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 JOINT TIMING OFFSET AND CHANNEL ESTIMATION USING FRACTIONAL FOURIER TRANSFO...IJCNCJournal
This paper proposes a new method for joint timing offset and channel estimation in OFDM systems using fractional Fourier transform and constant amplitude zero autocorrelation sequences. After estimating the timing offset in the frequency domain, compensation is performed in the time domain. Channel estimation then uses least squares with discrete Fourier transform and linear interpolation to recover the transmitted signal. Simulation results show the proposed method achieves good performance in terms of mean square error for timing offset estimation compared to other techniques, especially for fast fading channels. It also estimates the channel well while maintaining throughput.
Performance Analysis of M-ary Optical CDMA in Presence of Chromatic DispersionIDES Editor
The performance of M-ary optical code division
multiple access (OCDMA) is analytically investigated in
presence of chromatic dispersion. The study is carried out for
single mode dispersion shifted and non dispersion shifted
fibers. Walsh code is used as user address. The p-i-n
photodetector is used for optoelectronic conversion process.
In our proposed model 16 different symbols are modulated
with different intensity levels and detected by direct detection
technique. The numerical results show that, the reconstruction
of the transmitted symbol is strongly dependent on the received
symbols magnitude which is reduced by fiber length and
symbol rate. It is found that the proposed OCDMA system
shows better performance when dispersion shifted fiber is
used as a communication medium.
This document discusses image analysis using wavelet transformation. It provides an overview of digital image processing and compares Fourier transforms, short-term Fourier transforms, and wavelet transforms. Wavelet transforms provide better time-frequency localization than Fourier transforms. The document demonstrates Haar wavelets and how they can be used to decompose an image into different frequency subbands. It discusses applications of wavelet transforms such as image compression, denoising, and feature extraction. The document includes MATLAB code for performing wavelet decomposition on an image.
Wavelet packets provide an adaptive decomposition that overcomes limitations of the discrete wavelet transform (DWT). In wavelet packets, signal decomposition using high-pass and low-pass filters is applied recursively to both low-pass and high-pass outputs, allowing more flexible time-frequency analysis. This results in a redundant dictionary with increased flexibility but also higher computational costs. Pruning algorithms are used to select an optimal subset of bases for a given application based on cost functions related to properties like sparsity, entropy, or energy concentration.
Speech Processing in Stressing Co-Channel Interference Using the Wigner Distr...CSCJournals
The Fractional Fourier Transform (FrFT) can provide significant interference suppression (IS) over other techniques in real-life non-stationary environments because it can operate with very few samples. However, the optimum rotational parameter ‘a’ must first be estimated. Recently, a new method to estimate ‘a’ based on the value that minimizes the projection of the product of the Wigner Distributions (WDs) of the signal-of-interest (SOI) and interference was proposed. This is more easily calculated by recognizing its equivalency to choosing ‘a’ for which the product of the energies of the SOI and interference in the FrFT domain is minimized, termed the WD-FrFT algorithm. The algorithm was shown to estimate ‘a’ more accurately than minimum mean square error FrFT (MMSE-FrFT) methods and perform far better than MMSE Fast Fourier Transform (MMSE-FFT) methods, which only operate in the frequency domain. The WD-FrFT algorithm significantly improves interference suppression (IS) capability, even at low signal-to-noise ratio (SNR). In this paper, we apply the proposed WD-FrFT technique to recovering a speech signal in non-stationary co-channel interference. Using mean-square error (MSE) between the SOI and its estimate as the performance metric, we show that the technique greatly outperforms the conventional methods, MMSE-FrFT and MMSE-FFT, which fail with just one non-stationary interferer, and continues to perform well in the presence of severe co-channel interference (CCI) consisting of multiple, equal power, non-stationary interferers. This method therefore has great potential for separating co-channel signals in harsh, noisy, non-stationary environments.
Audio coding of harmonic signals is a challenging task for conventional MDCT coding schemes. In this paper we introduce a novel algorithm for improved transform coding of harmonic audio. The algorithm does not deploy the conventional scheme of splitting the input signal into a spectrum envelope and a residual, but models the spectral peak regions. Test results indicate that the presented algorithm outperforms the conventional coding concept.
It is a basic ppt of pattern recognition using wavelates and contourlets.... I will describe the algo into next slide... Thank you... It is a good ppt you can learn the basic of this project
A JOINT TIMING OFFSET AND CHANNEL ESTIMATION USING FRACTIONAL FOURIER TRANSFO...IJCNCJournal
This paper proposes a new method for joint timing offset and channel estimation in OFDM systems using fractional Fourier transform and constant amplitude zero autocorrelation sequences. After estimating the timing offset in the frequency domain, compensation is performed in the time domain. Channel estimation then uses least squares with discrete Fourier transform and linear interpolation to recover the transmitted signal. Simulation results show the proposed method achieves good performance in terms of mean square error for timing offset estimation compared to other techniques, especially for fast fading channels. It also estimates the channel well while maintaining throughput.
Performance Analysis of M-ary Optical CDMA in Presence of Chromatic DispersionIDES Editor
The performance of M-ary optical code division
multiple access (OCDMA) is analytically investigated in
presence of chromatic dispersion. The study is carried out for
single mode dispersion shifted and non dispersion shifted
fibers. Walsh code is used as user address. The p-i-n
photodetector is used for optoelectronic conversion process.
In our proposed model 16 different symbols are modulated
with different intensity levels and detected by direct detection
technique. The numerical results show that, the reconstruction
of the transmitted symbol is strongly dependent on the received
symbols magnitude which is reduced by fiber length and
symbol rate. It is found that the proposed OCDMA system
shows better performance when dispersion shifted fiber is
used as a communication medium.
This document discusses image analysis using wavelet transformation. It provides an overview of digital image processing and compares Fourier transforms, short-term Fourier transforms, and wavelet transforms. Wavelet transforms provide better time-frequency localization than Fourier transforms. The document demonstrates Haar wavelets and how they can be used to decompose an image into different frequency subbands. It discusses applications of wavelet transforms such as image compression, denoising, and feature extraction. The document includes MATLAB code for performing wavelet decomposition on an image.
Wavelet packets provide an adaptive decomposition that overcomes limitations of the discrete wavelet transform (DWT). In wavelet packets, signal decomposition using high-pass and low-pass filters is applied recursively to both low-pass and high-pass outputs, allowing more flexible time-frequency analysis. This results in a redundant dictionary with increased flexibility but also higher computational costs. Pruning algorithms are used to select an optimal subset of bases for a given application based on cost functions related to properties like sparsity, entropy, or energy concentration.
