This paper applies a compressed algorithm to improve the spectrum sensing performance of cognitive radio technology.
At the fusion center, the recovery error in the analog to information converter (AIC) when reconstructing the
transmit signal from the received time-discrete signal causes degradation of the detection performance. Therefore, we
propose a subspace pursuit (SP) algorithm to reduce the recovery error and thereby enhance the detection performance.
In this study, we employ a wide-band, low SNR, distributed compressed sensing regime to analyze and evaluate the
proposed approach. Simulations are provided to demonstrate the performance of the proposed algorithm.
Projected Barzilai-Borwein Methods Applied to Distributed Compressive Spectru...Polytechnique Montreal
Cognitive radio allows unlicensed (cognitive) users to use licensed frequency bands by exploiting spectrum sensing techniques to detect whether or not the licensed (primary) users are present. In this paper, we present a compressed sensing applied to spectrum-occupancy detection in wide-band applications. The collected analog signals from each cognitive radio (CR) receiver at a fusion center are transformed to discrete-time signals by using analog-to-information converter (AIC) and then employed to calculate the autocorrelation. For signal reconstruction, we exploit a novel approach to solve the optimization problem consisting of minimizing both a quadratic (l2) error term and an l1-regularization term. In specific, we propose the Basic gradient projection (GP) and projected Barzilai-Borwein (PBB) algorithm to offer a better performance in terms of the mean squared error of the power spectrum density estimate and the detection probability of licensed signal occupancy.
Performance of cognitive radio networks with maximal ratio combining over cor...Polytechnique Montreal
In this paper, we apply the maximal ratio combining (MRC) technique to achieve higher detection probability in cognitive radio networks over correlated Rayleigh fading channels. We present a simple approach to derive the probability of detection in closed-form expression. The numerical results reveal that the detection performance is a monotonically increasing function with respect to the number of antennas. Moreover, we provide sets of complementary receiver operating characteristic (ROC) curves to illustrate the effect of antenna correlation on the sensing performance of cognitive radio networks employing MRC schemes in some respective scenarios.
Many algorithms have been developed to find sparse representation over redundant dictionaries or
transform. This paper presents a novel method on compressive sensing (CS)-based image compression
using sparse basis on CDF9/7 wavelet transform. The measurement matrix is applied to the three levels of
wavelet transform coefficients of the input image for compressive sampling. We have used three different
measurement matrix as Gaussian matrix, Bernoulli measurement matrix and random orthogonal matrix.
The orthogonal matching pursuit (OMP) and Basis Pursuit (BP) are applied to reconstruct each level of
wavelet transform separately. Experimental results demonstrate that the proposed method given better
quality of compressed image than existing methods in terms of proposed image quality evaluation indexes
and other objective (PSNR/UIQI/SSIM) measurements.
Optimum range of angle tracking radars: a theoretical computingIJECEIAES
In this paper, we determine an optimal range for angle tracking radars (ATRs) based on evaluating the standard deviation of all kinds of errors in a tracking system. In the past, this optimal range has often been computed by the simulation of the total error components; however, we are going to introduce a closed form for this computation which allows us to obtain the optimal range directly. Thus, for this purpose, we firstly solve an optimization problem to achieve the closed form of the optimal range (Ropt.) and then, we compute it by doing a simple simulation. The results show that both theoretical and simulation-based computations are similar to each other.
A Novel CAZAC Sequence Based Timing Synchronization Scheme for OFDM SystemIJAAS Team
Several classical timing synchronization schemes have been proposed for the timing synchronization in OFDM systems based on the correlation between identical parts of OFDM symbol. These schemes show poor performance due to the presence of plateau and significant side lobe. In this paper we present a timing synchronization schemes with timing metric based on a Constant Amplitude Zero Auto Correlation (CAZAC) sequence. The performance of the proposed timing synchronization scheme is better than the classical techniques.
Band Clustering for the Lossless Compression of AVIRIS Hyperspectral ImagesIDES Editor
Hyperspectral images can be efficiently compressed
through a linear predictive model, as for example the one
used in the SLSQ algorithm. In this paper we exploit this
predictive model on the AVIRIS images by individuating,
through an off-line approach, a common subset of bands, which
are not spectrally related with any other bands. These bands
are not useful as prediction reference for the SLSQ 3-D
predictive model and we need to encode them via other
prediction strategies which consider only spatial correlation.
We have obtained this subset by clustering the AVIRIS bands
via the clustering by compression approach. The main result
of this paper is the list of the bands, not related with the
others, for AVIRIS images. The clustering trees obtained for
AVIRIS and the relationship among bands they depict is also
an interesting starting point for future research.
A novel and efficient mixed-signal compressed sensing for wide-band cognitive...Polytechnique Montreal
In cognitive radio (CR) networks, unlicensed (cognitive) users can exploit the licensed frequency bands by using spectrum sensing techniques to identify spectrum holes. This paper proposes a distributed compressive spectrum sensing scheme, in which the modulated wide-band converter can apply compressed sensing (CS) directly to analog signals at the sub-Nyquist rate and the central fusion receives signals from multiple CRs and exploits the multiple-measurements-vectors (MMV) subspace pursuit (M-SP) algorithm to jointly reconstruct the spectral support of the wide-band signal. This support is then used to detect whether the licensed bands are occupy or not. Finally, extensive simulation results show the advantages of the proposed scheme. Besides, we also compare the performance of M-SP with M-orthogonal matching pursuit (M-OMP) algorithms.
Projected Barzilai-Borwein Methods Applied to Distributed Compressive Spectru...Polytechnique Montreal
Cognitive radio allows unlicensed (cognitive) users to use licensed frequency bands by exploiting spectrum sensing techniques to detect whether or not the licensed (primary) users are present. In this paper, we present a compressed sensing applied to spectrum-occupancy detection in wide-band applications. The collected analog signals from each cognitive radio (CR) receiver at a fusion center are transformed to discrete-time signals by using analog-to-information converter (AIC) and then employed to calculate the autocorrelation. For signal reconstruction, we exploit a novel approach to solve the optimization problem consisting of minimizing both a quadratic (l2) error term and an l1-regularization term. In specific, we propose the Basic gradient projection (GP) and projected Barzilai-Borwein (PBB) algorithm to offer a better performance in terms of the mean squared error of the power spectrum density estimate and the detection probability of licensed signal occupancy.
Performance of cognitive radio networks with maximal ratio combining over cor...Polytechnique Montreal
In this paper, we apply the maximal ratio combining (MRC) technique to achieve higher detection probability in cognitive radio networks over correlated Rayleigh fading channels. We present a simple approach to derive the probability of detection in closed-form expression. The numerical results reveal that the detection performance is a monotonically increasing function with respect to the number of antennas. Moreover, we provide sets of complementary receiver operating characteristic (ROC) curves to illustrate the effect of antenna correlation on the sensing performance of cognitive radio networks employing MRC schemes in some respective scenarios.
Many algorithms have been developed to find sparse representation over redundant dictionaries or
transform. This paper presents a novel method on compressive sensing (CS)-based image compression
using sparse basis on CDF9/7 wavelet transform. The measurement matrix is applied to the three levels of
wavelet transform coefficients of the input image for compressive sampling. We have used three different
measurement matrix as Gaussian matrix, Bernoulli measurement matrix and random orthogonal matrix.
The orthogonal matching pursuit (OMP) and Basis Pursuit (BP) are applied to reconstruct each level of
wavelet transform separately. Experimental results demonstrate that the proposed method given better
quality of compressed image than existing methods in terms of proposed image quality evaluation indexes
and other objective (PSNR/UIQI/SSIM) measurements.
Optimum range of angle tracking radars: a theoretical computingIJECEIAES
In this paper, we determine an optimal range for angle tracking radars (ATRs) based on evaluating the standard deviation of all kinds of errors in a tracking system. In the past, this optimal range has often been computed by the simulation of the total error components; however, we are going to introduce a closed form for this computation which allows us to obtain the optimal range directly. Thus, for this purpose, we firstly solve an optimization problem to achieve the closed form of the optimal range (Ropt.) and then, we compute it by doing a simple simulation. The results show that both theoretical and simulation-based computations are similar to each other.
