Theoretical results for fast determination of the number of antennas in MIMO transmission systems

Multi-Input Multi-Output transmission has been a topic of great interest for the last few years due to the huge spectral efficiency gain it can provide over rich scattering transmission channels, such as indoor (for wireless local area networks) or urban outdoor (for mobile wireless communications). However, since each additional antenna has a cost and requires additional circuits for processing, one of the first question people in charge of realizing actual systems (and not only simulations) usually ask is: what is the required number of antennas? In this paper, we use random matrices theory to derive a theoretical approximation of the error rate with respect to the number of antennas. Thanks to this result, long simulations can be avoided and the required number of antennas can be easily determined.