In-phase Components Research Articles

On the Capacity-Achieving Input of the Gaussian Channel With Polar Quantization

The polar receiver architecture is a receiver design that captures the envelope and phase information of the signal rather than its in-phase and quadrature components. Several studies have demonstrated the robustness of polar receivers to phase noise and other nonlinearities. Yet, the information-theoretic limits of polar receivers with finite-precision quantizers have not been investigated in the literature. The main contribution of this work is to identify the optimal signaling strategy for the additive white Gaussian noise (AWGN) channel with polar quantization at the output. More precisely, we show that the capacity-achieving modulation scheme has an amplitude phase shift keying (APSK) structure. Using this result, the capacity of the AWGN channel with polar quantization at the output is established by numerically optimizing the probability mass function of the amplitude. The capacity of the polar-quantized AWGN channel with $b_1$-bit phase quantizer and optimized single-bit magnitude quantizer is also presented. Our numerical findings suggest the existence of signal-to-noise ratio (SNR) thresholds, above which the number of amplitude levels of the optimal APSK scheme and their respective probabilities change abruptly. Moreover, the manner in which the capacity-achieving input evolves with increasing SNR depends on the number of phase quantization bits.

A Joint Automatic Modulation Classification Scheme in Spatial Cognitive Communication.

Automatic modulation discrimination (AMC) is one of the critical technologies in spatial cognitive communication systems. Building a high-performance AMC model in intelligent receivers can help to realize adaptive signal synchronization and demodulation. However, tackling the intra-class diversity problem is challenging to AMC based on deep learning (DL), as 16QAM and 64QAM are not easily distinguished by DL networks. In order to overcome the problem, this paper proposes a joint AMC model that combines DL and expert features. In this model, the former builds a neural network that can extract the time series and phase features of in-phase and quadrature component (IQ) samples, which improves the feature extraction capability of the network in similar models; the latter achieves accurate classification of QAM signals by constructing effective feature parameters. Experimental results demonstrate that our proposed joint AMC model performs better than the benchmark networks. The classification accuracy is increased by 11.5% at a 10 dB signal-to-noise ratio (SNR). At the same time, it also improves the discrimination of QAM signals.

Experimental and numerical analysis of eddy current sensor signal induced by out-of-plane fiber waviness in carbon fiber composites

Eddy current sensor signals induced by out-of-plane waviness in carbon fiber composites were investigated. Cross-ply laminates with artificial out-of-plane waviness were fabricated. The samples were scanned using an eddy current probe to measure the in-phase and quadrature phase components of the pickup coil voltage with respect to the excitation. A two-dimensional map of the pickup coil voltage amplitude indicated that it was difficult to distinguish signal changes in the waviness zone from signal changes caused by inhomogeneous electrical properties. By selecting the optimum image phase and probe rotation angle, the signal-to-noise ratio was improved greatly and the waviness was visualized without being masked by signal changes in the non-defective zone. Finite element analysis of eddy current testing was performed for various waviness amplitudes and wavelengths to obtain the relationship between the waviness dimension and the pickup coil voltage. The finite element analysis validated the enhanced sensitivity to waviness observed experimentally.

Shunt active power filtering with reference current generation based on dual second order generalized integrator and LMS algorithm

For reducing the carbon emissions from utility sector, it is important to improve the efficiency of network and electrical loads. Current harmonics are responsible for the degradation of the system as well as load efficiency. The propagation of current harmonics into the grid can be prevented with shunt active power filters (SAPFs). Reference current generation (RCG) is critical for SAPF operation. This paper presents the control of SAPF with RCG based on least mean square (LMS) and dual second order generalized integrator (SOGI). The two SOGIs separately process grid voltage and load current to determine the respective fundamental in-phase component (FPC) and fundamental quadrature component (FQC). FPC and FQC of grid voltage are used to determine the phase angle of fundamental grid voltage. With LMS algorithm the distorted current can be decomposed into fundamental active (FA), fundamental reactive (FR) and harmonic components. However, the dynamic response of LMS based estimation is poor when the same learning rate is used for all components. FQC of load current, estimated with SOGI, can be processed by LMS algorithm to separate FA and FR components. RCG can be implemented with the computed phase angle and FA component. In LMS algorithm, as only two components are to be separated, two different learning rates can be easily specified. This results in faster dynamic response for LMS algorithm and has consequent positive impact on RCG and SAPF operation. Also, the computational complexity is considerably reduced. The performance of SAPF with the proposed extraction algorithm is analyzed for different operating conditions and comparative analysis is carried out.

