The increasing interest for wireless communication services and scarcity of radio spectrum resources have created the need for a more flexible and efficient usage of the radio frequency bands. Cognitive Radio (CR) eme...The increasing interest for wireless communication services and scarcity of radio spectrum resources have created the need for a more flexible and efficient usage of the radio frequency bands. Cognitive Radio (CR) emerges as an important trend for a solution to this problem. Spectrum sensing is a crucial function in a CR system. Cooperative spectrum sensing can overcome fading and shadowing effects, and hence increase the reliability of primary user detection. In this paper we consider a system model of a dedicated detect-andforward wireless sensor network (DetF WSN) for cooperative spectrum sensing with k-out-of-n decision fusion in the presence of reporting channels errors. Using this model we consider the design of a spatial reuse media access control (MAC) protocol based on TDMA/OFDMA to resolve conflicts and conserve resources for intra-WSN communication. The influence of the MAC protocol on spectrum sensing performance of the WSN is a key consideration. Two design approaches, using greedy and adaptive simulated annealing (ASA) algorithms, are considered in detail. Performance results assuming a grid network in a Rician fading environment are presented for the two design approaches.展开更多
Spectrum sensing is the key problem for Cognitive Radio(CR) systems.A method based on the Peak-to-Average Amplitude-Ratio(PAAR) of the Spatial Spectrum(SS) of the received signals is proposed to sense the available sp...Spectrum sensing is the key problem for Cognitive Radio(CR) systems.A method based on the Peak-to-Average Amplitude-Ratio(PAAR) of the Spatial Spectrum(SS) of the received signals is proposed to sense the available spectrum for the cognitive users with the help of the multiple antennas at the receiver of the cognitive users.The greatest advantage of the new method is that it requires no information of the noise power and is free of the noise power uncertainty.Both the simulation and the analytical results show that the proposed method is robust to noise uncertainty,and greatly outperform the classical Energy Detector(ED) method.展开更多
In this paper, a new spatial coherence model of seismic ground motions is proposed by a fitting procedure. The analytical expressions of modal combination （correlation） coefficients of structural response are develo...In this paper, a new spatial coherence model of seismic ground motions is proposed by a fitting procedure. The analytical expressions of modal combination （correlation） coefficients of structural response are developed for multi-support seismic excitations. The coefficients from both the numerical integration and analytical solutions are compared to verify the accuracy of the solutions. It is shown that the analytical expressions of numerical modal combination coefficients are of high accuracy. The results of random responses of an example bridge show that the analytical modal combination coefficients developed in this paper are accurate enough to meet the requirements needed in practice. In addition, the computational efficiency of the analytical solutions of the modal combination coefficients is demonstrated by the response computation of the example bridge. It is found that the time required for the structural response analysis by using the analytical modal combination coefficients is less than 1/20 of that using numerical integral methods.展开更多
Microphone array-based sound source localization(SSL)is a challenging task in adverse acoustic scenarios.To address this,a novel SSL algorithm based on deep neural network(DNN)using steered response power-phase transf...Microphone array-based sound source localization(SSL)is a challenging task in adverse acoustic scenarios.To address this,a novel SSL algorithm based on deep neural network(DNN)using steered response power-phase transform(SRP-PHAT)spatial spectrum as input feature is presented in this paper.Since the SRP-PHAT spatial power spectrum contains spatial location information,it is adopted as the input feature for sound source localization.DNN is exploited to extract the efficient location information from SRP-PHAT spatial power spectrum due to its advantage on extracting high-level features.SRP-PHAT at each steering position within a frame is arranged into a vector,which is treated as DNN input.A DNN model which can map the SRP-PHAT spatial spectrum to the azimuth of sound source is learned from the training signals.The azimuth of sound source is estimated through trained DNN model from the testing signals.Experiment results demonstrate that the proposed algorithm significantly improves localization performance whether the training and testing condition setup are the same or not,and is more robust to noise and reverberation.展开更多
A realistic population density distribution scenario in conjunction with the spatial dynamic spectrum allocation （DSA） is taken into account to mitigate the spectrum wastage in terms of extra guard bands. For the in...A realistic population density distribution scenario in conjunction with the spatial dynamic spectrum allocation （DSA） is taken into account to mitigate the spectrum wastage in terms of extra guard bands. For the insertion of the extra guard bands, an efficient strategy based on self-assessment is applied to each victim cell individually and independently. Consequently, it is no more required to spread the extra guard band over the whole DSA region. Simulation results StlOW an improvement of 3% -4% in percentage of satisfied users for Universal Mobile Telecommunications System （UMTS） network and 4%-5% for Digital Video Broadcasting Terrestrial （DVB-T） network.展开更多
