Linear precoding for improving the performance of a point-to-point multiple-input multiple-output (MIMO) system has been studied intensively during the last four decades. In practical applications, the symbols to be transmitted are taken from a discrete alphabet, such as quadrature amplitude modulation (QAM), and it is of interest to find the optimal linear precoder for a certain performance measure of the MIMO channel. This thesis studies the design of linear precoders for non-singular MIMO channels with additive white Gaussian noise and lattice-type inputs, namely the transmitted symbols are crafted from a lattice....[ Read more ]

Linear precoding for improving the performance of a point-to-point multiple-input multiple-output (MIMO) system has been studied intensively during the last four decades. In practical applications, the symbols to be transmitted are taken from a discrete alphabet, such as quadrature amplitude modulation (QAM), and it is of interest to find the optimal linear precoder for a certain performance measure of the MIMO channel. This thesis studies the design of linear precoders for non-singular MIMO channels with additive white Gaussian noise and lattice-type inputs, namely the transmitted symbols are crafted from a lattice.

The objective is to find a precoder that maximizes the minimum distance of the received lattice points, subject to an average energy constraint. It is shown that the optimal precoder only produces a finite number of different lattices, namely perfect lattices, at the receiver. The well-known densest lattice packings are instances of perfect lattices, however it is analytically shown that the densest lattices are not always the solution. This is a counter-intuitive result at first sight, since previous work in the area showed a tight connection between densest lattices and minimum distance. Since there are only finitely many different perfect lattices for a given dimension, they can theoretically be enumerated off-line. A new upper bound on the optimal minimum distance is derived, which significantly improves upon a previously reported bound. Based on this bound, we propose an enumeration algorithm that produces a finite codebook of optimal precoders.

Finally the theoretical results are applied to the finite alphabet case to construct precoders and improved upon them by adding lower rank perfect lattices into the list of finite codebook. Simulation results show that our proposed precoders perform extremely close to the optimal and outperform all previous competing schemes.