Lattice-Reduction for Power Optimisation Using the Fast Least-Squares Solution-Seeker Algorithm

The power constraint factor in precoding methods plays an important role in the reduction of SER at the receiver. The value of this scaling factor lies in the individual power assigned to the transmit symbols prior the transmission. Such assignment will depend entirely on the matrix condition of the channel, in this case the eigenvalue´s power of the channel inverse. Thus, the minimisation of this power constraint will rely on closing the power gap among the transmit symbols, and one solution is to use an auxiliary vector for fixing the matrix condition. This is equivalent to solving the integer least-squares problem. For achieving this specific goal there are two effective choices: the lattice-reduction, whose objective is to reduce the basis of any given matrix, and the sphere techniques which enumerate all the lattice points inside a sphere centered at the query point. Both choices aim for finding or fitting an approximated least-squares solution occasioning astonishing results in performance when minimising the scaling factor prior to transmit.