A Novel CAZAC Sequence Based Timing Synchronization Scheme for OFDM SystemIJAAS Team
Several classical timing synchronization schemes have been proposed for the timing synchronization in OFDM systems based on the correlation between identical parts of OFDM symbol. These schemes show poor performance due to the presence of plateau and significant side lobe. In this paper we present a timing synchronization schemes with timing metric based on a Constant Amplitude Zero Auto Correlation (CAZAC) sequence. The performance of the proposed timing synchronization scheme is better than the classical techniques.
Band Clustering for the Lossless Compression of AVIRIS Hyperspectral ImagesIDES Editor
Hyperspectral images can be efficiently compressed
through a linear predictive model, as for example the one
used in the SLSQ algorithm. In this paper we exploit this
predictive model on the AVIRIS images by individuating,
through an off-line approach, a common subset of bands, which
are not spectrally related with any other bands. These bands
are not useful as prediction reference for the SLSQ 3-D
predictive model and we need to encode them via other
prediction strategies which consider only spatial correlation.
We have obtained this subset by clustering the AVIRIS bands
via the clustering by compression approach. The main result
of this paper is the list of the bands, not related with the
others, for AVIRIS images. The clustering trees obtained for
AVIRIS and the relationship among bands they depict is also
an interesting starting point for future research.
A novel and efficient mixed-signal compressed sensing for wide-band cognitive...Polytechnique Montreal
In cognitive radio (CR) networks, unlicensed (cognitive) users can exploit the licensed frequency bands by using spectrum sensing techniques to identify spectrum holes. This paper proposes a distributed compressive spectrum sensing scheme, in which the modulated wide-band converter can apply compressed sensing (CS) directly to analog signals at the sub-Nyquist rate and the central fusion receives signals from multiple CRs and exploits the multiple-measurements-vectors (MMV) subspace pursuit (M-SP) algorithm to jointly reconstruct the spectral support of the wide-band signal. This support is then used to detect whether the licensed bands are occupy or not. Finally, extensive simulation results show the advantages of the proposed scheme. Besides, we also compare the performance of M-SP with M-orthogonal matching pursuit (M-OMP) algorithms.
Improved Timing Estimation Using Iterative Normalization Technique for OFDM S...IJECEIAES
Conventional timing estimation schemes based on autocorrelation experience perfor- mance degradation in the multipath channel environment with high delay spread. To overcome this problem, we proposed an improvement of the timing estimation for the OFDM system based on statistical change of symmetrical correlator. The new method uses iterative normalization technique to the correlator output before the detection based on statistical change of symmetric correlator is applied. Thus, it increases the detection probability and achieves better performance than previously published methods in the multipath environment. Computer simulation shows that our method is very robust in the fading multipath channel.
This paper presents a trifocal Rotman Lens Design
approach. The effects of focal ratio and element spacing on
the performance of Rotman Lens are described. A three beam
prototype feeding 4 element antenna array working in L-band
has been simulated using RLD v1.7 software. Simulated
results show that the simulated lens has a return loss of –
12.4dB at 1.8GHz. Beam to array port phase error variation
with change in the focal ratio and element spacing has also
been investigated.
A New Approach for Speech Enhancement Based On Eigenvalue Spectral SubtractionCSCJournals
In this paper, a phase space reconstruction-based method is proposed for speech enhancement. The method embeds the noisy signal into a high dimensional reconstructed phase space and uses Spectral Subtraction idea. The advantages of the proposed method are fast performance, high SNR and good MOS. In order to evaluate the proposed method, ten signals of TIMIT database mixed with the white additive Gaussian noise and then the method was implemented. The efficiency of the proposed method was evaluated by using qualitative and quantitative criteria.
Method for Converter Synchronization with RF InjectionCSCJournals
This paper presents an injection method for synchronizing analog to digital converters (ADC). This approach can eliminate the need for precision routed discrete synchronization signals of current technologies, such as JESD204. By eliminating the setup and hold time requirements at the conversion (or near conversion) clock rate, higher sample rate systems can be synchronized. Measured data from an existing multiple ADC conversion system was used to evaluate the method. Coherent beams were simulated to measure the effectiveness of the method. The results show near theoretical coherent processing gain.
OPTIMAL BEAM STEERING ANGLES OF A SENSOR ARRAY FOR A MULTIPLE SOURCE SCENARIOcsandit
We present the gradient and Hessian of the trace of the multivariate Cramér-Rao bound (CRB)
formula for unknown impinging angles of plane waves with non-unitary beamspace measurements,. These gradient and Hessian can be used to find the optimal beamspace
transformation matrix, i.e., the optimum beamsteering angles, using the Newton-Raphson iteration. These trace formulas are particularly useful to deal with the multiple source senario.
We also show the mean squred error (MSE) performance gain of the optimally steered beamspace measurements compared with the usuall DFT steered measurements, when the angle
of arrivals (AOAs) are estimated with stochastic maximum likelihood (SMLE) algorithm.
Interferogram Filtering Using Gaussians Scale Mixtures in Steerable Wavelet D...CSCJournals
An interferogram filtering is presented in this paper. The main concern of the proposed scheme is to lower the residues count mean while preserving the location and jump height of the lines of phase discontinuity. The proposed method is based on a statistical model of the coefficients of multi-scale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian vector and a hidden positive scalar multiplier. Under this model, the Bayesian least squares estimate of each coefficient reduces to a weighted average of the local linear estimates over all possible values of the hidden multiplier variable. The performance of this method substantially has the advantages of reducing number of residuals without affecting line of height discontinuity.
GPR Probing of Smoothly Layered Subsurface Medium: 3D Analytical ModelLeonid Krinitsky
An analytical approach to GPR probing of a
horizontally layered subsurface medium is developed, based on the coupled-wave WKB approximation. An empirical model of current in dipole transmitter antenna is used.
Poster for our conference paper titled "4K Ultra High Definition Video Coding using Homogeneous Motion Discovery Oriented Prediction" published in the Digital Image Computing: Techniques and Applications (DICTA) 2017 conference.
Abstract: State of the art video compression techniques use the motion model to approximate geometric boundaries of moving objects where motion discontinuities occur. Motion hints based inter-frame prediction paradigm moves away from this redundant approach and employs an innovative framework consisting of motion hint fields that are continuous and invertible, at least, over their respective domains. However, estimation of motion hint is computationally demanding, in particular for high resolution video sequences. Discovery of homogeneous motion models and their associated masks over the current frame and then use these models and masks to form a prediction of the current frame, provides a computationally simpler approach to video coding compared to motion hint. In this paper, the potential of this coherent motion model based approach, equipped with bigger blocks, is investigated for coding 4K Ultra High Definition (UHD) video sequences. Experimental results show a savings in bit rate of 4.68% is achievable over standalone HEVC.
A Scheme for Joint Signal Reconstruction in Wireless Multimedia Sensor Networksijma
In context aware wireless multimedia sensor networks, scenarios are usually such that
signals of multiple distributed sensors contain a common sparse component and each individual
signal owns an innovation sparse component. So distributed compressive sensing based on joint
sparsity of a signal ensemble concept exploits both these intra- and inter- signal correlation structures
and compress signals to the extent possible. This paper proposes an optimized reconstruction
scheme based on joint sparsity model which is derived from the distributed compressive sensing. In
this regard, based on distributed compressive sensing, a joint reconstruction scheme is proposed to
compress and reconstruct ensemble of signals even in large scale data transmission. Furthermore,
simulation results show the effectiveness of the proposed method in diverse compression ratios and
processing times in comparison with the joint sparsity model and individual compressive sensing
reconstruction methods.
Data Driven Choice of Threshold in Cepstrum Based Spectrum Estimatesipij
The technique of cepstrum thresholding, which is shown to be an effective, yet simple, way of obtaining a smoothed non parametric spectrum estimate of a stationary signal. The major problem of this method is the choice of the threshold value for variance reduction of spectrum estimates. This paper proposes a new threshold selection method which is based on cross validation schemes such as Leave-One-Out, LeaveTwo-Out and Leave-Half-Out. This new methods are easy to describe, simple to implement, and does not impose severe conditions on the unknown spectrum. Numerical results suggest that this new methods are shown to be in agreement with those obtained when the spectrum is fully known.