Estimating grapevine-relevant physicochemical soil zones using apparent electrical conductivity and in-phase data from EMI methods

This study explores the ability of the frequency domain electromagnetic induction (EMI) method to produce physicochemical soil maps with relevance to grapevine vigor. The study was conducted in the Médoc area of the Bordeaux wine region in France. A flexible clustering approach was used with both the apparent electrical conductivity and the in-phase components of EMI measurements. Soil zones with distinct physicochemical signatures were successfully identified, primarily due to the inclusion of in-phase data in the clustering method. Importantly, this approach does not use prior information to guide zone classification and does not require calibration of EMI measurements. Extensive soil texture and physicochemical measurements were used to compare the different zones identified by the clustering approach. Grapevine vigor was assessed using normalized vegetation index (NDVI) data to help conceptualize the critical physicochemical variables of the soil. It was evident that NDVI and EMI data were correlated to organic matter, nitrogen, CEC, pH, CaO, and copper concentration in one of the investigated sites. Unlike previous work in other Bordeaux soil viticulture areas, soil texture at these sites was relatively homogenous and consequently did not influence plant vigor substantially. This work demonstrates the value of the in-phase component of EMI measurements to estimate soil zonation. More generally, this work demonstrates the ability of coupled EMI and NDVI surveys to inform viticulture at scales relevant to management decisions.

Automatic Modulation and Recognition of Robot Communication Signal Based on Deep Learning Neural Network

In order to solve the problem that the traditional method of manually extracting expert features for communication signal recognition has large limitations and low accuracy under low signal-to-noise ratio, this paper proposes an automatic modulation and recognition method of robot communication signal based on deep learning neural network. In this method, the received signal is preprocessed to obtain the complex baseband signal including in-phase component and quadrature component. The signal is used as the data set of the input convolution neural network model. The model structure and the super parameters such as convolution kernel, step size, characteristic graph, and activation function are adjusted through multiple training, and the trained model is used to extract and recognize the features of the communication signal. It realizes the identification and classification of seven types of digital communication signals: 2FSK, 4FSK, BPSK, 8PSK, QPSK, QAM16, and QAM64. The experimental results show that the average recognition accuracy of the seven signals has reached 94.61% when the signal-to-noise ratio is 0 dB. Conclusion. The algorithm is proved to be effective and has high accuracy under the condition of low signal-to-noise ratio.

Nonlinear MIMO Communication With π-Periodic Phase Measurements

This paper proposes a nonlinear MIMO scheme named as halved-phase only MIMO (HPO-MIMO), whose base station (BS) is equipped with multiple HPO radio-frequency (RF) chains extracting <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pi $ </tex-math></inline-formula> -periodic phase measurements from RF signals directly by phase detectors, and single classical RF chain sampling the combination of all the RF signals from HPO-RF chains. Compared to MIMO, HPO-RF receivers are simplified significantly, and have much lower power consumption and fabrication cost. Two types of channel estimators and multiuser detectors are developed for HPO-MIMO from the perspectives of numerical optimization and Bayesian inference. Firstly, because <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pi $ </tex-math></inline-formula> -periodic phases provide tan-relationships between the Inphase (I) and Quadrature (Q) components, the channel estimation (CE) and multiuser detection (MUD) problems are resolved by minimizing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{2}$ </tex-math></inline-formula> -norm cost functions with unit-norm constraint on the recovered vector. Their solutions are obtained by deriving the eigenvector corresponding to the minimum eigenvalue through shifted power method (SPW). Secondly, the CE and MUD problems are categorized as generalized linear mixing problems under (un-)quantized <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pi $ </tex-math></inline-formula> -periodic phase measurements, and then handled by generalized approximate message passing (GAMP), where closed-form solutions for mean-and-variance messages involving <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pi $ </tex-math></inline-formula> -periodic phases are derived. Finally, magnitude and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pi $ </tex-math></inline-formula> -phase ambiguities persisting in signal recovery are removed based on the complex-valued full measurements from the single classical RF chain. Simulation results show that GAMP-type algorithms outperform SPW-type ones, and handle nonlinear phase quantization losses. 16-sector quantized HPO-MIMO could work as well as its un-quantized correspondence. HPO-MIMO reserves the MIMO advantages, but is more energy-efficient than the latter.

