Vertical boxes algorithm (VBA) for non-cooperative automatic discrimination between digital signals with amplitude information (AI) from those without AI is presented. The problem is not new and several solutions have been proposed. Unlike them VBA needs no information about propagation conditions and the received signal parameters. No SNR and noise distribution assumptions are made, no carrier frequency and no thresholds are required. The only assumption made is the symbol rate interval which may be as wide as desired. The signal is considered only in the time domain. VBA also distinguishes between some other classes of signals.
New Data Association Technique for Target Tracking in Dense Clutter Environme...CSCJournals
Improving data association process by increasing the probability of detecting valid data points (measurements obtained from radar/sonar system) in the presence of noise for target tracking are discussed in manuscript. We develop a novel algorithm by filtering gate for target tracking in dense clutter environment. This algorithm is less sensitive to false alarm (clutter) in gate size than conventional approaches as probabilistic data association filter (PDAF) which has data association algorithm that begin to fail due to the increase in the false alarm rate or low probability of target detection. This new selection filtered gate method combines a conventional threshold based algorithm with geometric metric measure based on one type of the filtering methods that depends on the idea of adaptive clutter suppression methods. An adaptive search based on the distance threshold measure is then used to detect valid filtered data point for target tracking. Simulation results demonstrate the effectiveness and better performance when compared to conventional algorithm.
Empirical mode decomposition and normal shrink tresholding for speech denoisingijitjournal
In this paper a signal denoising scheme based on Empirical mode decomposition (EMD) is presented. the
noisy signal is decomposed in an adaptive manner by the EMD algorithm which allows to obtain intrinsic
oscillatory called Intrinsic mode functions (IMFs)component by a process called sifting process. The basic
principle of the method is to decompose a speech signal corrupted by additive white Gaussian random
noise into segments each frame is categorised as either signal-dominant or noise-dominant then
reconstruct the signal with IMFs signal dominant frame previously filtered or thresholded.It is shown, on
the basis of intensivesimulations that EMD improves the signal to noise ratio and address the problem of
signal degradation. The denoising method is applied to real signal with different noise levels and the
results compared to Winner and universal threshold of DONOHO and JOHNSTONE [11] with soft and
hard tresholding.Theeffect of level noise value on the performances of the proposed denoising is analysed.
Conditional Averaging a New Algorithm for Digital FilterIDES Editor
This paper aims at designing a new algorithm for
digital filters. The traditional methods like FIR, IIR have been
improved in recent times with new approaches. However, the
developments have used complex arithmetic calculation and
dedicated DSP processors. In this research project, effort has
been made to reduce such complexities using a procedure
based on the technique of Conditional Averaging. The entire
algorithm is developed using more of conditional statements
and less of arithmetic calculations.
Digital signals are filtered at different stages of
signal processing. However high speed processor is used for
different calculations associated with filtration process. An
averaging is one such scheme used in simple FIR filter, which
performs low pass filtering operation. Conditional Averaging
is a new technique, which is one of the improvements in
continuous time averaging. Conditional Averaging algorithm
is explained in this practice with different examples for the
design of low pass filter. This algorithm has been successfully
tested using digital starter kit with TMS3206416v DSP
processor. Using code composer studio, the entire algorithm is
written in C/C++ language and compiled into an assembly
language. Conditional averaging can be implemented with any
general purpose processor to arrive at other types of filters
with certain necessary modifications.
Performance Analysis of Group-Blind Multiuser Detectors for Synchronous CDMAidescitation
Blind multiuser detectors are attractive for the
suppression of interference in a CDMA environment. This
paper deals with the performance of group blind multiuser
detector for synchronous CDMA is analyzed. The blind multi
user detectors are Direct Matrix Inversion(DMI),Subspace
and group blind multiuser detector. The performance
analysis is performed by means of the Signal to Interference
Noise Ratio(SINR) and Bit Error Rate(BER). The numerical
results are plotted as variation of SINR Vs SNR, K and M,
SINR with respect to correlation coefficient( ) and BER
Vs Number of samples(M) for three detectors using
MATLAB software. The gain rises in group blind multiuser
detector over the DMI and subspace detectors. The
comparison is carried out for equicorrelated signals for
mathematical simplicity.
Blind Audio Source Separation (Bass): An Unsuperwised Approach IJEEE
Audio processing is an area where signal separation is considered as a fascinating works, potentially offering a vivid range of new scope and experience in professional and personal context. The objective of Blind Audio Source Separation is to separate audio signals from multiple independent sources in an unknown mixing environment. This paper addresses the key challenges in BASS and unsupervised approaches to counter these challenges. Comparative performance analysis of Fast-ICA algorithm and Convex Divergence ICA for Blind Source Separation is presented with the help of experimental result. Result reflects Convex Divergence ICA with α=-1 gives more accurate estimate in comparison of Fast ICA..
New Data Association Technique for Target Tracking in Dense Clutter Environme...CSCJournals
Improving data association process by increasing the probability of detecting valid data points (measurements obtained from radar/sonar system) in the presence of noise for target tracking are discussed in manuscript. We develop a novel algorithm by filtering gate for target tracking in dense clutter environment. This algorithm is less sensitive to false alarm (clutter) in gate size than conventional approaches as probabilistic data association filter (PDAF) which has data association algorithm that begin to fail due to the increase in the false alarm rate or low probability of target detection. This new selection filtered gate method combines a conventional threshold based algorithm with geometric metric measure based on one type of the filtering methods that depends on the idea of adaptive clutter suppression methods. An adaptive search based on the distance threshold measure is then used to detect valid filtered data point for target tracking. Simulation results demonstrate the effectiveness and better performance when compared to conventional algorithm.
Empirical mode decomposition and normal shrink tresholding for speech denoisingijitjournal
In this paper a signal denoising scheme based on Empirical mode decomposition (EMD) is presented. the
noisy signal is decomposed in an adaptive manner by the EMD algorithm which allows to obtain intrinsic
oscillatory called Intrinsic mode functions (IMFs)component by a process called sifting process. The basic
principle of the method is to decompose a speech signal corrupted by additive white Gaussian random
noise into segments each frame is categorised as either signal-dominant or noise-dominant then
reconstruct the signal with IMFs signal dominant frame previously filtered or thresholded.It is shown, on
the basis of intensivesimulations that EMD improves the signal to noise ratio and address the problem of
signal degradation. The denoising method is applied to real signal with different noise levels and the
results compared to Winner and universal threshold of DONOHO and JOHNSTONE [11] with soft and
hard tresholding.Theeffect of level noise value on the performances of the proposed denoising is analysed.
Conditional Averaging a New Algorithm for Digital FilterIDES Editor
This paper aims at designing a new algorithm for
digital filters. The traditional methods like FIR, IIR have been
improved in recent times with new approaches. However, the
developments have used complex arithmetic calculation and
dedicated DSP processors. In this research project, effort has
been made to reduce such complexities using a procedure
based on the technique of Conditional Averaging. The entire
algorithm is developed using more of conditional statements
and less of arithmetic calculations.
Digital signals are filtered at different stages of
signal processing. However high speed processor is used for
different calculations associated with filtration process. An
averaging is one such scheme used in simple FIR filter, which
performs low pass filtering operation. Conditional Averaging
is a new technique, which is one of the improvements in
continuous time averaging. Conditional Averaging algorithm
is explained in this practice with different examples for the
design of low pass filter. This algorithm has been successfully
tested using digital starter kit with TMS3206416v DSP
processor. Using code composer studio, the entire algorithm is
written in C/C++ language and compiled into an assembly
language. Conditional averaging can be implemented with any
general purpose processor to arrive at other types of filters
with certain necessary modifications.
