Optimal finite duration pulses for OFDM

doi:10.1109/26.476088

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Optimal finite duration pulses for OFDM

Journal Article•DOI•

Optimal finite duration pulses for OFDM

A. Vahlin¹, N. Holte¹•Institutions (1)

Norwegian Institute of Technology¹

28 Nov 1994-Vol. 44, Iss: 1, pp 10-14

TL;DR: Pulses of finite duration for use in orthogonal frequency division multiplexing (OFDM) using offset QAM modulation is presented and an optimization procedure which minimizes the out-of-band energy under the constraints of zero intersymbol and interchannel interference is presented.

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Abstract: This paper presents pulses of finite duration for use in orthogonal frequency division multiplexing (OFDM) using offset QAM modulation. In such a system the pulses will overlap in both frequency and time without intersymbol or interchannel interference. The pulses are generated by an optimization procedure which minimizes the out-of-band energy under the constraints of zero intersymbol and interchannel interference. Low out-of-band energy is important to achieve high bandwidth efficiency, especially when the number of channels is small. The optimization procedure leads to an integral equation which is solved by expanding the pulse in truncated prolate spheroidal wave functions. Examples of optimized pulses and their spectrum are presented for lengths of 2 and 4 symbol intervals.

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Journal Article•DOI•

Analysis and design of OFDM/OQAM systems based on filterbank theory

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Pierre Siohan¹, C. Siclet¹, N. Lacaille²•Institutions (2)

Orange S.A.¹, Universite de technologie de Belfort-Montbeliard²

01 May 2002-IEEE Transactions on Signal Processing

TL;DR: A discrete-time analysis of the orthogonal frequency division multiplex/offset QAM (OFDM/OQAM) multicarrier modulation technique, leading to a modulated transmultiplexer, is presented.

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Abstract: A discrete-time analysis of the orthogonal frequency division multiplex/offset QAM (OFDM/OQAM) multicarrier modulation technique, leading to a modulated transmultiplexer, is presented. The conditions of discrete orthogonality are established with respect to the polyphase components of the OFDM/OQAM prototype filter, which is assumed to be symmetrical and with arbitrary length. Fast implementation schemes of the OFDM/OQAM modulator and demodulator are provided, which are based on the inverse fast Fourier transform. Non-orthogonal prototypes create intersymbol and interchannel interferences (ISI and ICI) that, in the case of a distortion-free transmission, are expressed by a closed-form expression. A large set of design examples is presented for OFDM/OQAM systems with the number of subcarriers going from four up to 2048, which also allows a comparison between different approaches to get well-localized prototypes.

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1,020 citations

Cites background or methods from "Optimal finite duration pulses for ..."

...As for OFDPs, their expression in continuous-time is as follows [6], [20]:...
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...where is the th prolate spheroidal wave function truncated to the interval and where are some real-valued coefficients obtained thanks to an optimization procedure [20]....
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...Let us refer to the optimization method of the lattice coefficients according to the criterion as the optimized lattice (OL), knowing naturally that more generally, the optimization of the lattice coefficients can be carried out with different types of criteria, including, as in [20], the maximization of the in-band energy....
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...for instance, [19]); 2) a family of pulses introduced by Vahlin and Holte in [20], which we will call optimal finite duration pulses (OFDPs); 3) a new family of functions called extended Gaussian functions (EGFs); see [21]....
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...These prototype filters have been computed thanks to the values of the coefficients given in [20]....
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Journal Article•DOI•

Nonorthogonal pulseshapes for multicarrier communications in doubly dispersive channels

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Werner Kozek, Andreas F. Molisch¹•Institutions (1)

Vienna University of Technology¹

01 Oct 1998-IEEE Journal on Selected Areas in Communications

TL;DR: This work derives the expected intersymbol/interchannel interference of such a nonorthogonal FDM (NOFDM) system under the assumption of a wide-sense stationary uncorrelated scattering (WSSUS) channel and compares OFDM and NOFDM schemes with regard to robustness against delay/Doppler spread.