In noncommutative space, we examine the problem of a noninteracting and harmonically trapped Bose- Einstein condensate, and derive a simple analytic expression for the effect of spatial noncommutatlvity on energy spec...In noncommutative space, we examine the problem of a noninteracting and harmonically trapped Bose- Einstein condensate, and derive a simple analytic expression for the effect of spatial noncommutatlvity on energy spectrum of the condensate, it indicates that the ground-state energy incorporating the spatial noncommutativity is reduced to a lower level, which depends upon the noncommutativity parameter 8. The gap between the noncommutative space and commutative one for the ground-state level of the condensate should be a signal of spatial noncommutativity.展开更多
Based on the statistical characteristics of remote sensing data, the spatial geometric structure characteristics of spectral data and distribution of background, interference and alteration information in characterist...Based on the statistical characteristics of remote sensing data, the spatial geometric structure characteristics of spectral data and distribution of background, interference and alteration information in characteristic space were researched through the analysis of two-dimensional and three-dimensional scatter diagrams. The results indicate that the hyper-space of remote sensing multi-data aggregation belongs to low-dimensional geometric structure, i.e. hyperplane form, and anomalous point groups including alteration information usually dissociate out of hyperplane. Scatter diagrams of remote sensing data band are mainly presented as two distribution forms of single-ellipse and dual-ellipse. Clarifying the relations of three objects of background, disturbance and alteration information in remote sensing images provides an important technical thought and guidance for accurately detecting and extracting remote sensing alteration information.展开更多
The problem of bearing estimation of coherent signal impingiog on an array ofarbitrary geometry is studied.Both approaches are developed,the first one synthesizes theobserved array data into the outputs of a linear un...The problem of bearing estimation of coherent signal impingiog on an array ofarbitrary geometry is studied.Both approaches are developed,the first one synthesizes theobserved array data into the outputs of a linear uniform array and then processes them viaconventional techniques such as spatial smoothing etc.The second approach is based on theinvariant subspace rotation operation which is equivalent to the translational displacement ofthe artay,linearly independent signal vectors are obtained thereby to span perfectly the signalsubspace.As compared with the conventional processing techniques,the approach based oninvariant subspace rotation does not lead to an effective decrease in aperture size and thereforea decrease in resolution capability.The computer simulations are conducted to demonstrate theeffectiveness of the presented approaches.展开更多
Fourier ptychographic microscopy(FPM)is a newly developed imaging technique which stands out by virtue of its high-resolution and wide FOV.It improves a microscope's imaging perfor-mance beyond the diffraction lim...Fourier ptychographic microscopy(FPM)is a newly developed imaging technique which stands out by virtue of its high-resolution and wide FOV.It improves a microscope's imaging perfor-mance beyond the diffraction limit of the employed optical components by illuminating the sample with oblique waves of different incident angles,similar to the concept of synthetic aperture.We propose to use an objective lens with high-NA to generate oblique illuminating waves in FPM.We demonstrate utilizing an objective lens with higher NA to iluminate the sample leads to better resolution by simulations,in which a resolution of 0.28 pum is achieved by using a high-NA illuminating objective lens(NA=1.49)and a low-NA collecting objective lens(NA=0.2)in coherent imaging(λ=488 nm).We then deeply study FPM's exact relevance of convergence speed to spatial spectrum overlap in frequency domain.The simulation results show that an overlap of about 60%is the optimal choice to acquire a high-quality recovery(520*520 pixels)with about 2 min's computing time.In addition,we testify the robustness of the algorithm of FPM to additive noises and its suitability for phase objects,which further proves FPM's potential application in biomedical imaging.展开更多
As a promising solution, virtualization is vigorously developed to eliminate the ossification of traditional Internet infrastructure and enhance the flexibility in sharing the substrate network (SN) resources includin...As a promising solution, virtualization is vigorously developed to eliminate the ossification of traditional Internet infrastructure and enhance the flexibility in sharing the substrate network (SN) resources including computing, storage, bandwidth, etc. With network virtualization, cloud service providers can utilize the shared substrate resources to provision virtual networks (VNs) and facilitate a wide and diverse range of applications. As more and more internet applications migrate to the cloud, the resource efficiency and the survivability of VNs, such as single link failure or large-scale disaster survivability, have become crucial issues. Elastic optical networks have emerged in recent years as a strategy for dealing with the divergence of network application bandwidth needs. The network capacity has been constrained due to the usage of only two multiplexing dimensions. As transmission rates rise, so does the demand for network failure protection. Due to their end-to-end solutions, those safe-guarding paths are of particular importance among the protection methods. Due to their end-to-end solutions, those safeguarding paths are of particular importance among the protection methods. This paper presents approaches that provide a failure-independent route-protecting p-cycle for path protection in space-division multiplexed elastic optical networks. This letter looks at two SDM network challenges and presents a heuristic technique (k-shortest path) for each. In the first approach, we study a virtual network embedding (SVNE) problem and propose an algorithm for EONs, which can combat against single-link failures. We evaluate the proposed POPETA algorithm and compare its performance with some counterpart algorithms. Simulation results demonstrate that the proposed algorithm can achieve satisfactory performance in terms of spectrum utilization and blocking ratio, even if with a higher backup redundancy ratio.展开更多