Performance Analysis of Group-Blind Multiuser Detectors for Synchronous CDMAidescitation
Blind multiuser detectors are attractive for the
suppression of interference in a CDMA environment. This
paper deals with the performance of group blind multiuser
detector for synchronous CDMA is analyzed. The blind multi
user detectors are Direct Matrix Inversion(DMI),Subspace
and group blind multiuser detector. The performance
analysis is performed by means of the Signal to Interference
Noise Ratio(SINR) and Bit Error Rate(BER). The numerical
results are plotted as variation of SINR Vs SNR, K and M,
SINR with respect to correlation coefficient( ) and BER
Vs Number of samples(M) for three detectors using
MATLAB software. The gain rises in group blind multiuser
detector over the DMI and subspace detectors. The
comparison is carried out for equicorrelated signals for
mathematical simplicity.
Blind Audio Source Separation (Bass): An Unsuperwised Approach IJEEE
Audio processing is an area where signal separation is considered as a fascinating works, potentially offering a vivid range of new scope and experience in professional and personal context. The objective of Blind Audio Source Separation is to separate audio signals from multiple independent sources in an unknown mixing environment. This paper addresses the key challenges in BASS and unsupervised approaches to counter these challenges. Comparative performance analysis of Fast-ICA algorithm and Convex Divergence ICA for Blind Source Separation is presented with the help of experimental result. Result reflects Convex Divergence ICA with α=-1 gives more accurate estimate in comparison of Fast ICA..
A Template Matching Approach to Classification of QAM Modulation using Geneti...CSCJournals
The automatic recognition of the modulation format of a detected signal, the intermediate step between signal detection and demodulation, is a major task of an intelligent receiver, with various civilian and military applications. Obviously, with no knowledge of the transmitted data and many unknown parameters at the receiver, such as the signal power, carrier frequency and phase offsets, timing information, etc., blind identification of the modulation is a difficult task. This becomes even more challenging in real-world. In this paper modulation classification for QAM is performed by Genetic Algorithm followed by Template matching, considering the constellation of the received signal. In addition this classification finds the decision boundary of the signal which is critical information for bit detection. I have proposed and implemented a technique that casts modulation recognition into shape recognition. Constellation diagram is a traditional and powerful tool for design and evaluation of digital modulations. The simulation results show the capability of this method for modulation classification with high accuracy and appropriate convergence in the presence of noise.
Spectrum Sensing Detection with Sequential Forward Search in Comparison to Kn...IJMTST Journal
FCC is currently working on the concept of white space users “borrowing” spectrum from free license
holders temporarily to improve the spectrum utilization.
This project provides a relation between a Pf and the SNR value of any spectrum detector to have a
certain performance. Previous spectrum sensing detection techniques are only suitable for Low SNR and
are based on signal information values. But these methods are purely narrow band spectrum applications
In order to overcome the above said drawbacks we propose a novel method of spectrum sensing method
and is suitable for low and high SNR values, the sensed spectrum applicable for wide band applications.
Our proposed method does not require signal information at the receiver and channel information, because
this flexibility sensing rate is very high compared to previous techniques.
allocation of entropy are convex cone, this report shows the 3D view of convex cone of allocation of entropy for bipartite and tripartite quantum system
Application of Hilbert-Huang Transform in the Field of Power Quality Events A...idescitation
This paper deals with the analysis of PQ
abnormalities using Hilbert–Huang Transform (HHT). HHT
can be applied to both non-stationary as well as non-linear
signals and it provides the energy-frequency-time
representation of the signal. HHT is a time–frequency analysis
method having low order of complexity and does not include
the frequency resolution and time resolution fundamentals.
So, it has the potential to outperform the frequency resolution
and time resolution based methods. Several cases have been
considered to present the efficiency of HHT. For the case
study, various PQ abnormalities like voltage sag, swell and
harmonics with sag are considered. These PQ abnormalities
are subjected to HHT and the results are shown in the form of
IMFs, instantaneous frequency, absolute value, phase and
Hilbert Huang Spectrum. The results shows that the HHT
performs better than the any other time resolution and
frequency resolution based methods.
Our statistical machine translation platform and hybrid features were presented at the European Commission offices in Luxembourg last Tuesday 22nd September. It is one of the tools that the European Union will consider, among other machine translation commercial solutions, as a tool to help its mandate for CEF (Connecting Europe Facility). Pangeanic’s CEO, Manuel Herranz, presented the current state-of-the-art that PangeaMT version 3 represents. Representatives from the EU were particularly interested in the solid data management features, machine translation engine retraining routines, data cleaning and automated engine training and creation features. One of key features with the new PangeaMT version is the possibility to change translation algorithms and use rule-based systems like Apertium and Thot as well as the default Moses. It is also compatible with 3rd-party calls from other systems. Its powerful API can also provide machine translated output to requests anywhere in the world, although the platform is designed for onsite use at translation companies and organizations. PangeaMT is also compatible with several popular translation formats like ttx, sdlxliff, memoq, memsource, and most xml-based Tikal formats.
Restaurant technology used to be about what happens within your four walls, getting food from the kitchen to your guests. Now it's much more - see the technology trends popping up in restaurants this year.
Trend removal from raman spectra with local variance estimation and cubic spl...csijjournal
Trend removal is an important problem in most communication systems. Here, we show a proposed
algorithm for trend (background) removal from Raman Spectra by merging local variance estimation and
cubic spline interpolation methods. We found that Raman spectrum does not need a smoothing process to
remove trend from noisy signals. Employing this technique results in more speedy and noiseless systems
than other techniques that use wavelet transformation to suppress noise.
TREND REMOVAL FROM RAMAN SPECTRA WITH LOCAL VARIANCE ESTIMATION AND CUBIC SPL...csijjournal
Trend removal is an important problem in most communication systems. Here, we show a proposed algorithm for trend (background) removal from Raman Spectra by merging local variance estimation and cubic spline interpolation methods. We found that Raman spectrum does not need a smoothing process to remove trend from noisy signals. Employing this technique results in more speedy and noiseless systems than other techniques that use wavelet transformation to suppress noise
Trend Removal from Raman Spectra With Local Variance Estimation and Cubic Spl...csijjournal
Abstract
Trend removal is an important problem in most communication systems. Here, we show a proposed algorithm for trend (background) removal from Raman Spectra by merging local variance estimation and cubic spline interpolation methods. We found that Raman spectrum does not need a smoothing process to remove trend from noisy signals. Employing this technique results in more speedy and noiseless systems than other techniques that use wavelet transformation to suppress noise.
Keywords
Raman spectroscopy, Background correction method, Local variance, Cubic spline interpolation.
TREND REMOVAL FROM RAMAN SPECTRA WITH LOCAL VARIANCE ESTIMATION AND CUBIC SPL...csijjournal
Trend removal is an important problem in most communication systems. Here, we show a proposed algorithm for trend (background) removal from Raman Spectra by merging local variance estimation and cubic spline interpolation methods. We found that Raman spectrum does not need a smoothing process to remove trend from noisy signals. Employing this technique results in more speedy and noiseless systems than other techniques that use wavelet transformation to suppress noise.
