  In this paper, assuming multi-antenna transmitter and receivers, we consider
multicast beamformer design for the weighted max-min-fairness (WMMF) problem in
a multi-stream multi-group communication setup. Unlike the single-stream
scenario, the WMMF objective in this setup is not equivalent to maximizing the
minimum weighted SINR due to the summation over the rates of multiple streams.
Therefore, the non-convex problem at hand is first approximated with a convex
one and then solved using Karush-Kuhn-Tucker (KKT) conditions. Then, a
practically appealing closed-form solution is derived, as a function of dual
variables, for both transmit and receive beamformers. Finally, we use an
iterative solution based on the sub-gradient method to solve for the mutually
coupled and interdependent dual variables. The proposed solution does not rely
on generic solvers and does not require any bisection loop for finding the
achievable rate of various streams. As a result, it significantly outperforms
the state-of-art in terms of computational cost and convergence speed.
