource allocation in modern wireless communication systems. In the literature, there exist many noise power estimation methods that can be classified based on underlying theoretical principle; the most common are spectral averaging, eigenvalues of sample covariance matrix, information theory, and statistical signal analysis. However, how these estimation methods compare against each other in terms of accuracy, stability, and complexity is not well studied, and the focus instead remains on the enhancement of individual methods. In this paper, we adopt a common simulation methodology to perform a detailed performance evaluation of the prominent estimation techniques. The basis of our comparison is the signal-to-noise ratio estimation in the simulated industrial, scientific and medical band transmission, while the reference noise signal is acquired from an industrial production plant using a software-defined radio platform, USRP-2932. In addition, we analyze the impact of different techniques for noise-samples’ separation on the estimation process. As a response to defects in the existing techniques, we propose a novel noise-samples’ separation algorithm based on the adaptation of rank-order filtering. Our analysis shows that the proposed solution, apart from its low complexity, has a very good root-mean-squared error of 0.5 dB and smaller than 0.1-dB resolution, thus achieving a performance comparable with the methods exploiting information theory concepts.

Edge-Fitting Based Energy Detection for Cognitive Radios

Two well-known drawbacks of energy detection sensing are its poor performance at low SNR and dependency on the accurate knowledge of noise power. To overcome these challenges in the context of wideband sensing, this paper proposes a spectrum sensing algorithm, inspired from edge detection techniques used in image processing. It is an improved, detailed and extended version of the gradient based method reported earlier (Koley et al. IEEE Communications Letters 19, 391–394, 2015). It is characterized by (i) histogram based noise power estimation for dynamic threshold computation (ii) preprocessing to obtain high detection probability with fewer numbers of samples and (iii) use of edge values as decision metric. Monte Carlo simulations as well as real-time wideband-sensed data captured through a Universal Software Radio Peripheral (USRP) is used to evaluate the performance of the algorithm. Mathematical formulations for the position of “SNR wall” and detection performance at different signal bandwidths is derived. Computational complexity of the edge-fitting scheme is shown to be lower than some of the wavelet approaches.

Coherent Power Measurements with a Compact Airborne Ka-Band Precipitation Radar

AbstractCoherent power is an alternative to the conventional noise-subtracted power technique for measuring weather radar signal power. The inherent noise-canceling feature of coherent power eliminates the need for estimating and subtracting the noise component, which is required when performing conventional signal power estimation at low signal-to-noise ratio. The coherent power technique is particularly useful when averaging a high number of samples to improve sensitivity to weak signals. In such cases, the signal power is small compared to the noise power and the required accuracy of the estimated noise power may be difficult to achieve. This paper compares conventional signal power estimation with the coherent power measurement technique by investigating bias, standard deviation, and probability of false alarm and detection rates as a function of signal-to-noise ratio and threshold level. This comparison is performed using analytical expressions, numerical simulations, and analysis of cloud and precipitation data collected with the airborne solid-state Ka-band precipitation radar (KPR) operated by the University of Wyoming.

Throughput of an Energy Harvesting Cognitive Radio Network Based on Prediction of Primary User

In this paper, a novel prediction based cooperative spectrum sensing scheme is investigated on the performance of an energy harvesting cognitive radio (CR) network. The spectrum sensing scheme is redesigned to protect the quality of service (QoS) of primary user (PU) and to improve the utilization of spectrum holes. The decision about the PU spectrum status and energy harvesting (RF and non-RF) of a CR node are based on prediction as well as sensing at individual CR level. We consider simultaneous spectrum sensing and energy harvesting scenario through the incorporation of an energy splitting device. A CR harvests from non-RF resources if both the decisions (decision of prediction and decision of spectrum sensing) do not match or if both the decisions match in favor of the absence of PU. On contrary, it harvests from RF resources while both the decisions match in favor of the presence of PU. A CR node transmits only if both decisions indicate the absence of PU. A CR user opportunistically uses the PU spectrum for its transmission purpose under a collision constraint. The collision constraint gives an extra protection to the QoS of PU on rearrival of PU. Novel analytical expressions for detection performance, harvested energy, and network throughput are developed. The impact of prediction and other network parameters such as number of detection frames, number of cooperative CR user, splitting parameter, collision probability on throughput performance is investigated. Improvement in spectrum reuse and energy penalty during harvesting is indicated. Impact of noise power estimation on the sensing performance is also studied.

Non‐linear shrinkage‐based precision matrix estimation for space–time adaptive processing

Space–time adaptive processing (STAP) is usually adopted in airborne and spaceborne radars for clutter suppression and slow moving target detection. However, for traditional sample covariance matrix inversion algorithm, there are usually not enough independent and identically distributed secondary samples to achieve a satisfactory performance. The diagonal loading methods are usually utilised to solve this finite sample problem. Nevertheless, the performance of diagonal loading STAP can be further improved by directly estimating the precision matrix and non-linearly shrinking the eigenvalues of the samples covariance matrix. This study proposes a non-linear shrinkage-based precision matrix estimation algorithm for STAP. Also, a noise power estimation method is provided so that the proposed algorithm still works well even if the noise power is not known previously. The proposed algorithm has much better performance than the diagonal loading methods whether the sample size is smaller or larger than the dimension of the covariance matrix. Besides, in the condition that the clutter-to-noise ratio is large, which is often encountered in practice, the proposed algorithm also shows a comparatively good performance. Simulations are performed to validate the proposed algorithm.

Robust dual‐sensor data sea‐surface ghost attenuation for quality control purposes

ABSTRACTThree‐dimensional receiver ghost attenuation (deghosting) of dual‐sensor towed‐streamer data is straightforward, in principle. In its simplest form, it requires applying a three‐dimensional frequency–wavenumber filter to the vertical component of the particle motion data to correct for the amplitude reduction on the vertical component of non‐normal incidence plane waves before combining with the pressure data. More elaborate techniques use three‐dimensional filters to both components before summation, for example, for ghost wavelet dephasing and mitigation of noise of different strengths on the individual components in optimum deghosting. The problem with all these techniques is, of course, that it is usually impossible to transform the data into the crossline wavenumber domain because of aliasing. Hence, usually, a two‐dimensional version of deghosting is applied to the data in the frequency–inline wavenumber domain. We investigate going down the “dimensionality ladder” one more step to a one‐dimensional weighted summation of the records of the collocated sensors to create an approximate deghosting procedure. We specifically consider amplitude‐balancing weights computed via a standard automatic gain control before summation, reminiscent of a diversity stack of the dual‐sensor recordings. This technique is independent of the actual streamer depth and insensitive to variations in the sea‐surface reflection coefficient. The automatic gain control weights serve two purposes: (i) to approximately correct for the geometric amplitude loss of the Z data and (ii) to mitigate noise strength variations on the two components. Here, Z denotes the vertical component of the velocity of particle motion scaled by the seismic impedance of the near‐sensor water volume. The weights are time‐varying and can also be made frequency‐band dependent, adapting better to frequency variations of the noise. The investigated process is a very robust, almost fully hands‐off, approximate three‐dimensional deghosting step for dual‐sensor data, requiring no spatial filtering and no explicit estimates of noise power. We argue that this technique performs well in terms of ghost attenuation (albeit, not exact ghost removal) and balancing the signal‐to‐noise ratio in the output data. For instances where full three‐dimensional receiver deghosting is the final product, the proposed technique is appropriate for efficient quality control of the data acquired and in aiding the parameterisation of the subsequent deghosting processing.