Cooperative Spectrum Sensing Technique Based on Blind Detection MethodINFOGAIN PUBLICATION
Spectrum sensing is a key task for cognitive radio. Our motivation is to increase the probability of detection of spectrum sensing in cognitive radio. The spectrum-sensing algorithms are proposed based on the statistical methods like EVD,CVD of a covariance matrix. In this Two test statistics are then extracted from the sample covariance matrix. The decision on the signal presence is made by comparing the two test statistics.The Detection probability and the associated threshold are found based on the statistical theory. In this paper, we study the collaborative sensing as a means to improve the performance of the proposed spectrum sensing technique and show their effect on cooperative cognitive radio network. Simulations results and performances evaluation are done in Matlab and the results are tabulated.
A Combined Voice Activity Detector Based On Singular Value Decomposition and ...CSCJournals
voice activity detector (VAD) is used to separate the speech data included parts from silence parts of the signal. In this paper a new VAD algorithm is represented on the basis of singular value decomposition. There are two sections to perform the feature vector extraction. In first section voiced frames are separated from unvoiced and silence frames. In second section unvoiced frames are silence frames. To perform the above sections, first, windowing the noisy signal then Hankel’s matrix is formed for each frame. The basis of statistical feature extraction of purposed system is slope of singular value curve related to each frame by using linear regression. It is shown that the slope of singular values curve per different SNRs in voiced frames is more than the other types and this property can be to achieve the goal the first part can be used. High similarity between feature vector of unvoiced and silence frame caused to approach for separation of the two categories above cannot be used. So in the second part, the frequency characteristics for identification of unvoiced frames from silent frames have been used. Simulation results show that high speed and accuracy are the advantages of the proposed system.
Blind, Non-stationary Source Separation Using Variational Mode Decomposition ...CSCJournals
The Fourier Transform (FT) is the single best-known technique for viewing and reconstructing signals. It has many uses in all realms of signal processing, communications, image processing, radar, optics, etc. The premise of the FT is to decompose a signal into its frequency components, where a coefficient is determined to represent the amplitude of each frequency component. It is rarely ever emphasized, however, that this coefficient is a constant. The implication of that fact is that Fourier Analysis (FA) is limited in its accuracy at representing signals that are time-varying, e.g. non-stationary. Another novel technique called empirical mode decomposition (EMD) was introduced in the late 1990s to overcome the limits of FA, but the EMD was shown to have stability issues in reconstructing non-stationary signals in the presence of noise or sampling errors. More recently, a technique called variational mode decomposition (VMD) was introduced that overcomes the limitations of both aforementioned methods. This is a powerful technique that can reconstruct non-stationary signals blindly. It is only limited in the choice of the number of modes, K, in the decomposition. In this paper, we discuss how K may be determined a priori, using several examples. We also present a new approach that applies VMD to the problem of blind source separation (BSS) of two signals, estimating the strong powered signal, termed the interferer, first and then extracting the weaker one, termed the signal-of-interest (SOI). The baseline approach is to use all the predetermined K modes to reconstruct the interferer and then subtract its estimate from the received signal to estimate the SOI. We then devise an approach to choose a subset of the K modes to better estimate the interferer, termed culling, based on a very rough a priori frequency estimate of the weak SOI. We show that the VMD method with culling results in improvement in the mean-square error (MSE) of the estimates over the baseline approach by nearly an order of magnitude.
A Template Matching Approach to Classification of QAM Modulation using Geneti...CSCJournals
The automatic recognition of the modulation format of a detected signal, the intermediate step between signal detection and demodulation, is a major task of an intelligent receiver, with various civilian and military applications. Obviously, with no knowledge of the transmitted data and many unknown parameters at the receiver, such as the signal power, carrier frequency and phase offsets, timing information, etc., blind identification of the modulation is a difficult task. This becomes even more challenging in real-world. In this paper modulation classification for QAM is performed by Genetic Algorithm followed by Template matching, considering the constellation of the received signal. In addition this classification finds the decision boundary of the signal which is critical information for bit detection. I have proposed and implemented a technique that casts modulation recognition into shape recognition. Constellation diagram is a traditional and powerful tool for design and evaluation of digital modulations. The simulation results show the capability of this method for modulation classification with high accuracy and appropriate convergence in the presence of noise.
Spectrum Sensing Detection with Sequential Forward Search in Comparison to Kn...IJMTST Journal
FCC is currently working on the concept of white space users “borrowing” spectrum from free license
holders temporarily to improve the spectrum utilization.
This project provides a relation between a Pf and the SNR value of any spectrum detector to have a
certain performance. Previous spectrum sensing detection techniques are only suitable for Low SNR and
are based on signal information values. But these methods are purely narrow band spectrum applications
In order to overcome the above said drawbacks we propose a novel method of spectrum sensing method
and is suitable for low and high SNR values, the sensed spectrum applicable for wide band applications.
Our proposed method does not require signal information at the receiver and channel information, because
this flexibility sensing rate is very high compared to previous techniques.
allocation of entropy are convex cone, this report shows the 3D view of convex cone of allocation of entropy for bipartite and tripartite quantum system
Application of Hilbert-Huang Transform in the Field of Power Quality Events A...idescitation
This paper deals with the analysis of PQ
abnormalities using Hilbert–Huang Transform (HHT). HHT
can be applied to both non-stationary as well as non-linear
signals and it provides the energy-frequency-time
representation of the signal. HHT is a time–frequency analysis
method having low order of complexity and does not include
the frequency resolution and time resolution fundamentals.
So, it has the potential to outperform the frequency resolution
and time resolution based methods. Several cases have been
considered to present the efficiency of HHT. For the case
study, various PQ abnormalities like voltage sag, swell and
harmonics with sag are considered. These PQ abnormalities
are subjected to HHT and the results are shown in the form of
IMFs, instantaneous frequency, absolute value, phase and
Hilbert Huang Spectrum. The results shows that the HHT
performs better than the any other time resolution and
frequency resolution based methods.
Our statistical machine translation platform and hybrid features were presented at the European Commission offices in Luxembourg last Tuesday 22nd September. It is one of the tools that the European Union will consider, among other machine translation commercial solutions, as a tool to help its mandate for CEF (Connecting Europe Facility). Pangeanic’s CEO, Manuel Herranz, presented the current state-of-the-art that PangeaMT version 3 represents. Representatives from the EU were particularly interested in the solid data management features, machine translation engine retraining routines, data cleaning and automated engine training and creation features. One of key features with the new PangeaMT version is the possibility to change translation algorithms and use rule-based systems like Apertium and Thot as well as the default Moses. It is also compatible with 3rd-party calls from other systems. Its powerful API can also provide machine translated output to requests anywhere in the world, although the platform is designed for onsite use at translation companies and organizations. PangeaMT is also compatible with several popular translation formats like ttx, sdlxliff, memoq, memsource, and most xml-based Tikal formats.
Restaurant technology used to be about what happens within your four walls, getting food from the kitchen to your guests. Now it's much more - see the technology trends popping up in restaurants this year.
Trend removal from raman spectra with local variance estimation and cubic spl...csijjournal
Trend removal is an important problem in most communication systems. Here, we show a proposed
algorithm for trend (background) removal from Raman Spectra by merging local variance estimation and
cubic spline interpolation methods. We found that Raman spectrum does not need a smoothing process to
remove trend from noisy signals. Employing this technique results in more speedy and noiseless systems
than other techniques that use wavelet transformation to suppress noise.