Speech Processing in Stressing Co-Channel Interference Using the Wigner Distr...CSCJournals
The Fractional Fourier Transform (FrFT) can provide significant interference suppression (IS) over other techniques in real-life non-stationary environments because it can operate with very few samples. However, the optimum rotational parameter ‘a’ must first be estimated. Recently, a new method to estimate ‘a’ based on the value that minimizes the projection of the product of the Wigner Distributions (WDs) of the signal-of-interest (SOI) and interference was proposed. This is more easily calculated by recognizing its equivalency to choosing ‘a’ for which the product of the energies of the SOI and interference in the FrFT domain is minimized, termed the WD-FrFT algorithm. The algorithm was shown to estimate ‘a’ more accurately than minimum mean square error FrFT (MMSE-FrFT) methods and perform far better than MMSE Fast Fourier Transform (MMSE-FFT) methods, which only operate in the frequency domain. The WD-FrFT algorithm significantly improves interference suppression (IS) capability, even at low signal-to-noise ratio (SNR). In this paper, we apply the proposed WD-FrFT technique to recovering a speech signal in non-stationary co-channel interference. Using mean-square error (MSE) between the SOI and its estimate as the performance metric, we show that the technique greatly outperforms the conventional methods, MMSE-FrFT and MMSE-FFT, which fail with just one non-stationary interferer, and continues to perform well in the presence of severe co-channel interference (CCI) consisting of multiple, equal power, non-stationary interferers. This method therefore has great potential for separating co-channel signals in harsh, noisy, non-stationary environments.
Audio coding of harmonic signals is a challenging task for conventional MDCT coding schemes. In this paper we introduce a novel algorithm for improved transform coding of harmonic audio. The algorithm does not deploy the conventional scheme of splitting the input signal into a spectrum envelope and a residual, but models the spectral peak regions. Test results indicate that the presented algorithm outperforms the conventional coding concept.
It is a basic ppt of pattern recognition using wavelates and contourlets.... I will describe the algo into next slide... Thank you... It is a good ppt you can learn the basic of this project
An introduction to discrete wavelet transformsLily Rose
This document provides an overview of wavelet transforms and their applications. It introduces continuous and discrete wavelet transforms, including multiresolution analysis and the fast wavelet transform. It discusses how wavelet transforms can be used for image compression, edge detection, and digital watermarking due to properties like decomposing images into different frequency subbands. The fast wavelet transform allows efficient computation of wavelet coefficients by exploiting relationships between scales.
This document provides an overview of wavelet transformation and discrete wavelet transform (DWT). It discusses working with wavelets by convolving signals with wavelet filters and storing the results in coefficients. Properties of wavelets include maximum frequency depending on signal length and recursive partitioning of lowest band. DWT requires an orthonormal wavelet basis and uses scaling functions and wavelets. 2D wavelet transform uses separable transforms with low and high pass filters in each direction. Experimental results show decompositions of images at different levels.
The document discusses performing a discrete wavelet transform (DWT) on a 1D signal using MATLAB. It loads a test signal, performs a 5-level DWT decomposition using the coif3 wavelet, then reconstructs the approximation and detail signals at each level. Plots of the original, approximation, and detail signals are generated.
Wavelet transform is one of the important methods of compressing image data so that it takes up less memory. Wavelet based compression techniques have advantages such as multi-resolution, scalability and tolerable degradation over other techniques.
SIR Analysis of Overloaded CDMA System Using Orthogonal Gold CodesIDES Editor
This document summarizes a research paper that proposes a technique for overloaded CDMA systems using orthogonal gold codes.
1) The technique assigns one set of orthogonal gold codes to the first N users and another set to additional users, but overlays them with different PN sequences. Detection is done iteratively in two steps to detect signals from each user set.
2) A multistage conventional and weighted linear parallel interference cancellation approach is used to cancel interference between the two user sets. Expressions for the signal to interference ratio at the output of the second and third cancellation stages are derived.
3) Simulation results show that the proposed technique can accommodate N users without interference and additional users at the cost of a small
This document discusses the discrete wavelet transform (DWT) and its implementation in MATLAB. It begins with an introduction to DWTs, explaining that they decompose signals into different frequency bands using low-pass and high-pass filters. It then describes how 2D DWTs are implemented by applying 1D transforms separately to rows and columns, producing subbands that emphasize different types of edges. The document provides steps for performing DWTs in MATLAB, including single-level and multi-level decomposition and reconstruction. It concludes by showing decomposed images and discussing how DWTs separate approximation and detail information.
A seminar on INTRODUCTION TO MULTI-RESOLUTION AND WAVELET TRANSFORMमनीष राठौर
This document provides an introduction to multi-resolution analysis and wavelet transforms. It discusses that multi-resolution analysis analyzes signals at varying levels of detail or resolutions simultaneously. The Fourier transform has limitations for non-stationary signals as it does not provide time information. The short-term Fourier transform was developed to analyze non-stationary signals, but it has limitations in time-frequency resolution. Wavelet transforms were developed to analyze signals using variable time-frequency resolutions. Wavelet transforms have features like varying time-frequency resolutions and are suitable for analyzing non-stationary signals. They have applications in fields like signal compression, noise removal, and image processing.
Performance of MMSE Denoise Signal Using LS-MMSE TechniqueIJMER
This paper presents performance of mmse denoises signal using consistent cycle spinning (ccs) and least square (LS) techniques. In the past decade, TV denoise technique is used to reduced the noisy signal. The main drawback is the low quality signal and high MMSE signal. Presently, we
proposed the CCS-MMSE and LS-MMSE technique .The CCS-MMSE technique consists of two steps. They are wavelet based denoise and consistent cycle spinning. The wavelet denoise is powerful decorrelating effect on many signal domains. The consistent cycle spinning is used to estimation the
MMSE in the signal domain. The LS-MMSE is better estimation of MMSE signal domain compare to
CCS-MMSE.The experimental result shows the average MMSE reduction using various techniques.
IOSR Journal of Electronics and Communication Engineering(IOSR-JECE) is an open access international journal that provides rapid publication (within a month) of articles in all areas of electronics and communication engineering and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in electronics and communication engineering. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Images may contain different types of noises. Removing noise from image is often the first step in image processing, and remains a challenging problem in spite of sophistication of recent research. This ppt presents an efficient image denoising scheme and their reconstruction based on Discrete Wavelet Transform (DWT) and Inverse Discrete Wavelet Transform (IDWT).
Performance of enhanced lte otdoa position ing approach through nakagami-m fa...Elmourabit Ilham
This document analyzes the performance of an enhanced LTE OTDOA positioning technique called Adaptive OTDOA (A-OTDOA) through a Nakagami-m fading channel. A-OTDOA uses adaptive filters to cancel noise from received positioning reference signals before estimating time differences of arrival, improving accuracy. The document introduces A-OTDOA and the Normalized Least Mean Square adaptive algorithm used. It then discusses modeling the propagation environment, including Nakagami-m fading channels, to test A-OTDOA's performance in a worst-case scenario without line of sight.
