Orthogonal transmultiplexers in communication: A review
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paper_title: Wavelet and subband transforms: fundamentals and communication applications

paper_content:

Subband and wavelet transforms have been a subject of great interest, especially in the fields of signal processing and applied mathematics. This article presents a tutorial on this subject, emphasizing the fundamentals and the reason for its success, importance, and potential. Subband and wavelet transform applications in communications are also reviewed. These application areas include interference excision, spread spectrum codes based on subband transform bases, CDMA, and discrete multitone transceivers.
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paper_title: Performance of an Efficient Parallel Data Transmission System

paper_content:

A parallel quadrature AM data transmission system may be implemented with a number of overlapping channels, each carrying a signaling rate b , spaced b/2 apart in frequency. When a large number of channels are used, the system allows transmission speeds very close to the Nyquist rate, with little sensitivity to delay and amplitude distortion of the transmission medium. The receiver requires precise phasing of the demodulating carriers and sampling times in order to keep crosstalk between channels small. In the presence of delay and amplitude distortion, better results are obtained when half cosine roll-offs are used for shaping each channel than for full cosine roll-off. This transmission scheme appears to be a promising technique for achieving good performance at high information rates over bandlimited dispersive transmission media.
---
paper_title: Frequency domain data transmission using reduced computational complexity algorithms

paper_content:

In this paper we describe a frequency domain data transmission method to be used for digital data transmission over analog telephone lines which exploits recently derived reduced computational complexity algorithms, such as the Winograd Fourier Transform, to achieve a significantly lower computational rate than comparable time domain QAM modems implemented digitally using signal processing techniques. In addition to the lower computational rate, the proposed method also allows for better channel bandwidth utilization by allowing optimal signal power allocation based on the channel's signal to noise versus frequency characteristics. Experimental results on this method are presented, indicating that it may be possible to send over 10,000 BPS over an unconditioned telephone line while maintaining a 10-5BER.
---
paper_title: Data Transmission by FrequencyDivision Multiplexing Using the Discrete Fourier Transform

paper_content:

The Fourier transform data communication system is a realization of frequency-division multiplexing (FDM) in which discrete Fourier transforms are computed as part of the modulation and demodulation processes. In addition to eliminating the banks of subcarrier oscillators and coherent demodulators usually required in FDM systems, a completely digital implementation can be built around a special-purpose computer performing the fast Fourier transform. In this paper, the system is described and the effects of linear channel distortion are investigated. Signal design criteria and equalization algorithms are derived and explained. A differential phase modulation scheme is presented that obviates any equalization.
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paper_title: TDM-FDM Transmultiplexer: Digital Polyphase and FFT

paper_content:

The cascading of a discrete Fourier transform processor and a digital polyphase network is shown to reduce the computation rate in frequency multiplexing-demultiplexing systems to a value close to minimum. Implementation advantages of that technique are pointed out. The highest efficiency is achieved when the number of channels is close to a power of 2, which is demonstrated by the 60-channel frequency-division-multiplexing (FDM)-2 × 30-channel time-division-multiplexing (TDM) transmultiplexer; a rough estimate of the computation rate is carried out in a practical case and appears to be quite within reach of the present technological capabilities. Significant cost advantage over equivalent analog equipment is expected. A digital version of the 12-channel FDM system using the same technique is also considered.
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paper_title: Perfect transmultiplexers

paper_content:

The mathematical equivalence of transmultiplexers and sub-band coders with reconstruction of the original signals is shown. Critical time sampling in sub-band coders corresponds to critical frequency sampling in transmultiplexers. In both cases, non-ideal band-pass filters are sufficient to reconstruct the original signals without aliasing (in sub-band coders) and without crosstalk (in transmultiplexers). The equivalence between the two systems allows the use of results from sub-band coders (like the QMF and pseudo-QMF concepts) for the design of transmultiplexers. The price to be paid is a synchronous up- and down-sampling between transmitter and receiver, as well as a good channel characteristic. Simulation results are given for the non-ideal case. All results are obtained through a matrix analysis of the filter bank problem.
---
paper_title: The multitone channel

paper_content:

The maximum bit rate of multitone QAM (quadrature amplitude modulation) over a general linear channel is found. First, the overall bit rate for an AWGN channel with a two-level transfer function is maximized, using a multitone QAM system. The power distribution between the tones and the number of bits/symbol per tone is optimized for a given symbol error rate. Extending these results to the general channel, it is shown that the optimum power division for multitone signals is similar to the water-pouring solution of information theory. Furthermore, multitone QAM performance is about 9 dB worse than the channel capacity, independent of the channel characteristics. The multitone results throughout are compared to those of an equivalent single-tone linearly equalized system. The comparison shows that the multitone system is useful for some channels, e.g. those with deep nulls in the transfer function. The maximum bit error rate over a twisted-pair channel which is performance dominated by near-end crosstalk (NEXT) is also found. >
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paper_title: A new look at digital orthogonal transmultiplexers for CDMA communications

paper_content:

