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.

A statistical model for crosstalk in twisted pair cables is presented, where all individual pair combinations in the cable are modeled separately. The model is realistic because all parameters are based on measurements, and an extensive set of crosstalk measurements will be necessary in order to describe all relevant pair combinations. The model is well suited for simulations of crosstalk, and Monte Carlo simulations in particular. In this paper, the model has been used to calculate the performance for partial crosstalk cancellation in one particular 10-pair cable. The results show that 10 dB crosstalk reduction may be obtained by canceling the approximately 50% of the disturbers both for far end and near end crosstalk.

Simulation of Crosstalk in Twisted Pair Cables

An MMSE per channel fractionally spaced equalizer is developed for an OFDM/OQAM system with a time varying channel, under the assumption of perfect channel knowledge at the receiver. The equalizer is analyzed for an example with a doubly dispersive channel with Jakes Doppler spectrum and an exponential delay profile, and where the transmitter and receiver filters are square root of cosine rolloff. The performance is measured in terms of ergodic channel capacity, which will be an upper bound for the throughput of the system, assuming perfect channel estimation and ideal channel coding. The results show that the channel capacity may be significantly increased by using an equalizer of finite length, instead of a one-tap equalizer. The channel capacity is for instance increased by 60 % for E s /N 0 = 20 dB in a channel with spreading factor 0.01.

MMSE equalization of OFDM/OQAM systems for channels with time and frequency dispersion

New blind carrier frequency offset (CFO) estimation methods based on the correlation function of the subchannel signals are presented for OFDM/OQAM systems The proposed estimators are robust to multipath effects due to the narrowband property of the subchannels in OFDM systems 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 method based on the signal before demodulation

SPC08-4: Blind Carrier Frequency Offset Estimation for OFDM/OQAM Systems Based on Subchannel Signals

This work presents a new and more accurate crosstalk model that is used for calculating the probability distributions of crosstalk power sum for M randomly selected pairs in an N-pair twisted pair cable. The calculation is based on averaged measurements of crosstalk in each individual pair combination. Probability distributions are calculated both for near end crosstalk (NEXT) and far end crosstalk (FEXT) in one specific type of commonly used cable that contains one 10-pair binder group. The results for the 10-pair cable show the same type of variation for the 99% point of crosstalk power sum as in the standard model used for DSL systems, which is based on 50-pair binder groups. However, the parameters are different for the two cases. For the 10-pair cable, there is a smaller variation in crosstalk as a function of the active number of pairs. The results for FEXT in a 10-pair group are in close correspondence with the standard model, while the level of NEXT is 1 2.5 dB weaker in the 10-pair group than in the standard model.

An analytical model for the probability distributions of crosstalk power sum for a subset of pairs in a twisted pair cable

The high sensitivity to carrier frequency offset of OFDM systems compared to single carrier systems is well known. In this paper we study how this can be remedied for OFDM/OQAM systems by appropriate pulse shaping. Building on earlier methods for minimizing out-of-band energy, a procedure for pulse shape design is derived. The new pulses are optimal with respect to interference in OFDM/OQAM systems. It is also demonstrated that, in this respect, OFDM/OQAM outperforms OFDM/QAM systems using rectangular pulses.

N. Holte

Papers

Simulation of Crosstalk in Twisted Pair Cables

MMSE equalization of OFDM/OQAM systems for channels with time and frequency dispersion

SPC08-4: Blind Carrier Frequency Offset Estimation for OFDM/OQAM Systems Based on Subchannel Signals

An analytical model for the probability distributions of crosstalk power sum for a subset of pairs in a twisted pair cable

Design of robust pulses to carrier frequency offset for OFDM/OQAM system