A Conic Quadratic Programming Approach to Physical Layer Multicasting for Large-Scale Antenna Arrays

We investigate the problem of downlink physical layer multicasting that aims at minimizing the transmit power with a massive antenna array installed at the transmitter site. We take a solution based on semidefinite relaxation (SDR) as our benchmark. It is shown that instead of working on the semidefinite program (SDP) naturally produced by the SDR, the dual counterpart of the same problem may provide a more efficient numerical implementation. Later, by using a successive convex approximation strategy, we arrive at a provably convergent iterative second-order cone programming (SOCP) solution. Our thorough numerical investigations report that the newly proposed SOCP solution offers improved power efficiency and a massively reduced computational complexity. Therefore, the SOCP solution is seen as a suitable candidate for obtaining beamformers that minimize transmit power, especially, when a very large number of antennas is used at the transmitter.