This proyect is based on the study of the massive MIMO channel properties, in particular, we have been studying the orthogonality and the capacity of the channel in order to have a better performance when we want to decode the message received. The main reason why we want to study the performance of the orthogonality is because if we are facing an orthogonal channel we get an easier decodification of the receiving signal due to the reduction of the signal processing complexity. In order to achieve that study, we have used the algebraic properties of the orthogonality defect of the channel matrix, this orthogonality defect is based on the properties of the norm of a matrix. As we can check along the proyect, the orthogonality defect is getting better when the number of users is larger. On the other hand, if the number of antennas in the system is bigger the orthogonality defect is worse, this is because the more antennas the system has the more interaction between signals is obtained. The other study performed is the capacity as a result of its evolution with MIMO. The measurement of the capacity system can vary depending on the knowledge of the channel state we have. If we do not know the channel state we can set an stochastic aproximation of it, whereas if we know it, we can get a better performance of the capacity as long as the pilot used for knowing the channel state is not infected. According to the capacity study, we have been measuring it once the received signal is decoded, in other words, when the filter of the receiver has been applied, and without any knowledge about the channel state. As we will follow in this proyect, the capacity is directly proportional to the number of antennas, as well as to the number of users.