Ill-posedness formulation of the emission source localization in the radio- d...Ahmed Ammar Rebai PhD
To contact the authors : tarek.salhi@gmail.com and ahmed.rebai2@gmail.com
In the field of radio detection in astroparticle physics, many studies have shown the strong dependence of the solution of the radio-transient sources localization problem (the radio-shower time of arrival on antennas) such solutions are purely numerical artifacts. Based on a detailed analysis of some already published results of radio-detection experiments like : CODALEMA 3 in France, AERA in Argentina and TREND in China, we demonstrate the ill-posed character of this problem in the sens of Hadamard. Two approaches have been used as the existence of solutions degeneration and the bad conditioning of the mathematical formulation problem. A comparison between experimental results and simulations have been made, to highlight the mathematical studies. Many properties of the non-linear least square function are discussed such as the configuration of the set of solutions and the bias.
Improved Timing Estimation Using Iterative Normalization Technique for OFDM S...IJECEIAES
Conventional timing estimation schemes based on autocorrelation experience perfor- mance degradation in the multipath channel environment with high delay spread. To overcome this problem, we proposed an improvement of the timing estimation for the OFDM system based on statistical change of symmetrical correlator. The new method uses iterative normalization technique to the correlator output before the detection based on statistical change of symmetric correlator is applied. Thus, it increases the detection probability and achieves better performance than previously published methods in the multipath environment. Computer simulation shows that our method is very robust in the fading multipath channel.
This paper presents a trifocal Rotman Lens Design
approach. The effects of focal ratio and element spacing on
the performance of Rotman Lens are described. A three beam
prototype feeding 4 element antenna array working in L-band
has been simulated using RLD v1.7 software. Simulated
results show that the simulated lens has a return loss of –
12.4dB at 1.8GHz. Beam to array port phase error variation
with change in the focal ratio and element spacing has also
been investigated.
A New Approach for Speech Enhancement Based On Eigenvalue Spectral SubtractionCSCJournals
In this paper, a phase space reconstruction-based method is proposed for speech enhancement. The method embeds the noisy signal into a high dimensional reconstructed phase space and uses Spectral Subtraction idea. The advantages of the proposed method are fast performance, high SNR and good MOS. In order to evaluate the proposed method, ten signals of TIMIT database mixed with the white additive Gaussian noise and then the method was implemented. The efficiency of the proposed method was evaluated by using qualitative and quantitative criteria.
Method for Converter Synchronization with RF InjectionCSCJournals
This paper presents an injection method for synchronizing analog to digital converters (ADC). This approach can eliminate the need for precision routed discrete synchronization signals of current technologies, such as JESD204. By eliminating the setup and hold time requirements at the conversion (or near conversion) clock rate, higher sample rate systems can be synchronized. Measured data from an existing multiple ADC conversion system was used to evaluate the method. Coherent beams were simulated to measure the effectiveness of the method. The results show near theoretical coherent processing gain.
OPTIMAL BEAM STEERING ANGLES OF A SENSOR ARRAY FOR A MULTIPLE SOURCE SCENARIOcsandit
We present the gradient and Hessian of the trace of the multivariate Cramér-Rao bound (CRB)
formula for unknown impinging angles of plane waves with non-unitary beamspace measurements,. These gradient and Hessian can be used to find the optimal beamspace
transformation matrix, i.e., the optimum beamsteering angles, using the Newton-Raphson iteration. These trace formulas are particularly useful to deal with the multiple source senario.
We also show the mean squred error (MSE) performance gain of the optimally steered beamspace measurements compared with the usuall DFT steered measurements, when the angle
of arrivals (AOAs) are estimated with stochastic maximum likelihood (SMLE) algorithm.
Interferogram Filtering Using Gaussians Scale Mixtures in Steerable Wavelet D...CSCJournals
An interferogram filtering is presented in this paper. The main concern of the proposed scheme is to lower the residues count mean while preserving the location and jump height of the lines of phase discontinuity. The proposed method is based on a statistical model of the coefficients of multi-scale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian vector and a hidden positive scalar multiplier. Under this model, the Bayesian least squares estimate of each coefficient reduces to a weighted average of the local linear estimates over all possible values of the hidden multiplier variable. The performance of this method substantially has the advantages of reducing number of residuals without affecting line of height discontinuity.
GPR Probing of Smoothly Layered Subsurface Medium: 3D Analytical ModelLeonid Krinitsky
An analytical approach to GPR probing of a
horizontally layered subsurface medium is developed, based on the coupled-wave WKB approximation. An empirical model of current in dipole transmitter antenna is used.
Poster for our conference paper titled "4K Ultra High Definition Video Coding using Homogeneous Motion Discovery Oriented Prediction" published in the Digital Image Computing: Techniques and Applications (DICTA) 2017 conference.
Abstract: State of the art video compression techniques use the motion model to approximate geometric boundaries of moving objects where motion discontinuities occur. Motion hints based inter-frame prediction paradigm moves away from this redundant approach and employs an innovative framework consisting of motion hint fields that are continuous and invertible, at least, over their respective domains. However, estimation of motion hint is computationally demanding, in particular for high resolution video sequences. Discovery of homogeneous motion models and their associated masks over the current frame and then use these models and masks to form a prediction of the current frame, provides a computationally simpler approach to video coding compared to motion hint. In this paper, the potential of this coherent motion model based approach, equipped with bigger blocks, is investigated for coding 4K Ultra High Definition (UHD) video sequences. Experimental results show a savings in bit rate of 4.68% is achievable over standalone HEVC.
A Scheme for Joint Signal Reconstruction in Wireless Multimedia Sensor Networksijma
In context aware wireless multimedia sensor networks, scenarios are usually such that
signals of multiple distributed sensors contain a common sparse component and each individual
signal owns an innovation sparse component. So distributed compressive sensing based on joint
sparsity of a signal ensemble concept exploits both these intra- and inter- signal correlation structures
and compress signals to the extent possible. This paper proposes an optimized reconstruction
scheme based on joint sparsity model which is derived from the distributed compressive sensing. In
this regard, based on distributed compressive sensing, a joint reconstruction scheme is proposed to
compress and reconstruct ensemble of signals even in large scale data transmission. Furthermore,
simulation results show the effectiveness of the proposed method in diverse compression ratios and
processing times in comparison with the joint sparsity model and individual compressive sensing
reconstruction methods.
Data Driven Choice of Threshold in Cepstrum Based Spectrum Estimatesipij
The technique of cepstrum thresholding, which is shown to be an effective, yet simple, way of obtaining a smoothed non parametric spectrum estimate of a stationary signal. The major problem of this method is the choice of the threshold value for variance reduction of spectrum estimates. This paper proposes a new threshold selection method which is based on cross validation schemes such as Leave-One-Out, LeaveTwo-Out and Leave-Half-Out. This new methods are easy to describe, simple to implement, and does not impose severe conditions on the unknown spectrum. Numerical results suggest that this new methods are shown to be in agreement with those obtained when the spectrum is fully known.
Ill-posedness formulation of the emission source localization in the radio- d...Ahmed Ammar Rebai PhD
To contact the authors : tarek.salhi@gmail.com and ahmed.rebai2@gmail.com
In the field of radio detection in astroparticle physics, many studies have shown the strong dependence of the solution of the radio-transient sources localization problem (the radio-shower time of arrival on antennas) such solutions are purely numerical artifacts. Based on a detailed analysis of some already published results of radio-detection experiments like : CODALEMA 3 in France, AERA in Argentina and TREND in China, we demonstrate the ill-posed character of this problem in the sens of Hadamard. Two approaches have been used as the existence of solutions degeneration and the bad conditioning of the mathematical formulation problem. A comparison between experimental results and simulations have been made, to highlight the mathematical studies. Many properties of the non-linear least square function are discussed such as the configuration of the set of solutions and the bias.
