Extended LLL algorithm for efficient signal precoding in multiuser communication systems

The lattice reduction method proposed by Lenstra, Lenstra and Lovasz (LLL algorithm) is extensively employed to perform precoding in multiuser downlink communications and also to improve suboptimal detectors in MIMO point-to-point systems. Existing implementations of this algorithm provide as an output a matrix that contains the transformations to be done over the initial channel matrix in order to get a transformed matrix with less correlated columns. However, there are some specific applications where the inverse of this transformation matrix is also required, and this must be calculated after the LLL algorithm. In this work we propose an efficient way to calculate the inverse of the transformation matrix inside the LLL algorithm to avoid the necessity of a matrix inversion, reducing in this way the computational cost.