Although the classical spectral representation method(SRM)has been widely used in the generation of spatially varying ground motions,there are still challenges in efficient simulation of the non-stationary stochastic ...Although the classical spectral representation method(SRM)has been widely used in the generation of spatially varying ground motions,there are still challenges in efficient simulation of the non-stationary stochastic vector process in practice.The first problem is the inherent limitation and inflexibility of the deterministic time/frequency modulation function.Another difficulty is the estimation of evolutionary power spectral density(EPSD)with quite a few samples.To tackle these problems,the wavelet packet transform(WPT)algorithm is utilized to build a time-varying spectrum of seed recording which describes the energy distribution in the time-frequency domain.The time-varying spectrum is proven to preserve the time and frequency marginal property as theoretical EPSD will do for the stationary process.For the simulation of spatially varying ground motions,the auto-EPSD for all locations is directly estimated using the time-varying spectrum of seed recording rather than matching predefined EPSD models.Then the constructed spectral matrix is incorporated in SRM to simulate spatially varying non-stationary ground motions using efficient Cholesky decomposition techniques.In addition to a good match with the target coherency model,two numerical examples indicate that the generated time histories retain the physical properties of the prescribed seed recording,including waveform,temporal/spectral non-stationarity,normalized energy buildup,and significant duration.展开更多
In array signal processing, 2-D spatial-spectrum estimation is required to determine DOA of multiple signals. The circular array of sensors is found to possess several nice properties for DOA estimation of wide-band s...In array signal processing, 2-D spatial-spectrum estimation is required to determine DOA of multiple signals. The circular array of sensors is found to possess several nice properties for DOA estimation of wide-band sources. C. U. Padmini, et al.(1994) had suggested that the frequency-direction ambiguity in azimuth estimation of wide-baud signals received by a uniform linear array (ULA) can be avoided by using a circular array, even without the use of any delay elements. In 2-D spatial-spectrum estimation for wide-band signals, the authors find that it is impossible to avoid the ambiguity in source frequency-elevation angle pairs using a circular array. In this paper, interpolated circular arrays are used to perform 2-D spatial-spectrum estimation for wide-band sources. In the estimation, a large aperture circular array (Υ】λmin/2) is found to possess superior resolution capability and robustness.展开更多
A novel spectrum hole detection mechanism is proposed to improve the detection probability in cognitive radio networks for several typical scenarios. By removing the influence of the spatial false alarm （SFA）, the s...A novel spectrum hole detection mechanism is proposed to improve the detection probability in cognitive radio networks for several typical scenarios. By removing the influence of the spatial false alarm （SFA）, the spectrum hole detection probability of the secondary user under path loss and multi-path fading is derived. Meanwhile, the spectrum hole detection probability of multi-users cooperative sensing and that of single-user sensing in multi-bands are derived for comparison. Theoretical analyses and simulation results show that the spectrum hole detection probability of the proposed mechanism is inversely proportional to the sampling times and the area of the sensing region. The detection performance of the multi-users sensing is better than that of single-user sensing when with the AND ~ogic fusion rule but worse when with the OR logic fusion rule. The detection probability is further decreased in the Rayleigh fading channel but it is greatly increased in multi-bands.展开更多
文摘The increasing interest for wireless communication services and scarcity of radio spectrum resources have created the need for a more flexible and efficient usage of the radio frequency bands. Cognitive Radio (CR) emerges as an important trend for a solution to this problem. Spectrum sensing is a crucial function in a CR system. Cooperative spectrum sensing can overcome fading and shadowing effects, and hence increase the reliability of primary user detection. In this paper we consider a system model of a dedicated detect-andforward wireless sensor network (DetF WSN) for cooperative spectrum sensing with k-out-of-n decision fusion in the presence of reporting channels errors. Using this model we consider the design of a spatial reuse media access control (MAC) protocol based on TDMA/OFDMA to resolve conflicts and conserve resources for intra-WSN communication. The influence of the MAC protocol on spectrum sensing performance of the WSN is a key consideration. Two design approaches, using greedy and adaptive simulated annealing (ASA) algorithms, are considered in detail. Performance results assuming a grid network in a Rician fading environment are presented for the two design approaches.
