  Multiple-input multiple-output (MIMO) systems are playing an important role
in the recent wireless communication. The complexity of the different systems
models challenge different researches to get a good complexity to performance
balance. Lattices Reduction Techniques and Lenstra-Lenstra-Lovasz (LLL)
algorithm bring more resources to investigate and can contribute to the
complexity reduction purposes. In this paper, we are looking to modify the LLL
algorithm to reduce the computation operations by exploiting the structure of
the upper triangular matrix without big performance degradation. Basically, the
first columns of the upper triangular matrix contain many zeroes, so the
algorithm will perform several operations with very limited income. We are
presenting a performance and complexity study and our proposal show that we can
gain in term of complexity while the performance results remains almost the
same.