A Straightforward Quadrature Signal Generator for Single-Phase SOGI-PLL With Low Susceptibility to Grid Harmonics

Suppressing the negative effects of grid voltage harmonics on the estimated frequency of a phase-locked loop (PLL) is a challenge in literature. This article proposes an easy-to-implement quadrature signal generator (QSG) to attenuate the oscillations on the estimated frequency in single-phase grid-connected inverters, which use second-order generalized integrator (SOGI)-PLL. It is shown that SOGI exerts a stronger filtering effect in generating the quadrature signal than the in-phase signal. Against this background, in this work, a modified integrator is introduced into the path of the in-quadrature signal to generate another in-phase component with much lower harmonic content. The proposed method imposes only a small computational burden on the existing SOGI-PLL compared to the previously presented methods that address the input voltage harmonic problem. Moreover, this method can work properly within the allowable range of grid voltage frequency deviations. The proposed integrator benefits from an error-decaying mechanism to overcome dc drift in pure integrators. The integrator has been designed based on theoretical equations. The validity of the proposed QSG and theoretical equations is evaluated using simulations and experimental studies. A fixed-point representation of the proposed QSG is also provided for implementation on low-cost microcontrollers.

Replay spoof detection using energy separation based instantaneous frequency estimation from quadrature and in-phase components

Replay attacks in speech are becoming easier to mount with the advent of high quality of recording and playback devices. This makes these replay attacks a major concern for the security of Automatic Speaker Verification (ASV) systems and voice assistants. In the past, auditory transform-based as well as Instantaneous Frequency (IF)-based features have been proposed for replay spoofed speech detection (SSD). In this context, IF has been estimated either by derivative of analytic phase via Hilbert transform, or by using high temporal resolution Teager Energy Operator (TEO)-based Energy Separation Algorithm (ESA). However, excellent temporal resolution of ESA comes with lacking in using relative phase information and vice-versa. To that effect, we propose novel Cochlear Filter Cepstral Coefficients-based Instantaneous Frequency using Quadrature Energy Separation Algorithm (CFCCIF-QESA) features, with excellent temporal resolution as well as relative phase information. CFCCIF-QESA is designed by exploiting relative phase shift to estimate IF, without estimating phase explicitly from the signal. To motivate and validate effectiveness of proposed QESA approach for IF estimation, we have employed information-theoretic measures, such as Mutual Information (MI), Kullback–Leibler (KL) divergence, and Jensen–Shannon (JS) divergence. The proposed CFCCIF-QESA feature set is extensively evaluated on standard statistically meaningful ASVSpoof 2017 version2.0 dataset. When evaluated on the ASVSpoof 2017 v2.0 dataset, CFCCIF-QESA achieves improved performance as compared to CFCCIF-ESA and CQCC feature sets on GMM, CNN, and LCNN classifiers. Furthermore, in the case of cross-database evaluation using ASVSpoof 2017 v2.0 and VSDC, CFCCIF-QESA also performs relatively better as compared to CFCCIF-ESA and CQCC on GMM classifier. However, for the case of self-classification on the ASVSpoof 2019 PA data, CFCCIF-QESA only outperforms CFCCIF-ESA. Whereas, on BTAS 2016 dataset, it performs relatively close to CFCCIF-ESA. Finally, results are presented for the case when the ASV system is not under attack.