This document discusses the use of an adaptive decision feedback equalizer (ADFE) to mitigate pulse dispersion in optical communication channels. It begins by describing different sources of dispersion in optical fibers. Then it proposes using a fractional spaced decision feedback equalizer (FSDFE) integrated with activity detection guidance (ADG) and tap decoupling (TD) to improve performance. Simulation results show the FSDFE can estimate the channel impulse response and minimize differences between the input and output. Adding ADG and TD further improves convergence rate, detection of inactive taps, and asymptotic performance. The ADFE is an effective technique for equalization and mitigating dispersion in optical links.
IRJET- Compressed Sensing based Modified Orthogonal Matching Pursuit in DTTV ...IRJET Journal
This document discusses a modified orthogonal matching pursuit algorithm used for channel estimation in digital terrestrial television systems. It proposes using compressed sensing based channel estimation at the receiver to eliminate sparse information. Thresholding is used to remove noise from the channel estimation and improve signal quality. Simulation results show that bit error rate decreases when the received signal power from different transmitters is almost equal.
1) There are different types of waveform coding including orthogonal, biorthogonal, and transorthogonal coding.
2) Orthogonal coding uses codewords that are mutually perpendicular to each other. Biorthogonal coding uses two sets of orthogonal codes where each codeword in one set has its antipodal codeword in the other set.
3) Transorthogonal coding generates codes from an orthogonal set by deleting the first digit of each codeword. It represents minimum energy equivalence and requires minimum energy per bit for a given symbol error rate.
This document describes two techniques for designing optical XNOR and NAND logic gates. The first technique uses a 2D array of coupled optical cavities with Kerr nonlinearity. Discrete cavity solitons are numerically simulated and used to demonstrate optical XNOR and NAND gates by controlling soliton interactions with a Gaussian beam. The second technique uses multi-mode interference waveguides to convert the phase of binary-phase-shift keying input signals to amplitude at the output, implementing optical XNOR and NAND logic. Numerical simulations using the finite element method show contrast ratios of 21.5 dB for the XNOR gate and 22.3 dB for the NAND gate.
Delta modulation is a type of pulse code modulation where the signal is encoded with 1-bit samples. It provides a staircase approximation of an oversampled input signal by increasing or decreasing the approximation by a fixed step size based on whether the input is above or below the approximation. Adaptive delta modulation improves performance by making the step size variable and adapting it based on the input signal, using a larger step size for steep signal segments and a smaller step size when the signal is changing slowly. Delta modulation is suitable for low bit rate applications like audio and speech processing due to its use of only 1 bit per sample, but can result in slope overload distortion or granular noise depending on the step size.
In this paper, a new algorithm for a high resolution
Direction Of Arrival (DOA) estimation method for multiple
wideband signals is proposed. The proposed method proceeds
in two steps. In the first step, the received signals data is
decomposed in a Toeplitz form using the first-order statistics.
In the second step, The QR decomposition is applied on the
constructed Toeplitz matrix. Compared with existing schemes,
the proposed scheme provides several advantages. First, it
requires computing the triangular matrix R or the orthogonal
matrix Q to find the DOA; these matrices can be computed
with O(n2) operation. However, most of the existing schemes
required eignvalue decomposition (EVD) for the covariance
matrix or singular value decomposition (SVD) for the data
matrix; using EVD or SVD requires much more complex
computational O(n3) operation. Second, the proposed scheme
is more suitable for high-speed communication since it
requires first-order statistics and a single snapshot. Third,
the proposed scheme can estimate the correlated wideband
signals without using spatial smoothing techniques; whereas,
already-existing schemes do not. Accuracy of the proposed
wideband DOA estimation method is evaluated through
computer simulation in comparison with a conventional
method.
1) The document discusses techniques for reducing the peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signals, including repeated clipping and filtering (RCF) and nonlinear commanding transform (NCT).
2) RCF projects clipping noise into the feasible extension area while removing out-of-band interference through filtering, but suffers from problems like in-band distortion, peak re-growth, and out-of-band radiation.
3) NCT aims to reduce PAPR by compressing peak signals and expanding small signals while maintaining constant average power through optimal parameter selection. The proposed NCT technique outperforms RCF in terms of lower clipping ratio,
The document discusses adaptive channel equalization using neural networks. It provides an overview of neural networks and their application to channel equalization. Specifically, it summarizes various neural network architectures that have been used for equalization, including multilayer perceptrons, functional link artificial neural networks, Chebyshev neural networks, and radial basis function networks. It compares the bit error rate performance of these different neural network equalizers with traditional linear equalizers such as LMS and RLS. Overall, the document finds that neural network equalizers can better handle nonlinear channel distortions compared to linear equalizers and that radial basis function networks provide particularly good performance for channel equalization applications.
IRJET- Reconstruction of Sparse Signals(Speech) Using Compressive SensingIRJET Journal
This document discusses reconstructing sparse speech signals using compressive sensing. Compressive sensing allows reconstructing signals from fewer samples than the Nyquist rate by exploiting signal sparsity. The paper proposes using the basis pursuit algorithm to reconstruct speech signals sampled below the Nyquist rate. Basis pursuit formulates reconstruction as an l1-norm optimization problem to find the sparsest solution matching the samples. The algorithm is implemented in MATLAB and results show basis pursuit can accurately reconstruct speech signals from undersampled measurements without noise.
At this present scenario, the demand of the system capacity is very high in wireless network. MIMO
technology is used from the last decade to provide this requirement for wireless network antenna
technology. MIMO channels are mostly used for advanced antenna array technology. But it is most
important to control the error rate with enhanced system capacity in MIMO for present-day progressive
wireless communication. This paper explores the frame error rate with respect to different path gain of
MIMO channel. This work has been done in different fading scenario and produces a comparative analysis
of MIMO on the basis of those fading models in various conditions. Here, it is to be considered that
modulation technique as QPSK to observe these comparative evaluations for different Doppler frequencies.
From the comparative analysis, minimum amount of frame error rate is viewed for Rician distribution at
LOS path Doppler shift of 0 Hz. At last, this work is concluded with a comparative bit error rate study on
the basis of singular parameters at different SNR levels to produce the system performance for uncoded
QPSK modulation.
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.
An introduction to discrete wavelet transformsLily Rose
This document provides an overview of wavelet transforms and their applications. It introduces continuous and discrete wavelet transforms, including multiresolution analysis and the fast wavelet transform. It discusses how wavelet transforms can be used for image compression, edge detection, and digital watermarking due to properties like decomposing images into different frequency subbands. The fast wavelet transform allows efficient computation of wavelet coefficients by exploiting relationships between scales.
This document provides an overview of wavelet transformation and discrete wavelet transform (DWT). It discusses working with wavelets by convolving signals with wavelet filters and storing the results in coefficients. Properties of wavelets include maximum frequency depending on signal length and recursive partitioning of lowest band. DWT requires an orthonormal wavelet basis and uses scaling functions and wavelets. 2D wavelet transform uses separable transforms with low and high pass filters in each direction. Experimental results show decompositions of images at different levels.
