It has been widely shown that the Sphere Decoding can be used to find the Maximum Likelihood (ML) solution with an expected complexity that is roughly cubic in the dimensions of the problem. However, the computational complexity becomes prohibitive if the Signal-to-Noise Ratio is too low and/or if the dimension of the problem is too large. That is why another technique denoted as Fixed-complexity Sphere Decoder (FSD) is an interesting approach. This algorithm needs a preprocessing step, and in this paper the QR-Decomposition-based preprocessing technique, which is not inconsequential, will be studied. Two different techniques are exposed, including the classical Gram Schmidt orthonormalization process. Their computational complexities and their impacts on the FSD computational complexity are studied. In the LTE context, the overall computational complexities of the two detection techniques are quantified and are shown to be dependent on the constellation size.