TREND REMOVAL FROM RAMAN SPECTRA WITH LOCAL VARIANCE ESTIMATION AND CUBIC SPL...csijjournal
Trend removal is an important problem in most communication systems. Here, we show a proposed algorithm for trend (background) removal from Raman Spectra by merging local variance estimation and cubic spline interpolation methods. We found that Raman spectrum does not need a smoothing process to remove trend from noisy signals. Employing this technique results in more speedy and noiseless systems than other techniques that use wavelet transformation to suppress noise
Trend Removal from Raman Spectra With Local Variance Estimation and Cubic Spl...csijjournal
Abstract
Trend removal is an important problem in most communication systems. Here, we show a proposed algorithm for trend (background) removal from Raman Spectra by merging local variance estimation and cubic spline interpolation methods. We found that Raman spectrum does not need a smoothing process to remove trend from noisy signals. Employing this technique results in more speedy and noiseless systems than other techniques that use wavelet transformation to suppress noise.
Keywords
Raman spectroscopy, Background correction method, Local variance, Cubic spline interpolation.
TREND REMOVAL FROM RAMAN SPECTRA WITH LOCAL VARIANCE ESTIMATION AND CUBIC SPL...csijjournal
Trend removal is an important problem in most communication systems. Here, we show a proposed algorithm for trend (background) removal from Raman Spectra by merging local variance estimation and cubic spline interpolation methods. We found that Raman spectrum does not need a smoothing process to remove trend from noisy signals. Employing this technique results in more speedy and noiseless systems than other techniques that use wavelet transformation to suppress noise.
Cooperative Spectrum Sensing Technique Based on Blind Detection MethodINFOGAIN PUBLICATION
Spectrum sensing is a key task for cognitive radio. Our motivation is to increase the probability of detection of spectrum sensing in cognitive radio. The spectrum-sensing algorithms are proposed based on the statistical methods like EVD,CVD of a covariance matrix. In this Two test statistics are then extracted from the sample covariance matrix. The decision on the signal presence is made by comparing the two test statistics.The Detection probability and the associated threshold are found based on the statistical theory. In this paper, we study the collaborative sensing as a means to improve the performance of the proposed spectrum sensing technique and show their effect on cooperative cognitive radio network. Simulations results and performances evaluation are done in Matlab and the results are tabulated.
A Combined Voice Activity Detector Based On Singular Value Decomposition and ...CSCJournals
voice activity detector (VAD) is used to separate the speech data included parts from silence parts of the signal. In this paper a new VAD algorithm is represented on the basis of singular value decomposition. There are two sections to perform the feature vector extraction. In first section voiced frames are separated from unvoiced and silence frames. In second section unvoiced frames are silence frames. To perform the above sections, first, windowing the noisy signal then Hankel’s matrix is formed for each frame. The basis of statistical feature extraction of purposed system is slope of singular value curve related to each frame by using linear regression. It is shown that the slope of singular values curve per different SNRs in voiced frames is more than the other types and this property can be to achieve the goal the first part can be used. High similarity between feature vector of unvoiced and silence frame caused to approach for separation of the two categories above cannot be used. So in the second part, the frequency characteristics for identification of unvoiced frames from silent frames have been used. Simulation results show that high speed and accuracy are the advantages of the proposed system.
Blind, Non-stationary Source Separation Using Variational Mode Decomposition ...CSCJournals
The Fourier Transform (FT) is the single best-known technique for viewing and reconstructing signals. It has many uses in all realms of signal processing, communications, image processing, radar, optics, etc. The premise of the FT is to decompose a signal into its frequency components, where a coefficient is determined to represent the amplitude of each frequency component. It is rarely ever emphasized, however, that this coefficient is a constant. The implication of that fact is that Fourier Analysis (FA) is limited in its accuracy at representing signals that are time-varying, e.g. non-stationary. Another novel technique called empirical mode decomposition (EMD) was introduced in the late 1990s to overcome the limits of FA, but the EMD was shown to have stability issues in reconstructing non-stationary signals in the presence of noise or sampling errors. More recently, a technique called variational mode decomposition (VMD) was introduced that overcomes the limitations of both aforementioned methods. This is a powerful technique that can reconstruct non-stationary signals blindly. It is only limited in the choice of the number of modes, K, in the decomposition. In this paper, we discuss how K may be determined a priori, using several examples. We also present a new approach that applies VMD to the problem of blind source separation (BSS) of two signals, estimating the strong powered signal, termed the interferer, first and then extracting the weaker one, termed the signal-of-interest (SOI). The baseline approach is to use all the predetermined K modes to reconstruct the interferer and then subtract its estimate from the received signal to estimate the SOI. We then devise an approach to choose a subset of the K modes to better estimate the interferer, termed culling, based on a very rough a priori frequency estimate of the weak SOI. We show that the VMD method with culling results in improvement in the mean-square error (MSE) of the estimates over the baseline approach by nearly an order of magnitude.
Fault Tolerant Matrix Pencil Method for Direction of Arrival Estimationsipij
Continuing to estimate the Direction-of-arrival (DOA) of the signals impinging on the antenna array, even when a few elements of the underlying Uniform Linear Antenna Array (ULA) fail to work will be of practical interest in RADAR, SONAR and Wireless Radio Communication Systems. This paper proposes a new technique to estimate the DOAs when a few elements are malfunctioning. The technique combines Singular Value Thresholding (SVT) based Matrix Completion (MC) procedure with the Direct Data Domain (D3) based Matrix Pencil (MP) Method. When the element failure is observed, first, the MC is performed to recover the missing data from failed elements, and then the MP method is used to estimate the DOAs. We also, propose a very simple technique to detect the location of elements failed, which is required to perform MC procedure. We provide simulation studies to demonstrate the performance and usefulness of the proposed technique. The results indicate a better performance, of the proposed DOA estimation scheme under different antenna failure scenarios.
SIGNAL DETECTION IN MIMO COMMUNICATIONS SYSTEM WITH NON-GAUSSIAN NOISES BASED...ijwmn
In this paper, we study signal detection in multi-input-multi output (MIMO) communications system with non-Gaussian noises such as Middleton Class A noise, Gaussian mixtures and alpha stable distributions, using several deep neural network-based detector models such as FULLYCONNECTED and DETNET detector. By applying information theoretic criterion of Maximum Correntropy , SVD analysis on the channel matrix and reducing network complexity, the suggested deep neural network detector performs well in environments with non-Gaussian noises and, compared to the deep neural network-based detector with MSE loss function, achieves better performance.
Signal Detection in MIMO Communications System with Non-Gaussian Noises based...ijwmn
In this paper, we study signal detection in multi-input-multi output (MIMO) communications system with non-Gaussian noises such as Middleton Class A noise, Gaussian mixtures and alpha stable distributions, using several deep neural network-based detector models such as FULLYCONNECTED and DETNET detector. By applying information theoretic criterion of Maximum Correntropy , SVD analysis on the channel matrix and reducing network complexity, the suggested deep neural network detector performs well in environments with non-Gaussian noises and, compared to the deep neural network-based detector with MSE loss function, achieves better performance.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Investigation of the performance of multi-input multi-output detectors based...IJECEIAES
The next generation of wireless cellular communication networks must be energy efficient, extremely reliable, and have low latency, leading to the necessity of using algorithms based on deep neural networks (DNN) which have better bit error rate (BER) or symbol error rate (SER) performance than traditional complex multi-antenna or multi-input multi-output (MIMO) detectors. This paper examines deep neural networks and deep iterative detectors such as OAMP-Net based on information theory criteria such as maximum correntropy criterion (MCC) for the implementation of MIMO detectors in non-Gaussian environments, and the results illustrate that the proposed method has better BER or SER performance.
