Several approaches have recently been proposed for the efficient optimum or approximate solution of the detection problem in multiple-input multiple-output transmission systems. These are, however, difficult to compare. In the present work we briefly summarize the most popular and promising of these approaches and offer a way to visualize the tradeoff between complexity of the detection and the achievable power efficiency using "complexity-power diagrams". We conclude that the so-called sphere decoder algorithm is very attractive in terms of average complexity, while for low and constant processing delay lattice reduction with subsequent simple linear or nonlinear detection is more favorable

In multiple-symbol differential detection (MSDD) for power-efficient transmission over Rayleigh fading channels without channel state information, blocks of N received symbols are jointly processed to decide on N-1 data symbols. The search space for the maximum-likelihood (ML) estimate is therefore (complex) (N-1)-dimensional, and maximum-likelihood MSDD (ML-MSDD) quickly becomes computationally intractable as N grows. Mackenthun's low-complexity MSDD algorithm finds the ML estimate only for Rayleigh fading channels that are time-invariant over an N symbol period. For the general time-varying fading case, however, low-complexity ML-MSDD is an unsolved problem. In this letter, we solve this problem by applying sphere decoding (SD) to ML-MSDD for time-varying Rayleigh fading channels. The resulting technique is referred to as multiple-symbol differential sphere decoding (MSDSD).

In multiple-symbol differential detection (MSDD) for power-efficient transmission over fading channels without channel state information, blocks of N received symbols are jointly processed to decide on N - 1 data symbols. The search space for the maximum-likelihood (ML) estimate is therefore (complex) (N - 1)-dimensional, and MSDD quickly becomes computationally intractable as N grows. Sphere decoding (SD) is a widely used approach to find the ML estimate in such high-dimensional spaces. In this paper, we devise the application of SD to accomplish MSDD, and we refer to the resulting technique as multiple-symbol differential sphere decoding (MSDSD). We present an efficient algorithm for MSDSD, whose excellent performance versus complexity trade-off is verified by various simulation results and by comparisons with other, suboptimum approaches known from the literature.

Algorithms for the detection problem in multiple-input multiple-output (MIMO) transmission systems are compared, and the tradeoff between detection complexity and the achieved power-efficiency is visualized using "power-complexity" diagrams.

A precoding scheme for multiuser broadcast communications is described, which fills the gap between the low-complexity Tomlinson-Harashima precoding and the sphere decoder-based system of Peel et al. Simulation results show that, replacing the closest-point search with the Babai approximation, the full diversity order supported by the channel is available to each user, as in the system of Peel et al., and unlike Tomlinson-Harashima precoding, which suffers some diversity penalty. The complexity of the scheme is similar to that of Tomlinson-Harashima precoding.

In this paper, Tomlinson-Harashima Precoding for multiple-input/multiple-output systems including multiple-antenna and multiuser 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 nonlinear precoding.

The paper presents an improved version of precoding, i.e., nonlinear pre-equalization, for situations with one central transmitter (e.g., base station) and a number of distributed receivers (e.g., mobile terminals). The new method is based on Tomlinson-Harashima precoding, applied to multiple-input-multiple-output (MIMO) channels, and inspired by the concept of lattice-reduction-aided detection in MIMO communication systems. We show that, by using the proposed technique, a considerable degree of diversity can be gained over linear pre-equalization, as well as conventional precoding.

In this contribution we study transmission over MIMO channels, where channel state information available at the transmitter enables the use of precoding as weak as an optimization of rate and power distribution over the parallel subchannels in the transmission system (loading). It is shown that spatial loading provides substantial gains and a revised version of the V-BLAST algorithm is given to calculate the matrix filters required for Tomlinson-Harashima precoding, or equivalently decision-feedback equalization.

We consider the lattice-reduction-aided detection scheme for 2/spl times/2 channels recently proposed by H. Yao and G.W. Wornell (see Proc. IEEE Globecom, 2002). By using an equivalent real-valued substitute MIMO channel model, their lattice reduction algorithm can be replaced by the well-known LLL (Lenstra-Lenstra-Lovasz) algorithm (Lenstra, A.K. et al., 1982), which enables the application of the algorithm 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.