The document discusses performing a discrete wavelet transform (DWT) on a 1D signal using MATLAB. It loads a test signal, performs a 5-level DWT decomposition using the coif3 wavelet, then reconstructs the approximation and detail signals at each level. Plots of the original, approximation, and detail signals are generated.
Wavelet transform is one of the important methods of compressing image data so that it takes up less memory. Wavelet based compression techniques have advantages such as multi-resolution, scalability and tolerable degradation over other techniques.
SIR Analysis of Overloaded CDMA System Using Orthogonal Gold CodesIDES Editor
This document summarizes a research paper that proposes a technique for overloaded CDMA systems using orthogonal gold codes.
1) The technique assigns one set of orthogonal gold codes to the first N users and another set to additional users, but overlays them with different PN sequences. Detection is done iteratively in two steps to detect signals from each user set.
2) A multistage conventional and weighted linear parallel interference cancellation approach is used to cancel interference between the two user sets. Expressions for the signal to interference ratio at the output of the second and third cancellation stages are derived.
3) Simulation results show that the proposed technique can accommodate N users without interference and additional users at the cost of a small
This document discusses the discrete wavelet transform (DWT) and its implementation in MATLAB. It begins with an introduction to DWTs, explaining that they decompose signals into different frequency bands using low-pass and high-pass filters. It then describes how 2D DWTs are implemented by applying 1D transforms separately to rows and columns, producing subbands that emphasize different types of edges. The document provides steps for performing DWTs in MATLAB, including single-level and multi-level decomposition and reconstruction. It concludes by showing decomposed images and discussing how DWTs separate approximation and detail information.
A seminar on INTRODUCTION TO MULTI-RESOLUTION AND WAVELET TRANSFORMमनीष राठौर
This document provides an introduction to multi-resolution analysis and wavelet transforms. It discusses that multi-resolution analysis analyzes signals at varying levels of detail or resolutions simultaneously. The Fourier transform has limitations for non-stationary signals as it does not provide time information. The short-term Fourier transform was developed to analyze non-stationary signals, but it has limitations in time-frequency resolution. Wavelet transforms were developed to analyze signals using variable time-frequency resolutions. Wavelet transforms have features like varying time-frequency resolutions and are suitable for analyzing non-stationary signals. They have applications in fields like signal compression, noise removal, and image processing.
Performance of MMSE Denoise Signal Using LS-MMSE TechniqueIJMER
This paper presents performance of mmse denoises signal using consistent cycle spinning (ccs) and least square (LS) techniques. In the past decade, TV denoise technique is used to reduced the noisy signal. The main drawback is the low quality signal and high MMSE signal. Presently, we
proposed the CCS-MMSE and LS-MMSE technique .The CCS-MMSE technique consists of two steps. They are wavelet based denoise and consistent cycle spinning. The wavelet denoise is powerful decorrelating effect on many signal domains. The consistent cycle spinning is used to estimation the
MMSE in the signal domain. The LS-MMSE is better estimation of MMSE signal domain compare to
CCS-MMSE.The experimental result shows the average MMSE reduction using various techniques.
IOSR Journal of Electronics and Communication Engineering(IOSR-JECE) is an open access international journal that provides rapid publication (within a month) of articles in all areas of electronics and communication engineering and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in electronics and communication engineering. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Images may contain different types of noises. Removing noise from image is often the first step in image processing, and remains a challenging problem in spite of sophistication of recent research. This ppt presents an efficient image denoising scheme and their reconstruction based on Discrete Wavelet Transform (DWT) and Inverse Discrete Wavelet Transform (IDWT).
Performance of enhanced lte otdoa position ing approach through nakagami-m fa...Elmourabit Ilham
This document analyzes the performance of an enhanced LTE OTDOA positioning technique called Adaptive OTDOA (A-OTDOA) through a Nakagami-m fading channel. A-OTDOA uses adaptive filters to cancel noise from received positioning reference signals before estimating time differences of arrival, improving accuracy. The document introduces A-OTDOA and the Normalized Least Mean Square adaptive algorithm used. It then discusses modeling the propagation environment, including Nakagami-m fading channels, to test A-OTDOA's performance in a worst-case scenario without line of sight.
This document discusses the use of an adaptive decision feedback equalizer (ADFE) to mitigate pulse dispersion in optical communication channels. It begins by describing different sources of dispersion in optical fibers. Then it proposes using a fractional spaced decision feedback equalizer (FSDFE) integrated with activity detection guidance (ADG) and tap decoupling (TD) to improve performance. Simulation results show the FSDFE can estimate the channel impulse response and minimize differences between the input and output. Adding ADG and TD further improves convergence rate, detection of inactive taps, and asymptotic performance. The ADFE is an effective technique for equalization and mitigating dispersion in optical links.
IRJET- Compressed Sensing based Modified Orthogonal Matching Pursuit in DTTV ...IRJET Journal
This document discusses a modified orthogonal matching pursuit algorithm used for channel estimation in digital terrestrial television systems. It proposes using compressed sensing based channel estimation at the receiver to eliminate sparse information. Thresholding is used to remove noise from the channel estimation and improve signal quality. Simulation results show that bit error rate decreases when the received signal power from different transmitters is almost equal.
1) There are different types of waveform coding including orthogonal, biorthogonal, and transorthogonal coding.
2) Orthogonal coding uses codewords that are mutually perpendicular to each other. Biorthogonal coding uses two sets of orthogonal codes where each codeword in one set has its antipodal codeword in the other set.
3) Transorthogonal coding generates codes from an orthogonal set by deleting the first digit of each codeword. It represents minimum energy equivalence and requires minimum energy per bit for a given symbol error rate.
This document describes two techniques for designing optical XNOR and NAND logic gates. The first technique uses a 2D array of coupled optical cavities with Kerr nonlinearity. Discrete cavity solitons are numerically simulated and used to demonstrate optical XNOR and NAND gates by controlling soliton interactions with a Gaussian beam. The second technique uses multi-mode interference waveguides to convert the phase of binary-phase-shift keying input signals to amplitude at the output, implementing optical XNOR and NAND logic. Numerical simulations using the finite element method show contrast ratios of 21.5 dB for the XNOR gate and 22.3 dB for the NAND gate.
Delta modulation is a type of pulse code modulation where the signal is encoded with 1-bit samples. It provides a staircase approximation of an oversampled input signal by increasing or decreasing the approximation by a fixed step size based on whether the input is above or below the approximation. Adaptive delta modulation improves performance by making the step size variable and adapting it based on the input signal, using a larger step size for steep signal segments and a smaller step size when the signal is changing slowly. Delta modulation is suitable for low bit rate applications like audio and speech processing due to its use of only 1 bit per sample, but can result in slope overload distortion or granular noise depending on the step size.
