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.

-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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Absfracr-In this paper, Tomlinson-Harashima precoding, a nonlinear pre-equalization technique, is proposed for transmission over multiple-input/multiple-output channels. Instead of equalizing intersymbol interference (temporal equalization) here spatial equalization, i.e., equalization of multi-user interference is performed. If only a low-rate backward channel is available for communicating channel state information back from the receiver to the transmitter, a compromise precoder setting, calculated from (medium-term) average channel knowledge in combination with linear residual equalization at the receiver side is proposed. Compared to an optimal adjustment of the precoder, Le., perfect channel state information at the transmitter, only small losses have to be accepted.

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