terference-plus-noise ratio (SINR) for an mMIMO system, characterization of outage probability (OP) using only statis- tical CSI availability at the transmission side, and a design of transmit beamforming weights used in the minimization of the derived expression OP under power loading constraints. The organization after the introduction is as follows. In Section 3.2, we outline a system model of mMIMO, and, in Section 3.3, we characterize the OP of an mMIMO system. In Section 3.4, we derive a transmit beamforming design using a constrained optimization objective whose solution is obtained using an iterative method. In Section 3.5, we authenticate our results using simulation. Finally, in Section 3.6, we summarize our work. 3.2 SYSTEM MODEL We consider a downlink mMIMO scenario adopted from [16] as depicted in Figure 3.1, where BS having N transmit antennas communicate to K user devices having a single antenna element. Herein, N > K is considered as per the mMIMO scheme. Among the total number of users identified as K, we select the Kth user. Next, S is the data symbol which is multiplied with a transmit beam-vector wk of dimensions N x1 at the transmission stage. We assume that Sk is normalized, that is, for Ai. Now, from the aforementioned considerations, we mathematically express the signal received at the kth user as Beamforming Vectors User 1 User 2 User K FIGURE 3.1 Block diagram of downlink multi-user mMIMO system [16]. Beamforming in Massive MIMO Communications (3.1) where having dimension of 1xN is basically a kth channel vector, and it is zero-mean complex and circular Gaussian channel having covariance Rk, that is,h ~ CN(0, R ). In Equation 3.1, the 1st term indicates the desired signal of user k, while the 2nd term is representative of the co-channel interference received, and the 3rd term is addi- tive noise which is considered as zero-mean white noise with variance The To proceed further we adopt the framework in [16] in this section. Thus, we express the instantaneous SINR as Yk' where the subscrip