In this paper, a new algorithm for a high resolution
Direction Of Arrival (DOA) estimation method for multiple
wideband signals is proposed. The proposed method proceeds
in two steps. In the first step, the received signals data is
decomposed in a Toeplitz form using the first-order statistics.
In the second step, The QR decomposition is applied on the
constructed Toeplitz matrix. Compared with existing schemes,
the proposed scheme provides several advantages. First, it
requires computing the triangular matrix R or the orthogonal
matrix Q to find the DOA; these matrices can be computed
with O(n2) operation. However, most of the existing schemes
required eignvalue decomposition (EVD) for the covariance
matrix or singular value decomposition (SVD) for the data
matrix; using EVD or SVD requires much more complex
computational O(n3) operation. Second, the proposed scheme
is more suitable for high-speed communication since it
requires first-order statistics and a single snapshot. Third,
the proposed scheme can estimate the correlated wideband
signals without using spatial smoothing techniques; whereas,
already-existing schemes do not. Accuracy of the proposed
wideband DOA estimation method is evaluated through
computer simulation in comparison with a conventional
method.
1) The document discusses techniques for reducing the peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signals, including repeated clipping and filtering (RCF) and nonlinear commanding transform (NCT).
2) RCF projects clipping noise into the feasible extension area while removing out-of-band interference through filtering, but suffers from problems like in-band distortion, peak re-growth, and out-of-band radiation.
3) NCT aims to reduce PAPR by compressing peak signals and expanding small signals while maintaining constant average power through optimal parameter selection. The proposed NCT technique outperforms RCF in terms of lower clipping ratio,
The document discusses adaptive channel equalization using neural networks. It provides an overview of neural networks and their application to channel equalization. Specifically, it summarizes various neural network architectures that have been used for equalization, including multilayer perceptrons, functional link artificial neural networks, Chebyshev neural networks, and radial basis function networks. It compares the bit error rate performance of these different neural network equalizers with traditional linear equalizers such as LMS and RLS. Overall, the document finds that neural network equalizers can better handle nonlinear channel distortions compared to linear equalizers and that radial basis function networks provide particularly good performance for channel equalization applications.
IRJET- Reconstruction of Sparse Signals(Speech) Using Compressive SensingIRJET Journal
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QPSK modulation.
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Keywords
Raman spectroscopy, Background correction method, Local variance, Cubic spline interpolation.
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The document discusses single carrier transmission using LabVIEW & NI-USRP. It covers several topics:
1. Symbol synchronization using the maximum output energy solution which introduces an adaptive element to find the optimal sampling time that maximizes output power.
2. The role of pseudo-noise sequences in frame synchronization, which provide properties like balance and unpredictability needed for random sequences.
3. The Moose algorithm for carrier frequency offset estimation and correction which exploits least squares to determine the phase shift between training sequences and correct sample phases.
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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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This document provides an overview of channel estimation strategies used in orthogonal frequency division multiplexing (OFDM) systems. It describes the basic types of channel estimation methods: block-type pilot channel estimation and comb-type pilot channel estimation. For block-type estimation, pilots are inserted into all subcarriers of OFDM symbols periodically. This allows estimation of the channel conditions between pilot symbols. Estimation can be done with least squares (LS), minimum mean-square error (MMSE), or modified MMSE. For comb-type estimation, pilots are inserted into certain subcarriers of each symbol, requiring interpolation to estimate data subcarriers. The document compares the implementation complexity and performance of different estimation methods.
A review of literature shows that there is a variety of adaptive filters. In this research study, we propose a new type of an adaptive filter that increases the diversification used to compensate the chan-nel distortion effect in the MC-CDMA transmission. First, we show the expressions of the filter’s impulse responses in the case of a perfect channel. The adaptive filter has been simulated and experienced by blind equalization for different cases of Gaussian white noise in the case of an MC-CDMA transmission with orthogonal frequency baseband for a mobile radio downlink channel Bran A. The simulation results show the performance of the proposed identification and blind equalization algorithm for MC-CDMA transmission chain using IFFT.
SIDELOBE SUPPRESSION AND PAPR REDUCTION FOR COGNITIVE RADIO MIMO-OFDM SYSTEMS...ijistjournal
Orthogonal Frequency Division Multiplexing (OFDM) is deployed to overcome the interference. However, OFDM has a relatively large OOB emissions. In spectrum sharing approaches such as dynamic spectrum access networks, the OOB power levels of secondary transmissions should be kept below a certain level, in order not to interfere with primary transmissions. . The difficulties such as sidelobes and PAPR caused by OFDM is reduced by convex optimization and PTS technique respectively. In this technique each OFDM subcarrier is multiplied with a real-valued weight that is determined in order not to interfere with adjacent users. The problem with the SW technique is involving a very complex optimization. We propose a heuristic approach called convex optimization. It can achieve considerable sidelobe suppression while requiring significantly less computational resources than the optimal solution. Implementation results prove that it can be introduced for real-time transmissions. Optimizing the subcarrier weights and SINR is complex, for which we use the technique of convex optimization. For reducing the PAPR we use Partial Transmit Sequence (PTS) technique.
Orthogonal Frequency Division Multiplexing (OFDM) is deployed to overcome the interference. However,
OFDM has a relatively large OOB emissions. In spectrum sharing approaches such as dynamic spectrum
access networks, the OOB power levels of secondary transmissions should be kept below a certain level, in
order not to interfere with primary transmissions. . The difficulties such as sidelobes and PAPR caused by
OFDM is reduced by convex optimization and PTS technique respectively. In this technique each OFDM
subcarrier is multiplied with a real-valued weight that is determined in order not to interfere with adjacent
users. The problem with the SW technique is involving a very complex optimization. We propose a heuristic
approach called convex optimization. It can achieve considerable sidelobe suppression while requiring
significantly less computational resources than the optimal solution. Implementation results prove that it
can be introduced for real-time transmissions. Optimizing the subcarrier weights and SINR is complex, for
which we use the technique of convex optimization. For reducing the PAPR we use Partial Transmit
Sequence (PTS) technique.
Index terms : OFDM (Orthogonal Frequency Division Multiplexing), PAPR (Peak Average Power
Ratio), OOB (Out Of Band), IFFT (Inverse Fast Fourier Transform).