In the last few years Compressed Sampling (CS) has been well used in the area of signal processing and image compression. Recently, CS has been earning a great interest in the area of wireless communication networks. CS exploits the sparsity of the signal processed for digital acquisition to reduce the number of measurement, which leads to reductions in the size, power consumption, processing time and processing cost. This article presents application of CS for the spectrum sensing and channel estimation in Cognitive Radio (CR) networks. Basic approach of CS is introduced first, and then scheme for spectrum sensing and channel estimation for CR is discussed. First, fast and efficient compressed spectrum sensing (CSS) scheme is proposed to detect wideband spectrum, where samples are taken at sub-Nyquist rate and signal acquisition is terminated automatically once the samples are sufficient for the best spectral recovery and then, after the spectrum sensing, in the second phase notion of multipath sparsity is formalized and a novel approach based on Orthogonal Matching Pursuit (OMP) is discussed to estimate sparse multipath channels for CR networks. The effectiveness of the proposed scheme is demonstrated through comparisons with the existing conventional spectrum sensing and channel estimation methods.
Numerical Investigation of Multilayer Fractal FSSIJMER
Numerical investigations are presented for a multilayer frequency selective surface with Koch
fractal (levels 1 and 2) conducting patch elements. The structure investigated is obtained using two FSS
screens separated by an air gap layer. For the proposed investigation were used three different values an
air gap height. The results obtained using the numerical method were compared with other technique and
using the commercial software Ansoft DesignerTM. A good agreement was observed in terms of the
bandwidth.
Fixed Point Realization of Iterative LR-Aided Soft MIMO Decoding AlgorithmCSCJournals
Multiple-input multiple-output (MIMO) systems have been widely acclaimed in order to provide high data rates. Recently Lattice Reduction (LR) aided detectors have been proposed to achieve near Maximum Likelihood (ML) performance with low complexity. In this paper, we develop the fixed point design of an iterative soft decision based LR-aided K-best decoder, which reduces the complexity of existing sphere decoder. A simulation based word-length optimization is presented for physical implementation of the K-best decoder. Simulations show that the fixed point result of 16 bit precision can keep bit error rate (BER) degradation within 0.3 dB for 8×8 MIMO systems with different modulation schemes.
METHOD FOR THE DETECTION OF MIXED QPSK SIGNALS BASED ON THE CALCULATION OF FO...sipij
In this paper we propose the method for the detection of Carrier-in-Carrier signals using QPSK modulations. The method is based on the calculation of fourth-order cumulants. In accordance with the methodology based on the Receiver Operating Characteristic (ROC) curve, a threshold value for the decision rule is established. It was found that the proposed method provides the correct detection of the sum of QPSK signals for a wide range of signal-to-noise ratios and also for the different bandwidths of mixed signals. The obtained results indicate the high efficiency of the proposed detection method. The advantage of the proposed detection method over the “radiuses” method is also shown.
In order to improve sensing performance when the noise variance is not known, this paper considers a so-called
blind spectrum sensing technique that is based on eigenvalue models. In this paper, we employed the spiked population
models in order to identify the miss detection probability. At first, we try to estimate the unknown noise variance
based on the blind measurements at a secondary location. We then investigate the performance of detection, in terms
of both theoretical and empirical aspects, after applying this estimated noise variance result. In addition, we study the
effects of the number of SUs and the number of samples on the spectrum sensing performance.
A Threshold Enhancement Technique for Chaotic On-Off Keying SchemeCSCJournals
In this paper, an improvement for Chaotic ON-OFF (COOK) Keying scheme is proposed. The scheme enhances Bit Error Rate (BER) performance of standard COOK by keeping the signal elements at fixed distance from the threshold irrespective of noise power. Each transmitted chaotic segment is added to its flipped version before transmission. This reduces the effect of noise contribution at correlator of the receiver. The proposed system is tested in Additive White Gaussian Noise (AWGN) channel and compared with the standard COOK under different Eb/No levels. A theoretical estimate of BER is derived and compared with the simulation results. Effect of spreading factor increment in the proposed system is studied. Results show that the proposed scheme has a considerable advantage over the standard COOK at similar average bit energy and with higher values of spreading factors.
A Compressed Sensing Approach to Image Reconstructionijsrd.com
compressed sensing is a new technique that discards the Shannon Nyquist theorem for reconstructing a signal. It uses very few random measurements that were needed traditionally to recover any signal or image. The need of this technique comes from the fact that most of the information is provided by few of the signal coefficients, then why do we have to acquire all the data if it is thrown away without being used. A number of review articles and research papers have been published in this area. But with the increasing interest of practitioners in this emerging field it is mandatory to take a fresh look at this method and its implementations. The main aim of this paper is to review the compressive sensing theory and its applications.
Design of Linear Array Transducer Using Ultrasound Simulation Program Field-IIinventy
This paper analyze the effect of number of elements of linear array and frequency influence the
image quality in a homogenous medium. Linear arrays are most common for conventional ultrasound imaging,
because of the advantages of electronic focusing and steering. Propagation of ultrasound in biological tissues is
of nonlinear in nature. But linear approximation in far-field is promising solution to model and simulate the
real time ultrasound wave propagation. The simulation of ultrasound imaging using linear acoustics has been
most widely used for understanding focusing, image formation and flow estimation, and it has become a
standard tool in ultrasound research. . In this paper the ultrasound field generated from linear array transducer
and propagation through biological tissues is modeled and simulated using FIELD II program.
Channel and clipping level estimation for ofdm in io t –based networks a reviewIJARIIT
Internet of Things (IoT) is the idea to connect all devices to the internet. To implement such systems, we need to design
low cost and less complex transmitters and make the receiver side complex. Now days OFDM is mainly used for communication
due to its great advantages. But it faces the main problem such as PAPR due to the non-linear performance of High power
amplifiers. There are so many methods are available to reduce the effect of PAPR in OFDM transmission, among this clipping
is the simplest one. In this paper, we propose two algorithms to find the clipping level as well as the channel estimation. The
efficiency of these algorithms is evaluated by using CLRB calculation.
A new look on performance of small-cell network with design of multiple anten...journalBEEI
A downlink of small-cell network is studied in this paper studies in term of outage performance. We benefit by design of multiple antennas at the base station and fullduplex transmission mode. The scenario of multiple surrounded small-cell networks is considered to look the impact of interference. We derive the closed-form expression of outage probability to show performance of mobile user. We investigate target rate is main factor affecting to outage performance. According to the considered system, simulation results indicate reasonable value of outage probability and throughput as well. Finally, Monte-Carlo simulation method is deployed to determine exactness of main results found in this article. Finally, the considered system can exhibit improved performance if controlling interference term.
Adaptive Channel Equalization using Multilayer Perceptron Neural Networks wit...IOSRJVSP
This research addresses the problem inter-symbol interference (ISI) using equalization techniques for time dispersive channels with additive white Gaussian noise (AWGN). The channel equalizer is modelled as a non-linear Multilayer Perceptron (MLP) structure. The Back Propagation (BP) algorithm is used to optimize the synaptic weights of the equalizer during the training mode. In the typical BP algorithm, the error signal is propagated from the output layer to the input layer while the learning rate parameter is held constant. In this study, the BP algorithm is modified so as to allow for the learning rate to be variable at each iteration and this achieves a faster convergence. The proposed algorithm is used to train the MLP based decision feedback equalizer (DFE) for time dispersive ISI channels. The equalizer is tested for a random input sequence of BPSK signals and its performance analysed in terms of the Bit Error Rates and speed of convergence. Simulation results show that the proposed algorithm improves the Bit Error Rate (BER) and rate of convergence.
Design and Optimal Configuration of Full-Duplex MAC Protocol for Cognitive Ra...Polytechnique Montreal
In this paper, we propose an adaptive medium access control (MAC) protocol for
full-duplex (FD) cognitive radio networks in which FD secondary users (SUs) perform channel contention
followed by concurrent spectrum sensing and transmission, and transmission only with maximum power
in two different stages (called the FD sensing and transmission stages, respectively) in each contention
and access cycle. The proposed FD cognitive MAC (FDC-MAC) protocol does not require synchronization
among SUs, and it efciently utilizes the spectrum and mitigates the self-interference in the FD transceiver.
We develop a mathematical model to analyze the throughput performance of the FDC-MAC protocol, where
both half-duplex (HD) transmission and FD transmission modes are considered in the transmission stage.