Enhanced Transmission and Receiver Diversity in Orthogonal Frequency Division...IJECEIAES
This paper deals with the blind channel estimation technique in OFDM system with receiver diversity to analyze the bit error rate with respect to the number of symbols. The paper clearly brings out the advantage that is being offered by the use of Blind channel estimation technique in terms of SNR requirements. Also a comparative study has been made for the analysis of BER variation with the amount i.e. number of symbols being transmitted. The work also explores the possibility of obtaining an optimum value of number of receivers that may lead to desired BER for threshold value of SNR in an OFDM system.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
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A Strategic Approach: GenAI in EducationPeter Windle
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Non-parametric Vertical Box Algorithm for Detecting Amplitude Information in the Received Digital Signal
1. Maria Beljaeva
Signal Processing: An International Journal (SPIJ), Volume (7) : Issue (1) : 2013 1
Non-parametric Vertical Box Algorithm for Detecting Amplitude
Information in the Received Digital Signal
Maria Beljaeva maria.beljaeva29@gmail.com
Scientific Centre of Applied Electrodynamics
Saint Petersburg, 190103, Russian Federation
Abstract
Vertical boxes algorithm (VBA) for non-cooperative automatic discrimination between digital
signals with amplitude information (AI) from those without AI is presented. The problem is not
new and several solutions have been proposed. Unlike them VBA needs no information about
propagation conditions and the received signal parameters. No SNR and noise distribution
assumptions are made, no carrier frequency and no thresholds are required. The only
assumption made is the symbol rate interval which may be as wide as desired. The signal is
considered only in the time domain. VBA also distinguishes between some other classes of
signals.
Keywords: Modulation Recognition, Modulation Classification, Vertical Box Control Chart, Non-
parametric.
1. INTRODUCTION
The less we know the more difficult it is to make a well-founded decision. Therefore while
studying a high-uncertainty problem one hardly can resist the temptation to introduce several,
sometimes unfounded, assumptions that simplify the problem statement. Modulation recognition
(MR) problem of determining the received signal modulation type is not an exception. Far less
methods are proposed for blind modulation recognition than for MR problems with some a priori
information about the received signal.
There are two sources of uncertainty in MR problem. The first one is the channel nature that
influences noise character and its intensity. MR methods of both Maximum Likelihood (ML) and
Feature Based (FB) classes [1] are based on strict assumptions about noise distribution. The
former because they are based on Parametric Hypothesis Testing [2] and the latter because they
use thresholds to which the sample characteristics (features) of the signal are compared.
Threshold values are calculated by means of simulation [3], and simulation requires information,
in particular information about corresponding random variable distributions.
The Gaussian distribution of the background noise is the most common assumption. But
‘To begin, distributions are never normal’ [4]. In fact the shot effect showed by Rice [5] to be the
source of Gaussian noise is not the only reason of signal corruption. The received radio signal
has passed through the medium which properties are varying in time and space and cannot be
controlled completely. Nobody can foreknow the proper noise distribution kind and the only
reason for using the Gаussian one is that ‘Everyone believes in the normal law, the experimenters
because they imagine that it is a mathematical theorem, and the mathematicians because they
think it is an experimental fact’ [6]. Some empirical data show non-gaussianity of real HF signals
in [7].
Other distributions are assumed sometimes [8,9] but none of them is suitable for general case.
2. Maria Beljaeva
Signal Processing: An International Journal (SPIJ), Volume (7) : Issue (1) : 2013 2
Ergo, free distribution (non-parametric) methods are to be used for modulation recognition
problems.
The second source of uncertainty is the transmitter emitting the signal. It produces different kinds
of uncertainty: the set of possible modulating schemes and the values of signal parameters such
as career, baud rate or SNR. The receiver knows some of this data in the cooperative case. The
lack of knowledge of any kind complicates MR problem and requires special methods for its
solution. For example many ML and FB methods [1] assume the carrier and phase offset are
known and cannot work if they aren’t; cluster methods [10] work well if number of clusters is
known a priory etc. In the non-cooperative case the receiver knows nothing except the sequence
of corrupted samples. The uncertainty in this situation is of greatest possible level. Many authors
(see [1]) recommend prior processing (preprocessing) of the received signal in order to estimate
some of its aforementioned parameters and then use the obtained values. Thus MR becomes a
two-stage process. It seems to be too long and complicated because it requires additional studies
of the robustness of MR methods to unavoidable estimation errors. We prefer another way in this
paper that is to analyse the sample sequence itself without intermediate steps.
So it would be useful to form some idea of received signal modulation type when nothing
is known except the distorted signal itself, not even the kind of distortion.
MR algorithms often have binary tree structure [3,11-15,19,21]. At each node decision is made
whether the received signal belongs to certain class or not. Does the signal contain amplitude
information (AI) or does it not is usually among these alternatives. Hereafter AI modulation set will
mean all kinds of AM and QAM while nonAI one will mean frequency and phase modulations or
just a non-modulated carrier.
Deciding if AI is present in the received signal or not is an important stage of MR, something like
a stage of differential diagnosis in medicine when exclusion of some diagnosis reduces the set of
alternatives.
To distinguish between AI and nonAI modulation of the received signal in non-cooperative
conditions several methods were proposed. Aisbett [16] and Chan & Gadboys [17] assumed
noise to be Gaussian and exploited its characteristic properties.
In order to decide is there AI in the received signal or not Ketterer [18] compares the variance of
envelope with threshold. This method requires knowledge of SNR which is not available in real
non-cooperative situation. Azzouz & Nandi [3] calculate statistical characteristic (extracted
feature) maxγ of the received signal and compare it with the threshold )(t maxγ which value is
determined by means of simulation, and again Gaussian assumption is made. So )(t maxγ may
become useless if the noise has some other distribution. Another matter is that the signal
envelope spectrum is used to calculate maxγ . This approach is viable only if symbol rate sr is big
enough so that few symbols would be located in the time interval
s
0
FFT
f
N
T = (here 0N is Fourier
transform number of points and sf is sampling rate). Indeed, the example in [3] has
kHz1200fs = , 0N =2048, kHz5.12rs = so that about 21 symbols come during 0N samples. But if
Hz500rs = then AI modulation would not be recognized, since symbol duration would exceed
FFTT . In more recent papers [19, 20] several time domain extracted features intended to solve
AI/nonAI problem were proposed, however without any decision rules with them. In [21] peak
number of the amplitude component derived from the DoE (Difference of Estimator filter) is used
as extracted feature but, as before, the threshold is calculated under the noise normality
assumption.
3. Maria Beljaeva
Signal Processing: An International Journal (SPIJ), Volume (7) : Issue (1) : 2013 3
In this paper we propose a new Vertical boxes algorithm (VBA) for distinguishing between
AI and nonAI modulation in the received digital signal in case when available information
uncertainty is maximal i.e. the only data used is the sequence of corrupted real samples )t(x i .
