Recursive covariance design for multiple antenna physical layer multicasting

We consider the multiple antenna multicasting channel, in which a common message is simultaneously transmitted to multiple users in a wireless cellular network, under the assumption that channel state information (CSI) is perfectly available at the transmitter. In this paper, we develop a simple recursive algorithm to determine the co- variance matrix of the transmitted signal vector. For a large number of transmit antennas or a large number of users, we show that the growth rate of the maximum achievable rate of the proposed scheme is the same as that of the optimal scheme while reducing computational complexity dramatically.