Then, we study the FDC-MAC conguration optimization through adaptively controlling the spectrum
sensing duration and transmit power level in the FD sensing stage.We prove that there exists optimal sensing
time and transmit power to achieve the maximum throughput, and we develop an algorithm to congure
the proposed FDC-MAC protocol. Extensive numerical results are presented to illustrate the optimal
FDC-MAC conguration and the impacts of protocol parameters and the self-interference cancellation
quality on the throughput performance. Moreover, we demonstrate the signicant throughput gains of the
FDC-MAC protocol with respect to the existing HD MAC and single-stage FD MAC protocols
Joint Cooperative Spectrum Sensing and MAC Protocol Design for Multi-channel ...Polytechnique Montreal
In this paper, we propose a semi-distributed cooperative spectrum sen
sing (SDCSS) and channel access framework
for multi-channel cognitive radio networks (CRNs). In particular, we c
onsider a SDCSS scheme where secondary
users (SUs) perform sensing and exchange sensing outcomes with ea
ch other to locate spectrum holes. In addition,
we devise the
p
-persistent CSMA-based cognitive MAC protocol integrating the SDCSS to
enable efficient spectrum
sharing among SUs. We then perform throughput analysis and develop
an algorithm to determine the spectrum
sensing and access parameters to maximize the throughput for a given
allocation of channel sensing sets. Moreover,
we consider the spectrum sensing set optimization problem for SUs to maxim
ize the overall system throughput. We
present both exhaustive search and low-complexity greedy algorithms
to determine the sensing sets for SUs and
analyze their complexity. We also show how our design and analysis can be
extended to consider reporting errors.
Finally, extensive numerical results are presented to demonstrate the sig
nificant performance gain of our optimized
design framework with respect to non-optimized designs as well as the imp
acts of different protocol parameters on
the throughput performance.
In this paper, we consider the joint optimal sensing
and distributed MAC protocol design for cognitive radio
networks. Specifically, we design a synchronized MAC protocol
for dynamic spectrum sharing among multiple secondary
users, which incorporates spectrum sensing for protecting active
primary users. We perform saturation throughput analysis for
the proposed MAC protocol that explicitly captures spectrum
sensing performance. Then, we find its optimal configuration
by formulating a throughput maximization problem subject to
detection probability constraints for primary users. In particular,
the optimal solution of this optimization problem returns the
required sensing time for primary users’ protection and optimal
contention window for maximizing total throughput of the
secondary network. Finally, numerical results are presented to
illustrate a significant performance gain of the optimal sensing
and protocol configuration.
In a communications system, the channel is affected by an additive white Gaussian noise (AWGN)
and a fading due to a distance between a transmitter and a receiver. Especially, there are many kinds of
channel fadings. Depending on the moving speeds of transmitters or receivers, a fading type can be a slow
fading or a fast fading (i.e., the product of 0.1 and coherence time than smaller or larger than the symbol
period of signal are corresponding to fast and slow fadings). Moreover, a channel can be referred as a
selective fading or a flat fading corresponding to the product of 0.1 and coherence bandwidth than smaller
or larger than the bandwidth of signal. These above effects can suffer received signals at a destination.
Hence the performance of received signals in term of bit-error-rate (BER) is much degraded.
In order to overcome these issues, communications systems would be carefully designed. In detail,
application systems operating over the AWGN channels would use coding schemes to combat an additive
white noise. However, if environment is affected by fading, coding techniques only solve a fast fading.
It implies that, coding schemes degrade received signals when they go through slow fading channels. In
this case, an interleaving technique would be added to a communications system. In order to overcome
the fading channels, besides, using an interleaver as above, we can exploit the diversity of multi-path. It
implies that the effects of fading can be combated by transmitting the original signals over multiple paths
(experiencing independent fading) and then combining all received signals at the receiver. There are many
kinds of diversities to mitigate this issue, such as diversity in time, frequency, and space. Correspondingly,
a lot of state-of-art methods are given, viz. diversity receiving and transmitting, OFDM, space-time block
codes, MIMO, Cooperation and etc.
In summary, the main scope of this report is modeling a communications system. First, I create a
basic communications system, where it includes the modulation/demodulation using a QPSK modulation,
a channel type is an AWGN channel. Secondly, a coder/decoder scheme is added to a transmitter/receiver to
improve received signals. Thirdly, the fading channel is considered when a receiver/transmitter is moving.
It means that the slow fading is mentioned. The performance is shown to prove that the received signal
2
is degraded whether a coding scheme is used or not. Finally, an interleaver/deinterleaver is used to solve
this problem.
Besides, the performance in terms of BER is used to verify a validity of these above techniques in a
communications system.
Capacity Performance Analysis for Decode-and-Forward OFDMDual-Hop SystemPolytechnique Montreal
In this paper, we propose an exact analytical technique to evaluate the average capacity of a dual-hop OFDM relay system with decode-and-forward protocol in an independent and identical distribution (i.i.d.) Rayleigh fading channel. Four schemes, (no) matching “and” or “or” (no) power allocation, will be considered. First, the probability density function (pdf) for the end-to-end power channel gain for each scheme is described. Then, based on these pdf functions, we will give the expressions of the average capacity. Monte Carlo simulation results will be shown to confirm the analytical results for both the pdf functions and average capacities.
Tech report: Fair Channel Allocation and Access Design for Cognitive Ad Hoc N...Polytechnique Montreal
supplement to Globecom paper: L. T. Tan and L. B. Le, ``Fair Channel Allocation and Access Design for Cognitive Ad Hoc Networks,'' in 2012 IEEE Global Communications Conference (IEEE GLOBECOM 2012), Anaheim, California, USA, pp. 1162-1167, December, 2012.
General analytical framework for cooperative sensing and access trade-off opt...Polytechnique Montreal
In this paper, we investigate the joint cooperative spectrum sensing and access design problem for multi-channel cognitive radio networks. A general heterogeneous setting is considered where the probabilities that different channels are available, SNRs of the signals received at secondary users (SUs) due to transmissions from primary users (PUs) for different users and channels can be different. We assume a cooperative sensing strategy with a general a-out-of-b aggregation rule and design a synchronized MAC protocol so that SUs can exploit available channels. We analyze the sensing performance and the throughput achieved by the joint sensing and access design. Based on this analysis, we develop algorithms to find optimal parameters for the sensing and access protocols and to determine channel assignment for SUs to maximize the system throughput. Finally, numerical results are presented to verify the effectiveness of our design and demonstrate the relative performance of our proposed algorithms and the optimal ones.
Channel assignment for throughput maximization in cognitive radio networks Polytechnique Montreal
In this paper, we consider the channel allocation problem for throughput maximization in cognitive radio networks with hardware-constrained secondary users. Specifically, we assume that secondary users exploit spectrum holes on a set of channels where each secondary user can use at most one available channel for communication. We develop two channel assignment algorithms that can efficiently utilize spectrum opportunities on these channels. In the first algorithm, secondary users are assigned distinct sets of channels. We show that this algorithm achieves the maximum throughput limit if the number of channels is sufficiently large. In addition, we propose an overlapping channel assignment algorithm, that can improve the throughput performance compared to the non-overlapping channel assignment algorithm. In addition, we design a distributed MAC protocol for access contention resolution and integrate the derived MAC protocol overhead into the second channel assignment algorithm. Finally, numerical results are presented to validate the theoretical results and illustrate the performance gain due to the overlapping channel assignment algorithm.
Fair channel allocation and access design for cognitive ad hoc networksPolytechnique Montreal
We investigate the fair channel assignment and access design problem for cognitive radio ad hoc network in this paper. In particular, we consider a scenario where ad hoc network nodes have hardware constraints which allow them to access at most one channel at any time. We investigate a fair channel allocation problem where each node is allocated a subset of channels which are sensed and accessed periodically by their owners by using a MAC protocol. Toward this end, we analyze the complexity of the optimal brute-force search algorithm which finds the optimal solution for this NP-hard problem. We then develop low-complexity algorithms that can work efficiently with a MAC protocol algorithm, which resolves the access contention from neighboring secondary nodes. Also, we develop a throughput analytical model, which is used in the proposed channel allocation algorithm and for performance evaluation of its performance. Finally, we present extensive numerical results to demonstrate the efficacy of the proposed algorithms in achieving fair spectrum sharing among traffic flows in the network.