Ligand Modified and Light Switched On/Off Single-Chain Magnets of {Fe 2 Co} Coordination Polymers via Metal-to-Metal Charge Transfer

Ligand Modified and Light Switched On/Off Single-Chain Magnets of {Fe ₂ Co} Coordination Polymers via Metal-to-Metal Charge Transfer

RanNet: Learning Residual-Attention Structure in CNNs for Automatic Modulation Classification

With the rapid emergence of advanced technologies for wireless communications, automatic modulation classification (AMC) has been deployed in the physical layer to blindly identify the modulation fashion of an incoming signal at the receiver and consequently improve the efficiency of spectrum utilization and management. Although recent works on AMC have adopted deep learning with convolutional neural networks (CNNs) to deal with large-confusing signal data, they have shown to be vulnerable to channel deterioration by primitive architectures. In this letter, we design a high-performance CNN architecture, namely Residual-attention Convolutional Network (RanNet), that mainly involves multiple advanced processing blocks to learn intrinsic features of combined waveform data (including in-phase, quadrature, amplitude, and phase components). Each block incorporates attention connection and skip connection in a sophisticated-designed structure to strengthen relevant features and weaken irrelevant features while preventing the network from vanishing gradient. Simulation results on the RadioML 2018.01A dataset show that RanNet is robust to different channel impairments and outperforms state-of-the-art deep networks in terms of accuracy while having a reasonable complexity.

Ultrasonic array imaging of highly attenuative materials with spatio-temporal singular value decomposition

With the increasing use of high density polyethylene (HDPE) pipes in nuclear industry which puts safety at the forefront, ultrasonic array imaging methods play a vital role in the structural integrity of HDPE pipe materials. However, the viscoelastic attenuation of HDPE pipe materials significantly decreases the level of signals, leading to a low signal-to-noise ratio caused by electronic noise. In this work, a domain-adapted spatio-temporal singular value decomposition (STSVD) processing algorithm combined with the total focusing method is proposed to improve the ultrasonic array image quality. First, the real-valued radio frequency (RF) data or A-scan signals are demodulated into the complex analytic signals containing in-phase and quadrature (I/Q) components. Then, the STSVD processing algorithm is used to filter the I/Q data, and the filtered I/Q data is converted into RF signals. Finally, the total focusing method is applied to the processed RF signals to produce the image of the region under detection as a stage of post-processing. Experiments are carried out with an ultrasonic linear phased array in contact with the HDPE pipe materials containing multiple side-drilled holes and through-wall notches. Results show that the proposed method can produce images with high quality to provide good inspection and characterization of defects in highly attenuative materials, especially the deeper defects.

Understanding the neutron noise induced by fuel assembly vibrations in linear theory

This paper investigates the underlying physical mechanisms involved in the monochromatic vibrations of fuel assemblies and their effects on the induced neutron noise throughout the core of nuclear reactors, in the framework of simplified benchmark configurations. Any vibrating fuel pin introduces noise sources at the frequency of vibrations, as well as at higher harmonics, the first one being the most significant of those. Depending on the harmonics considered, the position of the vibrating fuel pin, the size of the core and its macroscopic cross-sections, different noise responses are observed within the reactor core. Through the lens of a decomposition of the neutron noise into its point-kinetics component and its deviation from it, the spectrum of noise responses is explained and related to the spatial distribution of the amplitude and phase of the noise sources at the considered frequencies. At the frequency of vibration, possible out-of-phase behaviour of the induced neutron noise can be partially or totally shadowed by the in-phase point-kinetics component, the only exception being for central vibrations in symmetrical systems. At the frequency of the first higher harmonics, the structure of the induced neutron noise is more involved. Nevertheless, due to the compensation of the individual responses associated to the different components of the noise source at that frequency, point-kinetics has a significant contribution. The results of this work sheds new light on the complex spatial pattern of the neutron noise computed by realistic core simulators in case of vibrations of fuel assemblies.

Deep Learning-Based Indoor Localization Using Multi-View BLE Signal.

In this paper, we present a novel Deep Neural Network-based indoor localization method that estimates the position of a Bluetooth Low Energy (BLE) transmitter (tag) by using the received signals’ characteristics at multiple Anchor Points (APs). We use the received signal strength indicator (RSSI) value and the in-phase and quadrature-phase (IQ) components of the received BLE signals at a single time instance to simultaneously estimate the angle of arrival (AoA) at all APs. Through supervised learning on simulated data, various machine learning (ML) architectures are trained to perform AoA estimation using varying subsets of anchor points. In the final stage of the system, the estimated AoA values are fed to a positioning engine which uses the least squares (LS) algorithm to estimate the position of the tag. The proposed architectures are trained and rigorously tested on several simulated room scenarios and are shown to achieve a localization accuracy of 70 cm. Moreover, the proposed systems possess generalization capabilities by being robust to modifications in the room’s content or anchors’ configuration. Additionally, some of the proposed architectures have the ability to distribute the computational load over the APs.