基金Supported by the National Natural Science Foundation of China (No. 60602053)Program for New Century Excellent Talents in University (NCET-08-0891)+2 种基金the Natural Science Foundation of Shaanxi Province (2010JQ80241)the Natural Science Foundation of Hubei Province (2009 CDB308)the Fund from Education Department of Shaanxi Government (2010JK836)
文摘Spectrum sensing is the key problem for Cognitive Radio(CR) systems.A method based on the Peak-to-Average Amplitude-Ratio(PAAR) of the Spatial Spectrum(SS) of the received signals is proposed to sense the available spectrum for the cognitive users with the help of the multiple antennas at the receiver of the cognitive users.The greatest advantage of the new method is that it requires no information of the noise power and is free of the noise power uncertainty.Both the simulation and the analytical results show that the proposed method is robust to noise uncertainty,and greatly outperform the classical Energy Detector(ED) method.
基金National Natural Science Foundation of China Under Grant No. 50478112
文摘In this paper, a new spatial coherence model of seismic ground motions is proposed by a fitting procedure. The analytical expressions of modal combination （correlation） coefficients of structural response are developed for multi-support seismic excitations. The coefficients from both the numerical integration and analytical solutions are compared to verify the accuracy of the solutions. It is shown that the analytical expressions of numerical modal combination coefficients are of high accuracy. The results of random responses of an example bridge show that the analytical modal combination coefficients developed in this paper are accurate enough to meet the requirements needed in practice. In addition, the computational efficiency of the analytical solutions of the modal combination coefficients is demonstrated by the response computation of the example bridge. It is found that the time required for the structural response analysis by using the analytical modal combination coefficients is less than 1/20 of that using numerical integral methods.
基金This work is supported by the National Nature Science Foundation of China(NSFC)under Grant No.61571106Jiangsu Natural Science Foundation under Grant No.BK20170757the Natural Science Foundation of the Jiangsu Higher Education Institutions of China under grant No.17KJD510002.
文摘Microphone array-based sound source localization(SSL)is a challenging task in adverse acoustic scenarios.To address this,a novel SSL algorithm based on deep neural network(DNN)using steered response power-phase transform(SRP-PHAT)spatial spectrum as input feature is presented in this paper.Since the SRP-PHAT spatial power spectrum contains spatial location information,it is adopted as the input feature for sound source localization.DNN is exploited to extract the efficient location information from SRP-PHAT spatial power spectrum due to its advantage on extracting high-level features.SRP-PHAT at each steering position within a frame is arranged into a vector,which is treated as DNN input.A DNN model which can map the SRP-PHAT spatial spectrum to the azimuth of sound source is learned from the training signals.The azimuth of sound source is estimated through trained DNN model from the testing signals.Experiment results demonstrate that the proposed algorithm significantly improves localization performance whether the training and testing condition setup are the same or not,and is more robust to noise and reverberation.