Channel Assignment With Access Contention Resolution for Cognitive Radio Netw...Polytechnique Montreal
In this paper, we consider the channel assignment problem for cognitive radio networks with hardware-constrained secondary users (SUs). In particular, we assume that SUs exploit spectrum holes on a set of channels where each SU can use at most one available channel for communication. We present the optimal brute-force search algorithm to solve the corresponding nonlinear integer optimization problem and analyze its complexity. Because the optimal solution has exponential complexity with the numbers of channels and SUs, we develop two low-complexity channel assignment algorithms that can efficiently utilize the spectrum holes. In the first algorithm, SUs are assigned distinct sets of channels. We show that this algorithm achieves the maximum throughput limit if the number of channels is sufficiently large. In addition, we propose an overlapping channel assignment algorithm that can improve the throughput performance compared with its nonoverlapping channel assignment counterpart. Moreover, we design a distributed medium access control (MAC) protocol for access contention resolution and integrate it into the overlapping channel assignment algorithm. We then analyze the saturation throughput and the complexity of the proposed channel assignment algorithms. We also present several potential extensions, including the development of greedy channel assignment algorithms under the max-min fairness criterion and throughput analysis, considering sensing errors. Finally, numerical results are presented to validate the developed theoretical results and illustrate the performance gains due to the proposed channel assignment algorithms.
Distributed MAC Protocol for Cognitive Radio Networks: Design, Analysis, and ...Polytechnique Montreal
In this paper, we investigate the joint optimal sensing and distributed Medium Access Control (MAC) protocol design problem for cognitive radio (CR) networks. We consider both scenarios with single and multiple channels. For each scenario, we design a synchronized MAC protocol for dynamic spectrum sharing among multiple secondary users (SUs), which incorporates spectrum sensing for protecting active primary users (PUs). We perform saturation throughput analysis for the corresponding proposed MAC protocols that explicitly capture the spectrum-sensing performance. Then, we find their optimal configuration by formulating throughput maximization problems subject to detection probability constraints for PUs. In particular, the optimal solution of the optimization problem returns the required sensing time for PUs' protection and optimal contention window to maximize the total throughput of the secondary network. Finally, numerical results are presented to illustrate developed theoretical findings in this paper and significant performance gains of the optimal sensing and protocol configuration.
Essentials of Automations: Optimizing FME Workflows with ParametersSafe Software
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Pradeep Chinnala, Senior Consultant Automation Developer @WonderBotz and UiPath MVP
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
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2. Heatmap utilization for testing
3. Optimization of testing processes
4. Demo
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UiPath Test Automation using UiPath Test Suite series, part 4
Using Subspace Pursuit Algorithm to Improve Performance of the Distributed Compressive Wide-Band Spectrum Sensing
1. JOURNAL OF THE KOREAN INSTITUTE OF ELECTROMAGNETIC ENGINEERING AND SCIENCE, VOL. 11, NO. 4, DEC. 2011 JKIEES 2011-11-4-03
http://dx.doi.org/10.5515/JKIEES.2011.11.4.250
250
Using Subspace Pursuit Algorithm to Improve Performance of the
Distributed Compressive Wide-Band Spectrum Sensing
Le Thanh Tan․Hyung-Yun Kong
Abstract
This paper applies a compressed algorithm to improve the spectrum sensing performance of cognitive radio techno-
logy. At the fusion center, the recovery error in the analog to information converter (AIC) when reconstructing the
transmit signal from the received time-discrete signal causes degradation of the detection performance. Therefore, we
propose a subspace pursuit (SP) algorithm to reduce the recovery error and thereby enhance the detection performance.
In this study, we employ a wide-band, low SNR, distributed compressed sensing regime to analyze and evaluate the
proposed approach. Simulations are provided to demonstrate the performance of the proposed algorithm.
Key words: Wide-Band Spectrum Sensing, Subspace Pursuit Algorithm, Cognitive Radio, Compressed Sensing,
Power Spectrum Density Estimate.
Manuscript received July 19, 2011 ; revised October 25, 2011. (ID No. 20110719-022J)
School of Electrical Engineering, University of Ulsan, Ulsan, Korea.
Corresponding Author : Hyung-Yun Kong (e-mail : hkong@mail.ulsan.ac.kr)
Ⅰ. Introduction
Fueled by the dramatically increasing demand for high
quality of services, numerous novel wireless technologies
have been invented and are leading to a crowding of
spectrum allocation. This, in turn, raises the critical
problem that insufficient spectrum space is available for
new kinds of application. However, most of the licensed
bands are sporadically located and under-utilized, rather
than in actual shortage. In fact, less than 5 % of the total
licensed spectrum may be in use [1]. The Federal Co-
mmunications Commission (FCC) has therefore proposed
the idea of an open licensed frequency band, which un-
licensed users would be allowed to occupy opportu-
nistically. In addition, the IEEE 802.22 workgroup has
built the standards of WRAN based on cognitive radio
(CR) techniques [2]. CR is now considered as the most
competitive candidate for a secondary system that could
co-exist with the primary one.
Based on the ability to provide high data rates and
high quality of services, wide-band applications are re-
ceiving increasingly more attention recently. However,
wide-band applications in CR encounter considerable cha-
llenges in spectrum sensing. On the one hand, wide-band
sensing applications usually employ a large number of
RF devices to deal with the wide frequency range. On
the other hand, a trade-off exists between high-speed
processing units and detection performance due to the
sensing time constraints and insufficient samples.
In order to provide a reliable but low complexity
model, many studies have exploited a compressed sen-
sing (CS) framework for wide-band sensing. Initially, the
CS theory, which was innovated by Donoho [3], allowed
a highly sparse signal to be reconstructed from a small
number of measurements. In other words, this method is
able to compress the sparse signal at the sub-Nyquist rate
during sampling in the first stage. The reconstruction
stage requires state-of-the-art algorithms to solve the
convex optimization problem; for example, the basic
pursuit (BP) or orthogonal matching pursuit (OMP) [3],
[4]. Zhi et al. [5] next presented a single wide-band CR
model that uses CS based spectrum sensing schemes;
however, the input signal was still sampled by an ana-
log-to-digital convertor (ADC) operating at a Nyquist
rate. The authors in [6] improved compressive wide-band
spectrum sensing (CWSS) systems for single CR by em-
ploying an analog-to-information converter (AIC) [7]~
[9], which operates at a sub-Nyquist rate due to direct
application of CS to the analog signal. This group [10]
further extended their early work to multiple CRs in
order to design a distributed CWSS (DCWSS) based on
[11]. These studies simply applied wide-band spectrum
sensing to CS; hence, improvement of the model is still
required for greater robustness of the performance of
spectrum sensing.
In this work, we adopt CWSS and DCWSS schemes
for single and multiple CRs, respectively. In addition, we
propose the use of the subspace pursuit (SP) method [12]
in the reconstruction stage. The novel SP method pro-
vides the robustness to cope with inaccurate measure-
2. TAN and KONG : USING SUBSPACE PURSUIT ALGORITHM TO IMPROVE PERFORMANCE OF THE DISTRIBUTED COMPRESSIVE…
251
ment (due to noisy environment) as well as efficiency
and low complexity, owing to its restricted isometry pro-
perty (RIP) [13]. In an undesirable condition of low SNR
licensed signals, we also propose a DCWSS based SP
(DCWSSSP) method that jointly reconstructs the sparse
signal from multi-CR received signals. Finally, we com-
pare the performance of the DCWSSSP algorithm with
those of the schemes using compressive sampling mat-
ching pursuit (Cosamp) [12] and OMP [6], [10] to illu-
strate the accuracy of the proposed method.
The rest of this paper is organized as follows: section
Ⅱ presents the relevant concepts and terminology of the
CS reconstruction, while a compressive spectrum-sensing
scheme for single CR is presented in Section Ⅲ. An
extension to the collaborative compressed spectrum sens-
ing for multiple CR is shown in Section Ⅳ, while Sec-
tion V demonstrates the corroborating simulation results
to illustrate the effectiveness of the novel approach in
detecting the spectrum holes. Finally, concluding rema-
rks are given in Section Ⅳ.
Ⅱ. Preliminaries
2-1 Signal Model
We assume that the frequency range of the signal
consists of max I channels with equal bandwidth. The
spectrum-sensing model presented here includes a fusion
center that collects data from J CR nodes. An AIC is
used to sample the received signal at each CR node.