Orthogonal transmultiplexers have been successfully utilized for multiuser communications. They are of the FDMA type in their most common version. The transmultiplexers using frequency selective PR-QMFs as their user codes were reported in the literature. This approach conflicts with the requirements of a CDMA communications system. We introduce novel spread spectrum PR-QMF codes, wherein the orthogonality is distributed over both time and frequency domains. It is shown that the proposed multivalued spread spectrum PR-QMF codes with minimized auto and cross-correlation properties outperform the conventional binary Gold codes in CDMA communication scenarios considered in the article.
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paper_title: Filter banks allowing perfect reconstruction

paper_content:

Splitting a signal into N filtered channels subsampled by N is an important problem in digital signal processing. A fundamental property of such a system is that the original signal can be perfectly recovered from the subsampled channels. It is shown that this can always be done, and that FIR solutions exist. This is done by mapping the NM-dimensional nonlinear problem (where N is the number of channels and M the length of the FIR filters) into an M-dimensional linear problem. For N = 2, a general class of FIR solutions is derived, together with methods to find filters. The dual problem of mixing N signals into one channel upsampled by N is also addressed. Several applications are proposed. All results are obtained by looking at the N filter bank as a true N channel system, rather than N separate channels.
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paper_title: An Orthogonally Multiplexed QAM System Using the Discrete Fourier Transform

paper_content:

An orthogonally multiplexed QAM (O-QAM) system is a multichannel system with a baud rate spacing between adjacent carrier frequencies; this property is desirable to digitally implement the system using the discrete Fourier transformation (DFT). This paper provides a novel digital signal processing method based on an N /2-point DFT processing in the O-QAM system. A complexity comparison between a digital O-QAM system and a digital singlechannel QAM system shows that the digital O-QAM system using the new method is more economical than the digitally implemented conventional single-channel data transmission system.
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paper_title: Some results in the theory of crosstalk-free transmultiplexers

paper_content:

The crosstalk-free transmultiplexer (CF-TMUX) focuses on crosstalk cancellation (CC) rather than on suppressing it. The authors present an analysis of the CF-TMUX based on the polyphase component matrices of the filter banks used in TDM to FDM and FDM to TDM conversions, respectively. Thus a necessary and sufficient condition for complete CC is obtained. It is shown that the filters for a CF-TMUX are the same as the filters for a 1-skewed alias free QMF bank. In addition, if the QMF bank satisfies the perfect reconstruction (PR) property, then the TMUX also satisfies PR. The relation between CF-TMUX filters and alias-free QMF banks is used to obtain a direct design procedure for CF-TMUX filters (both FIR and IIR). It is also shown that approximately crosstalk-free TMUX filters can be obtained from any approximately alias-free QMC bank. Design examples and comparison tables are included. >
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paper_title: Multiresolution Signal Decomposition: Transforms, Subbands, and Wavelets

paper_content:

From the Publisher: ::: Multiresolution Signal Composition: Transforms, Subbands, and Wavelets, Second Edition is the first book to give a unified and coherent exposition of orthogonal signal decomposition techniques. Advances in the field of electrical engineering/computer science have occurred since the first edition was published in 1992. This second edition addresses new developments in applications-related chapters, especially in Chapter 4, "Filterbrook Families: Design and Performance," which is greatly expanded. Also included are the most recent applications of orthogonal transforms in digital communications and multimedia. ::: Multiresolution Signal Composition: Transforms, Subbands, and Wavelets, Second Edition is intended for graduate students and research and development practitioners engaged in signal processing applications in voice and image processing, multimedia, and telecommunications.
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paper_title: A new filter bank theory for time-frequency representation

paper_content:

This paper presents a new formalism for the description of analysis/synthesis systems based on filter banks. Although this work was done in the context of speech coding systems, the results apply to a far broader class of problems. This new formalism has three specific advantages. First, it allows for the description of many different techniques and approaches with one unifying theory. Second, it enables the decoupling of the effects of the various distorting elements in the system design process, allowing each to be addressed separately. Finally, it allows for the relatively simple invention of entirely new techniques in such a way that the relationship of the new approaches to previously developed techniques is always clear.
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paper_title: A procedure for designing exact reconstruction filter banks for tree-structured subband coders

paper_content:

In recent years, tree-structured analysis/reconstruction systems have been extensively studied for use in subband coders for speech. In such systems, it is important that the individual channel signals be decimated in such a way that the number of samples coded and transmitted does not exceed the number of samples in the original speech signal. Under this constraint, the systems presented in the past have sought to remove the aliasing distortion while minimizing the overall analysis/reconstruction distortion. In this paper, it is shown that it is possible to design tree-structured analysis/reconstruction systems which meet the sampling rate condition and which also result in exact reconstruction of the input signal. This paper develops the conditions for exact reconstruction and presents a general method for designing the corresponding high quality analysis and reconstruction filters.
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paper_title: Subband and Wavelet Transforms: Design and Applications

paper_content:

The contributors to Subband and Wavelet Transforms: Design and Applications are distinguished scholars, drawn from prominent research laboratories and universities around the world. The first six chapters of the book are devoted to theory and design, each having a unique focus and perspective. The remaining seven chapters use the foundation built in the first part to address specific applications. Some of these application areas are quite mature, while others are just emerging. An extensive bibliography is provided at the end of the book, which is used as a reference list for all chapters. This will help the interested readers to expand their study of this material. Subband and Wavelet Transforms: Design and Applications is an in-depth reference volume, treating the fundamentals and discussing emerging applications in which filter banks and wavelets are believed to be important. Audience: Intended for a broad readership, the book will be of particular interest to practicing engineers and scientists who wish to learn about utilization of these new developments, instructors teaching senior and graduate level engineering and applied mathematics courses in the field, and management personnel wishing to keep up with this rapidly developing technology.
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paper_title: Spread-signature CDMA: efficient multiuser communication in the presence of fading

paper_content:

A new class of orthogonal code-division multiple-access (CDMA) systems is developed for efficient multiuser communication in environments subject to multipath fading phenomena. The key characteristic of these new systems, which we refer to as "spread-signature CDMA" systems, is that the associated signature sequences are significantly longer than the interval between symbols. Using this approach, the transmission of each symbol of each user is, in effect, spread over a wide temporal and spectral extent, which is efficiently exploited to combat the effects of fading. These systems generalize and improve on the spread-response precoding systems. Both efficient signature sets and efficient receiver structures for such systems are developed. Several aspects of the performance of the resulting spread-signature CDMA systems are presented, including both the achievable bit-error rate characteristics and the effective capacity of such systems. The results suggest that spread-signature CDMA may be an attractive alternative to conventional CDMA in a variety of application scenarios. >
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paper_title: Some results in the theory of crosstalk-free transmultiplexers

paper_content:

The crosstalk-free transmultiplexer (CF-TMUX) focuses on crosstalk cancellation (CC) rather than on suppressing it. The authors present an analysis of the CF-TMUX based on the polyphase component matrices of the filter banks used in TDM to FDM and FDM to TDM conversions, respectively. Thus a necessary and sufficient condition for complete CC is obtained. It is shown that the filters for a CF-TMUX are the same as the filters for a 1-skewed alias free QMF bank. In addition, if the QMF bank satisfies the perfect reconstruction (PR) property, then the TMUX also satisfies PR. The relation between CF-TMUX filters and alias-free QMF banks is used to obtain a direct design procedure for CF-TMUX filters (both FIR and IIR). It is also shown that approximately crosstalk-free TMUX filters can be obtained from any approximately alias-free QMC bank. Design examples and comparison tables are included. >
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paper_title: On-signal decomposition techniques

paper_content:

Well-known block transforms and perfect reconstruction orthonormal filter banks are evaluated based on their frequency behavior and energy compaction. The filter banks outperform the block transforms for the signal sources considered. Although the latter are simpler to implement and already the choice of the existing video coding standards, filter banks with simple algorithms may well become the signal decomposition technique for the next generation video codecs, which require a multiresolution signal representation.
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paper_title: Statistically optimized PR-QMF design

paper_content:

A multivariable optimization problem is set to design 2-band PR-QMFs in this paper. The energy compaction, aliasing energy, step response, zero-mean high-pass filter, uncorrelated subband signals, constrained nonlinearity of the phase-response, and the given input statistics are simultaneously considered in the proposed optimal filter design technique. A set of optimal PR-QMF solutions and their optimization criteria along with their energy compaction performance are given for comparison. This approach of PR-QMF design leads to an input driven adaptive subband filter bank structure. It is expected that these optimal filters outperform the well-known fixed PR-QMFs in the literature for image and video coding applications.
---
paper_title: The multitone channel

paper_content:

The maximum bit rate of multitone QAM (quadrature amplitude modulation) over a general linear channel is found. First, the overall bit rate for an AWGN channel with a two-level transfer function is maximized, using a multitone QAM system. The power distribution between the tones and the number of bits/symbol per tone is optimized for a given symbol error rate. Extending these results to the general channel, it is shown that the optimum power division for multitone signals is similar to the water-pouring solution of information theory. Furthermore, multitone QAM performance is about 9 dB worse than the channel capacity, independent of the channel characteristics. The multitone results throughout are compared to those of an equivalent single-tone linearly equalized system. The comparison shows that the multitone system is useful for some channels, e.g. those with deep nulls in the transfer function. The maximum bit error rate over a twisted-pair channel which is performance dominated by near-end crosstalk (NEXT) is also found. >
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paper_title: Multirate filter banks for code-division multiple access systems

paper_content:

Direct sequence, code-division multiple access (CDMA) schemes offer an attractive alternative for sharing a transmission medium among many users, while requiring minimal co-operation among them. A number of signal processing issues are related to the receiver's task of multiuser information extraction and detection. In this paper, a discrete-time multirate formulation is introduced for asynchronous CDMA systems, which can incorporate multipath effects. In this framework, linear receivers are derived which can completely suppress multiuser interference (decorrelating receivers). A criterion is introduced, which guarantees the decorrelating property, while providing optimal solutions in the presence of noise. The synchronization problem in a multipath environment is also studied, and identifiability conditions are established. A subspace algorithm is proposed, to estimate the user's delays and multipath channels in a blind scenario.
---
paper_title: Multiresolution Signal Decomposition: Transforms, Subbands, and Wavelets

paper_content:

From the Publisher: ::: Multiresolution Signal Composition: Transforms, Subbands, and Wavelets, Second Edition is the first book to give a unified and coherent exposition of orthogonal signal decomposition techniques. Advances in the field of electrical engineering/computer science have occurred since the first edition was published in 1992. This second edition addresses new developments in applications-related chapters, especially in Chapter 4, "Filterbrook Families: Design and Performance," which is greatly expanded. Also included are the most recent applications of orthogonal transforms in digital communications and multimedia. ::: Multiresolution Signal Composition: Transforms, Subbands, and Wavelets, Second Edition is intended for graduate students and research and development practitioners engaged in signal processing applications in voice and image processing, multimedia, and telecommunications.
---
paper_title: A new look at digital orthogonal transmultiplexers for CDMA communications

paper_content:

Orthogonal transmultiplexers have been successfully utilized for multiuser communications. They are of the FDMA type in their most common version. The transmultiplexers using frequency selective PR-QMFs as their user codes were reported in the literature. This approach conflicts with the requirements of a CDMA communications system. We introduce novel spread spectrum PR-QMF codes, wherein the orthogonality is distributed over both time and frequency domains. It is shown that the proposed multivalued spread spectrum PR-QMF codes with minimized auto and cross-correlation properties outperform the conventional binary Gold codes in CDMA communication scenarios considered in the article.
---
paper_title: Subband and Wavelet Transforms: Design and Applications

paper_content:

The contributors to Subband and Wavelet Transforms: Design and Applications are distinguished scholars, drawn from prominent research laboratories and universities around the world. The first six chapters of the book are devoted to theory and design, each having a unique focus and perspective. The remaining seven chapters use the foundation built in the first part to address specific applications. Some of these application areas are quite mature, while others are just emerging. An extensive bibliography is provided at the end of the book, which is used as a reference list for all chapters. This will help the interested readers to expand their study of this material. Subband and Wavelet Transforms: Design and Applications is an in-depth reference volume, treating the fundamentals and discussing emerging applications in which filter banks and wavelets are believed to be important. Audience: Intended for a broad readership, the book will be of particular interest to practicing engineers and scientists who wish to learn about utilization of these new developments, instructors teaching senior and graduate level engineering and applied mathematics courses in the field, and management personnel wishing to keep up with this rapidly developing technology.
---
paper_title: Wavelet, Subband, and Block Transforms in Communications and Multimedia

paper_content:

From the Publisher: ::: Wavelet and subband transforms have been of great interest in the fields of engineering and applied mathematics. The theories of these powerful signal processing tools have matured and many applications utilizing them are emerging in different disciplines. This book, comprised of eleven chapter contributions from prominent researchers in the field, focuses on communications and multimedia applications of wavelet and subband transforms. Wavelet, Subband and Block Transforms in Communications and Multimedia will be of particular interest to engineers and scientists who want to learn about state-of-the-art subband and wavelet transform applications as well as their theoretical underpinnings. It can also serve as a supplementary book for graduate level engineering and applied mathematics courses on wavelet and subband transforms.
---
paper_title: Statistically optimized PR-QMF design

paper_content:

A multivariable optimization problem is set to design 2-band PR-QMFs in this paper. The energy compaction, aliasing energy, step response, zero-mean high-pass filter, uncorrelated subband signals, constrained nonlinearity of the phase-response, and the given input statistics are simultaneously considered in the proposed optimal filter design technique. A set of optimal PR-QMF solutions and their optimization criteria along with their energy compaction performance are given for comparison. This approach of PR-QMF design leads to an input driven adaptive subband filter bank structure. It is expected that these optimal filters outperform the well-known fixed PR-QMFs in the literature for image and video coding applications.
---
paper_title: The multitone channel

paper_content:

The maximum bit rate of multitone QAM (quadrature amplitude modulation) over a general linear channel is found. First, the overall bit rate for an AWGN channel with a two-level transfer function is maximized, using a multitone QAM system. The power distribution between the tones and the number of bits/symbol per tone is optimized for a given symbol error rate. Extending these results to the general channel, it is shown that the optimum power division for multitone signals is similar to the water-pouring solution of information theory. Furthermore, multitone QAM performance is about 9 dB worse than the channel capacity, independent of the channel characteristics. The multitone results throughout are compared to those of an equivalent single-tone linearly equalized system. The comparison shows that the multitone system is useful for some channels, e.g. those with deep nulls in the transfer function. The maximum bit error rate over a twisted-pair channel which is performance dominated by near-end crosstalk (NEXT) is also found. >
---
paper_title: Frequency domain data transmission using reduced computational complexity algorithms

paper_content:

In this paper we describe a frequency domain data transmission method to be used for digital data transmission over analog telephone lines which exploits recently derived reduced computational complexity algorithms, such as the Winograd Fourier Transform, to achieve a significantly lower computational rate than comparable time domain QAM modems implemented digitally using signal processing techniques. In addition to the lower computational rate, the proposed method also allows for better channel bandwidth utilization by allowing optimal signal power allocation based on the channel's signal to noise versus frequency characteristics. Experimental results on this method are presented, indicating that it may be possible to send over 10,000 BPS over an unconditioned telephone line while maintaining a 10-5BER.
---
paper_title: Multiresolution Signal Decomposition: Transforms, Subbands, and Wavelets

paper_content:

From the Publisher: ::: Multiresolution Signal Composition: Transforms, Subbands, and Wavelets, Second Edition is the first book to give a unified and coherent exposition of orthogonal signal decomposition techniques. Advances in the field of electrical engineering/computer science have occurred since the first edition was published in 1992. This second edition addresses new developments in applications-related chapters, especially in Chapter 4, "Filterbrook Families: Design and Performance," which is greatly expanded. Also included are the most recent applications of orthogonal transforms in digital communications and multimedia. ::: Multiresolution Signal Composition: Transforms, Subbands, and Wavelets, Second Edition is intended for graduate students and research and development practitioners engaged in signal processing applications in voice and image processing, multimedia, and telecommunications.
---
paper_title: Multirate Systems and Filter Banks

paper_content:

1. Introduction 2. Review of Discrete-Time Systems 3. Review of Digital Filters 4. Fundamentals of Multirate Systems 5. Maximally Decimated Filter Banks 6. Paraunitary Perfect Reconstruction Filter Banks 7. Linear Phase Perfect Reconstruction QMF Banks 8. Cosine Modulated Filter Banks 9. Finite Word Length Effects 10. Multirate Filter Bank Theory and Related Topics 11. The Wavelet Transform and Relation to Multirate Filter Banks 12. Multidimensional Multirate Systems 13. Review of Discrete-Time Multi-Input Multi-Output LTI Systems 14. Paraunitary and Lossless Systems Appendices Bibliography Index
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paper_title: A new look at digital orthogonal transmultiplexers for CDMA communications

paper_content:

Orthogonal transmultiplexers have been successfully utilized for multiuser communications. They are of the FDMA type in their most common version. The transmultiplexers using frequency selective PR-QMFs as their user codes were reported in the literature. This approach conflicts with the requirements of a CDMA communications system. We introduce novel spread spectrum PR-QMF codes, wherein the orthogonality is distributed over both time and frequency domains. It is shown that the proposed multivalued spread spectrum PR-QMF codes with minimized auto and cross-correlation properties outperform the conventional binary Gold codes in CDMA communication scenarios considered in the article.
---
paper_title: A distortion analysis and optimal design of orthogonal basis for DMT transceivers

paper_content:

An orthogonal transmultiplexer (synthesis/analysis filter bank) utilizing DFT (discrete fourier transform) basis is the current DMT (discrete multitone) standard for HDSL communications. The measures of the ICI and ISI distortions in a multicarrier modulation scheme are presented. The ICI and ISI performance of DFT along with other known linear transforms are compared. The issues of optimal basis design for a given channel are discussed. The available design tools of the subband transform theory are highlighted for the future performance improvements.
---
paper_title: Performance of an Efficient Parallel Data Transmission System

paper_content:

A parallel quadrature AM data transmission system may be implemented with a number of overlapping channels, each carrying a signaling rate b , spaced b/2 apart in frequency. When a large number of channels are used, the system allows transmission speeds very close to the Nyquist rate, with little sensitivity to delay and amplitude distortion of the transmission medium. The receiver requires precise phasing of the demodulating carriers and sampling times in order to keep crosstalk between channels small. In the presence of delay and amplitude distortion, better results are obtained when half cosine roll-offs are used for shaping each channel than for full cosine roll-off. This transmission scheme appears to be a promising technique for achieving good performance at high information rates over bandlimited dispersive transmission media.
---
paper_title: Data Transmission by FrequencyDivision Multiplexing Using the Discrete Fourier Transform

paper_content:

