Ivan W. Selesnick, Richard G. Baraniuk, and Nick G. Kingsbury: The Dual-Tree Complex Wavelet Transform Citat: "...trouble in paradise: four problems with real wavelets...one solution: complex wavelets...The second school seeks a redundant representation, with both wr(t) and wi(t) individually forming orthonormal or biorthogonal bases. The resulting CWT is a 2x redundant tight frame [26] in 1-D, with the power to overcome the four shortcomings...In this article, we will focus on a particularly natural approach to the second, redundant type of CWT, the dual-tree approach, which is based on two FB trees and thus two bases [55], [57]...From Figure 3, we see that we can reach quite close to the ideal even with quite short filters...As a result, the dual-tree CWT comes very close to mirroring the attractive properties of the Fourier transform, including a smooth, nonoscillating magnitude (see Figure 1); a nearly shift-invariant magnitude with a simple near-linear phase encoding of signal shifts; substantially reduced aliasing; and directional wavelets in higher dimensions. The only cost for all of this is a moderate redundancy: 2x redundancy in 1-D (2^d for d-dimensional signals, in general)...In the following, we describe three methods for FIR dual-tree filter design. Fast implementations of some of these filters have been recently described in[1]...MATLAB software for the dual-tree complex wavelet transform (and related algorithms) is available at the following locations on the web: http://taco.poly.edu/WaveletSoftware/Arkiveret 22. april 2015 hos Wayback Machine, http://www-sigproc.eng.cam.ac.uk/~ngk/, and http://dsp.rice.edu/..."
ieee802.org
IEEE 802.16 Broadband Wireless Access Working Group Citat: "...[pdf-side 3]...The following figure illustrates a comparable WOFDM power spectral density, illustrating the additional 35dB of stop-band, allowing much superior adjacent band rejection as compared to an OFDM PHY layer (Power Spectrum Magnitude in dB versus Frequency in MHz)...[pdf-side 6]...The PHY overhead for WOFDM is less than that of Fourier based OFDM modulations. OFDM Guard Intervals of 20% or more are typical for wireless thus giving Wavelet OFDM an advantage of roughly 20% in BW efficiency...[pdf-side 6]...In addition, pilot tones are not necessary for wavelets so that in comparison systems like 802.11a / HiperLan2 uses 4 out of 52 sub-bands for pilots which gives WOFDM another 8% advantage over typical OFDM implementations...[pdf-side 8]...The performance of wavelets in Gaussian noise is nominally the same as QAM and OFDM. However, wavelet modulations are intrinsically a convolutional modulation and further improvements appear possible for the “raw” modulation (i.e. before adding FEC). The effects of multi-path Rayleigh fading are negligible for wavelets when the mean delay is less that 10 % of the symbol time..."
Ivan W. Selesnick, Richard G. Baraniuk, and Nick G. Kingsbury: The Dual-Tree Complex Wavelet Transform Citat: "...trouble in paradise: four problems with real wavelets...one solution: complex wavelets...The second school seeks a redundant representation, with both wr(t) and wi(t) individually forming orthonormal or biorthogonal bases. The resulting CWT is a 2x redundant tight frame [26] in 1-D, with the power to overcome the four shortcomings...In this article, we will focus on a particularly natural approach to the second, redundant type of CWT, the dual-tree approach, which is based on two FB trees and thus two bases [55], [57]...From Figure 3, we see that we can reach quite close to the ideal even with quite short filters...As a result, the dual-tree CWT comes very close to mirroring the attractive properties of the Fourier transform, including a smooth, nonoscillating magnitude (see Figure 1); a nearly shift-invariant magnitude with a simple near-linear phase encoding of signal shifts; substantially reduced aliasing; and directional wavelets in higher dimensions. The only cost for all of this is a moderate redundancy: 2x redundancy in 1-D (2^d for d-dimensional signals, in general)...In the following, we describe three methods for FIR dual-tree filter design. Fast implementations of some of these filters have been recently described in[1]...MATLAB software for the dual-tree complex wavelet transform (and related algorithms) is available at the following locations on the web: http://taco.poly.edu/WaveletSoftware/Arkiveret 22. april 2015 hos Wayback Machine, http://www-sigproc.eng.cam.ac.uk/~ngk/, and http://dsp.rice.edu/..."