Finally, the determination of which bands are occupied
by licensed users (LUs) at the fusion center.
2-2 Compressed Sensing of Analog Signals and the
Restricted Isometric Property x(t), [0, ]t TÎ
We present an analog signal x(t), in a discrete format
as a finite weighted sum of the basic elements as [7]~
[9]:
1
( ) ( )
N
i i
i
x t s ty
=
= å (1)
where x is an 1N ´ vector x=Ψs , which is represented
in the sparse form of an 1N ´ vector s with K N<<
non-zero elements si via the N N´ matrix Ψ . CS de-
monstrates that x can be recovered using M N<<
measurements [13]. The measurements y are expressed
as:
y = Φx+ n = ΦΨs + n (2)
Several choices are available for the distribution of Φ,
such as the Gaussian, Bernoulli, or Fourier ensembles.
The reconstruction stage is performed by solving the
following standard approach to an objective function as
according to:
1s
min . .s y = ΦΨsst (3)
The problem (3) can be efficiently solved using BP or
some types of constructive algorithms such as matching
pursuit (MP) and OMP [3], [4].
In order to ensure the accuracy of each reconstruction
algorithm, the projected matrix Φ must satisfy the RIP
[14], which is presented as follows:
Definition 1 (Truncation): Let M N´
Î RF M N´
Î RF
M N´
Î RF and N
Îx R . The matrix TF with { }1, ,T NÌ L
has an i-th column ( )i TÎ in F and Tx is calculated
through TF .
Definition 2 (RIP): The matrix M N´
Î RF satisfies the
RIP with ( ), KK s for ,0 1KK M s£ £ £ , if
( ) ( )
2 2 2
2 2 2
1 1q q qK T Ks s- £ £ +F (4)
for all { }1, ,T NÌ L and for all T
qÎR , and ( )1 K T Ts l- £
( ) ( ) ( )min max1 1H H
K T T T T Ks l l s- £ £ £ +F F F F , where ( )min
H
T Tl F F
and ( )max
H
T Tl F F represent the minimal and maximal
eigenvalues of H
T TF F , respectively.
Ⅲ. Compressive Spectrum Sensing at a
Single CR [6], [10]
In this section, we summarize the procedures for the
receiving and reconstruction at each CR node.
Fig. 1 shows that the analog input x(t) is [ ]x
T
k kN ix += ,
and the output of AIC is y
T
k kM jy +
é ù= ë û where 0,1,2...k = ,
0, , 1i N= +K , and 0, , 1j M= +K . The AIC is modeled
by the M N´ projected matrix AF as
k A ky = Φ x (5)
Using some mathematical operations [6], [10], we ha-
ve
y xr = Φr (6)
where [ ]0 ( )xr
T
xr i= and 0 ( )yr
T
yr ié ù= ë û , 1, , 1i N N= - + +K
1, , 1i N N= - + +K are 2 1N ´ and 2 1M ´ autocorrelation vectors, res-
pectively.
Fig. 1. CS acquisition at an individual CR sensing receiver.
3. JOURNAL OF THE KOREAN INSTITUTE OF ELECTROMAGNETIC ENGINEERING AND SCIENCE, VOL. 11, NO. 4, DEC. 2011
252
After acquiring the output vector of the autocorrelation
operation, we use the wavelet-based approach as pre-
sented in [15], [16] to detect the band edge locations.
For an experiment when N M<< in [5], the edge
spectrum sz can be determination from measurements
and the relation between sz and xr is:
x sr = Gz (7)
where sz is the discrete 2 1N ´ vector and ( )
1
FW
-
=G G .
The 2 2N N´ matrices G , W, and F represent a first
derivative operation, Wavelet, and Fourier transforms,
respectively.
Combining (6) and (7), the optimization problem for
an edge spectrum reconstruction is given by:
1
min . .s y sz r = ΦGzs t (8)
To solve this problem, we use the CWSS based SP
(CWSSSP) that is presented in the next section. The
spectrum estimate can now be evaluated as a cumulative
sum of elements in vector ( )s s
ˆ ˆz =
T
z ié ùë û , 1, , 2i N= K .
Therefore, the estimated values of PSD are given by
( ) ( )x s
1
ˆ ˆ=
n
k
S n z k
=
å
(9)
Ⅳ. Collaborative Compressed Spectrum Sensing
In Fig. 2, ( )jx t is the input of AIC at the j-th CR
node. The output of AIC is processed to give the 2 1M ´
autocorrelation vector ,yr j . The fusion center collects the
autocorrelation vectors and applies the DCWSSSP app-
roach to reconstruct the J received PSD ,
ˆ
x jS ; 1, ,j J= K
and then obtains an average PSD. Finally, the center
determines whether the frequency ranges are occupied,
based on the average PSD.
4-1 Overview of the SP Approach [17]
The SP algorithm [17] is less complicated but it re-
sults in a comparable recovery performance to LP te-
Fig. 2. DCWSS for multiple CR nodes.
Fig. 3. Subspace pursuit algorithm applied to reconstruc-
tion.
chniques.
First, the matrix A = ΦG can be expressed in a row
of its columns as:
[ ]1 2 2A a a a N= L (10)
The next step is solving the problem (8) by using an
SP technique. We set the truncation for subspace AS of
the matrix 2 2M N´ A as in Definition 1, Section III
and ASspan( ) is represented to the space span of AS .
In addition, the matrix 2 2M N´ A also satisfies the
RIP, as in (4), Definition 2, Section III, by replacing M
by 2M, N by 2N, each TF by AS , and each F by A .
The l1-linear program approach can successfully
reconstruct a K-sparse signal if the RIP must be satisfied
with constants Ks , 2Ks and 3Ks , which have a con-
dition 2 3 1K K Ks s s+ + < [18]. However, in [14], the
authors improved the above condition to 2 2 1Ks < - .
For any given vector
2M
y Îr R , the projection of ry onto
the subspace ASspan( ) is denoted by ,ry p and can be
computed as:
( ) †
, , :r r A A A ry p y S S S yproj= =
(11)
Note that ( )
1†
A A A AH H
S S S S
-
= is the pseudo-inverse of
the matrix AS ,where subscript
H
denotes the conjugate
transposition. Corresponding to the projection vector, the
projection residue vector ,ry r is defined as
( ), ,, :r r A r ry r y S y y presid= = - (12)
Fig. 3 illustrates the schematic diagram of iterations in
the SP algorithm [17], demonstrating that the subspace is
updated during each iteration; i.e., elements can be added
to or deleted from the subspace.
The following subsection represents the algorithm to
solve the above problem.
4-2 The Jointly Recovery SP Algorithm
4. TAN and KONG : USING SUBSPACE PURSUIT ALGORITHM TO IMPROVE PERFORMANCE OF THE DISTRIBUTED COMPRESSIVE…
253
The advantage of the SP algorithm comparing with the
OMP method is the way to generate l
S , that is the
estimate of the correct support set S .
We describe the procedure of this algorithm as
follows:
1. Input:
․A 2 2M N´ matrix A.
․A 2M J´ input matrix ,1 ,2 ,y y yR r r r Jé ù= ë ûL recei-
ved from J CR sensing receivers.
2. Output: The 2N J´ estimated signal s s s sZ z z z=
,1 , 2 ,s s s sZ z z z Jé ù= ë ûL , the average of j PSD es-
timate vectors ( )
x
ˆS J
.
3. Procedure:
1) Initialization:
․For each j-th CR (j=1, …, J), we have
0
,
0 0 0
,1 ,2 ,
j
y j
j j j K
K indiceswith respecttothelargest
elementsin
S
u u u
ì üï ï
= í ý
ï ïî þ
é ù= ë û
H
A r
L
and then calculate
{ }0 0
0 0
1 2
j
o
K
S average S
u u u
=
é ù= ë ûL
,
Where ,
1
1 J
o o
k k j
jJ
u u
=
= å .
․The projection residue vector for the j-th CR is
( )0
0
ˆ, , ,r r Ar j y j S
r e s id= .
2) Iteration: The following steps will be performed at
every l th- iteration.
