A projected fast ISTA algorithm for joint beam forming and antenna selection in massive MIMO

The joint beam-forming and antenna selection problem encountered in modern multi-user massive multiple input multiple output (MIMO) communication systems is solved using the projected fast iterative shrinkage-thresholding algorithm (ISTA). The algorithm aim is to find the suboptimal set of transmitting antennas and to calculate the suboptimal beam-forming weights which maximize the users' achievable data rates. These requirements should be achieved quickly to maintain the system quality and reliability. The numerical analysis shows that the same rates are achieved using projected ISTA and projected fast ISTA. It also shows that the convergence rates for projected fast ISTA are much better than that of projected ISTA, and these rates are independent of the problem size. The paper concluded that the projected fast ISTA is suitable for multiuser massive MIMO systems due to the fast convergence rates and the implementation simplicity even for large system dimensions.