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Abstract-In this paper, Tomlinson-Harashima precoding for multiple-input/multiple-output systems including multiple-antenna and multi-user systems is studied. It is shown that nonlinear preequalization offers significant advantages over linear preequalization which increases average transmit power. Moreover, it outperforms decision-feedback equalization at the receiver side which is applicable if joint processing at the receiver side is possible, and which suffers from error propagation. A number of aspects of practical importance are studied. Loading, i.e., the optimum distribution of transmit power and rate is discussed in detail. It is shown that the capacity of the underlying MIMO channel can be utilized asymptotically by means of non-linear precoding.

A new loading algorithm for discrete multitone transmission is proposed. Thereby rate is not distributed according to channel capacity, but rate and transmit power are assigned to maximize the signal-to-noise ratio in each carrier. Because closed form expressions can be derived the algorithm is of very low complexity, even lower than the loading algorithm recently proposed by Chow et al. [ 3 ] . Nevertheless achievable performance is higher or at least the same. Results for a typical high rate transmission over twisted pair lines are presented.

-We consider the lattice-reduction-aided detection scheme for 2×2 channels recently proposed by Yao and Wornell [11]. Using an equivalent real-valued substitute MIMO channel model their lattice reduction algorithm can be replaced by the well-known LLL algorithm, which enables the application to MIMO systems with arbitrary numbers of dimensions. We show how lattice reduction can also be favourably applied in systems that use precoding and give simulation results that underline the usefulness of this approach. I. INTRODUCTIONIn a recent publication by Yao and Wornell [11] a novel scheme for improved detection of signals transmitted over multiple-input/multiple-output (MIMO) systems was presented. The astonishing property of this scheme is that it results in error rate curves that parallel those for maximumlikelihood (ML) detection (with some penalty in power efficiency), at only a fraction of the complexity.In the present work we show how their approach fits in the general (maximum-likelihood) lattice decoding framework of [1] and extend the work of [11], which presented an optimum algorithm for 2 × 2 complex MIMO systems based on Gaussian reduction [3], to higher-dimensional settings. The key point is the application of the (sub-optimum) basis reduction algorithm by A. K. Lenstra, H. W. Lenstra and L. Lovász ("LLL algorithm",[9]). Note that this algorithm has also been used in connection with efficient near-ML decoding of differential space-time codes in [2]. Furthermore, we will show how this approach can be applied in precoding/preequalization schemes.

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Resonance Raman spectroscopy/microscopy was used to study individualized single-walled carbon nanotubes (SWNTs) both in aqueous suspensions as well as after spin-coating onto Si/SiO2 surfaces. Four different SWNT materials containing nanotubes with diameters ranging from 0.7 to 1.6 nm were used. Comparison with Raman data obtained for suspensions shows that the surface does not dramatically affect the electronic properties of the deposited tubes. Raman features observed for deposited SWNTs are similar to what was measured for nanotubes directly fabricated on surfaces using chemical vapor deposition (CVD) methods. In particular, individual semiconducting tubes could be distinguished from metallic tubes by their different G-mode line shapes. It could also be shown that the high-power, short-time sonication used to generate individualized SWNT suspensions does not induce defects in great quantities. However, (additional) defects can be generated by laser irradiation of deposited SWNTs in air, thus giving rise to an increase of the D-mode intensity for even quite low power densities (approximately 10(4) W/cm2).