The Fourier transform data communication system is a realization of frequency-division multiplexing (FDM) in which discrete Fourier transforms are computed as part of the modulation and demodulation processes. In addition to eliminating the banks of subcarrier oscillators and coherent demodulators usually required in FDM systems, a completely digital implementation can be built around a special-purpose computer performing the fast Fourier transform. In this paper, the system is described and the effects of linear channel distortion are investigated. Signal design criteria and equalization algorithms are derived and explained. A differential phase modulation scheme is presented that obviates any equalization.
---
paper_title: Performance analysis and optimal structuring of subchannels for discrete multitone transceivers

paper_content:

A smart algorithm for the decomposition of a channel into its subchannel in the discrete multitone communications is proposed in this paper. This algorithm evaluates the unevenness and energy distribution of the channel spectrum in order to get a variable adaptive partitioning of the channel. It is shown that the proposed algorithm leads to a near optimum performance of the discrete multitone transceiver. This flexible and smart splitting of the channel suffers less from the aliasing problem that exists in blind decompositions using fixed transforms. This paper extends the fixed discrete multitone to the flexible unequal bandwidth multichannel concept which has significant potentials for performance improvements in high-speed digital communications.
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paper_title: Wavelet-packet-based multiple-access communication

paper_content:

We explore the role that the wavelet packet transform can play in increasing multiple access communication throughput via waveform design and receiver design. Wavelet packets offer a flexible framework which allows us to select and refine signature waveforms at intermediate time-frequency levels leading to the development of efficient methods for near optimal receiver implementation. The optimal receiver will jointly demodulate all of the received waveforms and has a complexity which is exponential in the number of users, while a suboptimal version will attempt to do the same with a greatly reduced computational complexity. We believe that our wavelet packet recursive joint detection system described in this paper offers a good alternative approach to existing comparable methods. Specifically, our preliminary analysis and simulation results indicate the potential for a marked computational improvement over the optimal detector and additional flexibility and efficiency over other proposed joint detection schemes for multiple access communication.
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paper_title: Linear phase cosine modulated maximally decimated filter banks with perfect reconstruction

paper_content:

We propose a novel way to design maximally decimated FIR cosine modulated filter banks, in which each analysis and synthesis filter has a linear phase. The system can be designed to have either the approximate reconstruction property (pseudo-QMF system) or perfect reconstruction property (PR system). In the PR case, the system is a paraunitary filter bank. As in earlier work on cosine modulated systems, all the analysis filters come from an FIR prototype filter. However, unlike in any of the previous designs, all but two of the analysis filters have a total bandwidth of 2/spl pi//M rather than /spl pi//M (where 2M is the number of channels in our notation). A simple interpretation is possible in terms of the complex (hypothetical) analytic signal corresponding to each bandpass subband. The coding gain of the new system is comparable with that of a traditional M-channel system (rather than a 2M-channel system). This is primarily because there are typically two bandpass filters with the same passband support. Correspondingly, the cost of the system (in terms of complexity of implementation) is also comparable with that of an M-channel system. We also demonstrate that very good attenuation characteristics can be obtained with the new system.
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paper_title: Oversampled filter banks

paper_content:

Perfect reconstruction oversampled filter banks are equivalent to a particular class of frames in l/sup 2/(Z). These frames are the subject of this paper. First, the necessary and sufficient conditions of a filter bank for implementing a frame or a tight frame expansion are established, as well as a necessary and sufficient condition for perfect reconstruction using FIR filters after an FIR analysis. Complete parameterizations of oversampled filter banks satisfying these conditions are given. Further, we study the condition under which the frame dual to the frame associated with an FIR filter bank is also FIR and give a parameterization of a class of filter banks satisfying this property. Then, we focus on non-subsampled filter banks. Non-subsampled filter banks implement transforms similar to continuous-time transforms and allow for very flexible design. We investigate the relations of these filter banks to continuous-time filtering and illustrate the design flexibility by giving a procedure for designing maximally flat two-channel filter banks that yield highly regular wavelets with a given number of vanishing moments.
---
paper_title: A distortion analysis and optimal design of orthogonal basis for DMT transceivers

paper_content:

An orthogonal transmultiplexer (synthesis/analysis filter bank) utilizing DFT (discrete fourier transform) basis is the current DMT (discrete multitone) standard for HDSL communications. The measures of the ICI and ISI distortions in a multicarrier modulation scheme are presented. The ICI and ISI performance of DFT along with other known linear transforms are compared. The issues of optimal basis design for a given channel are discussed. The available design tools of the subband transform theory are highlighted for the future performance improvements.
---
paper_title: Perfect transmultiplexers

paper_content:

