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Advanced equalization and coded-modulation strategies for multiple-input/multiple-output (MIMO) communication are considered. The focus is on techniques that are suited for the application in multiuser MIMO uplink transmission (MIMO multiple-access channel) or multiuser MIMO downlink transmission (MIMO broadcast channel). This particularly includes lattice-reduction-aided (LRA) schemes which have become popular in recent years. In LRA schemes, the MIMO channel matrix is factorized into two parts: a unimodular integer matrix and a residual non-integer matrix. Given that factorization, only the non-integer part is conventionally equalized, either by means of linear equalization or the application of the principle of successive interference cancellation (SIC). In contrast to that, the integer interference can be resolved without any performance-harming noise enhancement. From a mathematical point of view, the integer matrix describes a change to a more suited basis for channel equalization. Consequently, the channel factorization can be obtained by well-known lattice-basis-reduction algorithms, e.g., the Lenstra–Lenstra–Lovász (LLL) algorithm. However, concentrating on the treatment of the multiuser MIMO interference, LRA schemes have most often been treated uncoded, i.e., neglecting the combination with a convenient coded-modulation approach. This situation has changed with the concept of integer-forcing (IF) equalization. In IF schemes, the channel matrix is factorized, too. Nevertheless, the integer interference is resolved over the finite field of the channel code—creating a close coupling between channel equalization and coded modulation. For the finite-field integer matrix, the unimodularity constraint as present in LRA schemes can be relaxed to a full-rank constraint. This not only brings up the question if, in classical LRA schemes, the unimodularity constraint is really necessary, but also if the LRA techniques have really been operated in an optimum or at least in a close-to-optimum way. Hence, in this thesis, strategies and approaches are identified that enable a performance gain over the state-of-the-art application of LRA receiver- or transmitter-side equalization. First, this involves the choice of the signal constellation. In particular, constellations over the Eisenstein integers—the hexagonal lattice over the complex plane—are studied. These signal constellations as well as conventional quadrature amplitude modulation (QAM) ones are combined with coded-modulation schemes that are suited for the application in multiuser MIMO communications using binary or non-binary low-density parity-check (LDPC) codes. Moreover, criteria and algorithms for lattice basis reduction are reviewed and extended for lattices over Eisenstein integers. These considerations also include the abovementioned relaxation to full-rank integer matrices, which is specifically known as successive minima problem. A recapitulation of conventional linear and SIC-based equalization schemes is provided, where the famous V-BLAST detection strategy is regarded from the perspective of lattice theory. Following this, optimum or close-to-optimum channel factorization strategies and related algorithms are worked out for LRA transmitter- and receiver-side schemes. It is shown that the classical unimodularity constraint can indeed be relaxed—generalizing the “lattice-reduction-aided” to “lattice-aided” (LA) schemes. The combination of these LA approaches with coded-modulation strategies is studied and the differences to the corresponding IF schemes are clarified; a discussion on the convenience of both philosophies in multiuser MIMO uplink and downlink transmission is given. The theoretical derivations in this thesis are supported by results obtained from Monte-Carlo simulations. This particularly includes the evaluation of the transmission performance if binary source symbols are transmitted.

Advanced equalization and coded-modulation strategies for multiple-input/multiple-output (MIMO) communication are considered. The focus is on techniques that are suited for the application in multiuser MIMO uplink transmission (MIMO multiple-access channel) or multiuser MIMO downlink transmission (MIMO broadcast channel). This particularly includes lattice-reduction-aided (LRA) schemes which have become popular in recent years. In LRA schemes, the MIMO channel matrix is factorized into two parts: a unimodular integer matrix and a residual non-integer matrix. Given that factorization, only the non-integer part is conventionally equalized, either by means of linear equalization or the application of the principle of successive interference cancellation (SIC). In contrast to that, the integer interference can be resolved without any performance-harming noise enhancement. From a mathematical point of view, the integer matrix describes a change to a more suited basis for channel equalization. Consequently, the channel factorization can be obtained by well-known lattice-basis-reduction algorithms, e.g., the Lenstra–Lenstra–Lovász (LLL) algorithm. However, concentrating on the treatment of the multiuser MIMO interference, LRA schemes have most often been treated uncoded, i.e., neglecting the combination with a convenient coded-modulation approach. This situation has changed with the concept of integer-forcing (IF) equalization. In IF schemes, the channel matrix is factorized, too. Nevertheless, the integer interference is resolved over the finite field of the channel code—creating a close coupling between channel equalization and coded modulation. For the finite-field integer matrix, the unimodularity constraint as present in LRA schemes can be relaxed to a full-rank constraint. This not only brings up the question if, in classical LRA schemes, the unimodularity constraint is really necessary, but also if the LRA techniques have really been operated in an optimum or at least in a close-to-optimum way. Hence, in this thesis, strategies and approaches are identified that enable a performance gain over the state-of-the-art application of LRA receiver- or transmitter-side equalization. First, this involves the choice of the signal constellation. In particular, constellations over the Eisenstein integers—the hexagonal lattice over the complex plane—are studied. These signal constellations as well as conventional quadrature amplitude modulation (QAM) ones are combined with coded-modulation schemes that are suited for the application in multiuser MIMO communications using binary or non-binary low-density parity-check (LDPC) codes. Moreover, criteria and algorithms for lattice basis reduction are reviewed and extended for lattices over Eisenstein integers. These considerations also include the abovementioned relaxation to full-rank integer matrices, which is specifically known as successive minima problem. A recapitulation of conventional linear and SIC-based equalization schemes is provided, where the famous V-BLAST detection strategy is regarded from the perspective of lattice theory. Following this, optimum or close-to-optimum channel factorization strategies and related algorithms are worked out for LRA transmitter- and receiver-side schemes. It is shown that the classical unimodularity constraint can indeed be relaxed—generalizing the “lattice-reduction-aided” to “lattice-aided” (LA) schemes. The combination of these LA approaches with coded-modulation strategies is studied and the differences to the corresponding IF schemes are clarified; a discussion on the convenience of both philosophies in multiuser MIMO uplink and downlink transmission is given. The theoretical derivations in this thesis are supported by results obtained from Monte-Carlo simulations. This particularly includes the evaluation of the transmission performance if binary source symbols are transmitted.