ICI and PAPR enhancement in MIMO-OFDM system using RNS codingIJECEIAES
The Inter-Carrier-Interference (ICI) is considered a bottleneck in the utilization of Multiple-Input-Multiple-Output Orthogonal Frequency Division Multiplexing (MIMO-OFDM) systems, due to the sensitivity of the OFDM towards frequency offsets which lead to loss of orthogonality, interference and performance degradation. In this paper Residue Numbers as a coding scheme is impeded in MIMO-OFDM systems, where the ICI levels is measured and evaluated with respect to conventional ICI mitigation techniques implemented in MIMO-OFDM. The Carrier-to-Interference Ratio (CIR), the system Bit-Error-Rate (BER) and the Complementary Cumulative Distribution Function (CCDF) for MIMO-OFDM system with Residue Number System (RNS) coding are analyzed and evaluated. The results had demonstrated a performance of transmission model with and without RNS.
Bit Error Rate Performance of MIMO Spatial Multiplexing with MPSK Modulation ...ijsrd.com
Wireless communication is one of the most effective areas of technology development of our time. Wireless communications today covers a very wide array of applications. In this, we study the performance of general MIMO system, the general V-BLAST architecture with MPSK Modulation in Rayleigh fading channels. Based on bit error rate, we show the performance of the 2x2 schemes with MPSK Modulation in noisy environment. We also show the bit error rate performance of 2x2, 3x3, 4x4 systems with BPSK modulation. We see that the bit error rate performance of 2x2 systems with QPSK modulation gives us the best performance among other schemes analysed here.
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.
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Blind, Non-stationary Source Separation Using Variational Mode Decomposition with Mode Culling
1. Seema Sud
Signal Processing: An International Journal (SPIJ), Volume (13) : Issue (2) : 2020 11
Blind, Non-stationary Source Separation Using Variational Mode
Decomposition with Mode Culling
Seema Sud seema.sud@aero.org
Communication Technologies and Engineering Division
The Aerospace Corporation
Chantilly, VA 20151, USA
Abstract
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.
Keywords: Blind Source Separation (BSS), Culling, Non-stationary, Variational Mode
Decomposition (VMD).
1. INTRODUCTION
The problem of blind source separation (BSS) using a single receiver is a challenging one. The
problem is compounded by real world artifacts of signals that are non-stationary, pass through
non-linear and/or non-stationary channels, and perhaps are distorted by passing through non-
linear amplifiers. The non-stationarity is by far a bigger limiting factor than non-linearity [1]. Two
novel techniques have been developed to perform signal extraction in non-stationary conditions,
far surpassing the performance of conventional methods including Fourier analysis, wavelet
processing, principal components analysis (PCA), and singular value decomposition (SVD). The
first method, called empirical mode decomposition (EMD), constructs a signal using a series of
intrinsic mode decompositions, by isolating frequency components from high to low. This is
performed by an averaging process of the envelopes created by local minima and maxima of the
signals [2]. The second method, called variational mode decomposition (VMD) is a novel
technique that overcomes some of the limitations associated with EMD, such as noise and
Approved for public release. OTR 2020-00547.
2. Seema Sud
Signal Processing: An International Journal (SPIJ), Volume (13) : Issue (2) : 2020 12
sampling rate sensitivities [1]. VMD operates by constructing a signal from a set of modes, where
each mode is formed using a Wiener filter constructed around a particular center frequency. Both
the modes and frequencies are estimated. The modes themselves are selected to be narrowband
about the center frequency.
In [1], the authors demonstrated superior performance of VMD in reconstructing a signal in the
presence of noise. However, there has been limited application to studying the algorithm’s usage
to separate two signals, whereby both a signal-of-interest (SOI) and the interferer are to be
estimated. This is the classical problem of BSS. In [3], VMD was applied to separation of a
sinusoidal signal from speech, using PCA also, but the application was limited to this single use
case. In addition, the issue of selection of the number of modes, K, is yet to be addressed.
In this paper, we describe applying VMD using several unknown, non-stationary SOI and
interferer combinations, where we assume without loss of generality that the interferer is stronger
than the SOI. Through this, we observe a natural selection of K based on an estimate of the
number of narrowband components of signals. We generalize this to selecting K based on the
type of interferer present. We then use the selected value of K to estimate the higher powered
interferer, and then subtract this estimate from the received signal to extract the weaker powered
signal-of-interest (SOI); this is our baseline VMD BSS algorithm. Next, we propose a modification
to this VMD baseline approach, wherein certain modes of the decomposition are removed in
estimating the interferer, based on an assumption of the SOI’s amplitude or frequency, so as to
not include spurious modes that belong to the SOI. This is shown to provide an improvement in
MSE of the interferer and hence also of the SOI. Significant improvement over the baseline
algorithm is seen over a range of carrier-to-interference ratios (CIRs), which is the power ratio
between the SOI and interferer, as well as signal-to-noise-ratios (SNRs).
An outline of the paper is as follows: Section 2 first discusses the VMD algorithm, introduced in
[1]. Section 3 presents the signal model and problem. Section 4 shows a performance analysis
with several signal types, including tones, chirps, speech, and a digitally modulated quaternary
phase shift keyed (QPSK) signal to demonstrate how the number of modes may be selected.
Section 5 describes the two proposed algorithms: the baseline VMD BSS algorithm and the
improved culling method and presents their performance with some examples. Finally, concluding
remarks are given in Section 6.
2. BACKGROUND: VARIATIONAL MODE DECOMPOSITION (VMD)
As discussed in [3] and originally presented in [1], a signal x(t) may be viewed as the sum of a set
of modes, constructed from the VMD using a series of transformations. First, we use a Hilbert
Transform (HT) to compute an analytic (complex) version of the real mode, denoted uk, to be
estimated; its associated center frequency will be denoted k. Next, the mode is translated via an
exponential shift to baseband, using k as the shifting frequency. Third, the center frequency and
bandwidth of the mode are estimated, by assuming the baseband signal takes on a narrow band
about the zero frequency. The bandwidth is estimated by computing the magnitude squared,
often referred to as the L
2
norm, of the gradient of this translated signal. Hence, the problem
formulation is based on minimizing this bandwidth. The steps are repeated to compute
subsequent modes, until K, the predetermined number of modes, has been reached. The sum of
all the modes approximates the original signal, x(t), resulting in a constrained problem written as:
(1)
where k = 1, 2, …, K. The term in parenthesis is applied to compute the Hilbert Transform of uk(t),
* denotes convolution, the exponential term provides the translation of component k to
3. Seema Sud
Signal Processing: An International Journal (SPIJ), Volume (13) : Issue (2) : 2020 13
baseband, and the partial derivative t is the gradient of the result. Finally, the norm of the entire
term is computed using ||
.
||
2
. This problem is solved by augmenting with additional constraints:
The first constraint is a parameter, , used to adjust the weight of the first term in the Eq. (1)
depending on the noise. The more the noise, the smaller the . The second constraint is a
Lagrange multiplier, , used to adhere strictly to the constraint dictated by the second term in Eq.
(1). These two constraints result in the updated problem formulation.