The mathematical equivalence of transmultiplexers and sub-band coders with reconstruction of the original signals is shown. Critical time sampling in sub-band coders corresponds to critical frequency sampling in transmultiplexers. In both cases, non-ideal band-pass filters are sufficient to reconstruct the original signals without aliasing (in sub-band coders) and without crosstalk (in transmultiplexers). The equivalence between the two systems allows the use of results from sub-band coders (like the QMF and pseudo-QMF concepts) for the design of transmultiplexers. The price to be paid is a synchronous up- and down-sampling between transmitter and receiver, as well as a good channel characteristic. Simulation results are given for the non-ideal case. All results are obtained through a matrix analysis of the filter bank problem.
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paper_title: MDFT filter banks with perfect reconstruction

paper_content:

The Modified DFT (MDFT) polyphase filter bank has been introduced. It has been shown that this filter bank is able to cancel adjacent channel alias spectra resulting in almost perfect reconstruction. Compared to cosine modulated filter banks, the MDFT filter bank offers advantages such as linear phase analysis and synthesis filters, complex valued signal processing with a different mapping into the subbands and low propagation delays. In this paper, it is shown that the MDFT filter bank structure provides a cancellation of all odd alias spectra. Furthermore, it is demonstrated that even perfect reconstruction can be obtained by an appropriate filter design.
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paper_title: Blind equalization of OFDM systems based on the minimization of a quadratic criterion

paper_content:

Classical multicarrier systems based on the discrete Fourier transform (DFT) make use of a "guard interval" (GI) in order to enable a low complexity equalization scheme. This "guard interval" consists of a redundant prefix cyclically appended to each bloc of modulated symbols so as to exploit the cyclic convolution property of the DFT. Therefore, besides decreasing the useful transmitted symbol rate, this technique is very specific to DFT-based OFDM systems. In order to implement a digital modulator, an oversampled version of the continuous signal that would be produced by the all-analog ideal modulator is often computed. This amounts to appending null symbols to the block of symbols to be modulated. This work shows that forcing the presence of these null symbols at the appropriate places on the receiver side is sufficient to equalize the channel. Here, a linear equalizer is adapted by minimizing a quadratic criterion based on the energy of the subband signals that should be zero. Since no knowledge upon the "useful data" is required, this method performs blind equalization. Moreover, it requires neither a guard interval nor any reference symbol. As a result, for a given channel bit-rate budget, the data rate is increased.
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paper_title: Signal Processing With Lapped Transforms

paper_content:

Applications of transforms in signal processing signal processing in subbands lapped orthogonal transforms the modulated lapped transform heirarchical lapped transforms applications of lapped transforms.
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paper_title: Performance analysis and optimal structuring of subchannels for discrete multitone transceivers

paper_content:

A smart algorithm for the decomposition of a channel into its subchannel in the discrete multitone communications is proposed in this paper. This algorithm evaluates the unevenness and energy distribution of the channel spectrum in order to get a variable adaptive partitioning of the channel. It is shown that the proposed algorithm leads to a near optimum performance of the discrete multitone transceiver. This flexible and smart splitting of the channel suffers less from the aliasing problem that exists in blind decompositions using fixed transforms. This paper extends the fixed discrete multitone to the flexible unequal bandwidth multichannel concept which has significant potentials for performance improvements in high-speed digital communications.
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paper_title: Wavelet packet modulation: a generalized method for orthogonally multiplexed communications

paper_content:

Building on recently introduced multidimensional signalling techniques, a multirate wavelet based modulation format is presented which can utilize existing channels designed for conventional QAM. Customizable wavelet packet basis functions are employed as novel pulse shapes upon which independent QAM data at lower rates are placed. The advantages include dimensionality in both time and frequency for flexible channel exploitation and an efficient all digital filter bank implementation. >
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paper_title: A discrete multitone transceiver system for HDSL applications

paper_content:

A discrete multitone (DMT) transceiver design for high bit rate digital subscriber line (HDSL) access is presented and analyzed. The DMT transmitter and receiver structure and algorithms are detailed, and the computational requirements of DMT for HDSL are estimated. At a sampling rate of 640 kHz, using an appropriate combination of a short finite-impulse-response (FIR) equalizer and a length-512 DMT system, 1.6 Mb/s data transmission is possible within the carrier serving area (CSA) at an error rate of 10/sup -7/ on a single twisted pair. A significant performance margin can be achieved when two coordinated twisted pairs are used to deliver a total data rate of 1.6 Mb/s. In terms of a performance-per-computation figure of merit, the DMT system is an excellent candidate for HDSL implementation. >
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paper_title: Bandlimited orthogonal wavelet symbols

paper_content:

This paper presents methods for constructing bandlimited wavelets whose time-shifted and dyadically dilated replicates form orthonormal sets. The wavelets sets constructed have desirable spectral spreading properties when used as symbols for encoding digital communication signals, as has been proposed in recent literature. >
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paper_title: Analysis/Synthesis filter bank design based on time domain aliasing cancellation

paper_content:

A single-sideband analysis/synthesis system is proposed which provides perfect reconstruction of a signal from a set of critically sampled analysis signals. The technique is developed in terms of a weighted overlap-add method of analysis/synthesis and allows overlap between adjacent time windows. This implies that time domain aliasing is introduced in the analysis; however, this aliasing is cancelled in the synthesis process, and the system can provide perfect reconstruction. Achieving perfect reconstruction places constraints on the time domain window shape which are equivalent to those placed on the frequency domain shape of analysis/synthesis channels used in recently proposed critically sampled systems based on frequency domain aliasing cancellation [7], [8]. In fact, a duality exists between the new technique and the frequency domain techniques of [7] and [8], The proposed technique is more efficient than frequency domain designs for a given number of analysis/synthesis channels, and can provide reasonably band-limited channel responses. The technique could be particularly useful in applications where critically sampled analysis/synthesis is desirable, e.g., coding.
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paper_title: A new look at digital orthogonal transmultiplexers for CDMA communications

paper_content:

Orthogonal transmultiplexers have been successfully utilized for multiuser communications. They are of the FDMA type in their most common version. The transmultiplexers using frequency selective PR-QMFs as their user codes were reported in the literature. This approach conflicts with the requirements of a CDMA communications system. We introduce novel spread spectrum PR-QMF codes, wherein the orthogonality is distributed over both time and frequency domains. It is shown that the proposed multivalued spread spectrum PR-QMF codes with minimized auto and cross-correlation properties outperform the conventional binary Gold codes in CDMA communication scenarios considered in the article.
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paper_title: An Orthogonally Multiplexed QAM System Using the Discrete Fourier Transform

paper_content:

An orthogonally multiplexed QAM (O-QAM) system is a multichannel system with a baud rate spacing between adjacent carrier frequencies; this property is desirable to digitally implement the system using the discrete Fourier transformation (DFT). This paper provides a novel digital signal processing method based on an N /2-point DFT processing in the O-QAM system. A complexity comparison between a digital O-QAM system and a digital singlechannel QAM system shows that the digital O-QAM system using the new method is more economical than the digitally implemented conventional single-channel data transmission system.
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paper_title: Performance of coherent OFDM-CDMA for broadband mobile communications

paper_content:

Uncoded orthogonal frequency division multiplexing (OFDM) transmission technique applied in a multipath environment has a bit error rate (BER) comparable with a narrowband radio channel because the fading of each subcarrier is frequency-nonselective. To overcome this behaviour and to reduce the BER, a combination of OFDM and CDMA has been proposed recently. In an OFDM-CDMA system the energy of each information symbol is spread over several subcarriers. Therefore a diversity gain can be obtained in a broadband fading channel.
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Title: Orthogonal Transmultiplexers in Communication: A Review

Section 1: SYNTHESIS/ANALYSIS FILTER BANK AND ORTHOGONALITY
Description 1: Discuss the perfect reconstruction (PR) properties and synthesis/analysis configuration of filter banks as a transmultiplexer structure, including time-frequency interpretation and optimal design methodologies.

Section 2: Time-Frequency Interpretation and Optimal Basis Design for TDMA, FDMA, and CDMA Communications
Description 2: Explore the orthogonality and time-frequency properties of subcarriers, involving the design of the most suitable basis for different types of transmultiplexer platforms.

Section 3: ORTHOGONAL TRANSMULTIPLEXER: SINGLE AND MULTIUSER COMMUNICATIONS
Description 3: Discuss popular and emerging communication applications of orthogonal transmultiplexers, focusing on performance issues and application-specific requirements of synthesis/analysis filters with a time-frequency perspective.

Section 4: DMT Modulation
Description 4: Examine DMT (OFDM)-based applications like ADSL/VDSL and DAB, provide a mathematical foundation, and discuss channel equalization techniques and future research directions.

Section 5: Spread Spectrum PR-QMF Codes for CDMA
Description 5: Explain the use of orthogonal synthesis/analysis filter banks for CDMA communications, focusing on user codes and their time-frequency optimization.

Section 6: LPI Communications
Description 6: Discuss the use of time and frequency spread functions in LPI communications, including frequency hopping techniques and matched filter bank configurations.

Section 7: CONCLUSIONS
Description 7: Conclude with an overview of the application of orthogonal synthesis/analysis filterbanks in single and multiuser communication systems, presenting a unified theoretical framework and suggesting several research topics for future study.