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.

-In this paper we consider transmission over MIMO channels with channel state information available at the transmitter. This enables the use of precoding as well as an optimization of rate and power distribution over the parallel subchannels in the transmission system (loading). We show that spatial loading provides substantial gains and give a revised version of the V-BLAST algorithm to calculate the matrix filters required for precoding or decision feedback equalization in systems with loading.Keywords: V-BLAST, Tomlinson-Harashima precoding, loading, MIMO-DFE, equalization, MIMO channels I. INTRODUCTION Since the recent results of Foschini and Gans [1], multiple-input multiple-output (MIMO) systems have received considerable attention. In particular, systems that employ multiple transmit and receive antennas have been extensively studied, since it was shown that the spectral efficiency of such systems can in principle grow linearly with the minimum of the number of transmit antennas and the number of receive antennas. Especially popular are so-called BLAST systems, that make use of a special detection scheme. Here we consider uncoded transmission only, hence we concentrate on the V-BLAST variant of the algorithm [2].Moreover, our interest is in such systems where, in addition to the usual assumptions, channel state information (CSI) is available at the transmitter, as well. This is naturally the case for time-division duplex systems (provided the "ping-pong" time is small relative to the fading coherence time), otherwise it can be accomplished via some backward channel. Having CSI available at the transmitter, techniques such as preequalization [3], [4] and loading [5], [6], i.e., an adaption of the transmit signal to the current channel characteristic, can be applied.After introducing the channel model considered, we discuss the concept of MIMO precoding. Following a short discussion of loading options, we give a revised version of the V-BLAST algorithm to calculate the matrix filters used in the precoding structure and conclude with some simulation results and a discussion of possible applications.

In this paper we consider transmission over MIMO channels with channel state information available at the transmitter. This enables an optimization of the rate and power distribution over the parallel subchannels in the transmission system (loading). We show that spatial loading provides substantial gains and give an algorithm to calculate the matrix filters required for decision feedback equalization (DFE) in systems with loading. Introduction-We study the transmission over MIMO channels, described in the discrete time equivalent complex baseband model by = ¡ £ ¢ + ¤. For simplicity we assume an equal number of K transmit and receive antennas. The matrix