The only assumption made is about the symbol frequency interval which can be chosen as wide
as desired. No SNR or noise distribution assumptions are required, no carrier frequency
estimation is done.
VBA seems to be a promising algorithm. Developed only to solve AI vs nonAI problem it
distinguishes also between any modulated signal and career or noise and detects PM2 in the
received signal. VBA may be efficiently applied to every recognition problem reducible to
detecting of low and high periods existence in time series.
The rest of the paper is organized as follows. Section 2 presents VBA, in Section 3 we discuss it’s
holes and shortcomings, and describe necessary improvements. Section 4 presents simulation
results, the uses of VBA to recognize some other signals are considered in Section 5. Section 6
concludes the paper.
2. VBA
2.1. Algorithm Description
To detect, without going to frequency domain, whether the received signal is modulated in any
way one needs to find out whether signal oscillogram fluctuations cannot be explained only by
noise. AI oscillogram consists of periods of different height. For example there are low and high
periods in AM2 signal depending on the symbol transmitted (figure1).
FIGURE 1: High and Low Periods of AM2 Signal, SNR=20dB.
4. Maria Beljaeva
Signal Processing: An International Journal (SPIJ), Volume (7) : Issue (1) : 2013 4
The less is SNR the more difficult it is to detect the presence of two kinds of periods especially
because we do not know the moments when symbols change. Thus the AM2 recognition problem
reminds the change-point one of identifying stochastic process changes at unknown times [22]. In
our recognition algorithm we use the idea of Vertical Box Control Chart [23], that is, controlling
the number of random process observations which fall into the box moving along the time axis.
In-control state remains until this number jumps i.e. changes for more than a certain threshold,
then the out-of-control state is diagnosed. In our approach we replace one moving box by many
stationary ones and use non-parametric statistical test instead of comparing with threshold.
Another statistical test is used to process results.
Vertical box (V-box) is a rectangle with one side on horizontal axis. Let ]f,f[ maxsmbminsmb be the
interval of possible symbol frequency, sf the sample frequency, and
maxsmb
box f
1t = . (1)
Consider the received signal waveform )t(x over interval )T,0( , where boxKtT = , K is some
integer, the choice of which will be discussed below. Now sample size is ]Tf[N s= , and time
sample moments are
s
i
f
i
t = , N,...,1i = . VBA consists of six steps:
Step a). Center the signal and flip it positive (figure 2a).
Let
∑
=
−=
N
1j
jii )t(x
N
1
)t(x)t(s
Now average values in periods of different heights are different. Centering is necessary because
noise distribution may be asymmetrical.
Step b). Build a sequence of V-boxes over s(t) (figure 2b). Let )t(smaxs i
N,...,1i
max
=
= . Draw
K vertical boxes with height maxs based on consecutive subintervals of length boxt . Divide each
V-box in two halves by a horizontal line.
Step c). Split all V-boxes into low and high classes according to how many samples
fall under the middle line (figure 2c). Let iv be the number of samples in the ith V-box below
the middle line:
∑
≤≤−
χ=
boxbox tijt)1i(:j
jiv , (2)
where
<
=χ
else0
2
s
)j(sif1 max
j .
Let ∑
=
=
K
1i
iv v
K
1
m . We call the ith V-box low if vm)i(v > and high otherwise. Now we have a
sequence of low and high boxes. Neighboring boxes may belong either to different or to the same
classes.
Step d). Transform the sequence of boxes into the sequence of coffers of
alternating classes (figure 2d). Join every subsequence of the same class boxes into one coffer
5. Maria Beljaeva
Signal Processing: An International Journal (SPIJ), Volume (7) : Issue (1) : 2013 5
assigning the same class to it. That gives us a sequence of coffers of varying length with
alternating classes. By M denote number of coffers.
Step e). Make coffer borders more precise i.e. more close to symbol borders (figure
2e). Join each coffer ( ]1mmm a,aC += with its right neighbor’s left half
+
=′ ++
+
2
aa
,aC 2m1m
1m
and compare the union’s mean with m th coffer’s mean: if
∑∑
′∪∈∈ ′
<
CmCjt:j
j
mCjt:j
j
m
)t(s
)C(L
1
)t(s
)C(L
1
where )C(L is number of samples into C, then the m th coffer’s right border is left in place,
otherwise it is shifted to
2
aa 2m1m ++ +
. Do the same thing with the left borders. Now coffers are
close to symbols if there is AM (figure 2e) and entirely random otherwise. In the first case sample
distributions in neighboring coffers differ, in the second they do not. Note that some symbol may
be missed (as the 9th one in figure 2e) if SNR is low.
FIGURE 2: (a)-(e) Steps of VBA. SNR=3dB.
Step f). Compare sample distributions inside neighboring coffers content by statistical
test. We split all M coffers into
=µ
2
M
successive non-overlapping pairs, each of them
consisting of two coffers of different classes.
Then we use the well-known Mann–Whitney-–Wilcoxon (MWW) non-parametrical test [24] with
significance level U, implemented by the MATLAB function ranksum, to test sample distribution
sameness within each pair. µ test results form vector { }µ= R,...R,RR 21 of random independent
components where 1R k = (“failure”) if distributions in k th pair are different or 0Rk = (“success”)
otherwise. Let 1µ be number of units in R . Obviously we decide “AI” if µ=µ1 and “nonAI” if
01 =µ . But simulations show that such certain results usually occur when SNR is high enough
(more than 10-15dB). Otherwise R usually becomes a mixed array of zeroes and ones. For
6. Maria Beljaeva
Signal Processing: An International Journal (SPIJ), Volume (7) : Issue (1) : 2013 6
example in figure 2 { }0111R = , which means that distributions in the 1st & 2nd coffers are not
equal ( 1R1 = ), and the same goes for 3rd & 4th and 5th & 6th distributions ( 1RR 32 == ).
Distributions in 7th & 8th coffers passed MWW test successfully and could therefore be equal.
The 9th coffer has no pair and is not taken into consideration.
Step g). Use another statistical test to analyze the results of step “f”. The conditional
probability { }nonAI|1RP i = is less than U by the construction of R . We check the hypothesis that
the success probability sp is also less than U, using a test involving a single binomial probability
[2] which is implemented by the MATLAB function finv. If the hypothesis is confirmed on
significance level U′ our algorithm says “nonAI”, otherwise it says “AI”. Simulations show that in
the absence of noise VBA recognizes AM2 signals with confidence when symbol length is no less
than boxt .
2.1. The choice of K
Simulations show that for dB5SNR > VBA gives good results if M is near 10. Obviously M is
strongly related to symbol variation number (SVN). When noise is absent these numbers are
equal or differ by 1. The more is noise the more they differ. The distribution of SVN is binomial,
and according to [24] (table D) 0K =30 symbols are needed to obtain 10 symbol variations with
probability 0.95 assuming that symbol probabilities are equal. So 0KK = is recommended in a
special case when symbol length is equal to boxt (1).
Now suppose symbol length equals boxLt ,. where 1L > . Again 0K symbols are needed
therefore K should be equal to [ ]LK0 . Now if symbol length varies from maxsmbf1 to minsmbf1
we would need
minsmb
maxsmb
f
f
L = (3)
to recognize AM2. Thus the total sample number is
[ ] [ ]sbox0VBA ftLKNˆ ×= . (4)
Note that the 1st factor is the number of V-boxes, while the 2nd one is the number of samples per
V-box. Using (1,2), we get
=
minsmb
s
0VBA
f
f
KNˆ .