rice.edu
dsp.rice.edu
Ivan W. Selesnick, Richard G. Baraniuk, and Nick G. Kingsbury: The Dual-Tree Complex Wavelet Transform Citat: "...trouble in paradise: four problems with real wavelets...one solution: complex wavelets...The second school seeks a redundant representation, with both wr(t) and wi(t) individually forming orthonormal or biorthogonal bases. The resulting CWT is a 2x redundant tight frame [26] in 1-D, with the power to overcome the four shortcomings...In this article, we will focus on a particularly natural approach to the second, redundant type of CWT, the dual-tree approach, which is based on two FB trees and thus two bases [55], [57]...From Figure 3, we see that we can reach quite close to the ideal even with quite short filters...As a result, the dual-tree CWT comes very close to mirroring the attractive properties of the Fourier transform, including a smooth, nonoscillating magnitude (see Figure 1); a nearly shift-invariant magnitude with a simple near-linear phase encoding of signal shifts; substantially reduced aliasing; and directional wavelets in higher dimensions. The only cost for all of this is a moderate redundancy: 2x redundancy in 1-D (2^d for d-dimensional signals, in general)...In the following, we describe three methods for FIR dual-tree filter design. Fast implementations of some of these filters have been recently described in[1]...MATLAB software for the dual-tree complex wavelet transform (and related algorithms) is available at the following locations on the web: http://taco.poly.edu/WaveletSoftware/Arkiveret 22. april 2015 hos Wayback Machine, http://www-sigproc.eng.cam.ac.uk/~ngk/, and http://dsp.rice.edu/..."
Performance Comparison of Wavelet and FFT Based Multiuser MIMO OFDM over Wireless Rayleigh Fading ChannelArkiveret 15. april 2015 hos Wayback Machine Citat: "...We can have all the benefits of OFDM even if we replace traditional sinusoid carriers of the fourier based OFDM with suitable wavelets. Wavelet based systems have been shown to have better immunity to impulse and narrowband noises than Fourier OFDM [3, 4] also the interference power can to a large extent, be mitigated [5]...Also the performance of equalization in wavelet system is better than conventional OFDM [6]. Wavelet packet modulation will have much lower side lobes in transmitted signals which reduce the inter-carrier interference (ICI) and narrowband interference (NBI) [7]...This article compares the performances of wavelet and FFT based OFDM systems in multiuser environment in terms of error performance and through an extensive computer simulation it is shown that wavelet outperforms the FFT based OFDM...."
2008: Multy (multi?) binary turbo coded wofdm performance in flat rayleigh fading channels Citat: "...V. CONCLUSIONS AND FURTHER WORK. In this paper we evaluate the BER performance of MBTC associated with two multicarrier modulation techniques: OFDM and its wavelet based version, in a flat fading channel. The WOFDM provides better results than OFDM, especially for high values of the Doppler shift parameter, which quantifies the time variability of the channel. Furthermore, the coded WOFDM performance shows no significant dependency on the wavelets mother used for DWT computation. A surprising result of our simulations is that, unlike for the un-coded system, the BER and FER performance for the MBTC-WOFDM is better for higher values of the Doppler shift..."
utt.ro
cmpicsu.utt.ro
Wavelet OFDM Performance in Flat Fading Channels. Marius OlteanArkiveret 15. april 2015 hos Wayback Machine Citat: "...Abstract – This paper represents an investigation of the wavelet based multi-carrier modulation performance in flat fading channels. The fading envelope is distributed according to a Rayleigh probability density function....Besides its incontestable advantages, OFDM presents some well known drawbacks as: diminished spectral efficiency because of the cyclic prefix (CP) overhead, slow decay of the out-of-band side-lobes, high sensitivity to time and frequency synchronization, increased peak-to- average-power ratio [1,2]....The authors in [5] have shown that wavelet-based OFDM (WOFDM) has better spectral efficiency, is simpler and at least as rapid as OFDM in practical implementations......"