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Abstract: A new approach to multicarrier digital communication over time-varying, frequency selective fading channels is presented. We propose a transmission signal set whose basic structure is similar to standard orthogonal frequency division multiple access (OFDM)-setups, i.e., a system of functions generated by time and frequency-shifted versions of a pulse-like prototype function known as a Weyl-Heisenberg (WH) system. Unlike previous OFDM studies, however, which are restricted to the case of orthonormal pulses, we consider nonorthogonal pulses that are adapted to realistically available a priori knowledge of the channel. Perfect transmultiplexing in the case of an ideal channel is incorporated as a mathematical side-constraint. We derive the expected intersymbol/interchannel interference of such a nonorthogonal FDM (NOFDM) system under the assumption of a wide-sense stationary uncorrelated scattering (WSSUS) channel. Based on this result, we compare OFDM and NOFDM schemes with regard to robustness against delay/Doppler spread.

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388 citations

Cites methods from "Optimal finite duration pulses for ..."

...Reference [ 9 ] recommends the use of time-limited prolate spheroidal wave function which offers minimum bandwidth for a fixed temporal support....
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Journal Article•DOI•

A Survey on Multicarrier Communications: Prototype Filters, Lattice Structures, and Implementation Aspects

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Alphan Sahin¹, Ismail Guvenc², Huseyin Arslan¹•Institutions (2)

University of South Florida¹, Florida International University²

23 Jan 2014-IEEE Communications Surveys and Tutorials

TL;DR: In this article, the authors present a unified review of waveform design options for multicarrier schemes, and pave the way for the evolution of the multic-carrier schemes from the current state of the art to future technologies.

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Abstract: Due to their numerous advantages, communications over multicarrier schemes constitute an appealing approach for broadband wireless systems. Especially, the strong penetration of orthogonal frequency division multiplexing (OFDM) into the communications standards has triggered heavy investigation on multicarrier systems, leading to re-consideration of different approaches as an alternative to OFDM. The goal of the present survey is not only to provide a unified review of waveform design options for multicarrier schemes, but also to pave the way for the evolution of the multicarrier schemes from the current state of the art to future technologies. In particular, a generalized framework on multicarrier schemes is presented, based on what to transmit, i.e., symbols, how to transmit, i.e., filters, and where/when to transmit, i.e., lattice. Capitalizing on this framework, different variations of orthogonal, bi-orthogonal, and non-orthogonal multicarrier schemes are discussed. In addition, filter designs for various multicarrier systems are reviewed considering four different design perspectives: energy concentration, rapid decay, spectrum nulling, and channel/hardware characteristics. Subsequently, evaluation tools which may be used to compare different filters in multicarrier schemes are studied. Finally, multicarrier schemes are evaluated from the perspective of practical implementation aspects, such as lattice adaptation, equalization, synchronization, multiple antennas, and hardware impairments.

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316 citations

Journal Article•DOI•

Optimal OFDM design for time-frequency dispersive channels

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Thomas Strohmer¹, S. Beaver¹•Institutions (1)

University of California, Davis¹

28 Jul 2003-IEEE Transactions on Communications

TL;DR: This work presents a general framework for pulse shape design and shows how to design lattice-OFDM systems (lattice and pulse shape) optimally for time and frequency-dispersive channels in order to minimize the joint ISI/ICI.

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Abstract: Transmission over wireless channels is subject to time dispersion due to multipath propagation and to frequency dispersion due to the Doppler effect. Standard orthogonal frequency-division multiplexing (OFDM) systems, using a guard-time interval or cyclic prefix, combat intersymbol interference (ISI), but provide no protection against interchannel interference (ICI). This drawback has led to the introduction of pulse-shaping OFDM systems. We first present a general framework for pulse shape design. Our analysis shows that certain pulse shapes proposed in the literature are, in fact, optimal in a well-defined sense. Furthermore, our approach provides a simple way to adapt the pulse shape to varying channel conditions. We then show that (pulse-shaping) OFDM systems based on rectangular time-frequency lattices are not optimal for time- and frequency-dispersive wireless channels. This motivates the introduction of lattice-OFDM (LOFDM) systems which are based on general time-frequency lattices. Using results from sphere packing theory, we show how to design LOFDM systems (lattice and pulse shape) optimally for timeand frequency-dispersive channels in order to minimize the joint ISI/ICI. Our theoretical analysis is confirmed by numerical simulations, showing that LOFDM systems outperform traditional pulse-shaping OFDM systems with respect to robustness against ISI/ICI.