(2)
After some mathematical manipulation (details provided in [1]), the solution is obtained by
initializing: n = 0, k = 1, u1
0
=
0
= 1
0
= 0, and computing the modes and frequencies as:
(3)
and
(4)
where
(5)
and is a time step constant. We iterate from k = 1, 2, …, K and also from n = 0, 1, …, N-1 until
the modes and frequencies converge; for our simulations, we let N = 500. Note that one limit with
the VMD algorithm is in selection of the number of modes, similar to selection of the number of
signals when using PCA. If underselected, the interferer is not fully captured but if overestimated,
then partial SOI cancellation occurs. In both cases, errors in estimating the interferer and SOI
occur. In the next section, we discuss how K can be selected based on the expected types of
signal.
3. SIGNAL MODEL
Let us assume we collect a signal that takes the form:
(6)
where x(t) is a SOI, I(t) is an interfering signal, and n(t) is noise, modeled as additive white
Gaussian noise (AWGN). The goal is to blindly separate and estimate both the non-stationary
SOI and non-stationary interferer in the presence of the noise, hence this is a BSS problem. The
amplitude of the interferer is set to unity, without loss of generality. The amplitude of the SOI, Ax,
is set to achieve a certain SOI to interferer ratio, denoted as a carrier-to-interference (CIR), in dB,
computed by:
(7)
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Signal Processing: An International Journal (SPIJ), Volume (13) : Issue (2) : 2020 14
Furthermore, the noise standard deviation, n, is set to achieve a desired carrier-to-noise ratio
(C/N), also in dB, given by:
(8)
Without loss of generality, we assume: (1) that the amplitude of I(t) is unity, so that we vary the
amplitude of the SOI alone; and (2) Ax < 1, meaning the interferer is stronger than the SOI; if Ax >
1 we would treat the SOI as the interferer. An important consequence of the second assumption
is that the VMD will estimate the interfering signal first; we limit our attention therefore to the case
where -10 < CIR < 0 dB, resulting in 0.1 < Ax < 1. We also limit our attention to 0 < C/N < 15 dB.
For our first proposed, baseline, approach, we input y(t) to the VMD algorithm, and the output
modes are used to compute the estimate of I(t), denoted (t) as:
(9)
We again emphasize that this equation is based on the assumption that the interferer power is
higher, hence it will be estimated first by VMD. We then estimate the SOI as:
(10)
Finally, performance is determined by computing the mean-square error (MSE) between the true
signals and their estimates, using:
(11)
and
(12)
For the purpose of analysis, we assume four types of SOI and interferer types. These are as
follows:
Tone: x(t)/I(t) = , where ft is the tone frequency;
Chirp: x(t)/I(t) = , where fd is the initial frequency of the chirp, and is the
rate of change in the frequency in Hz/sec;
QPSK: x(t)/I(t) = A(t) + jB(t), where A, B take on values of {-1, +1} and are randomly
generated;
Speech: x(t)/I(t) = , where
(13)
and where ai(t) is the amplitude of component i, which will be time-varying, i.e. non-stationary, fci
is its center frequency, fi(t) is the frequency modulation, i = 1, 2, …, Ns, and Ns is the number of
signals combined to form the speech signal [4].
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Signal Processing: An International Journal (SPIJ), Volume (13) : Issue (2) : 2020 15
For simulation purposes, we let 1 < ft < 5 kHz, fd = 40 kHz, = 10 kHz/s, and 1 < fc < 1; 000 Hz,
and Ns = 6.
In the next section, we study the performance of VMD as a BSS algorithm, using Eqs. (11) and
(12) as the performance metrics, with combinations of the above four signal types representing
the interferer and SOI pair. After that, we discuss how to cull some modes in Eq. (9) to improve
the MSEs of both signals.
4. PREDICTION OF THE NUMBER OF MODES FOR BLIND SOURCE
SEPARATION (BSS)
Fig. 1 shows several examples of interferer and SOI pairs, where the number of modes K is
plotted vs. the MSE between the tru/e interferer (or SOI) and its estimate, using CN = 15 dB and
CIR = -10 dB. The first two cases show one and three tone interferers, respectively, with a
speech SOI. The optimum number of modes K when the interferer is a tone is equal to the
number of tones. If its underestimated, then a tone may not be cancelled, resulting in errors to
both tone and SOI estimates. Overestimation also results in slight increase in errors; this is
expected because now a portion of the SOI is being cancelled, but the increase is small because
the speech signal contains many spectral components.
The third plot shows a QPSK interferer. Here, the number of modes is roughly equal to the
number of lobes in the QPSK signal spectrum. A larger hit to the MSE of the SOI is seen if the
number of modes is underestimated, because this does not result in adequate cancellation of an
in-band lobe. If the QPSK signal is wideband, a few modes are still needed to capture the wider
main lobe. Hence, a good value of K is about 6 to 10. In the fourth plot, a speech signal is the
interferer. This is the most unstructured of all the interferers, with several narrowband spectral
components, and hence the most modes are required. Still, the number of modes needed to
estimate the signal can be assumed to be fairly small, i.e. K < 10.
When the interferer is a chirp, as in the fifth, sixth, and seventh plots, the number of modes
required depends on the chirp bandwidth, with more modes for wider chirps. However, even in
this case, only about K = 6 to 10 modes is needed. Note that if the number of modes is estimated
to be too high, then slight errors occur in the estimation of both the interferer and speech signals.
If it’s too low, larger errors can occur for estimation of the SOI, as the interferer is not being
adequately cancelled. Furthermore, for the wideband chirp case, underestimating the modes
results in significant errors for both signals, so overestimation is better.
In the final plot where the interferer is a speech signal and the SOI is a chirp, we still require K = 6
to 10. This is the most stressing of all the cases with significant spectral overlap of the signals, so
we see a degradation in the MSE performance. However, the algorithm can still separate the
signals and does not require any increase in K. Hence, we see that VMD in general operates with
small values of K, smaller for tones/narrowband chirps, larger for wideband chirps/QPSK, and
largest for speech. A summary of the number of modes for the signal pairs is in Table I.
The next section describes our second proposed approach to reduce the MSE by frequency- or
amplitude-based mode culling.
5. IMPROVED ALGORITHM USING FREQUENCY-BASED MODE CULLING
Revisiting Eqs. (6) and (9), we explore ways to improve the MSEs of interferer and SOI. The
selected method involves an initial estimate of the frequency bands at which a strong SOI
component may exist. Then, the modes uk associated with those frequencies, k, are removed
from Eq. (9) to obtain an improved estimate of the interferer. We write the summation as before,
but subtract every mode j, where j is estimated to be a frequency of X(), and where X() =
FFT{x(t)}, i.e.
6. Seema Sud
Signal Processing: An International Journal (SPIJ), Volume (13) : Issue (2) : 2020 16
FIGURE 1: Number of Modes, K, vs. Mean-Square Error (MSE); C/N = 15 dB, CIR = -10 dB.
