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.

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

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.

Nonorthogonal pulseshapes for multicarrier communications in doubly dispersive channels

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.

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

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.

Optimal OFDM design for time-frequency dispersive channels

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.

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.

Optimal finite duration pulses for OFDM

Optimal pulses with minimum ICI power at a given CFO point for OFDM/QAM systems are found analytically. A lower bound of the ICI power is introduced as a measure of the robustness to CFO for a given pulse. Numerical comparison verifies that the optimal pulse is more robust to CFO than previously suggested pulses at the selected CFO point.

Optimal Pulses Robust to Carrier Frequency Offset for OFDM/QAM Systems

This paper treats the problems of digital TV terrestrial broadcasting in presence of co-channel interference from analogue TV services. The channel capacity is calculated for the optimum distribution of the transmitted power. An OFDM scheme is presented which is designed to be robust to the analogue TV interference. Power and number of bits per symbol are assigned to each OFDM channel to give the maximum data rate for a given signal to interference ratio. Simulations of the proposed scheme, for 8 MHz bandwidth and interference from a system G PAL signal, show that acceptable error rate can be achieved for e.g. 27 Mbit/s and 39 Mbit/s at signal to interference ratios of -6 dB and 0 dB, respectively. The proposed scheme is suitable for the next generation terrestrial TV networks which are going to coexist with the current analogue systems. >

OFDM for broadcasting in presence of analogue co-channel interference

Digital block-based predistortion (PD) is an efficient scheme to linearize power amplifiers (PA). The performance of this method highly depends on the estimation accuracy of the amplifier characteristics. In this paper, the PA characteristics are approximated by piecewise continuous polynomials in the form of splines. The approximation is based on a block of observed data at the input and output of the PA. This approach leads to a linear parametric approximation problem with moderate implementation complexity, and it also gives the best possible fit to a given set of observations. With cubic splines it is possible to get a fairly accurate estimate even with a short block of data, and hence a fast convergence of the PD algorithm. The performance of the method has been evaluated for an example selected from an application in mobile satellite communications with burst transmission. We use a model of a 2 Watts class A PA that is based on measurements, and the calculations are performed for 16-QAM modulation. The mean square approximation error, the power spectrum and the error vector magnitude (EVM) of the received signal have been analyzed by simulations. For 6 dB back-off, the adjacent channel power ratio (ACPR) level is reduced by approximately 15 dB relative to a transmitter without predistortion, after an adaptation based on only 25 transmitted symbols.

Digital Predistortion of Power Amplifiers Based on Spline Approximations of the Amplifier Characteristics

Carrier frequency offset (CFO) in OFDM/OQAM systems can be estimated based on the conjugate correlation function of the received signals. Traditionally this is done before demodulation. We present new methods based on the subchannel signals. The proposed estimators are robust to multipath effects due to the narrowband property of the subchannels. The performance of the estimators is evaluated by asymptotic analysis and simulation results. Our results show that methods based on estimation in subchannels have better performance than estimators operating before demodulation.

N. Holte

Papers

Optimal finite duration pulses for OFDM

Optimal Pulses Robust to Carrier Frequency Offset for OFDM/QAM Systems

OFDM for broadcasting in presence of analogue co-channel interference

Digital Predistortion of Power Amplifiers Based on Spline Approximations of the Amplifier Characteristics

New Methods for Blind Fine Estimation of Carrier Frequency Offset in OFDM/OQAM Systems