基金The National High-Tech Research and Development Program of China ( No.2005AA123950)the National Science Foundation of China (No.90604035)
文摘A realistic population density distribution scenario in conjunction with the spatial dynamic spectrum allocation （DSA） is taken into account to mitigate the spectrum wastage in terms of extra guard bands. For the insertion of the extra guard bands, an efficient strategy based on self-assessment is applied to each victim cell individually and independently. Consequently, it is no more required to spread the extra guard band over the whole DSA region. Simulation results StlOW an improvement of 3% -4% in percentage of satisfied users for Universal Mobile Telecommunications System （UMTS） network and 4%-5% for Digital Video Broadcasting Terrestrial （DVB-T） network.
基金The project supported in part by National Natural Science Foundation of China under Grant No. 10174086. Luo greatly appreciates Prof. J.Z. Zhang for valuable discussions.
文摘In noncommutative space, we examine the problem of a noninteracting and harmonically trapped Bose- Einstein condensate, and derive a simple analytic expression for the effect of spatial noncommutatlvity on energy spectrum of the condensate, it indicates that the ground-state energy incorporating the spatial noncommutativity is reduced to a lower level, which depends upon the noncommutativity parameter 8. The gap between the noncommutative space and commutative one for the ground-state level of the condensate should be a signal of spatial noncommutativity.
基金Project(2006BAB01A06) supported by the National Science and Technology Pillar Program Project during the 11th Five-Year Plan PeriodProject(1212010761503) supported by Land and Resources Investigation Project
文摘Based on the statistical characteristics of remote sensing data, the spatial geometric structure characteristics of spectral data and distribution of background, interference and alteration information in characteristic space were researched through the analysis of two-dimensional and three-dimensional scatter diagrams. The results indicate that the hyper-space of remote sensing multi-data aggregation belongs to low-dimensional geometric structure, i.e. hyperplane form, and anomalous point groups including alteration information usually dissociate out of hyperplane. Scatter diagrams of remote sensing data band are mainly presented as two distribution forms of single-ellipse and dual-ellipse. Clarifying the relations of three objects of background, disturbance and alteration information in remote sensing images provides an important technical thought and guidance for accurately detecting and extracting remote sensing alteration information.
文摘The problem of bearing estimation of coherent signal impingiog on an array ofarbitrary geometry is studied.Both approaches are developed,the first one synthesizes theobserved array data into the outputs of a linear uniform array and then processes them viaconventional techniques such as spatial smoothing etc.The second approach is based on theinvariant subspace rotation operation which is equivalent to the translational displacement ofthe artay,linearly independent signal vectors are obtained thereby to span perfectly the signalsubspace.As compared with the conventional processing techniques,the approach based oninvariant subspace rotation does not lead to an effective decrease in aperture size and thereforea decrease in resolution capability.The computer simulations are conducted to demonstrate theeffectiveness of the presented approaches.
基金the National Basic Research Program of China(973 Program)(No.2015CB352003)the National Natural Science Foundation of China(No.61335003,61377013,61378051 and 61427818)+1 种基金NSFC of Zhejiang province LR16F050001,Innovation Joint Research Center for iCPS(2015XZZX005-01)Open Foundation of the State Key Laboratory of Modern Optical Instrumentation.
文摘Fourier ptychographic microscopy(FPM)is a newly developed imaging technique which stands out by virtue of its high-resolution and wide FOV.It improves a microscope's imaging perfor-mance beyond the diffraction limit of the employed optical components by illuminating the sample with oblique waves of different incident angles,similar to the concept of synthetic aperture.We propose to use an objective lens with high-NA to generate oblique illuminating waves in FPM.We demonstrate utilizing an objective lens with higher NA to iluminate the sample leads to better resolution by simulations,in which a resolution of 0.28 pum is achieved by using a high-NA illuminating objective lens(NA=1.49)and a low-NA collecting objective lens(NA=0.2)in coherent imaging(λ=488 nm).We then deeply study FPM's exact relevance of convergence speed to spatial spectrum overlap in frequency domain.The simulation results show that an overlap of about 60%is the optimal choice to acquire a high-quality recovery(520*520 pixels)with about 2 min's computing time.In addition,we testify the robustness of the algorithm of FPM to additive noises and its suitability for phase objects,which further proves FPM's potential application in biomedical imaging.