3. VBA DISCUSSION AND IMPROVEMENTS
3.1. VBA Holes and Shortcomings
First hole is the use of MWW test, which requires sample groups to be independent. That doesn’t
seem to be the case for coffers contents. At least the numbers of samples in different class
coffers are correlated. For example, if the i th box is high and the jth one is low, then iν , jν (2)
are order statistics ( iν has the smaller index than jν ). Since the latter are correlated, so are the
sample arrays within V-boxes, and, therefore, coffers’ contents. But correlation is weak and
medians of sample distributions within low and high coffers differ much more in AI case than in
nonAI, which is why MWW test distinguishes between them (see Section 4).
Second hole is the interpretation of MWW test results. Strictly speaking sample distributions in
different class boxes are not the same even in nonAI case. The means of these distributions are
different, again due to the way classes are chosen. But the difference is rather small and the test
usually doesn’t “feel” it when sample number within one V-box is not too large.
7. Maria Beljaeva
Signal Processing: An International Journal (SPIJ), Volume (7) : Issue (1) : 2013 7
First VBA shortcoming is that it’s sensitive to signal aliasing. Signal without modulation could be
mistakenly determined to be amplitude modulated (figure.3).
FIGURE 3: Non-modulated Carrier Looks like AI Signal Because of Aliasing.
Second shortcoming is that VBA is computationally slow because of large number of proceeded
samples. For example let 100Hzf minsmb = , HzK3f maxsmb = , MHz20fs = . According to (4)
6
VBA 106Nˆ ⋅= ; there are about 900 V-boxes with more than 6500 samples per box. Both
shortcomings can be removed by the same trick namely the randomization of sample times (see
below). The number of samples is lowered even more by using V-boxes of different lengths.
3.2. Improving VBA
Decreasing the Number of Samples per V-box
To determine the box’s class it’s enough to take much less samples than
minsmb
s
f
f
if they are
taken in uniformly distributed moments. Let us take D pseudorandom numbers D,...,1j,j =ξ ,
uniformly distributed in (0,1), and sample the signal at the moments boxjj)1i(D t)1i(t ξ+−=+− .
Thus there would be D samples within each V-box. Note that the same array { }iξ is used for all
V-boxes. Therefore the total sample size decreases significally from VBANˆ to KDNVBA = .
What’s more, this approach removes the first shortcoming too due to nonregularity of time
sampling.
Randomization also helps to diminish the second hole i.e. to reduce the tendency of the MWW
test to give the false positive result i.e. to detect AI when there is none. Create another sequence
of D′ samples exactly the same way as the first one (using another array of pseudorandom
numbers). This second sequence would then be used as input for the MWW test. If there is no AI
in the received signal then the only difference between low and high coffers would come from the
noise, hence it will be neutralized while comparing samples taken in another array moments
within coffers. Otherwise, if there is AI in the signal, changing the sample moments array will not
decrease the difference greatly. Now there are DD ′+ samples per V-box. Simulations show that
200DD =′= is a good choice.
Decreasing V-box number
Let us divide the symbol length interval [ ]
=
minsmbmaxsmb
maxsmbminsmb f
1,
f
1t,t to m
subintervals and denote points of division by 1m1,..., −ττ , maxsmbmminsmb0 t,t =τ=τ . Then we
use VBA with iboxt τ= in order to recognize AM in the received signal with the symbol length
belonging to [ ]1ii , +ττ . Now the total number of different length V-boxes is ( )m00 ,...,,mIK ττ ,
where
8. Maria Beljaeva
Signal Processing: An International Journal (SPIJ), Volume (7) : Issue (1) : 2013 8
( ) ∑
−
=
+
τ
τ
=ττ
1m
0i i
1i
m0 ,...,,mI . (5)
Now the problem is to find the best way of division.
Theorem. Let [ ],Lln=α
+α
<
+α
α
α=
+αα
otherwise1
1L
1
ifm
)1(
1
*
(6)
∗
=λ m
L .
Then
( )m0
1m,...,1,m
,...,,mImin ττ
−ττ
= { } ∗
=
∗
λ=
λτ
∗
m,mI
m
0i
i
0 (7)
Proof
Note that we can only vary 1m1,..., −ττ since 0τ and mτ are fixed. Assume that 2m = . According
to (5) ( )
1
2
0
1
210 ,,,2I
τ
τ
+
τ
τ
=τττ .
It has a minimum when 201 ττ=τ . It follows that for any 2m > , ( )m0,...,,mI ττ would be minimal
when the points of division satisfy simultaneous equations 1m,...1i,1i1ii −=ττ=τ +− . Therefore
1m,...1i,Lm
i
0i −=τ=τ . (8)
Substituting (8) to (5), we obtain
( ) m
1
m0 mL,...,,mI =ττ . (9)
Function x
Lx)x(f ⋅= has a unique minimum at Llnx = . Since m takes only integer values then,
in order to minimize I, it must be equal to α if )1(f)(f +α<α and to 1+α otherwise.
Now the total number of V-boxes is ∗
λ mK0 and the total sample number is equal to
)DD(mKN 21
*
0VBA +λ= (10)
instead of (4). Note that (10) does not include sampling rate because of sample time
randomization. Under the conditions of section 3 example 3m*
= , 1.3≈λ . If ,30K0 =
200DD 21 == then about 280 V-boxes and 112000 samples are needed. So in this example the
improved VBA reduces the required samples number in more than 50 times.
It’s possible to use parallel computations to speed up signal processing. There are *
m
subsequences of 0Kλ V-boxes in each one. The length of V-boxes in ith subsequence is
∗−
− =λτ=τ m,...1i,1i
01i . If all subsequences start to be proceeded simultaneously then the length
of the required signal piece T is equal to the length of the longest subsequence i.e 1m
00K ∗−
λτ .
9. Maria Beljaeva
Signal Processing: An International Journal (SPIJ), Volume (7) : Issue (1) : 2013 9
Under the conditions of section 3A example 1.030T 2 ≈τ= s. Keep in mind that such a long time
is the charge for symbol rate uncertainty. If, hypotheticaly, the symbol rate is known (as in [3])
then the signal duration about 0024.0
r
K
s
0
= s would be enough. It is about the same as required
by the algorithm described in [3]: the latter needs 0017.0
f
2048
s
≈ s but cannot recognize AI when
the symbol rate interval is as wide as in our example.
While proceeding ∗
m subsequences we obtain ∗
m results: ∗
m21 r,...,r,r , where 1ri = if AI is
recognized for symbol length belonging to ),( i1i ττ − , 0ri = otherwise. The final decision is made
as following: if 1&2*m ≥ε≤ or 2&2*m ≥ε> where ∑
∗
=
=ε
m
1i
ir then signal contains AI, otherwise
it does not.
Since VBA is built around the recognition of different height oscillogram periods it can detect the
presence of AI not only in AM2 signals but also in other AI modulated signals. Naturally the
detection probability depends on the difference between average heights of high and low periods.
4. SIMULATION
Simulation was performed under the conditions of section 3 example. Received signal was
simulated as follows. Sequence of equiprobable and independent zeros and ones modulated the
carrier, the result was corrupted by additive noise. 100 realizations were generated for every
variant.