web.archive.org: Wavelet University: Wavelets 101 - Wavelets for Dummies (Non-Mathematicians) Citat: "...If a single symbol of data were sent (the equivalent of the modulated and summed wavelets covering all of the available bands), then it would create a time limited signal as below...Through careful design and selection of phases and timing, these Wavelet Symbols can be overlapped in time; the spacing between successive symbols need only be a fraction of the width, or length, of the symbol it self..."
Wavelet OFDM Performance in Flat Fading Channels. Marius OlteanArkiveret 15. april 2015 hos Wayback Machine Citat: "...Abstract – This paper represents an investigation of the wavelet based multi-carrier modulation performance in flat fading channels. The fading envelope is distributed according to a Rayleigh probability density function....Besides its incontestable advantages, OFDM presents some well known drawbacks as: diminished spectral efficiency because of the cyclic prefix (CP) overhead, slow decay of the out-of-band side-lobes, high sensitivity to time and frequency synchronization, increased peak-to- average-power ratio [1,2]....The authors in [5] have shown that wavelet-based OFDM (WOFDM) has better spectral efficiency, is simpler and at least as rapid as OFDM in practical implementations......"
Performance Comparison of Wavelet and FFT Based Multiuser MIMO OFDM over Wireless Rayleigh Fading ChannelArkiveret 15. april 2015 hos Wayback Machine Citat: "...We can have all the benefits of OFDM even if we replace traditional sinusoid carriers of the fourier based OFDM with suitable wavelets. Wavelet based systems have been shown to have better immunity to impulse and narrowband noises than Fourier OFDM [3, 4] also the interference power can to a large extent, be mitigated [5]...Also the performance of equalization in wavelet system is better than conventional OFDM [6]. Wavelet packet modulation will have much lower side lobes in transmitted signals which reduce the inter-carrier interference (ICI) and narrowband interference (NBI) [7]...This article compares the performances of wavelet and FFT based OFDM systems in multiuser environment in terms of error performance and through an extensive computer simulation it is shown that wavelet outperforms the FFT based OFDM...."
Ivan W. Selesnick, Richard G. Baraniuk, and Nick G. Kingsbury: The Dual-Tree Complex Wavelet Transform Citat: "...trouble in paradise: four problems with real wavelets...one solution: complex wavelets...The second school seeks a redundant representation, with both wr(t) and wi(t) individually forming orthonormal or biorthogonal bases. The resulting CWT is a 2x redundant tight frame [26] in 1-D, with the power to overcome the four shortcomings...In this article, we will focus on a particularly natural approach to the second, redundant type of CWT, the dual-tree approach, which is based on two FB trees and thus two bases [55], [57]...From Figure 3, we see that we can reach quite close to the ideal even with quite short filters...As a result, the dual-tree CWT comes very close to mirroring the attractive properties of the Fourier transform, including a smooth, nonoscillating magnitude (see Figure 1); a nearly shift-invariant magnitude with a simple near-linear phase encoding of signal shifts; substantially reduced aliasing; and directional wavelets in higher dimensions. The only cost for all of this is a moderate redundancy: 2x redundancy in 1-D (2^d for d-dimensional signals, in general)...In the following, we describe three methods for FIR dual-tree filter design. Fast implementations of some of these filters have been recently described in[1]...MATLAB software for the dual-tree complex wavelet transform (and related algorithms) is available at the following locations on the web: http://taco.poly.edu/WaveletSoftware/Arkiveret 22. april 2015 hos Wayback Machine, http://www-sigproc.eng.cam.ac.uk/~ngk/, and http://dsp.rice.edu/..."
