In recent years single carrier modulation (SCM) has again become an interesting and complementary alternative to multicarrier modulations such as orthogonal frequency division multiplexing (OFDM). This has been largely due to the use of nonlinear equalizer structures implemented in part in the frequency domain by means of fast Fourier transforms, bringing the complexity close to that of OFDM. Here a nonlinear equalizer is formed with a linear filter to remove part of intersymbol interference, followed by a canceler of remaining interference by using previous detected data. Moreover, the capacity of SCM is similar to that of OFDM in highly dispersive channels only if a nonlinear equalizer is adopted at the receiver. Indeed, the study of efficient nonlinear frequency domain equalization techniques has further pushed the adoption of SCM in various standards. This tutorial paper aims at providing an overview of nonlinear equalization methods as a key ingredient in receivers of SCM for wideband transmission. We review both hybrid (with filters implemented both in time and frequency domain) and all-frequency-domain iterative structures. Application of nonlinear frequency domain equalizers to a multiple input multiple output scenario is also investigated, with a comparison of two architectures for interference reduction. We also present methods for channel estimation and alternatives for pilot insertion. The impact on SCM transmission of impairments such as phase noise, frequency offset and saturation due to high power amplifiers is also assessed. The comparison among the considered frequency domain equalization techniques is based both on complexity and performance, in terms of bit error rate or throughput.

Error-propagation phenomena and computational complexity of the filters' design are important drawbacks of existing decision-feedback equalizers (DFE) for dispersive channels. In this paper, we propose a new iterative block DFE (IBDFE) which operates iteratively on blocks of the received signal. Indeed, a suitable data-transmission format must be used to allow an efficient implementation of the equalizer in the frequency domain, by means of the discrete Fourier transform. Two design methods are considered. In the first method, hard detected data are used as input of the feedback, and filters are designed according to the correlation between detected and transmitted data. In the second method, the feedback signal is directly designed from soft detection of the equalized signal at the previous iteration. Estimators of the parameters involved in the IBDFE design are also derived. From performance simulations on a wireless dispersive fading channel, we observed that the IBDFE outperforms existing DFEs. Moreover, the IBDFE exhibits a reduction of the computational complexity when compared against existing schemes, both in signal processing and in filter design.

An iterative block decision feedback equaliser (IB-DFE) for single carrier modulation is proposed. Filtering operations are implemented by discrete Fourier transforms (DFTs) which yield a reduced computational complexity, for both filter design and signal processing, when compared to existing DFEs. Moreover, the new IB-DFE operates on blocks of the receive signal, thus allowing the use of error correction codes on the feedback data signal.

In a wide band and multipath rich environment, precise channel estimation allows authenticating the source and protecting the integrity of a message at the physical layer without the need of a pre-shared secret key. This allows also a reduction of the burden on the authentication protocols at higher layers. In this paper we develop an authentication scheme in the framework of hypothesis testing that suits a multiple wiretap channels environment with correlated fading, as is the case of multiple input multiple output (MIMO) systems and/or orthogonal frequency division multiplexing (OFDM) modulation. By allowing some degree of correlation among the channels, we formulate the optimal attack strategy for the cases of both single attempt and multiple repeated trials. For the latter scenario, due to the complexity of the optimal solution, we also develop a simpler suboptimal attack strategy. The performance of the proposed methods is evaluated in a MIMO/OFDM scenario and numerical results show the merits of the proposed approaches that can be adopted as a layer one authentication mechanism.

In mobile reception, the reliability of orthogonal frequency division multiplexing (OFDM) is limited because of the time-varying nature of the channel. This causes intercarrier interference (ICI) and increases inaccuracies in channel tracking. We model the ICI using derivatives of the channel amplitude. This allows us to design a relatively simple receiver scheme that iteratively cancels the ICI. The design of the canceler aims at maximizing the signal-to-noise-plus-ICI ratio at the detector input. We also propose a new channel estimator, and we show that it achieves reliable mobile reception in practical situations that are relevant to terrestrial Digital Video Broadcasting (DVB-T). Extensive simulations for a receiver with one or two antennas show that a small number of iterations between ICI cancellation and channel estimation allow a reliable reception at vehicle speeds above 100 km/h.