文摘As a promising solution, virtualization is vigorously developed to eliminate the ossification of traditional Internet infrastructure and enhance the flexibility in sharing the substrate network (SN) resources including computing, storage, bandwidth, etc. With network virtualization, cloud service providers can utilize the shared substrate resources to provision virtual networks (VNs) and facilitate a wide and diverse range of applications. As more and more internet applications migrate to the cloud, the resource efficiency and the survivability of VNs, such as single link failure or large-scale disaster survivability, have become crucial issues. Elastic optical networks have emerged in recent years as a strategy for dealing with the divergence of network application bandwidth needs. The network capacity has been constrained due to the usage of only two multiplexing dimensions. As transmission rates rise, so does the demand for network failure protection. Due to their end-to-end solutions, those safe-guarding paths are of particular importance among the protection methods. Due to their end-to-end solutions, those safeguarding paths are of particular importance among the protection methods. This paper presents approaches that provide a failure-independent route-protecting p-cycle for path protection in space-division multiplexed elastic optical networks. This letter looks at two SDM network challenges and presents a heuristic technique (k-shortest path) for each. In the first approach, we study a virtual network embedding (SVNE) problem and propose an algorithm for EONs, which can combat against single-link failures. We evaluate the proposed POPETA algorithm and compare its performance with some counterpart algorithms. Simulation results demonstrate that the proposed algorithm can achieve satisfactory performance in terms of spectrum utilization and blocking ratio, even if with a higher backup redundancy ratio.
基金National Key Research and Development Program of China under Grant No.2023YFE0102900National Natural Science Foundation of China under Grant Nos.52378506 and 52208164。
文摘Although the classical spectral representation method(SRM)has been widely used in the generation of spatially varying ground motions,there are still challenges in efficient simulation of the non-stationary stochastic vector process in practice.The first problem is the inherent limitation and inflexibility of the deterministic time/frequency modulation function.Another difficulty is the estimation of evolutionary power spectral density(EPSD)with quite a few samples.To tackle these problems,the wavelet packet transform(WPT)algorithm is utilized to build a time-varying spectrum of seed recording which describes the energy distribution in the time-frequency domain.The time-varying spectrum is proven to preserve the time and frequency marginal property as theoretical EPSD will do for the stationary process.For the simulation of spatially varying ground motions,the auto-EPSD for all locations is directly estimated using the time-varying spectrum of seed recording rather than matching predefined EPSD models.Then the constructed spectral matrix is incorporated in SRM to simulate spatially varying non-stationary ground motions using efficient Cholesky decomposition techniques.In addition to a good match with the target coherency model,two numerical examples indicate that the generated time histories retain the physical properties of the prescribed seed recording,including waveform,temporal/spectral non-stationarity,normalized energy buildup,and significant duration.
文摘In array signal processing, 2-D spatial-spectrum estimation is required to determine DOA of multiple signals. The circular array of sensors is found to possess several nice properties for DOA estimation of wide-band sources. C. U. Padmini, et al.(1994) had suggested that the frequency-direction ambiguity in azimuth estimation of wide-baud signals received by a uniform linear array (ULA) can be avoided by using a circular array, even without the use of any delay elements. In 2-D spatial-spectrum estimation for wide-band signals, the authors find that it is impossible to avoid the ambiguity in source frequency-elevation angle pairs using a circular array. In this paper, interpolated circular arrays are used to perform 2-D spatial-spectrum estimation for wide-band sources. In the estimation, a large aperture circular array (Υ】λmin/2) is found to possess superior resolution capability and robustness.
基金The National Science and Technology Major Project( No. 2011ZX03005-004-03)the National Natural Science Foundation of China ( No. 61171081, 60872004 )the Natural Science Foundation of Guangxi Province ( No. 2011GXNSFB018075)
文摘A novel spectrum hole detection mechanism is proposed to improve the detection probability in cognitive radio networks for several typical scenarios. By removing the influence of the spatial false alarm （SFA）, the spectrum hole detection probability of the secondary user under path loss and multi-path fading is derived. Meanwhile, the spectrum hole detection probability of multi-users cooperative sensing and that of single-user sensing in multi-bands are derived for comparison. Theoretical analyses and simulation results show that the spectrum hole detection probability of the proposed mechanism is inversely proportional to the sampling times and the area of the sensing region. The detection performance of the multi-users sensing is better than that of single-user sensing when with the AND ~ogic fusion rule but worse when with the OR logic fusion rule. The detection probability is further decreased in the Rayleigh fading channel but it is greatly increased in multi-bands.