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306 citations

Cites background or methods from "Optimal finite duration pulses for ..."

...Some of the proposed pulse shape design methods, however, involve the solution of highly nonlinear optimization problems [ 6 ], [7]....
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...Following other work on pulse-shaping OFDM [ 6 ]‐[8], [10], [23], we consider transmission systems with spectral efficiency (in practice, a higher spectral...
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...3 Alternatively, we can use a slightly different modulation scheme, known as OQAM-OFDM, see [ 6 ]....
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Posted Content•

A Survey on Multicarrier Communications: Prototype Filters, Lattice Structures, and Implementation Aspects

[...]

Alphan Sahin¹, Ismail Guvenc², Huseyin Arslan¹•Institutions (2)

University of South Florida¹, Florida International University²

14 Dec 2012-arXiv: Information Theory

TL;DR: The goal of the present survey is to provide a unified review of waveform design options for multicarrier schemes to pave the way for the evolution of the multicarriers schemes from the current state of the art to future technologies.

...read moreread less

Abstract: Due to their numerous advantages, communications over multicarrier schemes constitute an appealing approach for broadband wireless systems. Especially, the strong penetration of orthogonal frequency division multiplexing (OFDM) into the communications standards has triggered heavy investigation on multicarrier systems, leading to re-consideration of different approaches as an alternative to OFDM. The goal of the present survey is not only to provide a unified review of waveform design options for multicarrier schemes, but also to pave the way for the evolution of the multicarrier schemes from the current state of the art to future technologies. In particular, a generalized framework on multicarrier schemes is presented, based on what to transmit, i.e., symbols, how to transmit, i.e., filters, and where/when to transmit, i.e., lattice. Capitalizing on this framework, different variations of orthogonal, bi-orthogonal, and nonorthogonal multicarrier schemes are discussed. In addition, filter design for various multicarrier systems is reviewed considering four different design perspectives: energy concentration, rapid decay, spectrum nulling, and channel/hardware characteristics. Subsequently, evaluation tools which may be used to compare different filters in multicarrier schemes are studied. Finally, multicarrier schemes are evaluated from the view of the practical implementation issues, such as lattice adaptation, equalization, synchronization, multiple antennas, and hardware impairments.

...read moreread less

291 citations

Cites methods from "Optimal finite duration pulses for ..."

...0 0.5 1 1.5 2 2.5 3 3.5 4 −160 −140 −120 −100 −80 −60 −40 −20 0 f/F 10 lo g 1 0 (| P (f )| 2 ) Gaussian IOTA Hermite Prolate (K = 4) OFDP (K = 4) Kaiser (β = 10) (b) Energy distribution in frequency....
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...In this context, a basic single-tap equalization per subcarrier may be employed to recover the symbols [16], [21], [22], [74], [92]–[94]....
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...It is shown that these coefficients can be computed (for finite number of coefficientsbk,j) as dk,ρ,υ0 = jk∑ j=0 bk,je −(πρ/2ν2 0 )(2j+k) , 0 ≤ k ≤ K , (16) 0 0.5 1 1.5 2 2.5 3 3.5 4 −160 −140 −120 −100 −80 −60 −40 −20 0 10 lo g 1 0 |p (t )| 2 t/T Gaussian IOTA Hermite Prolate (K = 4) OFDP (K = 4) Kaiser (β = 10) (a) Energy distribution in time....
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...Equalization [52], [54], [55], [61], [106]–[108], [110], [112]– [115], [121] [167] [39], [40], [45], [46], [50], [51], [106], [107], [109], [110], [113]–[115], [123] [108], [111], [112], [121], [157], [168] [134], [165] [51], [106] [16], [21], [22], [93], [94] [74] [47]...
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...Considering this fact, Vahlin exploits PSWFs to realize a new family which is referred as optimal finite duration pulse (OFDP) [74] by generalizing the optimization procedure given for single carrier, presented in [73]....
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References

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Open Access

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Journal Article•DOI•

Multicarrier modulation for data transmission: an idea whose time has come

[...]