Time Domain Multiplexed LoRa Modulation Waveform Design for IoT Communication

Long-Range (LoRa) is one of the emerging technologies in low-power wide-area networks (LPWANs). In this letter, we proposed a Time Domain Multiplexed LoRa (TDM-LoRa) modulation to improve the throughput of conventional LoRa by using up-chirp and down-chirp simultaneously. A low complexity non-coherent algorithm for the TDM-LoRa modulation is also presented. We then derive an analytical expression for the bit error rate (BER) of non-coherent demodulation in the additive white Gaussian noise (AWGN) channel. In addition, a scheme that encodes information bits on both in-phase and quadrature components of the TDM-LoRa symbol is presented to further improve the system data rate. Performance analysis and simulation show that our proposed schemes can achieve better spectral efficiency (SE) and throughput without obvious bit error rate (BER) degradation compared to the LoRa Physical Layer (PHY) scheme.

New magnetic intermediate state, “B-phase,” in the cubic chiral magnet MnSi

It is well known that the archetype chiral magnet MnSi stabilizes a skyrmion lattice, termed “A-phase,” in a narrow temperature range in the vicinity of the paramagnetic boundary around Tc ∼ 29 K and Hc ∼ 2 kOe. Recently, it has been predicted that at much lower temperatures below Tc, the conical helicoid and the forced ferromagnetic (FFM) states could be separated by a new “unknown state.” In order to detect this “unknown state,” we explored the phase diagram of MnSi oriented single crystals as a function of the d.c. magnetic field (H⃗dc) and the temperature (T) by using a.c. magnetization measurements. For H⃗dc∥ 〈111〉, we observed a new region, termed “B-phase,” in the magnetic phase diagram, characterized by a flat-valley-like anomaly on the in-phase component of the a.c. magnetization (m′), over 3.5 ≤ Hdc ≤ 6.2 kOe just below the low temperature (T &amp;lt; 6 K) FFM boundary. The observed frequency independence over 0.3–1000 Hz and the absence of any measurable absorption in the a.c. magnetization (m″) in the “B-phase” suggest a static nature. The “B-phase” was not observed for either H⃗dc∥ 〈100〉 or 〈110〉, revealing that the magnetic anisotropy could play a role in the stabilization of the phase. The “B-phase” could be compatible with the theoretical predictions if the new magnetic state is supposedly related with a relative reorientation of the four helices in MnSi.

The Deserted Manor of Noer, Schleswig-Holstein, Germany. Geophysical Prospection Methods in Comparison

Manors are an important component of the cultural-economic history of Northern Germany and Southern Scandinavia. We present the results of a geophysical prospection that led to the identification of a previously unknown manor near the village of Noer, Schleswig-Holstein, Northern Germany. Although magnetic gradiometry provides a fast way to cover large areas, it does not provide accurate depth estimates, is affected by magnetic blanking and is unable to detect differences in water content. Therefore, we applied a combination of different geophysical methods to optimize the non-invasive reconstruction of the target and its surroundings not only with respect to building structures but also in relation to the surrounding landscape. In particular, a combination of magnetics, ground-penetrating radar (GPR), electromagnetic induction (EMI), electrical resistivity tomography (ERT), and soil samples were carried out to determine: (1) the object's exact location; (2) the building structure and state of preservation; and (3) any additional structures in the surrounding area. We detected a tripartite building of 22 by 27 m, with several inner walls, which was located underneath a topographic high on the surveyed field. The bulk structure is identifiable most clearly in the magnetic and EMI inphase component maps. GPR profiles and soil samples indicate flooring or foundations in part of the building. Their shallow depths of less than 2 m below the surface and debris clusters close to the surface indicate at least partial demolition. A surrounding wall was found about 5 m outside the building. The area in between shows no magnetic anomalies, lower resistivities in EMI and ERT, and low GPR reflection amplitudes. Soil samples suggest a moat or other water feature. Archaeological artifacts found at the location characterize the building as a 16th to 17th century brick manor. Other objects, like a suspected farmyard and access path could not be found. A comparison with historical sources suggest that the mansion is in relation to the manor Grönwohld. After a change of the owner it was degraded to a Meierhof, and subsequently the building decayed and was forgotten.

