Sebastian Stern

Lattice-reduction-aided preequalization over algebraic signal constellations

Lattice-reduction-aided (LRA) equalization techniques have become very popular in multiple-input/multiple-output (MIMO) multiuser communication as they obtain the full diversity order of the MIMO channel. For joint transmitter-side LRA preequalization or precoding on the broadcast channel, the signal constellation is required to be periodically extendable, which is typically achieved by employing square QAM constellations. However, recent enhancements of the LRA philosophy- named integer-forcing equalization-additionally demand the data symbols to be representable as elements of a finite field over the grid the signal points are drawn from. This significantly constraints the choice of the constellation, especially when considering the complex baseband and complex-valued constellations. To overcome the lack of flexibility, in this paper, we present constellations with algebraic properties for use in LRA preequalization directly enabling the desired finite-field property. In particular, fields of Gaussian primes (integer lattice) and Eisenstein primes (hexagonal lattice) are studied and compared to conventional constellations. The respective transmitter- and receiver-side operations are detailed and the adaptation of the channel matrix factorization is proposed. Numerical simulations cover the performance of such schemes.

Efficient assessment of the instantaneous power distributions of pulse-shaped single- and multi-carrier signals

We present a new approach for assessing the instantaneous power distributions of the continuous-time transmit signal (i.e., after pulse shaping) in single- and multi-carrier transmission schemes. On the one hand, an efficient calculation of the distribution for single-carrier signals via the fast Fourier transform (FFT) is given. On the other hand, tight approximations for multi-carrier transmission based on orthogonal frequency-division multiplexing (OFDM) are reviewed. Thereby, the effect of non-modulated carriers (guard bands) is taken into account. The impact of the roll-off factor of root-raised-cosine pulse shaping is analyzed and its converse influence on the peak-to-average power behavior of both modulation strategies is discussed. All theoretical derivations match very well with numerical results obtained from Monte-Carlo simulations.

Advanced factorization strategies for lattice-reduction-aided preequalization

Lattice-reduction-aided preequalization (LRA PE) is a powerful technique for interference handling on the multi-user multiple-input/multiple-output (MIMO) broadcast channel. However, recent advantages in the strongly related field of compute-and-forward and integer-forcing equalization have raised the question, if the factorization task present in LRA PE is really solved in an optimum way. In this paper, advanced factorization strategies are presented, significantly increasing the transmission performance. Specifically, the signal constellation and its related lattice as well as the factorization task/strategy are discussed. The impact of dropping the common unimodularity constraint in LRA PE is studied. Numerical simulations are given to show the effectiveness of all presented strategies.

Space-time codes based on rank-metric codes and their decoding.

In this paper, a new class of space-time block codes is proposed. The new construction is based on finite-field rank-metric codes in combination with a rank-metric-preserving mapping to the set of Eisenstein integers. It is shown that these codes achieve maximum diversity order and improve upon existing constructions. Moreover, a new decoding algorithm for these codes is presented, utilizing the algebraic structure of the underlying finite-field rank-metric codes and employing lattice-reduction-aided equalization. This decoder does not achieve the same performance as the classical maximum-likelihood decoding methods, but has polynomial complexity in the matrix dimension, making it usable for large field sizes and numbers of antennas.

V-BLAST in lattice reduction and integer forcing

Lattice-reduction-aided decision-feedback equalization (LRA DFE) and successive integer forcing are MIMO detection schemes which combine the equalization in a suited basis with the principle of successive interference cancellation (SIC). To this end, the reduction algorithm not only has to find a suited basis, but it should also provide an optimized detection order for SIC: the V-BLAST ordering, known to be optimal for conventional DFE. How these two tasks can be solved jointly has so far remained unclear in the literature. In this paper, we describe how the Lenstra-Lenstra-Lovász (LLL) reduction has to be adapted to achieve this aim. Moreover, we propose a weakened variant of the Hermite-Korkine-Zolotareff (HKZ) reduction that optimally solves both tasks jointly. Results obtained from numerical simulations complement the theoretical derivations.

Modulo-Type Precoding for Networks

In this chapter, we address scenarios where the tasks of (modulo-type) precoding for the multiple-input/multiple-output (MIMO) broadcast channel, network coding with its associated finite-field matrix channel, and channel coding meet or complement each other. By enlightening dualities, similarities, and differences between the areas and corresponding schemes, a deeper understanding of their mutual interaction is gained. Moreover, this allows for a transfer of schemes and strategies from one field to another one. Exemplarily, schemes operating at the intersection of complex-valued and finite-field/modulo processing are addressed. First, an overview on modulo-type precoding and its latest version via finite-field preprocessing is given; the connections and specific restrictions of the different approaches are illustrated. The advantages of modulo-type precoding are addressed when additional requirements, such as per-antenna power constraints and a reduced degree of coordination in a network MIMO scenario, are imposed. Finally, the application of precoding to finite-field channels is discussed, either as differential network coding or as selection precoding.