Modulation Types and Noise.
VBA was tested on 10 types of modulation: AM2, 4-level PAM, PSK2, PSK4, FSK2, FSK4, three
kinds of QAM8 shown at figure 4a-c, QAM16 (figure 4d), and non-modulated carrier.
FIGURE 4: Simulated Kinds of QAM.
Two kinds of noise distributions (Gaussian and a mixture of uniform and Rayleigh distributions)
and three SNR levels (10, 5, and 0 dB) were simulated.
Algorithm Parameters.
200DD =′= , 30K0 = , 05.0UU =′= .
A=1; carrier=7.5 MHz, modulation index 0.6 for AM2; modulation indices 0.2, 0.4, 0.6 for PAM.
Symbol
frequency do not influence the results thus their values were chosen arbitrarily.
Simulation Results are presented in Table 1. The numerator in each cell of Table 1 is the
probability for Gaussian noise while the denominator is the same for mixture noise. We see that
VBA confidently detects AI in all considered signals when dB5SNR ≥ . As SNR decreases the
correct decision probability decreases as well. Its rate of decrease is greater if the average
difference between low and high periods in the signal is smaller. That’s why AI in PAM4,
10. Maria Beljaeva
Signal Processing: An International Journal (SPIJ), Volume (7) : Issue (1) : 2013 10
QAM8(b), QAM16 is recognized with much less confidence than in the other modulation types
when SNR=0 (see the last line in Table 1).
carrier AM2 PAM4 PM2 PM4 FM2 FM4 QAM8(1, 2, 3) QAM16
10dB
0.97
0.97
1.0
1.0
0.98
1.0
0.97
0.94
0.96
0.98
0.97
0.99
0.99
0.98
1.0 , 0.99 , 1.0
1.0 1.0 1.0
0.99
0.98
5dB
0.98
0.96
0.99
1.0
0.99
0.97
0.95
0.99
0.98
0.97
0.97
0.98
0.98
0.95
0.99 , 1.0 , 1.0
1.0 1.0 1.0
0.99
1.0
0dB
0.98
0.97
0.94
0.92
0.34
0.23
0.98
0.97
0.96
0.98
0.97
0.97
0.99
0.98
1.0 , 0.75, 1.0
0.98 0.67 0.97
0.76
0.68
TABLE 1: Probability of Correct Decision «AI vs. nonAI». 93KK 0 =λ=
It is difficult to compare these results with those obtained previously because of difference in
basic assumptions. Methods [3,16,17,18-21] proposed for the AI vs non AI problem are based on
Gaussian hypothesis. Besides, some signal characteristics are assumed to be known, e.g. carrier
frequency in [3,20,21], and symbol rate in [20], and SNR in [16,18], although not all referenced
articles mention it. Moreover the probability of correct decision is not estimated in some articles at
all [16,19], while in others the problem is considered as a part of binary tree algorithm [3,19,21] so
only integral estimates are presented. Thus the only characteristic we can use to compare these
methods is signal-to-noise ratio, specifically its minimum value minSNR for which good
recognition results are claimed to be obtained. It equals -1dB in [16], 0dB in [19,20], 5dB in [3],
7dB in [17], and 10dB in [18,21]. Note that the best results in [16,20] require a priori knowledge of
the received signal characteristics. In the case SNR=0, [19] shows good results, but only for
those modulation kinds VBA recognizes with high probability too.
Now we can conclude that VBA detects the presence or absence of AI in the signal well when
neither it characteristics nor the noise level and distribution are known.
5. THE USE OF VBA FOR SOME OTHER PROBLEMS
Not only signals carrying true amplitude information are classified by VBA as AI modulated
signals but also all other signals with high and low periods. We shall call such signals a la AI
ones.
Let )t(
s ∆+
be the sum of signal and its shifted to t∆ copy and let )t(
s ∆∗
be their product:
)tt(s)t(s)t(s )t(
∆−+=∆+
(11)
)tt(s)t(s)t(s )t(
∆−=∆∗
(12)
Note that if )t(s is pure carrier or noise then )t(s )t( ∆+
is not a la AI signal (fig.5).
FIGURE 5: Sums of Carrier and Gaussian Noise With Their Shifted Copies; minsmbt2.1t =∆ ; SNR=20dB.
11. Maria Beljaeva
Signal Processing: An International Journal (SPIJ), Volume (7) : Issue (1) : 2013 11
On the contrary, )t(
s ∆+
is a la AI signal when )t(s carries frequency or phase modulation (fig.6).
Being flipped such a signal remains a la AI one, and VBA detects AI even when SNR is quite low
(e.g. 3dB in fig.7; R={1110}). Thus the presence of phase or frequency modulation in the received
signal is recognized by means of VBA.
To distinguish between phase and frequency modulations in the received signal let’s consider
)t(
s ∆∗
(fig.8).
Note that )t(
s ∆∗
is a la AI for all modulated signals and )t(
s ∆∗
is not a la AI only for PM2 signal.
So to distinguish PM2 from the other signals one has to apply VBA not only to the flipped signal
)t(
s ∆∗
as it is described in Section 2 but also to the signal shifted up:
)t(
)tT,0(t
)t(
up smin)t(s)t,t(s ∆∗
∆−∈
∆∗
+=∆ . (13)
FIGURE 6: Sums of Modulated Signals and Their Shifted Copies; minsmbt2.1t =∆ , SNR=20dB.
If the first answer is nonAI and the second is AI then the signal is PM2.
To distinguish between PM and FM signals the more accurate VBA modification is needed. It may
be achieved by breaking up boxes in more than two parts (step e, Section II), and it would take
more time. If we build coffers for )t,t(sup ∆ accurately enough, the scatter of samples within them
would differ when the received signal is FM and not differ when it is PM. So to distinguish one
from another one would have to compare scatters by some non-parametrical test for variances
[24].
12. Maria Beljaeva
Signal Processing: An International Journal (SPIJ), Volume (7) : Issue (1) : 2013 12
These and other distinguishing characteristics analyzable by means of VBA would be the subject
to further investigation. One more idea to be examined in the future is applying VBA to analogous
modulation recognition.
FIGURE 7: a) PM2-signal b) Its Shifted Copy c) Their Sum d) The Result of VBA: Four Pairs of Coffers.
13. Maria Beljaeva
Signal Processing: An International Journal (SPIJ), Volume (7) : Issue (1) : 2013 13
FIGURE 8: Products of Modulated Signals and Their Shifted Copies; minsmbt2.1t =∆ , SNR=20dB.
6. CONCLUSION
The idea of VBA is clear enough: the algorithm “sees” AI as a man does. In fact method [3] does
the same in frequency domain; the difference is that man looks at spectrum, not at oscillogram.
However in time domain it is possible to use non-parametrical statistical tests while at the
moment there are no such tests for frequency domain. That’s why there is no method of
recognizing modulation type in frequency domain automatically without choosing some
thresholds. This approach inevitably limits the assortment of considered modulation kinds and
types of noise while VBA realizes more general approach.
In practice, VBA’s advantage is that it doesn’t require any information not available in
reality, whilst other algorithms do. At the same time VBA works well under the same SNR
conditions as other algorithms.
VBA is simple and rough enough, and that is quite normal: problems with high degree of
uncertainty need rough solutions.
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