An FPGA-based multi-agent Reinforcement Learning timing synchronizer

In this paper we propose a Timing Recovery Loop for PSK and QAM modulations based on swarm Reinforcement Learning, suitable for FPGA implementation. We apply the Q-RTS algorithm, a hardware-oriented multi-agent version of Q-Learning, to a symbol synchronizer. One agent is in charge to synchronize the In-phase component and a second agent is applied to the Quadrature component. If compared to a loop based on a single-agent Q-Learning, we obtain improved synchronization capabilities in terms of recovery time and immunity to sub-optimal sampling. The Q-RTS timing recovery is up to 3 times faster than its Q-Learning counterpart. The implementation results show a low power consumption and a high throughput allowing the proposed synchronizer to be used in high-speed telecommunications systems.

Fully Complex Deep Learning Classifiers for Signal Modulation Recognition in Non-Cooperative Environment

Deep learning (DL) classifiers have significantly outperformed traditional likelihood-based or feature-based classifiers for signal modulation recognition in non-cooperative environments. However, despite these recent improvements, the conventional DL classifiers still have an unintended problem in handling the received signal in which the in-phase and quadrature components are separated. Even though the two components seem to be individually uncorrelated to each other, they are definitely the theoretical real and imaginary parts of a signal sample in the complex domain. Thus, it may be helpful for a classifier to regard and treat the modulated signal as a complex data array representing beneficial mutual information between the two real data arrays. In this paper, we propose two types of fully complex convolutional neural network (CNN) and residual neural network (ResNet) classifiers that deal with the complex data instead of the two separated data. First, we organize and define the core complex operations for implementing the complex DL classifiers. Next, the architectures of the proposed classifiers are realized by applying the structural optimizations and the regularization technique. Then, the various aspects of the classifiers’ performance are analyzed and explained for providing comprehensive and deep understandings: (a) the effectiveness of the complex signal handling, (b) the in-depth evaluation of classification accuracy, (c) the impact of the data size on performance, and (d) the computational complexity. The experimental results show that the proposed classifiers can provide the faster learning speed, the higher optimization, and the better generalization with sacrificing acceptable learning and classification costs. Especially, our approaches remarkably improve the performance on the mutually correlated modulation types (i.e., the phase-related modulations: PSK, APSK, and QAM) even in the less-scale datasets.

Two-Stage ML Detector Using Absolute Value of IQ Components and SVM for Adaptive OFDM-IM

Among various index modulation technology, adaptive orthogonal frequency division multiplexing with index modulation (A-OFDM-IM) improves reliability by solving the problem of deep fading. However, the maximal likelihood (ML) detector of A-OFDM-IM has high complexity by simultaneously performing active subcarrier detection and quadrature amplitude modulation (QAM) symbol demodulation. A simpler type of ML detector can be applied since the A-OFDM-IM has independent active states of each subcarrier and uses a single QAM constellation. In this paper, we propose two low-complexity detectors for the A-OFDM-IM. The proposed detectors have a two-stage receiving process, active subcarrier detection, and QAM demodulation. In active subcarrier detection, the presence or absence of the QAM symbol is more important than its information. Therefore we derive the thresholds using the absolute value of the in-phase and quadrature components of the received signal in the frequency domain. Using the absolute value, the distribution of noise added to inactive subcarrier is half normal. This is different from noise distribution of the ML detector, and the proposed detectors select the threshold considering the corresponding noise distribution. The first proposed detector uses a threshold derived by the ML estimation method. The second detector estimates the active subcarriers via a support vector machine. The proposed detectors have lower complexity than the ML detector because of the divided receiving process. Moreover, the theoretical analysis and simulation results show that the proposed detectors have better reliability than the ML detector due to different noise distribution and thresholds.