irectly, rather than for individual users. An important difference between the multi-user MIMO channel and the interference channels for which dirty paper techniques are designed is that the interference depends on the signal being designed. Block Diagonalization (BD) is a linear precoding technique for the downlink of MU-MIMO systems. It decomposes a MU-MIMO downlink channel into multiple parallel orthogonal single-user MIMO channels. The signal of each user is pre-processed at the transmitter using a modulation matrix that lies in the null space of all other users' channel matrices; thereby the multi-user interference in the system is effectively zero. Block diagonalization is restricted to channels where the number of transmit antennas N is greater or equal to the total number of receive antennas in the network Nr. Let's define precoder matrices FNu]ECN,XN, where CN,xNsi precoder matrix. We assume that Ns < N is the total number of the transmitted data streams, while Nsi Nri is the number of data streams transmitted to the ith user. We can find the optimal precoding matrix F such that multi-user interference is zero by choosing a precoding matrix Fi that lies in the null space of the other users' channel matrices. Thereby, a MU-MIMO downlink channel is decomposed into multiple parallel independent SU-MIMO channels. Minimum mean square error beamforming improves the system performance by allowing a certain amount of interference, especially for users equipped with a single antenna. However, it suffers from performance loss when it attempts to mitigate the interference between two closely-spaced antennas, a situation that usually occurs when the user terminal is equipped with more than one receive antenna. An improved version of this algorithm known as Successive MMSE (SMMSE) was developed to mitigate this problem by successively calculating the columns of the precoding matrix for each of the receive antennas separately. Linear equalization suffers from noise enhancement and hence has poor power efficiency in so