7. Seema Sud
Signal Processing: An International Journal (SPIJ), Volume (13) : Issue (2) : 2020 17
TABLE 1: Interferer, SOI, and Number of Modes.
(14)
Since certain modes have been removed in estimating the higher powered interferer, we term this
new approach as VMD with mode culling. Note that the j’s have to be estimated or guessed at,
since we do not know X(). This could be done by knowing what bands a particular SOI lies in or
knowing the type of signal under search, since most signals occupy specific frequency bands
designated by the International Telecommunications Union (ITU) internationally; in the United
States the Federal Communications Commission (FCC) determines frequency bands for specific
services. The SOI is still obtained from the new interferer estimate using Eq. (10), and MSEs are
computed as before from Eqs. (11) and (12).
Another way to do the mode culling is to try to estimate the amplitude of a SOI, which of course is
easiest to estimate with a narrowband or tone SOI, and then remove the uk(t)’s whose amplitude
is closest, i.e. the k
th
component where Ax max(uk(t)). We can write:
(15)
From the analysis conducted, the selection should be based on which parameter is easier to
estimate, i.e. more stationary over time. Removal of estimated SOI modes by culling has the
objective of better estimating the interferer, which in turn results in an improved estimate of the
SOI.
Fig. 2 illustrates the culling concept for a speech interferer overpowering a narrow tone SOI. We
take a guess as to the frequency of the SOI, choosing the k that most closely reflects that
frequency. We then remove the associated mode, u2 in this case, from the interferer estimation.
We compute the MSE of the resulting signals. The figure illustrates the MSEs of both SOI and
interferer, before and after culling. We also show the ratio of MSEs to determine how much
improvement the culling provides. An improvement of one to two orders of magnitude in both the
interferer and SOI are seen. This is explained by noting that the tone has a power that is higher
than some modes of the interferer, hence it will be included in the mode decomposition of the
interferer. By using its estimated frequency or amplitude to remove (cull) it, we can improve the
estimates of both signals. The improvement is seen across the whole range of C/N and CIR,
where the interferer MSE is substantially reduced because estimation error due to the presence
of the SOI is removed. Also, note that when the SOI is culled, the MSE performance of the
interferer is more constant across the range of CIR, which is expected because the SOI is
removed in obtaining the interferer estimate, so its power is not important. The resultant culling
also improves the SOI MSE for all C/N’s and CIR’s.
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Signal Processing: An International Journal (SPIJ), Volume (13) : Issue (2) : 2020 18
The next example is a more stressing case where there is a speech interferer riding on a chirp
SOI. There is overlap between the two in the spectral domain, and the amplitude of the SOI is
high enough so as to cause errors in estimating the interferer, and hence the SOI itself.
Estimating that the chirp is present over the first three frequencies, and culling these, we obtain
the result in Fig. 3. Both sets of plots again show the results over a range of C/N and CIR for
completeness. For the baseline algorithm, when CIR is very small, the MSE of the interferer is
low. This is because the interferer is much stronger than the SOI, so it can be easily estimated;
hence, the MSE of the SOI is smallest in this range, too. MSE of both interferer and SOI degrade
gracefully as C/N reduces. With culling, we see a similar improvement in the interferer’s MSE as
in the previous example; it is improved across the whole range of C/N and CIR, and is overall
reduced. Culling also significantly reduces the MSE of the SOI overall, except at very low CIR. At
low CIR, i.e. CIR = -10 dB, the culling approach does not work as well, since the modes estimate
the interferer, not the SOI, so culling introduces cancellation errors. The most significant
improvement in SOI MSE is seen at higher CIR. However, performance improvement at low CIR
is difficult. Hence, future effort can be directed at joint algorithms to improve performance at
higher CIR. If we look at the ratio of culled MSE to the baseline MSE, which is also plotted in
Figs. 2 and 3, both for the interferer and SOI, we see that up to one or two orders magnitude
improvement is with the culling approach. This occurs with both tone and chirp SOIs.
These results demonstrate that the culling approach offers improvement when compared to the
conventional VMD approach presented in [1]; EMD and other conventional methods such as
Fourier analysis, wavelet analysis, and PCA fail to perform here due to the presence of the
interfering signal. Thus, the VMD culling approach offers promise in blindly separating non-
stationary signals, surpassing the best currently available approach of the conventional VMD.
6. CONCLUSION
This paper describes the application of the variational mode decomposition (VMD) algorithm to
the problem of blind source separation (BSS). A higher powered interferer is estimated using
VMD first, and then subtracted from the received mixture to extract a lower powered signal-of-
interest (SOI). Typically, as we show with numerous examples and signal types, the number of
VMD modes can be less than K = 10. If the interferer can be effectively broken down into N
tones, then we should choose K = N for optimum performance. For wideband interferers, we
typically choose K = 6 to 10. We further describe an improvement to this blind estimation problem
by using a culling approach, wherein high powered frequency components of the SOI that may
contribute to the modes used to estimate the interferer are culled, by excluding those modes k
whose frequencies k correspond to frequency bands of the SOI. The culling approach improves
estimation of the interferer and SOI, typically producing mean-square error (MSE) reduction by an
order of magnitude or more. This is tested over a range of power levels and noise levels. Future
work includes the development of a joint blind source separation algorithm using the VMD
method and testing the algorithm with real data, such as speech signals collected in the presence
of other non-stationary interferers.
7. ACKNOWLEDGMENTS
The author thanks The Aerospace Corporation for funding this work and Alan Foonberg for
reviewing the paper.
8. REFERENCES
[1] K. Dragomiretskiy, and D. Zosso, “Variational Mode Decomposition,” IEEE Trans. on
Signal Proc., Vol. 62, No. 3, pp. 531-544, 2014.
[2] N.E. Huang, Z. Shen, S.R. Long, M.C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C.C. Tung, and
H.H. Liu, “The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and
Non-stationary Time Series Analysis”, Proc. Royal Soc. A: Math., Phys. Eng. Sci., Vol. 454,
No. 1971, pp. 903-995, Mar. 1998.
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Signal Processing: An International Journal (SPIJ), Volume (13) : Issue (2) : 2020 19
[3] P. Dey, U. Satija, and B. Ramkumar, “Single Channel Blind Source Separation Based on
Variational Mode Decomposition and PCA,” Proc. Annual IEEE India Conference
(INDICON), New Delhi, India, pp. 1-5, 2015.
[4] E. Lai, “Practical Digital Signal Processing”, Elsevier Science and Technology, Oxford, UK,
Jan. 2004.
FIGURE 2: Mean-Square Errors (MSEs); Speech Interferer and Tone SOI; K = 10.
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Signal Processing: An International Journal (SPIJ), Volume (13) : Issue (2) : 2020 20
FIGURE 3: Mean-Square Errors (MSEs); Speech Interferer and 10 Hz/s Chirp SOI; K = 10.