․For each j-th CR (j=1, …, J), we evaluate
{ }1 1
1 1 1
1 2
늿l l
j
l l l
K
S average S
u u u
- -
- - -
=
é ù= ë ûL
1
H 1
,
ˆ
A r
l
j l
r j
K indices respect tothelargest
elementsin
S -
-
ì üï ï
= í ý
ï ïî þ ,
1ˆl
jS -
(13)
where
1 1
,
1
1
, 1, 2, ,
J
l l
k k j
j
k K
J
u u- -
=
= =å K ,
(14)
and then 1 1ˆl l l
S S S- -
=% U .
․For each j-th CR, we set the projection coefficients:
†
, , ,z A rls p j y jS
= % .
․
,
l
j
s j
K indiceswith respecttothelargest
elementsin
S
ì ü
= í ý
î þz
; And we cal-
culate l
S using (13), (14) and replacing (l—1) with l.
․The residue vector of the projection for the j-th CR
is ( ), , ,r r A l
l
r j y j S
resid= .
3) Termination test: The SP iteration is terminated
when 1
, ,2 2
m in m inr rl l
r j r j
-
> , 1,2, ,j J= K . Then
let 1l l
S S -
= and quit the iteration. If the limit is
not reached, increase l and return to the iteration.
4) Store the results:
The estimated signal ˆzs, j satisfies { }1, ,
ˆz 0ls, j N T-
=L and
†
,
ˆz A rl ls, j y jS S
= . The j-th PSD estimate vector is
( ) ( )x , s ,
1
ˆ ˆS =
n
j j
k
n z k
=
å .
The average of J PSD estimate vectors is
(15)
4-3 Performances:
4-3-1 MSE Performance
The MSE of PSD from our approach is calculated as:
( )
( ) ( )
( )
2
2
2
2
ˆ
MSE = E
x x
x
S S
S
J J
J
J
ì ü-ï ï
í ý
ï ï
î þ (16)
where ( )ˆ
xS J
and ( )
xS J
denote the average PSD output and
the PSD, respectively for in case of signals sampled at
the Nyquist rate.
4-3-2 Probability of Detection
To compute the detection probability Pd, we apply the
energy detection method, where the test static is cal-
culated from the averaged PSD estimate ( )ˆ
xS J
[19]. As in
[10], we identify the static test as:
( )
( )
2
,
1 1 1 1
1
= ( )
IL J H
J
I h j
i I L j h
E X i
JH = - + = =
å åå (17)
where L is the total samples from each channel, I maxI=
1,2, ,I maxI= K , H is the total number of blocks, X repre-
sents the Fourier transform from x.
Using the Neyman-Pearson hypothesis test, we deter-
mine the decision threshold m [19]:
( )
( )
,
1
J
f
JH
JH
P
JH
mæ ö
Gç ÷
è ø= -
G (18)
, ,
5. JOURNAL OF THE KOREAN INSTITUTE OF ELECTROMAGNETIC ENGINEERING AND SCIENCE, VOL. 11, NO. 4, DEC. 2011
254
where (.,.)G is upper incomplete gamma function [20],
Sec. (8.350)], Γ(.) is the gamma function [20], Sec.
(13.10)]. Hence, the probability of detection ( )J
dP is eva-
luated as
( ) ( )
{ }
1
1
Pr
aI
J J
d I
I I
P E
a
m
=
= >å
(19)
where , 1, ,iI i a= K denote the indices of a active cha-
nnels.
Ⅴ. Simulation Results
In this section, the simulation results are shown to
evaluate the proposed approach. In this simulation mo-
del, the frequency band ranges from —38.05 to 38.05
MHz, which is the same as that described in [21], and
the number of channels is maxI=10 with 7.61 MHz
bandwidth. The OFDM frame length TF includes 68
symbols, and each of these super-frames contains four
frames. The number of carriers per symbol is C=1,705
with a duration TS, composed of a useful part TU and a
guard interval ∆ (set to 0 in this simulation).
For this scheme, the over-sampling factor is 02, and
only 50 % of the channels are active. The SNRs of the
active channels are assumed to be in the range [—10 dB,
—8 dB] and the AGWN variance is
2
1ns = . The smoo-
thing signal scheme is performed using a Gaussian
wavelet. The length of input signal is 2N=512 and the
compressed rate is varying from 5 % to 100 %, and
H=160, and ΦA has a zero-mean Gaussian ensemble wi-
th variance 1/M. The number of PSD samples of each
channel is L=25.
Fig. 4 illustrates the MSE performances for the SP,
OMP, iteratively reweighted least squares with regula-
rization (IRLS) [21] and Cosamp algorithms [22]. The
results show that better performance is achieved for SP
than for these other approaches, while all versions take
Table 1. Parameters for the simulations.
Parameter 2 k mode
Elementary period T 7 / 64 sm
Number of carriers C 1,705
Value of carrier number minC 0
Value of carrier number maxC 1,704
Duration of symbol part UT
2, 048
224
T
sm
´
Carrier spacing 1/ UT 4,464 Hz
Spacing between carriers minC and
( )max 1 / UC C T-
7.61 MHz
Fig. 4. MSE for SP, IRLS, OMP and Cosamp approaches
versus compression rate M/N for various numbers of
collaborating CRs (SNR=[—10 dB, —8 dB]).
the same time to reach convergence. The OMP algorithm
has the worst performance in the conditions used for this
simulation, with a low sampling factor corresponding to
low sparsity and the noisy environment. The SP algo-
rithm is robust in this case because it adds the good basis
candidates and it also removes the bad candidates. This
figure also shows the signal recovery quality, where
MSE decreases when the compression rate M/N increa-
ses. However, to complement this degradation, we take
advantage of the multi-CR scheme, where MSE can be
significantly reduced. Therefore, we reduce the cost of
high speed by using the CS method and we also improve
the MSE by exploiting the multiple CRs.
The detection performance is shown in Fig. 5, which
Fig. 5. Probabilities of detection Pd for SP and Cosamp ap-
proaches versus compression rate M/N for various num-
bers of collaborating CRs (SNR=[—10 dB, —8 dB]).
6. TAN and KONG : USING SUBSPACE PURSUIT ALGORITHM TO IMPROVE PERFORMANCE OF THE DISTRIBUTED COMPRESSIVE…
255
depicts the probability of detection ( )J
dP vs. the compre-
ssion ratio M/N when the number of CRs is J=1 and 5
at a given ( )J
fP of 0.01. This figure demonstrates that the
detection probability was high at a low compression ratio
M/N. The use of multiple CRs significantly improves the
detection probability. In addition, the probability of
detection is improved by the SP approach compared with
the IRLS and Cosamp algorithms.
Ⅵ. Conclusion
In this paper, we used the DCWSS and SP algorithm
to reduce the recovery error in the reconstruction stage in
the CRN. A new iterative algorithm, termed the DCW-
SSSP approach, is exploited for joint compressive spec-
trum sensing.
This research was supported by Basic Science
Research Program through the National Research
Foundation of Korea(NRF) funded by the Ministry of
Education, Science and Technology(No. 2010-0004-
865)
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7. JOURNAL OF THE KOREAN INSTITUTE OF ELECTROMAGNETIC ENGINEERING AND SCIENCE, VOL. 11, NO. 4, DEC. 2011
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Le Thanh Tan Hyung-Yun Kong
received the B.S. degrees in Telecommu-
nication Engineering from Poly-technique
University of Danang, Vietnam in 2005.
In 2008, he got the degree of Master
from Hochiminh University of Technol-
ogy, Vietnam in major of Electrical and
Electronics Engineering. Since 2010, he
has been studying Ph.D. program at
University of Ulsan, Korea. His major researches are Cogni-
tive Radio Network, Cooperative Communication.
received the M.E. and Ph.D. degrees in
electrical engineering from Polytechnic
University, Brooklyn, New York, USA,
in 1991 and 1996, respectively, He re-
ceived a B.E. in electrical engineering fr-
om New York Institute of Technology,
New York, in 1989. Since 1996, he has
been with LG electronics Co., Ltd., in
the multimedia research lab developing PCS mobile phone
systems, and from 1997 the LG chairman's office planning
future satellite communication systems. Currently he is a pro-
fessor in electrical engineering at the University of Ulsan,
Korea. His research area includes channel coding, detection and
estimation, cooperative communications, cognitive radio and
sensor networks. He is a member of IEEK, KICS, KIPS,
IEEE, and IEICE.