J.A.C. Bingham

01 May 1990-IEEE Communications Magazine

TL;DR: The general technique of parallel transmission on many carriers, called multicarrier modulation (MCM), is explained, and the performance that can be achieved on an undistorted channel and algorithms for achieving that performance are discussed.

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Abstract: The general technique of parallel transmission on many carriers, called multicarrier modulation (MCM), is explained. The performance that can be achieved on an undistorted channel and algorithms for achieving that performance are discussed. Ways of dealing with channel impairments and of improving the performance through coding are described, and implementation methods are considered. Duplex operation of MCM and the possible use of this on the general switched telephone network are examined. >

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3,995 citations

Journal Article•DOI•

Prolate spheroidal wave functions, fourier analysis and uncertainty — II

[...]

David Slepian, H. O. Pollak

01 Jan 1961-Bell System Technical Journal

TL;DR: In this paper, the authors apply the theory developed in the preceding paper to a number of questions about timelimited and bandlimited signals, and find the signals which do the best job of simultaneous time and frequency concentration.

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Abstract: The theory developed in the preceding paper1 is applied to a number of questions about timelimited and bandlimited signals. In particular, if a finite-energy signal is given, the possible proportions of its energy in a finite time interval and a finite frequency band are found, as well as the signals which do the best job of simultaneous time and frequency concentration.

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2,498 citations

Journal Article•DOI•

Synthesis of band-limited orthogonal signals for multichannel data transmission

[...]

Robert W. Chang

01 Dec 1966-Bell System Technical Journal

TL;DR: A principle of orthogonal multiplexing for transmitting a number of data messages simultaneously through a linear band-limited transmission medium at a maximum data rate without interchannel and intersymbol interferences is presented.

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Abstract: This paper presents a principle of orthogonal multiplexing for transmitting a number of data messages simultaneously through a linear band-limited transmission medium at a maximum data rate without interchannel and intersymbol interferences. A general method is given for synthesizing an infinite number of classes of band-limited orthogonal time functions in a limited frequency band. Stated in practical terms, the method permits the synthesis of a large class of practical transmitting filter characteristics for an arbitrarily given amplitude characteristic of the transmission medium. Rectangular-shaped ideal filters are not required. The synthesis procedure is convenient. Furthermore, the amplitude and the phase characteristics of the transmitting filters can be synthesized independently. Adaptive correlation reception can be used for data processing, since the received signals remain orthogonal no matter what the phase distortion is in the transmission medium. The system provides the same signal distance protection against channel noises as if the signals of each channel were transmitted through an independent medium and intersymbol interference in each channel were eliminated by reducing data rate.

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1,340 citations

Journal Article•DOI•

Performance of an Efficient Parallel Data Transmission System

[...]

B. Saltzberg¹•Institutions (1)

Bell Labs¹

01 Dec 1967-IEEE Transactions on Communications

TL;DR: A parallel quadrature AM data transmission system with a number of overlapping channels, each carrying a signaling rateb, spacedb/2apart in frequency appears to be a promising technique for achieving good performance at high information rates over bandlimited dispersive transmission media.

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Abstract: 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.

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972 citations

"Optimal finite duration pulses for ..." refers background or methods in this paper

...which corresponds to the integral equation ( 9 )....
[...]
...As h(t) is assumed even, coefficients a, are zero for odd z. Substituting the series expansion (10) in ( 9 ), using only even indices, the condition for h(t) becomes...
[...]
...equations, defined by (16) and (17), gives the coefficients a, in the series expansion of an h(t) which satisfies equations ( 9 ) and (6)....
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...Orthogonality conditions for this category were presented in [SI and an application with offset QAM (OQAM) can be found in [ 9 ]....
[...]
...As the integral operator on the left-hand side of ( 9 ) is compact and self adjoint, there exists a complete set of orthogonal eigenfunctions &(t), which are known as prolate spheroidal wave functions (PSWF’s), and corresponding distinct eigenvalues y; [12]....
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